Unit 7 — End of Topic Tests (reviewer copy: all keys and model answers visible)

[
 {
  "value": 0.0111,
  "misconception": "you divided the mass of one bearing by the total mass — the total goes on top",
  "feedback": "This answer is wrong — you divided the mass of one bearing by the total mass — the total goes on top"
 },
 {
  "value": 2624.4,
  "misconception": "you multiplied the two masses instead of dividing",
  "feedback": "This answer is wrong — you multiplied the two masses instead of dividing"
 },
 {
  "value": 900,
  "misconception": "you slipped a decimal place in the division — check by multiplying back: this count times the mass of one bearing comes to ten times the jar's total mass",
  "feedback": "This answer is wrong — you slipped a decimal place in the division — check by multiplying back: this count times the mass of one bearing comes to ten times the jar's total mass"
 }
]

{
 "keyExplanation": "Write down the values in the question:\ntotal mass = 486.0 g\nmass of one bearing = 5.4 g\nWrite down the equation:\nnumber of bearings = total mass / mass of one bearing\nSubstitute in the values, and calculate:\nnumber of bearings = 486.0 / 5.4\nnumber of bearings = 90",
 "anticipatedWrong": [
  {
   "value": 0.0111,
   "misconception": "you divided the mass of one bearing by the total mass — the total goes on top",
   "feedback": "This answer is wrong — you divided the mass of one bearing by the total mass — the total goes on top"
  },
  {
   "value": 2624.4,
   "misconception": "you multiplied the two masses instead of dividing",
   "feedback": "This answer is wrong — you multiplied the two masses instead of dividing"
  },
  {
   "value": 900,
   "misconception": "you slipped a decimal place in the division — check by multiplying back: this count times the mass of one bearing comes to ten times the jar's total mass",
   "feedback": "This answer is wrong — you slipped a decimal place in the division — check by multiplying back: this count times the mass of one bearing comes to ten times the jar's total mass"
  }
 ]
}

[
 {
  "value": 29,
  "misconception": "you read the atomic number — the smaller whole number counts protons and is not a mass",
  "feedback": "This answer is wrong — you read the atomic number — the smaller whole number counts protons and is not a mass"
 },
 {
  "value": 34.5,
  "misconception": "you subtracted the atomic number from the atomic mass — that neutron-count move belongs to isotope work, not molar mass",
  "feedback": "This answer is wrong — you subtracted the atomic number from the atomic mass — that neutron-count move belongs to isotope work, not molar mass"
 },
 {
  "value": 127.0,
  "misconception": "you doubled the printed value — the square's average atomic mass is already the whole molar mass for an element of single atoms",
  "feedback": "This answer is wrong — you doubled the printed value — the square's average atomic mass is already the whole molar mass for an element of single atoms"
 }
]

{
 "keyExplanation": "The square prints two numbers: the atomic number 29 and the average atomic mass 63.5. The average atomic mass, read in grams per mole, is the molar mass: copper's is 63.5 g/mol. The 29 counts protons and is never a mass.",
 "anticipatedWrong": [
  {
   "value": 29,
   "misconception": "you read the atomic number — the smaller whole number counts protons and is not a mass",
   "feedback": "This answer is wrong — you read the atomic number — the smaller whole number counts protons and is not a mass"
  },
  {
   "value": 34.5,
   "misconception": "you subtracted the atomic number from the atomic mass — that neutron-count move belongs to isotope work, not molar mass",
   "feedback": "This answer is wrong — you subtracted the atomic number from the atomic mass — that neutron-count move belongs to isotope work, not molar mass"
  },
  {
   "value": 127.0,
   "misconception": "you doubled the printed value — the square's average atomic mass is already the whole molar mass for an element of single atoms",
   "feedback": "This answer is wrong — you doubled the printed value — the square's average atomic mass is already the whole molar mass for an element of single atoms"
  }
 ]
}

[
 {
  "value": 31.0,
  "misconception": "you ignored the subscript — each P₄ molecule holds four atoms, so the atom's value quadruples",
  "feedback": "This answer is wrong — you ignored the subscript — each P₄ molecule holds four atoms, so the atom's value quadruples"
 },
 {
  "value": 35.0,
  "misconception": "you added the subscript as if it were a mass — the 4 is a count and multiplies",
  "feedback": "This answer is wrong — you added the subscript as if it were a mass — the 4 is a count and multiplies"
 },
 {
  "value": 7.75,
  "misconception": "you divided by the subscript instead of multiplying — the 4 counts atoms per molecule",
  "feedback": "This answer is wrong — you divided by the subscript instead of multiplying — the 4 counts atoms per molecule"
 }
]

{
 "keyExplanation": "The subscript counts the atoms in one molecule: 4.\nmolar mass of P₄ = 4 × 31.0\nmolar mass of P₄ = 124.0, reported as 124 g/mol (3 significant figures)\nEach P₄ molecule weighs four phosphorus atoms' worth.",
 "anticipatedWrong": [
  {
   "value": 31.0,
   "misconception": "you ignored the subscript — each P₄ molecule holds four atoms, so the atom's value quadruples",
   "feedback": "This answer is wrong — you ignored the subscript — each P₄ molecule holds four atoms, so the atom's value quadruples"
  },
  {
   "value": 35.0,
   "misconception": "you added the subscript as if it were a mass — the 4 is a count and multiplies",
   "feedback": "This answer is wrong — you added the subscript as if it were a mass — the 4 is a count and multiplies"
  },
  {
   "value": 7.75,
   "misconception": "you divided by the subscript instead of multiplying — the 4 counts atoms per molecule",
   "feedback": "This answer is wrong — you divided by the subscript instead of multiplying — the 4 counts atoms per molecule"
  }
 ]
}

[
 {
  "value": 185.4,
  "misconception": "you ignored the subscript — the formula counts four oxygens, not one",
  "feedback": "This answer is wrong — you ignored the subscript — the formula counts four oxygens, not one"
 },
 {
  "value": 741.6,
  "misconception": "you multiplied every element by the subscript — the 4 belongs to oxygen alone",
  "feedback": "This answer is wrong — you multiplied every element by the subscript — the 4 belongs to oxygen alone"
 },
 {
  "value": 189.4,
  "misconception": "you added the subscript as if it were a mass — the 4 is a count and multiplies the oxygen value",
  "feedback": "This answer is wrong — you added the subscript as if it were a mass — the 4 is a count and multiplies the oxygen value"
 }
]

{
 "keyExplanation": "Count the atoms the formula unit shows: 1 barium, 1 sulfur, and 4 oxygens.\nmolar mass of BaSO₄ = 137.3 + 32.1 + 4 × 16.0\nmolar mass of BaSO₄ = 233.4 g/mol\nThe subscript 4 multiplies oxygen only; barium and sulfur appear once each.",
 "anticipatedWrong": [
  {
   "value": 185.4,
   "misconception": "you ignored the subscript — the formula counts four oxygens, not one",
   "feedback": "This answer is wrong — you ignored the subscript — the formula counts four oxygens, not one"
  },
  {
   "value": 741.6,
   "misconception": "you multiplied every element by the subscript — the 4 belongs to oxygen alone",
   "feedback": "This answer is wrong — you multiplied every element by the subscript — the 4 belongs to oxygen alone"
  },
  {
   "value": 189.4,
   "misconception": "you added the subscript as if it were a mass — the 4 is a count and multiplies the oxygen value",
   "feedback": "This answer is wrong — you added the subscript as if it were a mass — the 4 is a count and multiplies the oxygen value"
  }
 ]
}

[
 {
  "value": 149.6,
  "misconception": "you ignored the subscript outside the parentheses — the 2 multiplies the whole NO₃ group",
  "feedback": "This answer is wrong — you ignored the subscript outside the parentheses — the 2 multiplies the whole NO₃ group"
 },
 {
  "value": 299.2,
  "misconception": "you multiplied the strontium as well — the outside subscript reaches only what sits inside the parentheses",
  "feedback": "This answer is wrong — you multiplied the strontium as well — the outside subscript reaches only what sits inside the parentheses"
 },
 {
  "value": 163.6,
  "misconception": "you applied the outside 2 only to the nitrogen — every atom inside the parentheses is doubled, all three oxygens included",
  "feedback": "This answer is wrong — you applied the outside 2 only to the nitrogen — every atom inside the parentheses is doubled, all three oxygens included"
 }
]

{
 "keyExplanation": "Inside the parentheses: 14.0 + 3 × 16.0 = 62.0\nMultiply by the outside subscript: 2 × 62.0 = 124.0\nAdd the atoms outside the parentheses: 87.6 + 124.0\nM = 211.6 g/mol",
 "anticipatedWrong": [
  {
   "value": 149.6,
   "misconception": "you ignored the subscript outside the parentheses — the 2 multiplies the whole NO₃ group",
   "feedback": "This answer is wrong — you ignored the subscript outside the parentheses — the 2 multiplies the whole NO₃ group"
  },
  {
   "value": 299.2,
   "misconception": "you multiplied the strontium as well — the outside subscript reaches only what sits inside the parentheses",
   "feedback": "This answer is wrong — you multiplied the strontium as well — the outside subscript reaches only what sits inside the parentheses"
  },
  {
   "value": 163.6,
   "misconception": "you applied the outside 2 only to the nitrogen — every atom inside the parentheses is doubled, all three oxygens included",
   "feedback": "This answer is wrong — you applied the outside 2 only to the nitrogen — every atom inside the parentheses is doubled, all three oxygens included"
  }
 ]
}

[
 {
  "value": 0.25,
  "misconception": "you divided the molar mass by the mass instead of the mass by the molar mass",
  "feedback": "This answer is wrong — you divided the molar mass by the mass instead of the mass by the molar mass"
 },
 {
  "value": 7779.24,
  "misconception": "you multiplied the mass by the molar mass instead of dividing",
  "feedback": "This answer is wrong — you multiplied the mass by the molar mass instead of dividing"
 },
 {
  "value": 40.0,
  "misconception": "you slipped a decimal place in the division — check by multiplying back: this count times 44.1 g/mol comes to ten times the tank's mass",
  "feedback": "This answer is wrong — you slipped a decimal place in the division — check by multiplying back: this count times 44.1 g/mol comes to ten times the tank's mass"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nm = 176.4 g\nM = 44.1 g/mol\nWrite down the equation:\nn = m / M\nSubstitute in the values, and calculate:\nn = 176.4 / 44.1\nn = 4.00 mol\nSanity check: a lab-to-tank-scale mole count lands around 0.01 to 10 mol — 4.00 mol passes.",
 "anticipatedWrong": [
  {
   "value": 0.25,
   "misconception": "you divided the molar mass by the mass instead of the mass by the molar mass",
   "feedback": "This answer is wrong — you divided the molar mass by the mass instead of the mass by the molar mass"
  },
  {
   "value": 7779.24,
   "misconception": "you multiplied the mass by the molar mass instead of dividing",
   "feedback": "This answer is wrong — you multiplied the mass by the molar mass instead of dividing"
  },
  {
   "value": 40.0,
   "misconception": "you slipped a decimal place in the division — check by multiplying back: this count times 44.1 g/mol comes to ten times the tank's mass",
   "feedback": "This answer is wrong — you slipped a decimal place in the division — check by multiplying back: this count times 44.1 g/mol comes to ten times the tank's mass"
  }
 ]
}

[
 {
  "value": 0.02506,
  "misconception": "you divided the moles by the molar mass instead of multiplying them",
  "feedback": "This answer is wrong — you divided the moles by the molar mass instead of multiplying them"
 },
 {
  "value": 39.9,
  "misconception": "you divided the molar mass by the moles instead of multiplying them",
  "feedback": "This answer is wrong — you divided the molar mass by the moles instead of multiplying them"
 },
 {
  "value": 63.84,
  "misconception": "you slipped a decimal place in the product — 4.00 portions of 159.6 g must weigh over six hundred grams",
  "feedback": "This answer is wrong — you slipped a decimal place in the product — 4.00 portions of 159.6 g must weigh over six hundred grams"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nn = 4.000 mol\nM = 159.6 g/mol\nWrite down the equation:\nn = m / M\nMake m the subject:\nm = n × M\nSubstitute in the values, and calculate:\nm = 4.000 × 159.6\nm = 638.4 g\nSanity check: more than 1 mol must weigh more than the 159.6 g molar mass — 638.4 g passes.",
 "anticipatedWrong": [
  {
   "value": 0.02506,
   "misconception": "you divided the moles by the molar mass instead of multiplying them",
   "feedback": "This answer is wrong — you divided the moles by the molar mass instead of multiplying them"
  },
  {
   "value": 39.9,
   "misconception": "you divided the molar mass by the moles instead of multiplying them",
   "feedback": "This answer is wrong — you divided the molar mass by the moles instead of multiplying them"
  },
  {
   "value": 63.84,
   "misconception": "you slipped a decimal place in the product — 4.00 portions of 159.6 g must weigh over six hundred grams",
   "feedback": "This answer is wrong — you slipped a decimal place in the product — 4.00 portions of 159.6 g must weigh over six hundred grams"
  }
 ]
}

[
 {
  "value": 0.0125,
  "misconception": "you divided the mass of one washer by the total mass — the total goes on top",
  "feedback": "This answer is wrong — you divided the mass of one washer by the total mass — the total goes on top"
 },
 {
  "value": 5120,
  "misconception": "you multiplied the two masses instead of dividing",
  "feedback": "This answer is wrong — you multiplied the two masses instead of dividing"
 },
 {
  "value": 800,
  "misconception": "you slipped a decimal place in the division — check by multiplying back: this count times the mass of one washer comes to ten times the crate's total mass",
  "feedback": "This answer is wrong — you slipped a decimal place in the division — check by multiplying back: this count times the mass of one washer comes to ten times the crate's total mass"
 }
]

{
 "keyExplanation": "Write down the values in the question:\ntotal mass = 640.0 g\nmass of one washer = 8.0 g\nWrite down the equation:\nnumber of washers = total mass / mass of one washer\nSubstitute in the values, and calculate:\nnumber of washers = 640.0 / 8.0\nnumber of washers = 80",
 "anticipatedWrong": [
  {
   "value": 0.0125,
   "misconception": "you divided the mass of one washer by the total mass — the total goes on top",
   "feedback": "This answer is wrong — you divided the mass of one washer by the total mass — the total goes on top"
  },
  {
   "value": 5120,
   "misconception": "you multiplied the two masses instead of dividing",
   "feedback": "This answer is wrong — you multiplied the two masses instead of dividing"
  },
  {
   "value": 800,
   "misconception": "you slipped a decimal place in the division — check by multiplying back: this count times the mass of one washer comes to ten times the crate's total mass",
   "feedback": "This answer is wrong — you slipped a decimal place in the division — check by multiplying back: this count times the mass of one washer comes to ten times the crate's total mass"
  }
 ]
}

[
 {
  "value": 50,
  "misconception": "you read the atomic number — the smaller whole number counts protons and is not a mass",
  "feedback": "This answer is wrong — you read the atomic number — the smaller whole number counts protons and is not a mass"
 },
 {
  "value": 68.7,
  "misconception": "you subtracted the atomic number from the atomic mass — that neutron-count move belongs to isotope work, not molar mass",
  "feedback": "This answer is wrong — you subtracted the atomic number from the atomic mass — that neutron-count move belongs to isotope work, not molar mass"
 },
 {
  "value": 237.4,
  "misconception": "you doubled the printed value — the square's average atomic mass is already the whole molar mass for an element of single atoms",
  "feedback": "This answer is wrong — you doubled the printed value — the square's average atomic mass is already the whole molar mass for an element of single atoms"
 }
]

{
 "keyExplanation": "The square prints the atomic number 50 and the average atomic mass 118.7. The average atomic mass, read in grams per mole, is the molar mass: tin's is 118.7 g/mol. The 50 counts protons and is never a mass.",
 "anticipatedWrong": [
  {
   "value": 50,
   "misconception": "you read the atomic number — the smaller whole number counts protons and is not a mass",
   "feedback": "This answer is wrong — you read the atomic number — the smaller whole number counts protons and is not a mass"
  },
  {
   "value": 68.7,
   "misconception": "you subtracted the atomic number from the atomic mass — that neutron-count move belongs to isotope work, not molar mass",
   "feedback": "This answer is wrong — you subtracted the atomic number from the atomic mass — that neutron-count move belongs to isotope work, not molar mass"
  },
  {
   "value": 237.4,
   "misconception": "you doubled the printed value — the square's average atomic mass is already the whole molar mass for an element of single atoms",
   "feedback": "This answer is wrong — you doubled the printed value — the square's average atomic mass is already the whole molar mass for an element of single atoms"
  }
 ]
}

[
 {
  "value": 126.9,
  "misconception": "you ignored the subscript — each I₂ molecule holds two atoms, so the atom's value doubles",
  "feedback": "This answer is wrong — you ignored the subscript — each I₂ molecule holds two atoms, so the atom's value doubles"
 },
 {
  "value": 128.9,
  "misconception": "you added the subscript as if it were a mass — the 2 is a count and multiplies",
  "feedback": "This answer is wrong — you added the subscript as if it were a mass — the 2 is a count and multiplies"
 },
 {
  "value": 63.45,
  "misconception": "you divided by the subscript instead of multiplying — the 2 counts atoms per molecule",
  "feedback": "This answer is wrong — you divided by the subscript instead of multiplying — the 2 counts atoms per molecule"
 }
]

{
 "keyExplanation": "The subscript counts the atoms in one molecule: 2.\nmolar mass of I₂ = 2 × 126.9\nmolar mass of I₂ = 253.8 g/mol\nEach iodine molecule weighs two iodine atoms' worth.",
 "anticipatedWrong": [
  {
   "value": 126.9,
   "misconception": "you ignored the subscript — each I₂ molecule holds two atoms, so the atom's value doubles",
   "feedback": "This answer is wrong — you ignored the subscript — each I₂ molecule holds two atoms, so the atom's value doubles"
  },
  {
   "value": 128.9,
   "misconception": "you added the subscript as if it were a mass — the 2 is a count and multiplies",
   "feedback": "This answer is wrong — you added the subscript as if it were a mass — the 2 is a count and multiplies"
  },
  {
   "value": 63.45,
   "misconception": "you divided by the subscript instead of multiplying — the 2 counts atoms per molecule",
   "feedback": "This answer is wrong — you divided by the subscript instead of multiplying — the 2 counts atoms per molecule"
  }
 ]
}

[
 {
  "value": 44.1,
  "misconception": "you ignored the subscript — the formula counts two S atoms, not one",
  "feedback": "This answer is wrong — you ignored the subscript — the formula counts two S atoms, not one"
 },
 {
  "value": 88.2,
  "misconception": "you multiplied every element by the subscript — the 2 belongs to S alone",
  "feedback": "This answer is wrong — you multiplied every element by the subscript — the 2 belongs to S alone"
 },
 {
  "value": 46.1,
  "misconception": "you added the subscript as if it were a mass — the 2 is a count and multiplies the S value",
  "feedback": "This answer is wrong — you added the subscript as if it were a mass — the 2 is a count and multiplies the S value"
 }
]

{
 "keyExplanation": "Count the atoms the formula shows: 1 carbon-family atom (C) and 2 sulfur-family atoms (S).\nmolar mass of CS₂ = 12.0 + 2 × 32.1\nmolar mass of CS₂ = 76.2 g/mol\nThe subscript 2 multiplies the S value only; C appears once.",
 "anticipatedWrong": [
  {
   "value": 44.1,
   "misconception": "you ignored the subscript — the formula counts two S atoms, not one",
   "feedback": "This answer is wrong — you ignored the subscript — the formula counts two S atoms, not one"
  },
  {
   "value": 88.2,
   "misconception": "you multiplied every element by the subscript — the 2 belongs to S alone",
   "feedback": "This answer is wrong — you multiplied every element by the subscript — the 2 belongs to S alone"
  },
  {
   "value": 46.1,
   "misconception": "you added the subscript as if it were a mass — the 2 is a count and multiplies the S value",
   "feedback": "This answer is wrong — you added the subscript as if it were a mass — the 2 is a count and multiplies the S value"
  }
 ]
}

[
 {
  "value": 200.1,
  "misconception": "you ignored the subscript outside the parentheses — the 3 multiplies the whole SO₄ group",
  "feedback": "This answer is wrong — you ignored the subscript outside the parentheses — the 3 multiplies the whole SO₄ group"
 },
 {
  "value": 340.3,
  "misconception": "you counted only one chromium — the subscript 2 after Cr doubles it",
  "feedback": "This answer is wrong — you counted only one chromium — the subscript 2 after Cr doubles it"
 },
 {
  "value": 600.3,
  "misconception": "you multiplied the chromium by 3 as well — the outside subscript reaches only what sits inside the parentheses",
  "feedback": "This answer is wrong — you multiplied the chromium by 3 as well — the outside subscript reaches only what sits inside the parentheses"
 }
]

{
 "keyExplanation": "Inside the parentheses: 32.1 + 4 × 16.0 = 96.1\nMultiply by the outside subscript: 3 × 96.1 = 288.3\nAdd the atoms outside the parentheses: 2 × 52.0 + 288.3\nM = 392.3 g/mol",
 "anticipatedWrong": [
  {
   "value": 200.1,
   "misconception": "you ignored the subscript outside the parentheses — the 3 multiplies the whole SO₄ group",
   "feedback": "This answer is wrong — you ignored the subscript outside the parentheses — the 3 multiplies the whole SO₄ group"
  },
  {
   "value": 340.3,
   "misconception": "you counted only one chromium — the subscript 2 after Cr doubles it",
   "feedback": "This answer is wrong — you counted only one chromium — the subscript 2 after Cr doubles it"
  },
  {
   "value": 600.3,
   "misconception": "you multiplied the chromium by 3 as well — the outside subscript reaches only what sits inside the parentheses",
   "feedback": "This answer is wrong — you multiplied the chromium by 3 as well — the outside subscript reaches only what sits inside the parentheses"
  }
 ]
}

[
 {
  "value": 0.286,
  "misconception": "you divided the molar mass by the mass instead of the mass by the molar mass",
  "feedback": "This answer is wrong — you divided the molar mass by the mass instead of the mass by the molar mass"
 },
 {
  "value": 2366,
  "misconception": "you multiplied the mass by the molar mass instead of dividing",
  "feedback": "This answer is wrong — you multiplied the mass by the molar mass instead of dividing"
 },
 {
  "value": 35.0,
  "misconception": "you slipped a decimal place in the division — check by multiplying back: this count times 26.0 g/mol comes to ten times the cylinder's mass",
  "feedback": "This answer is wrong — you slipped a decimal place in the division — check by multiplying back: this count times 26.0 g/mol comes to ten times the cylinder's mass"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nm = 91.0 g\nM = 26.0 g/mol\nWrite down the equation:\nn = m / M\nSubstitute in the values, and calculate:\nn = 91.0 / 26.0\nn = 3.50 mol\nSanity check: a cylinder-scale mole count lands around 0.01 to 10 mol — 3.50 mol passes.",
 "anticipatedWrong": [
  {
   "value": 0.286,
   "misconception": "you divided the molar mass by the mass instead of the mass by the molar mass",
   "feedback": "This answer is wrong — you divided the molar mass by the mass instead of the mass by the molar mass"
  },
  {
   "value": 2366,
   "misconception": "you multiplied the mass by the molar mass instead of dividing",
   "feedback": "This answer is wrong — you multiplied the mass by the molar mass instead of dividing"
  },
  {
   "value": 35.0,
   "misconception": "you slipped a decimal place in the division — check by multiplying back: this count times 26.0 g/mol comes to ten times the cylinder's mass",
   "feedback": "This answer is wrong — you slipped a decimal place in the division — check by multiplying back: this count times 26.0 g/mol comes to ten times the cylinder's mass"
  }
 ]
}

[
 {
  "value": 0.0154,
  "misconception": "you divided the moles by the molar mass instead of multiplying them",
  "feedback": "This answer is wrong — you divided the moles by the molar mass instead of multiplying them"
 },
 {
  "value": 64.95,
  "misconception": "you divided the molar mass by the moles instead of multiplying them",
  "feedback": "This answer is wrong — you divided the molar mass by the moles instead of multiplying them"
 },
 {
  "value": 25.98,
  "misconception": "you slipped a decimal place in the product — two portions of 129.9 g must weigh about 260 g",
  "feedback": "This answer is wrong — you slipped a decimal place in the product — two portions of 129.9 g must weigh about 260 g"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nn = 2.000 mol\nM = 129.9 g/mol\nWrite down the equation:\nn = m / M\nMake m the subject:\nm = n × M\nSubstitute in the values, and calculate:\nm = 2.000 × 129.9\nm = 259.8 g\nSanity check: more than 1 mol must weigh more than the 129.9 g molar mass — 259.8 g passes.",
 "anticipatedWrong": [
  {
   "value": 0.0154,
   "misconception": "you divided the moles by the molar mass instead of multiplying them",
   "feedback": "This answer is wrong — you divided the moles by the molar mass instead of multiplying them"
  },
  {
   "value": 64.95,
   "misconception": "you divided the molar mass by the moles instead of multiplying them",
   "feedback": "This answer is wrong — you divided the molar mass by the moles instead of multiplying them"
  },
  {
   "value": 25.98,
   "misconception": "you slipped a decimal place in the product — two portions of 129.9 g must weigh about 260 g",
   "feedback": "This answer is wrong — you slipped a decimal place in the product — two portions of 129.9 g must weigh about 260 g"
  }
 ]
}

[
 {
  "value": 0.0222,
  "misconception": "you divided the mass of one rivet by the total mass — the total goes on top",
  "feedback": "This answer is wrong — you divided the mass of one rivet by the total mass — the total goes on top"
 },
 {
  "value": 5951.25,
  "misconception": "you multiplied the two masses instead of dividing",
  "feedback": "This answer is wrong — you multiplied the two masses instead of dividing"
 },
 {
  "value": 450,
  "misconception": "you slipped a decimal place in the division — check by multiplying back: this count times the mass of one rivet comes to ten times the bin's total mass",
  "feedback": "This answer is wrong — you slipped a decimal place in the division — check by multiplying back: this count times the mass of one rivet comes to ten times the bin's total mass"
 }
]

{
 "keyExplanation": "Write down the values in the question:\ntotal mass = 517.5 g\nmass of one rivet = 11.5 g\nWrite down the equation:\nnumber of rivets = total mass / mass of one rivet\nSubstitute in the values, and calculate:\nnumber of rivets = 517.5 / 11.5\nnumber of rivets = 45",
 "anticipatedWrong": [
  {
   "value": 0.0222,
   "misconception": "you divided the mass of one rivet by the total mass — the total goes on top",
   "feedback": "This answer is wrong — you divided the mass of one rivet by the total mass — the total goes on top"
  },
  {
   "value": 5951.25,
   "misconception": "you multiplied the two masses instead of dividing",
   "feedback": "This answer is wrong — you multiplied the two masses instead of dividing"
  },
  {
   "value": 450,
   "misconception": "you slipped a decimal place in the division — check by multiplying back: this count times the mass of one rivet comes to ten times the bin's total mass",
   "feedback": "This answer is wrong — you slipped a decimal place in the division — check by multiplying back: this count times the mass of one rivet comes to ten times the bin's total mass"
  }
 ]
}

[
 {
  "value": 25,
  "misconception": "you read the atomic number — the smaller whole number counts protons and is not a mass",
  "feedback": "This answer is wrong — you read the atomic number — the smaller whole number counts protons and is not a mass"
 },
 {
  "value": 29.9,
  "misconception": "you subtracted the atomic number from the atomic mass — that neutron-count move belongs to isotope work, not molar mass",
  "feedback": "This answer is wrong — you subtracted the atomic number from the atomic mass — that neutron-count move belongs to isotope work, not molar mass"
 },
 {
  "value": 109.8,
  "misconception": "you doubled the printed value — the square's average atomic mass is already the whole molar mass for an element of single atoms",
  "feedback": "This answer is wrong — you doubled the printed value — the square's average atomic mass is already the whole molar mass for an element of single atoms"
 }
]

{
 "keyExplanation": "The square prints the atomic number 25 and the average atomic mass 54.9. The average atomic mass, read in grams per mole, is the molar mass: manganese's is 54.9 g/mol. The 25 counts protons and is never a mass.",
 "anticipatedWrong": [
  {
   "value": 25,
   "misconception": "you read the atomic number — the smaller whole number counts protons and is not a mass",
   "feedback": "This answer is wrong — you read the atomic number — the smaller whole number counts protons and is not a mass"
  },
  {
   "value": 29.9,
   "misconception": "you subtracted the atomic number from the atomic mass — that neutron-count move belongs to isotope work, not molar mass",
   "feedback": "This answer is wrong — you subtracted the atomic number from the atomic mass — that neutron-count move belongs to isotope work, not molar mass"
  },
  {
   "value": 109.8,
   "misconception": "you doubled the printed value — the square's average atomic mass is already the whole molar mass for an element of single atoms",
   "feedback": "This answer is wrong — you doubled the printed value — the square's average atomic mass is already the whole molar mass for an element of single atoms"
  }
 ]
}

[
 {
  "value": 32.1,
  "misconception": "you ignored the subscript — each S₈ molecule holds eight atoms, so the atom's value multiplies by 8",
  "feedback": "This answer is wrong — you ignored the subscript — each S₈ molecule holds eight atoms, so the atom's value multiplies by 8"
 },
 {
  "value": 40.1,
  "misconception": "you added the subscript as if it were a mass — the 8 is a count and multiplies",
  "feedback": "This answer is wrong — you added the subscript as if it were a mass — the 8 is a count and multiplies"
 },
 {
  "value": 4.0125,
  "misconception": "you divided by the subscript instead of multiplying — the 8 counts atoms per molecule",
  "feedback": "This answer is wrong — you divided by the subscript instead of multiplying — the 8 counts atoms per molecule"
 }
]

{
 "keyExplanation": "The square prints the average atomic mass 32.1. The subscript counts the atoms in one molecule: 8.\nmolar mass of S₈ = 8 × 32.1\nmolar mass of S₈ = 256.8, reported as 257 g/mol (3 significant figures)\nEach S₈ ring weighs eight sulfur atoms' worth.",
 "anticipatedWrong": [
  {
   "value": 32.1,
   "misconception": "you ignored the subscript — each S₈ molecule holds eight atoms, so the atom's value multiplies by 8",
   "feedback": "This answer is wrong — you ignored the subscript — each S₈ molecule holds eight atoms, so the atom's value multiplies by 8"
  },
  {
   "value": 40.1,
   "misconception": "you added the subscript as if it were a mass — the 8 is a count and multiplies",
   "feedback": "This answer is wrong — you added the subscript as if it were a mass — the 8 is a count and multiplies"
  },
  {
   "value": 4.0125,
   "misconception": "you divided by the subscript instead of multiplying — the 8 counts atoms per molecule",
   "feedback": "This answer is wrong — you divided by the subscript instead of multiplying — the 8 counts atoms per molecule"
  }
 ]
}

[
 {
  "value": 90.4,
  "misconception": "you ignored the subscript — the formula counts two chlorines, not one",
  "feedback": "This answer is wrong — you ignored the subscript — the formula counts two chlorines, not one"
 },
 {
  "value": 180.8,
  "misconception": "you multiplied every element by the subscript — the 2 belongs to chlorine alone",
  "feedback": "This answer is wrong — you multiplied every element by the subscript — the 2 belongs to chlorine alone"
 },
 {
  "value": 92.4,
  "misconception": "you added the subscript as if it were a mass — the 2 is a count and multiplies the chlorine value",
  "feedback": "This answer is wrong — you added the subscript as if it were a mass — the 2 is a count and multiplies the chlorine value"
 }
]

{
 "keyExplanation": "Count the atoms the formula unit shows: 1 manganese and 2 chlorines.\nmolar mass of MnCl₂ = 54.9 + 2 × 35.5\nmolar mass of MnCl₂ = 125.9 g/mol\nThe subscript 2 multiplies the chlorine value only; manganese appears once.",
 "anticipatedWrong": [
  {
   "value": 90.4,
   "misconception": "you ignored the subscript — the formula counts two chlorines, not one",
   "feedback": "This answer is wrong — you ignored the subscript — the formula counts two chlorines, not one"
  },
  {
   "value": 180.8,
   "misconception": "you multiplied every element by the subscript — the 2 belongs to chlorine alone",
   "feedback": "This answer is wrong — you multiplied every element by the subscript — the 2 belongs to chlorine alone"
  },
  {
   "value": 92.4,
   "misconception": "you added the subscript as if it were a mass — the 2 is a count and multiplies the chlorine value",
   "feedback": "This answer is wrong — you added the subscript as if it were a mass — the 2 is a count and multiplies the chlorine value"
  }
 ]
}

[
 {
  "value": 75.7,
  "misconception": "you ignored the subscript outside the parentheses — the 2 multiplies both the oxygen and the hydrogen",
  "feedback": "This answer is wrong — you ignored the subscript outside the parentheses — the 2 multiplies both the oxygen and the hydrogen"
 },
 {
  "value": 151.4,
  "misconception": "you multiplied the nickel as well — the outside subscript reaches only what sits inside the parentheses",
  "feedback": "This answer is wrong — you multiplied the nickel as well — the outside subscript reaches only what sits inside the parentheses"
 },
 {
  "value": 91.7,
  "misconception": "you applied the outside 2 only to the oxygen — every atom inside the parentheses is doubled, the hydrogen included",
  "feedback": "This answer is wrong — you applied the outside 2 only to the oxygen — every atom inside the parentheses is doubled, the hydrogen included"
 }
]

{
 "keyExplanation": "Inside the parentheses: 16.0 + 1.0 = 17.0\nMultiply by the outside subscript: 2 × 17.0 = 34.0\nAdd the atoms outside the parentheses: 58.7 + 34.0\nM = 92.7 g/mol",
 "anticipatedWrong": [
  {
   "value": 75.7,
   "misconception": "you ignored the subscript outside the parentheses — the 2 multiplies both the oxygen and the hydrogen",
   "feedback": "This answer is wrong — you ignored the subscript outside the parentheses — the 2 multiplies both the oxygen and the hydrogen"
  },
  {
   "value": 151.4,
   "misconception": "you multiplied the nickel as well — the outside subscript reaches only what sits inside the parentheses",
   "feedback": "This answer is wrong — you multiplied the nickel as well — the outside subscript reaches only what sits inside the parentheses"
  },
  {
   "value": 91.7,
   "misconception": "you applied the outside 2 only to the oxygen — every atom inside the parentheses is doubled, the hydrogen included",
   "feedback": "This answer is wrong — you applied the outside 2 only to the oxygen — every atom inside the parentheses is doubled, the hydrogen included"
  }
 ]
}

[
 {
  "value": 0.5,
  "misconception": "you divided the molar mass by the mass instead of the mass by the molar mass",
  "feedback": "This answer is wrong — you divided the molar mass by the mass instead of the mass by the molar mass"
 },
 {
  "value": 12199.22,
  "misconception": "you multiplied the mass by the molar mass instead of dividing",
  "feedback": "This answer is wrong — you multiplied the mass by the molar mass instead of dividing"
 },
 {
  "value": 20.0,
  "misconception": "you slipped a decimal place in the division — check by multiplying back: this count times 78.1 g/mol comes to ten times the drum's mass",
  "feedback": "This answer is wrong — you slipped a decimal place in the division — check by multiplying back: this count times 78.1 g/mol comes to ten times the drum's mass"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nm = 156.2 g\nM = 78.1 g/mol\nWrite down the equation:\nn = m / M\nSubstitute in the values, and calculate:\nn = 156.2 / 78.1\nn = 2.00 mol\nSanity check: a drum-scale mole count lands around 0.01 to 10 mol — 2.00 mol passes.",
 "anticipatedWrong": [
  {
   "value": 0.5,
   "misconception": "you divided the molar mass by the mass instead of the mass by the molar mass",
   "feedback": "This answer is wrong — you divided the molar mass by the mass instead of the mass by the molar mass"
  },
  {
   "value": 12199.22,
   "misconception": "you multiplied the mass by the molar mass instead of dividing",
   "feedback": "This answer is wrong — you multiplied the mass by the molar mass instead of dividing"
  },
  {
   "value": 20.0,
   "misconception": "you slipped a decimal place in the division — check by multiplying back: this count times 78.1 g/mol comes to ten times the drum's mass",
   "feedback": "This answer is wrong — you slipped a decimal place in the division — check by multiplying back: this count times 78.1 g/mol comes to ten times the drum's mass"
  }
 ]
}

[
 {
  "value": 0.01912,
  "misconception": "you divided the moles by the molar mass instead of multiplying them",
  "feedback": "This answer is wrong — you divided the moles by the molar mass instead of multiplying them"
 },
 {
  "value": 52.3,
  "misconception": "you divided the molar mass by the moles instead of multiplying them",
  "feedback": "This answer is wrong — you divided the molar mass by the moles instead of multiplying them"
 },
 {
  "value": 20.92,
  "misconception": "you slipped a decimal place in the product — two portions of 104.6 g must weigh about 200 g",
  "feedback": "This answer is wrong — you slipped a decimal place in the product — two portions of 104.6 g must weigh about 200 g"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nn = 2.000 mol\nM = 104.6 g/mol\nWrite down the equation:\nn = m / M\nMake m the subject:\nm = n × M\nSubstitute in the values, and calculate:\nm = 2.000 × 104.6\nm = 209.2 g\nSanity check: more than 1 mol must weigh more than the 104.6 g molar mass — 209.2 g passes.",
 "anticipatedWrong": [
  {
   "value": 0.01912,
   "misconception": "you divided the moles by the molar mass instead of multiplying them",
   "feedback": "This answer is wrong — you divided the moles by the molar mass instead of multiplying them"
  },
  {
   "value": 52.3,
   "misconception": "you divided the molar mass by the moles instead of multiplying them",
   "feedback": "This answer is wrong — you divided the molar mass by the moles instead of multiplying them"
  },
  {
   "value": 20.92,
   "misconception": "you slipped a decimal place in the product — two portions of 104.6 g must weigh about 200 g",
   "feedback": "This answer is wrong — you slipped a decimal place in the product — two portions of 104.6 g must weigh about 200 g"
  }
 ]
}

[
 {
  "value": 0.0278,
  "misconception": "you divided the mass of one dowel by the total mass — the total goes on top",
  "feedback": "This answer is wrong — you divided the mass of one dowel by the total mass — the total goes on top"
 },
 {
  "value": 2601,
  "misconception": "you multiplied the two masses instead of dividing",
  "feedback": "This answer is wrong — you multiplied the two masses instead of dividing"
 },
 {
  "value": 360,
  "misconception": "you slipped a decimal place in the division — check by multiplying back: this count times the mass of one dowel comes to ten times the carton's total mass",
  "feedback": "This answer is wrong — you slipped a decimal place in the division — check by multiplying back: this count times the mass of one dowel comes to ten times the carton's total mass"
 }
]

{
 "keyExplanation": "Write down the values in the question:\ntotal mass = 306.0 g\nmass of one dowel = 8.5 g\nWrite down the equation:\nnumber of dowels = total mass / mass of one dowel\nSubstitute in the values, and calculate:\nnumber of dowels = 306.0 / 8.5\nnumber of dowels = 36",
 "anticipatedWrong": [
  {
   "value": 0.0278,
   "misconception": "you divided the mass of one dowel by the total mass — the total goes on top",
   "feedback": "This answer is wrong — you divided the mass of one dowel by the total mass — the total goes on top"
  },
  {
   "value": 2601,
   "misconception": "you multiplied the two masses instead of dividing",
   "feedback": "This answer is wrong — you multiplied the two masses instead of dividing"
  },
  {
   "value": 360,
   "misconception": "you slipped a decimal place in the division — check by multiplying back: this count times the mass of one dowel comes to ten times the carton's total mass",
   "feedback": "This answer is wrong — you slipped a decimal place in the division — check by multiplying back: this count times the mass of one dowel comes to ten times the carton's total mass"
  }
 ]
}

[
 {
  "value": 48,
  "misconception": "you read the atomic number — the smaller whole number counts protons and is not a mass",
  "feedback": "This answer is wrong — you read the atomic number — the smaller whole number counts protons and is not a mass"
 },
 {
  "value": 64.4,
  "misconception": "you subtracted the atomic number from the atomic mass — that neutron-count move belongs to isotope work, not molar mass",
  "feedback": "This answer is wrong — you subtracted the atomic number from the atomic mass — that neutron-count move belongs to isotope work, not molar mass"
 },
 {
  "value": 224.8,
  "misconception": "you doubled the printed value — the square's average atomic mass is already the whole molar mass for an element of single atoms",
  "feedback": "This answer is wrong — you doubled the printed value — the square's average atomic mass is already the whole molar mass for an element of single atoms"
 }
]

{
 "keyExplanation": "The square prints the atomic number 48 and the average atomic mass 112.4. The average atomic mass, read in grams per mole, is the molar mass: cadmium's is 112.4 g/mol. The 48 counts protons and is never a mass.",
 "anticipatedWrong": [
  {
   "value": 48,
   "misconception": "you read the atomic number — the smaller whole number counts protons and is not a mass",
   "feedback": "This answer is wrong — you read the atomic number — the smaller whole number counts protons and is not a mass"
  },
  {
   "value": 64.4,
   "misconception": "you subtracted the atomic number from the atomic mass — that neutron-count move belongs to isotope work, not molar mass",
   "feedback": "This answer is wrong — you subtracted the atomic number from the atomic mass — that neutron-count move belongs to isotope work, not molar mass"
  },
  {
   "value": 224.8,
   "misconception": "you doubled the printed value — the square's average atomic mass is already the whole molar mass for an element of single atoms",
   "feedback": "This answer is wrong — you doubled the printed value — the square's average atomic mass is already the whole molar mass for an element of single atoms"
  }
 ]
}

[
 {
  "value": 16.0,
  "misconception": "you ignored the subscript — each O₃ molecule holds three atoms, so the atom's value triples",
  "feedback": "This answer is wrong — you ignored the subscript — each O₃ molecule holds three atoms, so the atom's value triples"
 },
 {
  "value": 19.0,
  "misconception": "you added the subscript as if it were a mass — the 3 is a count and multiplies",
  "feedback": "This answer is wrong — you added the subscript as if it were a mass — the 3 is a count and multiplies"
 },
 {
  "value": 5.33,
  "misconception": "you divided by the subscript instead of multiplying — the 3 counts atoms per molecule",
  "feedback": "This answer is wrong — you divided by the subscript instead of multiplying — the 3 counts atoms per molecule"
 }
]

{
 "keyExplanation": "The square prints the average atomic mass 16.0. The subscript counts the atoms in one molecule: 3.\nmolar mass of O₃ = 3 × 16.0\nmolar mass of O₃ = 48.0 g/mol\nEach ozone molecule weighs three atoms' worth of the element it is built from.",
 "anticipatedWrong": [
  {
   "value": 16.0,
   "misconception": "you ignored the subscript — each O₃ molecule holds three atoms, so the atom's value triples",
   "feedback": "This answer is wrong — you ignored the subscript — each O₃ molecule holds three atoms, so the atom's value triples"
  },
  {
   "value": 19.0,
   "misconception": "you added the subscript as if it were a mass — the 3 is a count and multiplies",
   "feedback": "This answer is wrong — you added the subscript as if it were a mass — the 3 is a count and multiplies"
  },
  {
   "value": 5.33,
   "misconception": "you divided by the subscript instead of multiplying — the 3 counts atoms per molecule",
   "feedback": "This answer is wrong — you divided by the subscript instead of multiplying — the 3 counts atoms per molecule"
  }
 ]
}

[
 {
  "value": 156.3,
  "misconception": "you ignored the subscript — the formula counts two fluorines, not one",
  "feedback": "This answer is wrong — you ignored the subscript — the formula counts two fluorines, not one"
 },
 {
  "value": 312.6,
  "misconception": "you multiplied every element by the subscript — the 2 belongs to fluorine alone",
  "feedback": "This answer is wrong — you multiplied every element by the subscript — the 2 belongs to fluorine alone"
 },
 {
  "value": 158.3,
  "misconception": "you added the subscript as if it were a mass — the 2 is a count and multiplies the fluorine value",
  "feedback": "This answer is wrong — you added the subscript as if it were a mass — the 2 is a count and multiplies the fluorine value"
 }
]

{
 "keyExplanation": "Count the atoms the formula unit shows: 1 barium and 2 fluorines.\nmolar mass of BaF₂ = 137.3 + 2 × 19.0\nmolar mass of BaF₂ = 175.3 g/mol\nThe subscript 2 multiplies the fluorine value only; barium appears once.",
 "anticipatedWrong": [
  {
   "value": 156.3,
   "misconception": "you ignored the subscript — the formula counts two fluorines, not one",
   "feedback": "This answer is wrong — you ignored the subscript — the formula counts two fluorines, not one"
  },
  {
   "value": 312.6,
   "misconception": "you multiplied every element by the subscript — the 2 belongs to fluorine alone",
   "feedback": "This answer is wrong — you multiplied every element by the subscript — the 2 belongs to fluorine alone"
  },
  {
   "value": 158.3,
   "misconception": "you added the subscript as if it were a mass — the 2 is a count and multiplies the fluorine value",
   "feedback": "This answer is wrong — you added the subscript as if it were a mass — the 2 is a count and multiplies the fluorine value"
  }
 ]
}

[
 {
  "value": 174.4,
  "misconception": "you ignored the subscript outside the parentheses — the 2 multiplies the whole NO₃ group",
  "feedback": "This answer is wrong — you ignored the subscript outside the parentheses — the 2 multiplies the whole NO₃ group"
 },
 {
  "value": 348.8,
  "misconception": "you multiplied the cadmium as well — the outside subscript reaches only what sits inside the parentheses",
  "feedback": "This answer is wrong — you multiplied the cadmium as well — the outside subscript reaches only what sits inside the parentheses"
 },
 {
  "value": 188.4,
  "misconception": "you applied the outside 2 only to the nitrogen — every atom inside the parentheses is doubled, all three oxygens included",
  "feedback": "This answer is wrong — you applied the outside 2 only to the nitrogen — every atom inside the parentheses is doubled, all three oxygens included"
 }
]

{
 "keyExplanation": "Inside the parentheses: 14.0 + 3 × 16.0 = 62.0\nMultiply by the outside subscript: 2 × 62.0 = 124.0\nAdd the atoms outside the parentheses: 112.4 + 124.0\nM = 236.4 g/mol",
 "anticipatedWrong": [
  {
   "value": 174.4,
   "misconception": "you ignored the subscript outside the parentheses — the 2 multiplies the whole NO₃ group",
   "feedback": "This answer is wrong — you ignored the subscript outside the parentheses — the 2 multiplies the whole NO₃ group"
  },
  {
   "value": 348.8,
   "misconception": "you multiplied the cadmium as well — the outside subscript reaches only what sits inside the parentheses",
   "feedback": "This answer is wrong — you multiplied the cadmium as well — the outside subscript reaches only what sits inside the parentheses"
  },
  {
   "value": 188.4,
   "misconception": "you applied the outside 2 only to the nitrogen — every atom inside the parentheses is doubled, all three oxygens included",
   "feedback": "This answer is wrong — you applied the outside 2 only to the nitrogen — every atom inside the parentheses is doubled, all three oxygens included"
  }
 ]
}

[
 {
  "value": 0.5,
  "misconception": "you divided the molar mass by the mass instead of the mass by the molar mass",
  "feedback": "This answer is wrong — you divided the molar mass by the mass instead of the mass by the molar mass"
 },
 {
  "value": 16964.82,
  "misconception": "you multiplied the mass by the molar mass instead of dividing",
  "feedback": "This answer is wrong — you multiplied the mass by the molar mass instead of dividing"
 },
 {
  "value": 20.0,
  "misconception": "you slipped a decimal place in the division — check by multiplying back: this count times 92.1 g/mol comes to ten times the bottle's mass",
  "feedback": "This answer is wrong — you slipped a decimal place in the division — check by multiplying back: this count times 92.1 g/mol comes to ten times the bottle's mass"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nm = 184.2 g\nM = 92.1 g/mol\nWrite down the equation:\nn = m / M\nSubstitute in the values, and calculate:\nn = 184.2 / 92.1\nn = 2.00 mol\nSanity check: a bottle-scale mole count lands around 0.01 to 10 mol — 2.00 mol passes.",
 "anticipatedWrong": [
  {
   "value": 0.5,
   "misconception": "you divided the molar mass by the mass instead of the mass by the molar mass",
   "feedback": "This answer is wrong — you divided the molar mass by the mass instead of the mass by the molar mass"
  },
  {
   "value": 16964.82,
   "misconception": "you multiplied the mass by the molar mass instead of dividing",
   "feedback": "This answer is wrong — you multiplied the mass by the molar mass instead of dividing"
  },
  {
   "value": 20.0,
   "misconception": "you slipped a decimal place in the division — check by multiplying back: this count times 92.1 g/mol comes to ten times the bottle's mass",
   "feedback": "This answer is wrong — you slipped a decimal place in the division — check by multiplying back: this count times 92.1 g/mol comes to ten times the bottle's mass"
  }
 ]
}

[
 {
  "value": 0.01067,
  "misconception": "you divided the moles by the molar mass instead of multiplying them",
  "feedback": "This answer is wrong — you divided the moles by the molar mass instead of multiplying them"
 },
 {
  "value": 93.7,
  "misconception": "you divided the molar mass by the moles instead of multiplying them",
  "feedback": "This answer is wrong — you divided the molar mass by the moles instead of multiplying them"
 },
 {
  "value": 37.48,
  "misconception": "you slipped a decimal place in the product — two portions of 187.4 g must weigh about 375 g",
  "feedback": "This answer is wrong — you slipped a decimal place in the product — two portions of 187.4 g must weigh about 375 g"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nn = 2.000 mol\nM = 187.4 g/mol\nWrite down the equation:\nn = m / M\nMake m the subject:\nm = n × M\nSubstitute in the values, and calculate:\nm = 2.000 × 187.4\nm = 374.8 g\nSanity check: more than 1 mol must weigh more than the 187.4 g molar mass — 374.8 g passes.",
 "anticipatedWrong": [
  {
   "value": 0.01067,
   "misconception": "you divided the moles by the molar mass instead of multiplying them",
   "feedback": "This answer is wrong — you divided the moles by the molar mass instead of multiplying them"
  },
  {
   "value": 93.7,
   "misconception": "you divided the molar mass by the moles instead of multiplying them",
   "feedback": "This answer is wrong — you divided the molar mass by the moles instead of multiplying them"
  },
  {
   "value": 37.48,
   "misconception": "you slipped a decimal place in the product — two portions of 187.4 g must weigh about 375 g",
   "feedback": "This answer is wrong — you slipped a decimal place in the product — two portions of 187.4 g must weigh about 375 g"
  }
 ]
}

[
 {
  "value": 0.037,
  "misconception": "you divided the mass of one grommet by the total mass — the total goes on top",
  "feedback": "This answer is wrong — you divided the mass of one grommet by the total mass — the total goes on top"
 },
 {
  "value": 1140.75,
  "misconception": "you multiplied the two masses instead of dividing",
  "feedback": "This answer is wrong — you multiplied the two masses instead of dividing"
 },
 {
  "value": 270,
  "misconception": "you slipped a decimal place in the division — check by multiplying back: this count times the mass of one grommet comes to ten times the canister's total mass",
  "feedback": "This answer is wrong — you slipped a decimal place in the division — check by multiplying back: this count times the mass of one grommet comes to ten times the canister's total mass"
 }
]

{
 "keyExplanation": "Write down the values in the question:\ntotal mass = 175.5 g\nmass of one grommet = 6.5 g\nWrite down the equation:\nnumber of grommets = total mass / mass of one grommet\nSubstitute in the values, and calculate:\nnumber of grommets = 175.5 / 6.5\nnumber of grommets = 27",
 "anticipatedWrong": [
  {
   "value": 0.037,
   "misconception": "you divided the mass of one grommet by the total mass — the total goes on top",
   "feedback": "This answer is wrong — you divided the mass of one grommet by the total mass — the total goes on top"
  },
  {
   "value": 1140.75,
   "misconception": "you multiplied the two masses instead of dividing",
   "feedback": "This answer is wrong — you multiplied the two masses instead of dividing"
  },
  {
   "value": 270,
   "misconception": "you slipped a decimal place in the division — check by multiplying back: this count times the mass of one grommet comes to ten times the canister's total mass",
   "feedback": "This answer is wrong — you slipped a decimal place in the division — check by multiplying back: this count times the mass of one grommet comes to ten times the canister's total mass"
  }
 ]
}

[
 {
  "value": 74,
  "misconception": "you read the atomic number — the smaller whole number counts protons and is not a mass",
  "feedback": "This answer is wrong — you read the atomic number — the smaller whole number counts protons and is not a mass"
 },
 {
  "value": 109.8,
  "misconception": "you subtracted the atomic number from the atomic mass — that neutron-count move belongs to isotope work, not molar mass",
  "feedback": "This answer is wrong — you subtracted the atomic number from the atomic mass — that neutron-count move belongs to isotope work, not molar mass"
 },
 {
  "value": 367.6,
  "misconception": "you doubled the printed value — the square's average atomic mass is already the whole molar mass for an element of single atoms",
  "feedback": "This answer is wrong — you doubled the printed value — the square's average atomic mass is already the whole molar mass for an element of single atoms"
 }
]

{
 "keyExplanation": "The square prints the atomic number 74 and the average atomic mass 183.8. The average atomic mass, read in grams per mole, is the molar mass: tungsten's is 183.8 g/mol. The 74 counts protons and is never a mass.",
 "anticipatedWrong": [
  {
   "value": 74,
   "misconception": "you read the atomic number — the smaller whole number counts protons and is not a mass",
   "feedback": "This answer is wrong — you read the atomic number — the smaller whole number counts protons and is not a mass"
  },
  {
   "value": 109.8,
   "misconception": "you subtracted the atomic number from the atomic mass — that neutron-count move belongs to isotope work, not molar mass",
   "feedback": "This answer is wrong — you subtracted the atomic number from the atomic mass — that neutron-count move belongs to isotope work, not molar mass"
  },
  {
   "value": 367.6,
   "misconception": "you doubled the printed value — the square's average atomic mass is already the whole molar mass for an element of single atoms",
   "feedback": "This answer is wrong — you doubled the printed value — the square's average atomic mass is already the whole molar mass for an element of single atoms"
  }
 ]
}

[
 {
  "value": 32.1,
  "misconception": "you ignored the subscript — each S₂ molecule holds two atoms, so the atom's value doubles",
  "feedback": "This answer is wrong — you ignored the subscript — each S₂ molecule holds two atoms, so the atom's value doubles"
 },
 {
  "value": 34.1,
  "misconception": "you added the subscript as if it were a mass — the 2 is a count and multiplies",
  "feedback": "This answer is wrong — you added the subscript as if it were a mass — the 2 is a count and multiplies"
 },
 {
  "value": 16.05,
  "misconception": "you divided by the subscript instead of multiplying — the 2 counts atoms per molecule",
  "feedback": "This answer is wrong — you divided by the subscript instead of multiplying — the 2 counts atoms per molecule"
 }
]

{
 "keyExplanation": "The square prints the average atomic mass 32.1. The subscript counts the atoms in one molecule: 2.\nmolar mass of S₂ = 2 × 32.1\nmolar mass of S₂ = 64.2 g/mol\nEach hot-vapor S₂ molecule weighs two sulfur atoms' worth.",
 "anticipatedWrong": [
  {
   "value": 32.1,
   "misconception": "you ignored the subscript — each S₂ molecule holds two atoms, so the atom's value doubles",
   "feedback": "This answer is wrong — you ignored the subscript — each S₂ molecule holds two atoms, so the atom's value doubles"
  },
  {
   "value": 34.1,
   "misconception": "you added the subscript as if it were a mass — the 2 is a count and multiplies",
   "feedback": "This answer is wrong — you added the subscript as if it were a mass — the 2 is a count and multiplies"
  },
  {
   "value": 16.05,
   "misconception": "you divided by the subscript instead of multiplying — the 2 counts atoms per molecule",
   "feedback": "This answer is wrong — you divided by the subscript instead of multiplying — the 2 counts atoms per molecule"
  }
 ]
}

[
 {
  "value": 107.2,
  "misconception": "you ignored the subscript — the formula counts two oxygens, not one",
  "feedback": "This answer is wrong — you ignored the subscript — the formula counts two oxygens, not one"
 },
 {
  "value": 214.4,
  "misconception": "you multiplied every element by the subscript — the 2 belongs to oxygen alone",
  "feedback": "This answer is wrong — you multiplied every element by the subscript — the 2 belongs to oxygen alone"
 },
 {
  "value": 109.2,
  "misconception": "you added the subscript as if it were a mass — the 2 is a count and multiplies the oxygen value",
  "feedback": "This answer is wrong — you added the subscript as if it were a mass — the 2 is a count and multiplies the oxygen value"
 }
]

{
 "keyExplanation": "Count the atoms the formula unit shows: 1 zirconium and 2 oxygens.\nmolar mass of ZrO₂ = 91.2 + 2 × 16.0\nmolar mass of ZrO₂ = 123.2 g/mol\nThe subscript 2 multiplies the oxygen value only; zirconium appears once.",
 "anticipatedWrong": [
  {
   "value": 107.2,
   "misconception": "you ignored the subscript — the formula counts two oxygens, not one",
   "feedback": "This answer is wrong — you ignored the subscript — the formula counts two oxygens, not one"
  },
  {
   "value": 214.4,
   "misconception": "you multiplied every element by the subscript — the 2 belongs to oxygen alone",
   "feedback": "This answer is wrong — you multiplied every element by the subscript — the 2 belongs to oxygen alone"
  },
  {
   "value": 109.2,
   "misconception": "you added the subscript as if it were a mass — the 2 is a count and multiplies the oxygen value",
   "feedback": "This answer is wrong — you added the subscript as if it were a mass — the 2 is a count and multiplies the oxygen value"
  }
 ]
}

[
 {
  "value": 114.1,
  "misconception": "you counted only one NH₄ group — the subscript 2 after the parentheses doubles the whole group",
  "feedback": "This answer is wrong — you counted only one NH₄ group — the subscript 2 after the parentheses doubles the whole group"
 },
 {
  "value": 228.2,
  "misconception": "you applied the 2 to the sulfate part as well — the subscript reaches only the group inside its own parentheses",
  "feedback": "This answer is wrong — you applied the 2 to the sulfate part as well — the subscript reaches only the group inside its own parentheses"
 },
 {
  "value": 116.1,
  "misconception": "you added the subscript as if it were a mass — the 2 is a count and multiplies the NH₄ group's value",
  "feedback": "This answer is wrong — you added the subscript as if it were a mass — the 2 is a count and multiplies the NH₄ group's value"
 }
]

{
 "keyExplanation": "Inside the parentheses: 14.0 + 4 × 1.0 = 18.0\nMultiply by the subscript after the parentheses: 2 × 18.0 = 36.0\nAdd the atoms outside the parentheses: 36.0 + 32.1 + 4 × 16.0\nM = 132.1 g/mol",
 "anticipatedWrong": [
  {
   "value": 114.1,
   "misconception": "you counted only one NH₄ group — the subscript 2 after the parentheses doubles the whole group",
   "feedback": "This answer is wrong — you counted only one NH₄ group — the subscript 2 after the parentheses doubles the whole group"
  },
  {
   "value": 228.2,
   "misconception": "you applied the 2 to the sulfate part as well — the subscript reaches only the group inside its own parentheses",
   "feedback": "This answer is wrong — you applied the 2 to the sulfate part as well — the subscript reaches only the group inside its own parentheses"
  },
  {
   "value": 116.1,
   "misconception": "you added the subscript as if it were a mass — the 2 is a count and multiplies the NH₄ group's value",
   "feedback": "This answer is wrong — you added the subscript as if it were a mass — the 2 is a count and multiplies the NH₄ group's value"
  }
 ]
}

[
 {
  "value": 0.2,
  "misconception": "you divided the molar mass by the mass instead of the mass by the molar mass",
  "feedback": "This answer is wrong — you divided the molar mass by the mass instead of the mass by the molar mass"
 },
 {
  "value": 19282.05,
  "misconception": "you multiplied the mass by the molar mass instead of dividing",
  "feedback": "This answer is wrong — you multiplied the mass by the molar mass instead of dividing"
 },
 {
  "value": 50.0,
  "misconception": "you slipped a decimal place in the division — check by multiplying back: this count times 62.1 g/mol comes to ten times the reservoir's mass",
  "feedback": "This answer is wrong — you slipped a decimal place in the division — check by multiplying back: this count times 62.1 g/mol comes to ten times the reservoir's mass"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nm = 310.5 g\nM = 62.1 g/mol\nWrite down the equation:\nn = m / M\nSubstitute in the values, and calculate:\nn = 310.5 / 62.1\nn = 5.00 mol\nSanity check: a reservoir-scale mole count lands around 0.01 to 10 mol — 5.00 mol passes.",
 "anticipatedWrong": [
  {
   "value": 0.2,
   "misconception": "you divided the molar mass by the mass instead of the mass by the molar mass",
   "feedback": "This answer is wrong — you divided the molar mass by the mass instead of the mass by the molar mass"
  },
  {
   "value": 19282.05,
   "misconception": "you multiplied the mass by the molar mass instead of dividing",
   "feedback": "This answer is wrong — you multiplied the mass by the molar mass instead of dividing"
  },
  {
   "value": 50.0,
   "misconception": "you slipped a decimal place in the division — check by multiplying back: this count times 62.1 g/mol comes to ten times the reservoir's mass",
   "feedback": "This answer is wrong — you slipped a decimal place in the division — check by multiplying back: this count times 62.1 g/mol comes to ten times the reservoir's mass"
  }
 ]
}

[
 {
  "value": 0.007423,
  "misconception": "you divided the moles by the molar mass instead of multiplying them",
  "feedback": "This answer is wrong — you divided the moles by the molar mass instead of multiplying them"
 },
 {
  "value": 134.72,
  "misconception": "you divided the molar mass by the moles instead of multiplying them",
  "feedback": "This answer is wrong — you divided the molar mass by the moles instead of multiplying them"
 },
 {
  "value": 21.05,
  "misconception": "you slipped a decimal place in the product — 1.25 portions of 168.4 g must weigh more than one portion, not far less",
  "feedback": "This answer is wrong — you slipped a decimal place in the product — 1.25 portions of 168.4 g must weigh more than one portion, not far less"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nn = 1.250 mol\nM = 168.4 g/mol\nWrite down the equation:\nn = m / M\nMake m the subject:\nm = n × M\nSubstitute in the values, and calculate:\nm = 1.250 × 168.4\nm = 210.5 g\nSanity check: more than 1 mol must weigh more than the 168.4 g molar mass — 210.5 g passes.",
 "anticipatedWrong": [
  {
   "value": 0.007423,
   "misconception": "you divided the moles by the molar mass instead of multiplying them",
   "feedback": "This answer is wrong — you divided the moles by the molar mass instead of multiplying them"
  },
  {
   "value": 134.72,
   "misconception": "you divided the molar mass by the moles instead of multiplying them",
   "feedback": "This answer is wrong — you divided the molar mass by the moles instead of multiplying them"
  },
  {
   "value": 21.05,
   "misconception": "you slipped a decimal place in the product — 1.25 portions of 168.4 g must weigh more than one portion, not far less",
   "feedback": "This answer is wrong — you slipped a decimal place in the product — 1.25 portions of 168.4 g must weigh more than one portion, not far less"
  }
 ]
}

[
 {
  "value": 6.642311524410495e-24,
  "misconception": "you divided by Avogadro's number instead of multiplying — each mole contributes 6.022 × 10²³ particles",
  "feedback": "This answer is wrong — you divided by Avogadro's number instead of multiplying — each mole contributes 6.022 × 10²³ particles"
 },
 {
  "value": 6.022e+23,
  "misconception": "you ignored the mole count and answered Nₐ itself",
  "feedback": "This answer is wrong — you ignored the mole count and answered Nₐ itself"
 },
 {
  "value": 2.4088e+23,
  "misconception": "you slipped one power of ten in the exponent",
  "feedback": "This answer is wrong — you slipped one power of ten in the exponent"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nn = 4.00 mol\nNₐ = 6.022 × 10²³ mol⁻¹\nWrite down the equation:\nN = n × Nₐ\nSubstitute in the values, and calculate:\nN = 4.00 × 6.022 × 10²³\nN = 2.4088 × 10²⁴ = 2.41 × 10²⁴ formula units (3 significant figures, set by the 3-significant-figure mole value)\nSanity check: a lab-scale count lands around 10²² to 10²⁵ — 2.41 × 10²⁴ passes.",
 "anticipatedWrong": [
  {
   "value": 6.642311524410495e-24,
   "misconception": "you divided by Avogadro's number instead of multiplying — each mole contributes 6.022 × 10²³ particles",
   "feedback": "This answer is wrong — you divided by Avogadro's number instead of multiplying — each mole contributes 6.022 × 10²³ particles"
  },
  {
   "value": 6.022e+23,
   "misconception": "you ignored the mole count and answered Nₐ itself",
   "feedback": "This answer is wrong — you ignored the mole count and answered Nₐ itself"
  },
  {
   "value": 2.4088e+23,
   "misconception": "you slipped one power of ten in the exponent",
   "feedback": "This answer is wrong — you slipped one power of ten in the exponent"
  }
 ]
}

[
 {
  "value": 2.7198363e+47,
  "misconception": "you multiplied by Avogadro's number instead of dividing — this direction travels toward moles",
  "feedback": "This answer is wrong — you multiplied by Avogadro's number instead of dividing — this direction travels toward moles"
 },
 {
  "value": 1.3333333333333333,
  "misconception": "you divided Avogadro's number by the particle count instead of the other way around",
  "feedback": "This answer is wrong — you divided Avogadro's number by the particle count instead of the other way around"
 },
 {
  "value": 7.5,
  "misconception": "you slipped one power of ten in the division",
  "feedback": "This answer is wrong — you slipped one power of ten in the division"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nN = 4.5165 × 10²³ atoms\nNₐ = 6.022 × 10²³ mol⁻¹\nWrite down the equation:\nN = n × Nₐ\nMake n the subject:\nn = N/Nₐ\nSubstitute in the values, and calculate:\nn = 4.5165 × 10²³ / (6.022 × 10²³)\nn = 0.750 mol\nSanity check: a count below 6.022 × 10²³ means less than 1 mol, and above it more than 1 mol.",
 "anticipatedWrong": [
  {
   "value": 2.7198363e+47,
   "misconception": "you multiplied by Avogadro's number instead of dividing — this direction travels toward moles",
   "feedback": "This answer is wrong — you multiplied by Avogadro's number instead of dividing — this direction travels toward moles"
  },
  {
   "value": 1.3333333333333333,
   "misconception": "you divided Avogadro's number by the particle count instead of the other way around",
   "feedback": "This answer is wrong — you divided Avogadro's number by the particle count instead of the other way around"
  },
  {
   "value": 7.5,
   "misconception": "you slipped one power of ten in the division",
   "feedback": "This answer is wrong — you slipped one power of ten in the division"
  }
 ]
}

[
 {
  "value": 2.0,
  "misconception": "you ignored the subscript and gave the moles of the compound itself",
  "feedback": "This answer is wrong — you ignored the subscript and gave the moles of the compound itself"
 },
 {
  "value": 0.6666666666666666,
  "misconception": "you divided the moles by the subscript instead of multiplying",
  "feedback": "This answer is wrong — you divided the moles by the subscript instead of multiplying"
 },
 {
  "value": 8.0,
  "misconception": "you multiplied by the molecule's total atom count (4) instead of bromine's subscript (3)",
  "feedback": "This answer is wrong — you multiplied by the molecule's total atom count (4) instead of bromine's subscript (3)"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmoles of PBr₃ = 2.00 mol\nsubscript of bromine in PBr₃ = 3\nWrite down the equation:\nmoles of bromine atoms = subscript × moles of compound\nSubstitute in the values, and calculate:\nmoles of bromine atoms = 3 × 2.00\nmoles of bromine atoms = 6.00 mol",
 "anticipatedWrong": [
  {
   "value": 2.0,
   "misconception": "you ignored the subscript and gave the moles of the compound itself",
   "feedback": "This answer is wrong — you ignored the subscript and gave the moles of the compound itself"
  },
  {
   "value": 0.6666666666666666,
   "misconception": "you divided the moles by the subscript instead of multiplying",
   "feedback": "This answer is wrong — you divided the moles by the subscript instead of multiplying"
  },
  {
   "value": 8.0,
   "misconception": "you multiplied by the molecule's total atom count (4) instead of bromine's subscript (3)",
   "feedback": "This answer is wrong — you multiplied by the molecule's total atom count (4) instead of bromine's subscript (3)"
  }
 ]
}

[
 {
  "value": 3.0,
  "misconception": "you ignored the subscript outside the parentheses — it multiplies everything inside",
  "feedback": "This answer is wrong — you ignored the subscript outside the parentheses — it multiplies everything inside"
 },
 {
  "value": 12.0,
  "misconception": "you applied the outer subscript twice",
  "feedback": "This answer is wrong — you applied the outer subscript twice"
 }
]

{
 "keyExplanation": "The subscript outside the parentheses multiplies everything inside, so each formula unit of Mg(ClO₃)₂ carries 2 × 1 = 2 chlorine atoms.\nWrite down the equation:\nmoles of Cl atoms = subscript × moles of compound\nSubstitute in the values, and calculate:\nmoles of Cl atoms = 2 × 3.00\nmoles of Cl atoms = 6.00 mol",
 "anticipatedWrong": [
  {
   "value": 3.0,
   "misconception": "you ignored the subscript outside the parentheses — it multiplies everything inside",
   "feedback": "This answer is wrong — you ignored the subscript outside the parentheses — it multiplies everything inside"
  },
  {
   "value": 12.0,
   "misconception": "you applied the outer subscript twice",
   "feedback": "This answer is wrong — you applied the outer subscript twice"
  }
 ]
}

[
 {
  "value": 5.4198e+25,
  "misconception": "you skipped the mass-to-moles step and multiplied the mass by Avogadro's number",
  "feedback": "This answer is wrong — you skipped the mass-to-moles step and multiplied the mass by Avogadro's number"
 },
 {
  "value": 1.2044e+24,
  "misconception": "you divided the molar mass by the mass in step 1, inverting the mole value",
  "feedback": "This answer is wrong — you divided the molar mass by the mass in step 1, inverting the mole value"
 },
 {
  "value": 8.302889405513118e-25,
  "misconception": "you divided by Avogadro's number instead of multiplying — a count below one fails any sense check",
  "feedback": "This answer is wrong — you divided by Avogadro's number instead of multiplying — a count below one fails any sense check"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nm = 90.0 g\nM = 180.0 g/mol\nNₐ = 6.022 × 10²³ mol⁻¹\nStep 1 — convert mass to moles:\nn = m/M\nn = 90.0 / 180.0\nn = 0.500 mol   (the mole checkpoint — lab-scale values land between about 0.01 and 10 mol)\nStep 2 — convert moles to molecules:\nN = n × Nₐ\nN = 0.500 × 6.022 × 10²³\nN = 3.011 × 10²³ = 3.01 × 10²³ molecules (3 significant figures, set by the least-precise given)",
 "anticipatedWrong": [
  {
   "value": 5.4198e+25,
   "misconception": "you skipped the mass-to-moles step and multiplied the mass by Avogadro's number",
   "feedback": "This answer is wrong — you skipped the mass-to-moles step and multiplied the mass by Avogadro's number"
  },
  {
   "value": 1.2044e+24,
   "misconception": "you divided the molar mass by the mass in step 1, inverting the mole value",
   "feedback": "This answer is wrong — you divided the molar mass by the mass in step 1, inverting the mole value"
  },
  {
   "value": 8.302889405513118e-25,
   "misconception": "you divided by Avogadro's number instead of multiplying — a count below one fails any sense check",
   "feedback": "This answer is wrong — you divided by Avogadro's number instead of multiplying — a count below one fails any sense check"
  }
 ]
}

[
 {
  "value": 208.2,
  "misconception": "you gave one full mole's mass — the sample is not 1 mol; divide the count by Nₐ first",
  "feedback": "This answer is wrong — you gave one full mole's mass — the sample is not 1 mol; divide the count by Nₐ first"
 },
 {
  "value": 173.5,
  "misconception": "you divided the molar mass by the moles instead of multiplying them",
  "feedback": "This answer is wrong — you divided the molar mass by the moles instead of multiplying them"
 },
 {
  "value": 1.50453648e+26,
  "misconception": "you skipped the particles-to-moles step and multiplied the particle count by the molar mass",
  "feedback": "This answer is wrong — you skipped the particles-to-moles step and multiplied the particle count by the molar mass"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nN = 7.2264 × 10²³ formula units\nM = 208.2 g/mol\nNₐ = 6.022 × 10²³ mol⁻¹\nStep 1 — convert formula units to moles:\nN = n × Nₐ\nMake n the subject:\nn = N/Nₐ\nn = 7.2264 × 10²³ / (6.022 × 10²³)\nn = 1.200 mol   (the mole checkpoint)\nStep 2 — convert moles to mass:\nn = m/M\nMake m the subject:\nm = n × M\nm = 1.200 × 208.2\nm = 249.84 g\nReported to 4 significant figures (set by M and Nₐ): m = 249.8 g",
 "anticipatedWrong": [
  {
   "value": 208.2,
   "misconception": "you gave one full mole's mass — the sample is not 1 mol; divide the count by Nₐ first",
   "feedback": "This answer is wrong — you gave one full mole's mass — the sample is not 1 mol; divide the count by Nₐ first"
  },
  {
   "value": 173.5,
   "misconception": "you divided the molar mass by the moles instead of multiplying them",
   "feedback": "This answer is wrong — you divided the molar mass by the moles instead of multiplying them"
  },
  {
   "value": 1.50453648e+26,
   "misconception": "you skipped the particles-to-moles step and multiplied the particle count by the molar mass",
   "feedback": "This answer is wrong — you skipped the particles-to-moles step and multiplied the particle count by the molar mass"
  }
 ]
}

[
 {
  "value": 374.595,
  "misconception": "you ran a second stage the question never asked for — multiplying by the molar mass gives the mass, not the moles",
  "feedback": "This answer is wrong — you ran a second stage the question never asked for — multiplying by the molar mass gives the mass, not the moles"
 },
 {
  "value": 7.07157438e+47,
  "misconception": "you multiplied by Avogadro's number — moles and particle count are route neighbors, and this direction divides",
  "feedback": "This answer is wrong — you multiplied by Avogadro's number — moles and particle count are route neighbors, and this direction divides"
 },
 {
  "value": 0.5128205128205128,
  "misconception": "you divided Avogadro's number by the particle count instead of the other way around",
  "feedback": "This answer is wrong — you divided Avogadro's number by the particle count instead of the other way around"
 }
]

{
 "keyExplanation": "Ask the two route questions first: the question GIVES a particle count and ASKS for moles.\nCount and moles sit next to each other on the route, so ONE equation finishes the job — the supplied molar mass is never needed.\nN = n × Nₐ\nMake n the subject:\nn = N/Nₐ\nn = 1.17429 × 10²⁴ / (6.022 × 10²³)\nn = 1.95 mol",
 "anticipatedWrong": [
  {
   "value": 374.595,
   "misconception": "you ran a second stage the question never asked for — multiplying by the molar mass gives the mass, not the moles",
   "feedback": "This answer is wrong — you ran a second stage the question never asked for — multiplying by the molar mass gives the mass, not the moles"
  },
  {
   "value": 7.07157438e+47,
   "misconception": "you multiplied by Avogadro's number — moles and particle count are route neighbors, and this direction divides",
   "feedback": "This answer is wrong — you multiplied by Avogadro's number — moles and particle count are route neighbors, and this direction divides"
  },
  {
   "value": 0.5128205128205128,
   "misconception": "you divided Avogadro's number by the particle count instead of the other way around",
   "feedback": "This answer is wrong — you divided Avogadro's number by the particle count instead of the other way around"
  }
 ]
}

[
 {
  "value": 1.328462304882099e-23,
  "misconception": "you divided by Avogadro's number instead of multiplying — each mole contributes 6.022 × 10²³ particles",
  "feedback": "This answer is wrong — you divided by Avogadro's number instead of multiplying — each mole contributes 6.022 × 10²³ particles"
 },
 {
  "value": 6.022e+23,
  "misconception": "you ignored the mole count and answered Nₐ itself",
  "feedback": "This answer is wrong — you ignored the mole count and answered Nₐ itself"
 },
 {
  "value": 4.8176e+23,
  "misconception": "you slipped one power of ten in the exponent",
  "feedback": "This answer is wrong — you slipped one power of ten in the exponent"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nn = 8.00 mol\nNₐ = 6.022 × 10²³ mol⁻¹\nWrite down the equation:\nN = n × Nₐ\nSubstitute in the values, and calculate:\nN = 8.00 × 6.022 × 10²³\nN = 4.8176 × 10²⁴ = 4.82 × 10²⁴ molecules (3 significant figures, set by the 3-significant-figure mole value)\nSanity check: a lab-scale count lands around 10²² to 10²⁵ — 4.82 × 10²⁴ passes.",
 "anticipatedWrong": [
  {
   "value": 1.328462304882099e-23,
   "misconception": "you divided by Avogadro's number instead of multiplying — each mole contributes 6.022 × 10²³ particles",
   "feedback": "This answer is wrong — you divided by Avogadro's number instead of multiplying — each mole contributes 6.022 × 10²³ particles"
  },
  {
   "value": 6.022e+23,
   "misconception": "you ignored the mole count and answered Nₐ itself",
   "feedback": "This answer is wrong — you ignored the mole count and answered Nₐ itself"
  },
  {
   "value": 4.8176e+23,
   "misconception": "you slipped one power of ten in the exponent",
   "feedback": "This answer is wrong — you slipped one power of ten in the exponent"
  }
 ]
}

[
 {
  "value": 1.63190178e+48,
  "misconception": "you multiplied by Avogadro's number instead of dividing — this direction travels toward moles",
  "feedback": "This answer is wrong — you multiplied by Avogadro's number instead of dividing — this direction travels toward moles"
 },
 {
  "value": 0.2222222222222222,
  "misconception": "you divided Avogadro's number by the particle count instead of the other way around",
  "feedback": "This answer is wrong — you divided Avogadro's number by the particle count instead of the other way around"
 },
 {
  "value": 45.0,
  "misconception": "you slipped one power of ten in the division",
  "feedback": "This answer is wrong — you slipped one power of ten in the division"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nN = 2.7099 × 10²⁴ molecules\nNₐ = 6.022 × 10²³ mol⁻¹\nWrite down the equation:\nN = n × Nₐ\nMake n the subject:\nn = N/Nₐ\nSubstitute in the values, and calculate:\nn = 2.7099 × 10²⁴ / (6.022 × 10²³)\nn = 4.50 mol\nSanity check: a count below 6.022 × 10²³ means less than 1 mol, and above it more than 1 mol.",
 "anticipatedWrong": [
  {
   "value": 1.63190178e+48,
   "misconception": "you multiplied by Avogadro's number instead of dividing — this direction travels toward moles",
   "feedback": "This answer is wrong — you multiplied by Avogadro's number instead of dividing — this direction travels toward moles"
  },
  {
   "value": 0.2222222222222222,
   "misconception": "you divided Avogadro's number by the particle count instead of the other way around",
   "feedback": "This answer is wrong — you divided Avogadro's number by the particle count instead of the other way around"
  },
  {
   "value": 45.0,
   "misconception": "you slipped one power of ten in the division",
   "feedback": "This answer is wrong — you slipped one power of ten in the division"
  }
 ]
}

[
 {
  "value": 4.0,
  "misconception": "you ignored the subscript and gave the moles of the compound itself",
  "feedback": "This answer is wrong — you ignored the subscript and gave the moles of the compound itself"
 },
 {
  "value": 1.3333333333333333,
  "misconception": "you divided the moles by the subscript instead of multiplying",
  "feedback": "This answer is wrong — you divided the moles by the subscript instead of multiplying"
 },
 {
  "value": 16.0,
  "misconception": "you multiplied by the formula unit's total atom count (4) instead of iodine's subscript (3)",
  "feedback": "This answer is wrong — you multiplied by the formula unit's total atom count (4) instead of iodine's subscript (3)"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmoles of AlI₃ = 4.00 mol\nsubscript of iodine in AlI₃ = 3\nWrite down the equation:\nmoles of iodine atoms = subscript × moles of compound\nSubstitute in the values, and calculate:\nmoles of iodine atoms = 3 × 4.00\nmoles of iodine atoms = 12.0 mol",
 "anticipatedWrong": [
  {
   "value": 4.0,
   "misconception": "you ignored the subscript and gave the moles of the compound itself",
   "feedback": "This answer is wrong — you ignored the subscript and gave the moles of the compound itself"
  },
  {
   "value": 1.3333333333333333,
   "misconception": "you divided the moles by the subscript instead of multiplying",
   "feedback": "This answer is wrong — you divided the moles by the subscript instead of multiplying"
  },
  {
   "value": 16.0,
   "misconception": "you multiplied by the formula unit's total atom count (4) instead of iodine's subscript (3)",
   "feedback": "This answer is wrong — you multiplied by the formula unit's total atom count (4) instead of iodine's subscript (3)"
  }
 ]
}

[
 {
  "value": 4.0,
  "misconception": "you ignored the subscript outside the parentheses — it multiplies everything inside",
  "feedback": "This answer is wrong — you ignored the subscript outside the parentheses — it multiplies everything inside"
 },
 {
  "value": 16.0,
  "misconception": "you applied the outer subscript twice",
  "feedback": "This answer is wrong — you applied the outer subscript twice"
 }
]

{
 "keyExplanation": "The subscript outside the parentheses multiplies everything inside, so each formula unit of Ba(ClO₃)₂ carries 2 × 1 = 2 chlorine atoms.\nWrite down the equation:\nmoles of Cl atoms = subscript × moles of compound\nSubstitute in the values, and calculate:\nmoles of Cl atoms = 2 × 4.00\nmoles of Cl atoms = 8.00 mol",
 "anticipatedWrong": [
  {
   "value": 4.0,
   "misconception": "you ignored the subscript outside the parentheses — it multiplies everything inside",
   "feedback": "This answer is wrong — you ignored the subscript outside the parentheses — it multiplies everything inside"
  },
  {
   "value": 16.0,
   "misconception": "you applied the outer subscript twice",
   "feedback": "This answer is wrong — you applied the outer subscript twice"
  }
 ]
}

[
 {
  "value": 1.1580306e+26,
  "misconception": "you skipped the mass-to-moles step and multiplied the mass by Avogadro's number",
  "feedback": "This answer is wrong — you skipped the mass-to-moles step and multiplied the mass by Avogadro's number"
 },
 {
  "value": 4.014666666666667e+23,
  "misconception": "you divided the molar mass by the mass in step 1, inverting the mole value",
  "feedback": "This answer is wrong — you divided the molar mass by the mass in step 1, inverting the mole value"
 },
 {
  "value": 2.4908668216539354e-24,
  "misconception": "you divided by Avogadro's number instead of multiplying — a count below one fails any sense check",
  "feedback": "This answer is wrong — you divided by Avogadro's number instead of multiplying — a count below one fails any sense check"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nm = 192.3 g\nM = 128.2 g/mol\nNₐ = 6.022 × 10²³ mol⁻¹\nStep 1 — convert mass to moles:\nn = m/M\nn = 192.3 / 128.2\nn = 1.500 mol   (the mole checkpoint — lab-scale values land between about 0.01 and 10 mol)\nStep 2 — convert moles to molecules:\nN = n × Nₐ\nN = 1.500 × 6.022 × 10²³\nN = 9.033 × 10²³ molecules",
 "anticipatedWrong": [
  {
   "value": 1.1580306e+26,
   "misconception": "you skipped the mass-to-moles step and multiplied the mass by Avogadro's number",
   "feedback": "This answer is wrong — you skipped the mass-to-moles step and multiplied the mass by Avogadro's number"
  },
  {
   "value": 4.014666666666667e+23,
   "misconception": "you divided the molar mass by the mass in step 1, inverting the mole value",
   "feedback": "This answer is wrong — you divided the molar mass by the mass in step 1, inverting the mole value"
  },
  {
   "value": 2.4908668216539354e-24,
   "misconception": "you divided by Avogadro's number instead of multiplying — a count below one fails any sense check",
   "feedback": "This answer is wrong — you divided by Avogadro's number instead of multiplying — a count below one fails any sense check"
  }
 ]
}

[
 {
  "value": 183.7,
  "misconception": "you gave one full mole's mass — the sample is not 1 mol; divide the count by Nₐ first",
  "feedback": "This answer is wrong — you gave one full mole's mass — the sample is not 1 mol; divide the count by Nₐ first"
 },
 {
  "value": 76.54166666666667,
  "misconception": "you divided the molar mass by the moles instead of multiplying them",
  "feedback": "This answer is wrong — you divided the molar mass by the moles instead of multiplying them"
 },
 {
  "value": 2.65497936e+26,
  "misconception": "you skipped the particles-to-moles step and multiplied the particle count by the molar mass",
  "feedback": "This answer is wrong — you skipped the particles-to-moles step and multiplied the particle count by the molar mass"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nN = 1.44528 × 10²⁴ formula units\nM = 183.7 g/mol\nNₐ = 6.022 × 10²³ mol⁻¹\nStep 1 — convert formula units to moles:\nN = n × Nₐ\nMake n the subject:\nn = N/Nₐ\nn = 1.44528 × 10²⁴ / (6.022 × 10²³)\nn = 2.400 mol   (the mole checkpoint)\nStep 2 — convert moles to mass:\nn = m/M\nMake m the subject:\nm = n × M\nm = 2.400 × 183.7\nm = 440.88 g\nReported to 4 significant figures (set by M and Nₐ): m = 440.9 g",
 "anticipatedWrong": [
  {
   "value": 183.7,
   "misconception": "you gave one full mole's mass — the sample is not 1 mol; divide the count by Nₐ first",
   "feedback": "This answer is wrong — you gave one full mole's mass — the sample is not 1 mol; divide the count by Nₐ first"
  },
  {
   "value": 76.54166666666667,
   "misconception": "you divided the molar mass by the moles instead of multiplying them",
   "feedback": "This answer is wrong — you divided the molar mass by the moles instead of multiplying them"
  },
  {
   "value": 2.65497936e+26,
   "misconception": "you skipped the particles-to-moles step and multiplied the particle count by the molar mass",
   "feedback": "This answer is wrong — you skipped the particles-to-moles step and multiplied the particle count by the molar mass"
  }
 ]
}

[
 {
  "value": 361.005,
  "misconception": "you ran a second stage the question never asked for — multiplying by the molar mass gives the mass, not the moles",
  "feedback": "This answer is wrong — you ran a second stage the question never asked for — multiplying by the molar mass gives the mass, not the moles"
 },
 {
  "value": 7.43421922e+47,
  "misconception": "you multiplied by Avogadro's number — moles and particle count are route neighbors, and this direction divides",
  "feedback": "This answer is wrong — you multiplied by Avogadro's number — moles and particle count are route neighbors, and this direction divides"
 },
 {
  "value": 0.4878048780487805,
  "misconception": "you divided Avogadro's number by the particle count instead of the other way around",
  "feedback": "This answer is wrong — you divided Avogadro's number by the particle count instead of the other way around"
 }
]

{
 "keyExplanation": "Ask the two route questions first: the question GIVES a particle count and ASKS for moles.\nCount and moles sit next to each other on the route, so ONE equation finishes the job — the supplied molar mass is never needed.\nN = n × Nₐ\nMake n the subject:\nn = N/Nₐ\nn = 1.23451 × 10²⁴ / (6.022 × 10²³)\nn = 2.05 mol",
 "anticipatedWrong": [
  {
   "value": 361.005,
   "misconception": "you ran a second stage the question never asked for — multiplying by the molar mass gives the mass, not the moles",
   "feedback": "This answer is wrong — you ran a second stage the question never asked for — multiplying by the molar mass gives the mass, not the moles"
  },
  {
   "value": 7.43421922e+47,
   "misconception": "you multiplied by Avogadro's number — moles and particle count are route neighbors, and this direction divides",
   "feedback": "This answer is wrong — you multiplied by Avogadro's number — moles and particle count are route neighbors, and this direction divides"
  },
  {
   "value": 0.4878048780487805,
   "misconception": "you divided Avogadro's number by the particle count instead of the other way around",
   "feedback": "This answer is wrong — you divided Avogadro's number by the particle count instead of the other way around"
  }
 ]
}

[
 {
  "value": 9.963467286615742e-24,
  "misconception": "you divided by Avogadro's number instead of multiplying — each mole contributes 6.022 × 10²³ particles",
  "feedback": "This answer is wrong — you divided by Avogadro's number instead of multiplying — each mole contributes 6.022 × 10²³ particles"
 },
 {
  "value": 6.022e+23,
  "misconception": "you ignored the mole count and answered Nₐ itself",
  "feedback": "This answer is wrong — you ignored the mole count and answered Nₐ itself"
 },
 {
  "value": 3.6132e+23,
  "misconception": "you slipped one power of ten in the exponent",
  "feedback": "This answer is wrong — you slipped one power of ten in the exponent"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nn = 6.00 mol\nNₐ = 6.022 × 10²³ mol⁻¹\nWrite down the equation:\nN = n × Nₐ\nSubstitute in the values, and calculate:\nN = 6.00 × 6.022 × 10²³\nN = 3.6132 × 10²⁴ = 3.61 × 10²⁴ molecules (3 significant figures, set by the 3-significant-figure mole value)\nSanity check: a lab-scale count lands around 10²² to 10²⁵ — 3.61 × 10²⁴ passes.",
 "anticipatedWrong": [
  {
   "value": 9.963467286615742e-24,
   "misconception": "you divided by Avogadro's number instead of multiplying — each mole contributes 6.022 × 10²³ particles",
   "feedback": "This answer is wrong — you divided by Avogadro's number instead of multiplying — each mole contributes 6.022 × 10²³ particles"
  },
  {
   "value": 6.022e+23,
   "misconception": "you ignored the mole count and answered Nₐ itself",
   "feedback": "This answer is wrong — you ignored the mole count and answered Nₐ itself"
  },
  {
   "value": 3.6132e+23,
   "misconception": "you slipped one power of ten in the exponent",
   "feedback": "This answer is wrong — you slipped one power of ten in the exponent"
  }
 ]
}

[
 {
  "value": 5.07702776e+47,
  "misconception": "you multiplied by Avogadro's number instead of dividing — this direction travels toward moles",
  "feedback": "This answer is wrong — you multiplied by Avogadro's number instead of dividing — this direction travels toward moles"
 },
 {
  "value": 0.7142857142857143,
  "misconception": "you divided Avogadro's number by the particle count instead of the other way around",
  "feedback": "This answer is wrong — you divided Avogadro's number by the particle count instead of the other way around"
 },
 {
  "value": 14.0,
  "misconception": "you slipped one power of ten in the division",
  "feedback": "This answer is wrong — you slipped one power of ten in the division"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nN = 8.4308 × 10²³ formula units\nNₐ = 6.022 × 10²³ mol⁻¹\nWrite down the equation:\nN = n × Nₐ\nMake n the subject:\nn = N/Nₐ\nSubstitute in the values, and calculate:\nn = 8.4308 × 10²³ / (6.022 × 10²³)\nn = 1.40 mol\nSanity check: a count below 6.022 × 10²³ means less than 1 mol, and above it more than 1 mol.",
 "anticipatedWrong": [
  {
   "value": 5.07702776e+47,
   "misconception": "you multiplied by Avogadro's number instead of dividing — this direction travels toward moles",
   "feedback": "This answer is wrong — you multiplied by Avogadro's number instead of dividing — this direction travels toward moles"
  },
  {
   "value": 0.7142857142857143,
   "misconception": "you divided Avogadro's number by the particle count instead of the other way around",
   "feedback": "This answer is wrong — you divided Avogadro's number by the particle count instead of the other way around"
  },
  {
   "value": 14.0,
   "misconception": "you slipped one power of ten in the division",
   "feedback": "This answer is wrong — you slipped one power of ten in the division"
  }
 ]
}

[
 {
  "value": 12.0,
  "misconception": "you doubled the moles — the unwritten subscript on Br is 1, so the atom moles equal the compound moles",
  "feedback": "This answer is wrong — you doubled the moles — the unwritten subscript on Br is 1, so the atom moles equal the compound moles"
 },
 {
  "value": 3.0,
  "misconception": "you halved the moles — nothing in IBr divides the amount; the subscript on Br is an unwritten 1",
  "feedback": "This answer is wrong — you halved the moles — nothing in IBr divides the amount; the subscript on Br is an unwritten 1"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmoles of IBr = 6.00 mol\nsubscript of bromine in IBr = 1 (a symbol with no written subscript counts as 1)\nWrite down the equation:\nmoles of bromine atoms = subscript × moles of compound\nSubstitute in the values, and calculate:\nmoles of bromine atoms = 1 × 6.00\nmoles of bromine atoms = 6.00 mol",
 "anticipatedWrong": [
  {
   "value": 12.0,
   "misconception": "you doubled the moles — the unwritten subscript on Br is 1, so the atom moles equal the compound moles",
   "feedback": "This answer is wrong — you doubled the moles — the unwritten subscript on Br is 1, so the atom moles equal the compound moles"
  },
  {
   "value": 3.0,
   "misconception": "you halved the moles — nothing in IBr divides the amount; the subscript on Br is an unwritten 1",
   "feedback": "This answer is wrong — you halved the moles — nothing in IBr divides the amount; the subscript on Br is an unwritten 1"
  }
 ]
}

[
 {
  "value": 7.0,
  "misconception": "you ignored the subscript outside the parentheses — it multiplies everything inside",
  "feedback": "This answer is wrong — you ignored the subscript outside the parentheses — it multiplies everything inside"
 },
 {
  "value": 28.0,
  "misconception": "you applied the outer subscript twice",
  "feedback": "This answer is wrong — you applied the outer subscript twice"
 }
]

{
 "keyExplanation": "The subscript outside the parentheses multiplies everything inside, so each formula unit of Sr(ClO₄)₂ carries 2 × 1 = 2 chlorine atoms.\nWrite down the equation:\nmoles of Cl atoms = subscript × moles of compound\nSubstitute in the values, and calculate:\nmoles of Cl atoms = 2 × 7.00\nmoles of Cl atoms = 14.0 mol",
 "anticipatedWrong": [
  {
   "value": 7.0,
   "misconception": "you ignored the subscript outside the parentheses — it multiplies everything inside",
   "feedback": "This answer is wrong — you ignored the subscript outside the parentheses — it multiplies everything inside"
  },
  {
   "value": 28.0,
   "misconception": "you applied the outer subscript twice",
   "feedback": "This answer is wrong — you applied the outer subscript twice"
  }
 ]
}

[
 {
  "value": 2.37869e+25,
  "misconception": "you skipped the mass-to-moles step and multiplied the mass by Avogadro's number",
  "feedback": "This answer is wrong — you skipped the mass-to-moles step and multiplied the mass by Avogadro's number"
 },
 {
  "value": 2.4088e+24,
  "misconception": "you divided the molar mass by the mass in step 1, inverting the mole value",
  "feedback": "This answer is wrong — you divided the molar mass by the mass in step 1, inverting the mole value"
 },
 {
  "value": 4.151444702756559e-25,
  "misconception": "you divided by Avogadro's number instead of multiplying — a count below one fails any sense check",
  "feedback": "This answer is wrong — you divided by Avogadro's number instead of multiplying — a count below one fails any sense check"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nm = 39.5 g\nM = 158.0 g/mol\nNₐ = 6.022 × 10²³ mol⁻¹\nStep 1 — convert mass to moles:\nn = m/M\nn = 39.5 / 158.0\nn = 0.250 mol   (the mole checkpoint — lab-scale values land between about 0.01 and 10 mol)\nStep 2 — convert moles to formula units:\nN = n × Nₐ\nN = 0.250 × 6.022 × 10²³\nN = 1.5055 × 10²³ = 1.51 × 10²³ formula units (3 significant figures, set by the least-precise given)",
 "anticipatedWrong": [
  {
   "value": 2.37869e+25,
   "misconception": "you skipped the mass-to-moles step and multiplied the mass by Avogadro's number",
   "feedback": "This answer is wrong — you skipped the mass-to-moles step and multiplied the mass by Avogadro's number"
  },
  {
   "value": 2.4088e+24,
   "misconception": "you divided the molar mass by the mass in step 1, inverting the mole value",
   "feedback": "This answer is wrong — you divided the molar mass by the mass in step 1, inverting the mole value"
  },
  {
   "value": 4.151444702756559e-25,
   "misconception": "you divided by Avogadro's number instead of multiplying — a count below one fails any sense check",
   "feedback": "This answer is wrong — you divided by Avogadro's number instead of multiplying — a count below one fails any sense check"
  }
 ]
}

[
 {
  "value": 297.1,
  "misconception": "you gave one full mole's mass — the sample is not 1 mol; divide the count by Nₐ first",
  "feedback": "This answer is wrong — you gave one full mole's mass — the sample is not 1 mol; divide the count by Nₐ first"
 },
 {
  "value": 114.26923076923077,
  "misconception": "you divided the molar mass by the moles instead of multiplying them",
  "feedback": "This answer is wrong — you divided the molar mass by the moles instead of multiplying them"
 },
 {
  "value": 4.65175412e+26,
  "misconception": "you skipped the particles-to-moles step and multiplied the particle count by the molar mass",
  "feedback": "This answer is wrong — you skipped the particles-to-moles step and multiplied the particle count by the molar mass"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nN = 1.56572 × 10²⁴ formula units\nM = 297.1 g/mol\nNₐ = 6.022 × 10²³ mol⁻¹\nStep 1 — convert formula units to moles:\nN = n × Nₐ\nMake n the subject:\nn = N/Nₐ\nn = 1.56572 × 10²⁴ / (6.022 × 10²³)\nn = 2.600 mol   (the mole checkpoint)\nStep 2 — convert moles to mass:\nn = m/M\nMake m the subject:\nm = n × M\nm = 2.600 × 297.1\nm = 772.46 g\nReported to 4 significant figures (set by M and Nₐ): m = 772.5 g",
 "anticipatedWrong": [
  {
   "value": 297.1,
   "misconception": "you gave one full mole's mass — the sample is not 1 mol; divide the count by Nₐ first",
   "feedback": "This answer is wrong — you gave one full mole's mass — the sample is not 1 mol; divide the count by Nₐ first"
  },
  {
   "value": 114.26923076923077,
   "misconception": "you divided the molar mass by the moles instead of multiplying them",
   "feedback": "This answer is wrong — you divided the molar mass by the moles instead of multiplying them"
  },
  {
   "value": 4.65175412e+26,
   "misconception": "you skipped the particles-to-moles step and multiplied the particle count by the molar mass",
   "feedback": "This answer is wrong — you skipped the particles-to-moles step and multiplied the particle count by the molar mass"
  }
 ]
}

[
 {
  "value": 155.244,
  "misconception": "you ran a second stage the question never asked for — multiplying by the molar mass gives the mass, not the moles",
  "feedback": "This answer is wrong — you ran a second stage the question never asked for — multiplying by the molar mass gives the mass, not the moles"
 },
 {
  "value": 3.698977368e+47,
  "misconception": "you multiplied by Avogadro's number — moles and particle count are route neighbors, and this direction divides",
  "feedback": "This answer is wrong — you multiplied by Avogadro's number — moles and particle count are route neighbors, and this direction divides"
 },
 {
  "value": 0.9803921568627451,
  "misconception": "you divided Avogadro's number by the particle count instead of the other way around",
  "feedback": "This answer is wrong — you divided Avogadro's number by the particle count instead of the other way around"
 }
]

{
 "keyExplanation": "Ask the two route questions first: the question GIVES a particle count and ASKS for moles.\nCount and moles sit next to each other on the route, so ONE equation finishes the job — the supplied molar mass is never needed.\nN = n × Nₐ\nMake n the subject:\nn = N/Nₐ\nn = 6.14244 × 10²³ / (6.022 × 10²³)\nn = 1.02 mol",
 "anticipatedWrong": [
  {
   "value": 155.244,
   "misconception": "you ran a second stage the question never asked for — multiplying by the molar mass gives the mass, not the moles",
   "feedback": "This answer is wrong — you ran a second stage the question never asked for — multiplying by the molar mass gives the mass, not the moles"
  },
  {
   "value": 3.698977368e+47,
   "misconception": "you multiplied by Avogadro's number — moles and particle count are route neighbors, and this direction divides",
   "feedback": "This answer is wrong — you multiplied by Avogadro's number — moles and particle count are route neighbors, and this direction divides"
  },
  {
   "value": 0.9803921568627451,
   "misconception": "you divided Avogadro's number by the particle count instead of the other way around",
   "feedback": "This answer is wrong — you divided Avogadro's number by the particle count instead of the other way around"
  }
 ]
}

[
 {
  "value": 1.1624045167718365e-23,
  "misconception": "you divided by Avogadro's number instead of multiplying — each mole contributes 6.022 × 10²³ particles",
  "feedback": "This answer is wrong — you divided by Avogadro's number instead of multiplying — each mole contributes 6.022 × 10²³ particles"
 },
 {
  "value": 6.022e+23,
  "misconception": "you ignored the mole count and answered Nₐ itself",
  "feedback": "This answer is wrong — you ignored the mole count and answered Nₐ itself"
 },
 {
  "value": 4.2154e+23,
  "misconception": "you slipped one power of ten in the exponent",
  "feedback": "This answer is wrong — you slipped one power of ten in the exponent"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nn = 7.00 mol\nNₐ = 6.022 × 10²³ mol⁻¹\nWrite down the equation:\nN = n × Nₐ\nSubstitute in the values, and calculate:\nN = 7.00 × 6.022 × 10²³\nN = 4.2154 × 10²⁴ = 4.22 × 10²⁴ formula units (3 significant figures, set by the 3-significant-figure mole value)\nSanity check: a lab-scale count lands around 10²² to 10²⁵ — 4.22 × 10²⁴ passes.",
 "anticipatedWrong": [
  {
   "value": 1.1624045167718365e-23,
   "misconception": "you divided by Avogadro's number instead of multiplying — each mole contributes 6.022 × 10²³ particles",
   "feedback": "This answer is wrong — you divided by Avogadro's number instead of multiplying — each mole contributes 6.022 × 10²³ particles"
  },
  {
   "value": 6.022e+23,
   "misconception": "you ignored the mole count and answered Nₐ itself",
   "feedback": "This answer is wrong — you ignored the mole count and answered Nₐ itself"
  },
  {
   "value": 4.2154e+23,
   "misconception": "you slipped one power of ten in the exponent",
   "feedback": "This answer is wrong — you slipped one power of ten in the exponent"
  }
 ]
}

[
 {
  "value": 3.98909324e+47,
  "misconception": "you multiplied by Avogadro's number instead of dividing — this direction travels toward moles",
  "feedback": "This answer is wrong — you multiplied by Avogadro's number instead of dividing — this direction travels toward moles"
 },
 {
  "value": 0.9090909090909091,
  "misconception": "you divided Avogadro's number by the particle count instead of the other way around",
  "feedback": "This answer is wrong — you divided Avogadro's number by the particle count instead of the other way around"
 },
 {
  "value": 11.0,
  "misconception": "you slipped one power of ten in the division",
  "feedback": "This answer is wrong — you slipped one power of ten in the division"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nN = 6.6242 × 10²³ formula units\nNₐ = 6.022 × 10²³ mol⁻¹\nWrite down the equation:\nN = n × Nₐ\nMake n the subject:\nn = N/Nₐ\nSubstitute in the values, and calculate:\nn = 6.6242 × 10²³ / (6.022 × 10²³)\nn = 1.10 mol\nSanity check: a count below 6.022 × 10²³ means less than 1 mol, and above it more than 1 mol.",
 "anticipatedWrong": [
  {
   "value": 3.98909324e+47,
   "misconception": "you multiplied by Avogadro's number instead of dividing — this direction travels toward moles",
   "feedback": "This answer is wrong — you multiplied by Avogadro's number instead of dividing — this direction travels toward moles"
  },
  {
   "value": 0.9090909090909091,
   "misconception": "you divided Avogadro's number by the particle count instead of the other way around",
   "feedback": "This answer is wrong — you divided Avogadro's number by the particle count instead of the other way around"
  },
  {
   "value": 11.0,
   "misconception": "you slipped one power of ten in the division",
   "feedback": "This answer is wrong — you slipped one power of ten in the division"
  }
 ]
}

[
 {
  "value": 3.0,
  "misconception": "you ignored the subscript and gave the moles of the compound itself",
  "feedback": "This answer is wrong — you ignored the subscript and gave the moles of the compound itself"
 },
 {
  "value": 0.75,
  "misconception": "you divided the moles by the subscript instead of multiplying",
  "feedback": "This answer is wrong — you divided the moles by the subscript instead of multiplying"
 },
 {
  "value": 30.0,
  "misconception": "you used oxygen's subscript instead of phosphorus's",
  "feedback": "This answer is wrong — you used oxygen's subscript instead of phosphorus's"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmoles of P₄O₁₀ = 3.00 mol\nsubscript of phosphorus in P₄O₁₀ = 4\nWrite down the equation:\nmoles of phosphorus atoms = subscript × moles of compound\nSubstitute in the values, and calculate:\nmoles of phosphorus atoms = 4 × 3.00\nmoles of phosphorus atoms = 12.0 mol",
 "anticipatedWrong": [
  {
   "value": 3.0,
   "misconception": "you ignored the subscript and gave the moles of the compound itself",
   "feedback": "This answer is wrong — you ignored the subscript and gave the moles of the compound itself"
  },
  {
   "value": 0.75,
   "misconception": "you divided the moles by the subscript instead of multiplying",
   "feedback": "This answer is wrong — you divided the moles by the subscript instead of multiplying"
  },
  {
   "value": 30.0,
   "misconception": "you used oxygen's subscript instead of phosphorus's",
   "feedback": "This answer is wrong — you used oxygen's subscript instead of phosphorus's"
  }
 ]
}

[
 {
  "value": 2.0,
  "misconception": "you ignored the subscript outside the parentheses — it multiplies everything inside",
  "feedback": "This answer is wrong — you ignored the subscript outside the parentheses — it multiplies everything inside"
 },
 {
  "value": 8.0,
  "misconception": "you applied the outer subscript twice",
  "feedback": "This answer is wrong — you applied the outer subscript twice"
 }
]

{
 "keyExplanation": "The subscript outside the parentheses multiplies everything inside, so each formula unit of Zn(ClO₃)₂ carries 2 × 1 = 2 chlorine atoms.\nWrite down the equation:\nmoles of Cl atoms = subscript × moles of compound\nSubstitute in the values, and calculate:\nmoles of Cl atoms = 2 × 2.00\nmoles of Cl atoms = 4.00 mol",
 "anticipatedWrong": [
  {
   "value": 2.0,
   "misconception": "you ignored the subscript outside the parentheses — it multiplies everything inside",
   "feedback": "This answer is wrong — you ignored the subscript outside the parentheses — it multiplies everything inside"
  },
  {
   "value": 8.0,
   "misconception": "you applied the outer subscript twice",
   "feedback": "This answer is wrong — you applied the outer subscript twice"
  }
 ]
}

[
 {
  "value": 1.3236356e+26,
  "misconception": "you skipped the mass-to-moles step and multiplied the mass by Avogadro's number",
  "feedback": "This answer is wrong — you skipped the mass-to-moles step and multiplied the mass by Avogadro's number"
 },
 {
  "value": 3.011e+23,
  "misconception": "you divided the molar mass by the mass in step 1, inverting the mole value",
  "feedback": "This answer is wrong — you divided the molar mass by the mass in step 1, inverting the mole value"
 },
 {
  "value": 3.321155762205247e-24,
  "misconception": "you divided by Avogadro's number instead of multiplying — a count below one fails any sense check",
  "feedback": "This answer is wrong — you divided by Avogadro's number instead of multiplying — a count below one fails any sense check"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nm = 219.8 g\nM = 109.9 g/mol\nNₐ = 6.022 × 10²³ mol⁻¹\nStep 1 — convert mass to moles:\nn = m/M\nn = 219.8 / 109.9\nn = 2.000 mol   (the mole checkpoint — lab-scale values land between about 0.01 and 10 mol)\nStep 2 — convert moles to formula units:\nN = n × Nₐ\nN = 2.000 × 6.022 × 10²³\nN = 1.2044 × 10²⁴ = 1.204 × 10²⁴ formula units (4 significant figures, set by the least-precise given)",
 "anticipatedWrong": [
  {
   "value": 1.3236356e+26,
   "misconception": "you skipped the mass-to-moles step and multiplied the mass by Avogadro's number",
   "feedback": "This answer is wrong — you skipped the mass-to-moles step and multiplied the mass by Avogadro's number"
  },
  {
   "value": 3.011e+23,
   "misconception": "you divided the molar mass by the mass in step 1, inverting the mole value",
   "feedback": "This answer is wrong — you divided the molar mass by the mass in step 1, inverting the mole value"
  },
  {
   "value": 3.321155762205247e-24,
   "misconception": "you divided by Avogadro's number instead of multiplying — a count below one fails any sense check",
   "feedback": "This answer is wrong — you divided by Avogadro's number instead of multiplying — a count below one fails any sense check"
  }
 ]
}

[
 {
  "value": 115.8,
  "misconception": "you gave one full mole's mass — the sample is not 1 mol; divide the count by Nₐ first",
  "feedback": "This answer is wrong — you gave one full mole's mass — the sample is not 1 mol; divide the count by Nₐ first"
 },
 {
  "value": 92.64,
  "misconception": "you divided the molar mass by the moles instead of multiplying them",
  "feedback": "This answer is wrong — you divided the molar mass by the moles instead of multiplying them"
 },
 {
  "value": 8.716845e+25,
  "misconception": "you skipped the particles-to-moles step and multiplied the particle count by the molar mass",
  "feedback": "This answer is wrong — you skipped the particles-to-moles step and multiplied the particle count by the molar mass"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nN = 7.5275 × 10²³ formula units\nM = 115.8 g/mol\nNₐ = 6.022 × 10²³ mol⁻¹\nStep 1 — convert formula units to moles:\nN = n × Nₐ\nMake n the subject:\nn = N/Nₐ\nn = 7.5275 × 10²³ / (6.022 × 10²³)\nn = 1.250 mol   (the mole checkpoint)\nStep 2 — convert moles to mass:\nn = m/M\nMake m the subject:\nm = n × M\nm = 1.250 × 115.8\nm = 144.75 g\nReported to 4 significant figures (set by M and Nₐ): m = 144.8 g",
 "anticipatedWrong": [
  {
   "value": 115.8,
   "misconception": "you gave one full mole's mass — the sample is not 1 mol; divide the count by Nₐ first",
   "feedback": "This answer is wrong — you gave one full mole's mass — the sample is not 1 mol; divide the count by Nₐ first"
  },
  {
   "value": 92.64,
   "misconception": "you divided the molar mass by the moles instead of multiplying them",
   "feedback": "This answer is wrong — you divided the molar mass by the moles instead of multiplying them"
  },
  {
   "value": 8.716845e+25,
   "misconception": "you skipped the particles-to-moles step and multiplied the particle count by the molar mass",
   "feedback": "This answer is wrong — you skipped the particles-to-moles step and multiplied the particle count by the molar mass"
  }
 ]
}

[
 {
  "value": 126.984,
  "misconception": "you ran a second stage the question never asked for — multiplying by the molar mass gives the mass, not the moles",
  "feedback": "This answer is wrong — you ran a second stage the question never asked for — multiplying by the molar mass gives the mass, not the moles"
 },
 {
  "value": 3.771506336e+47,
  "misconception": "you multiplied by Avogadro's number — moles and particle count are route neighbors, and this direction divides",
  "feedback": "This answer is wrong — you multiplied by Avogadro's number — moles and particle count are route neighbors, and this direction divides"
 },
 {
  "value": 0.9615384615384616,
  "misconception": "you divided Avogadro's number by the particle count instead of the other way around",
  "feedback": "This answer is wrong — you divided Avogadro's number by the particle count instead of the other way around"
 }
]

{
 "keyExplanation": "Ask the two route questions first: the question GIVES a particle count and ASKS for moles.\nCount and moles sit next to each other on the route, so ONE equation finishes the job — the supplied molar mass is never needed.\nN = n × Nₐ\nMake n the subject:\nn = N/Nₐ\nn = 6.26288 × 10²³ / (6.022 × 10²³)\nn = 1.04 mol",
 "anticipatedWrong": [
  {
   "value": 126.984,
   "misconception": "you ran a second stage the question never asked for — multiplying by the molar mass gives the mass, not the moles",
   "feedback": "This answer is wrong — you ran a second stage the question never asked for — multiplying by the molar mass gives the mass, not the moles"
  },
  {
   "value": 3.771506336e+47,
   "misconception": "you multiplied by Avogadro's number — moles and particle count are route neighbors, and this direction divides",
   "feedback": "This answer is wrong — you multiplied by Avogadro's number — moles and particle count are route neighbors, and this direction divides"
  },
  {
   "value": 0.9615384615384616,
   "misconception": "you divided Avogadro's number by the particle count instead of the other way around",
   "feedback": "This answer is wrong — you divided Avogadro's number by the particle count instead of the other way around"
  }
 ]
}

[
 {
  "value": 1.4945200929923614e-23,
  "misconception": "you divided by Avogadro's number instead of multiplying — each mole contributes 6.022 × 10²³ particles",
  "feedback": "This answer is wrong — you divided by Avogadro's number instead of multiplying — each mole contributes 6.022 × 10²³ particles"
 },
 {
  "value": 6.022e+23,
  "misconception": "you ignored the mole count and answered Nₐ itself",
  "feedback": "This answer is wrong — you ignored the mole count and answered Nₐ itself"
 },
 {
  "value": 5.4198e+23,
  "misconception": "you slipped one power of ten in the exponent",
  "feedback": "This answer is wrong — you slipped one power of ten in the exponent"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nn = 9.00 mol\nNₐ = 6.022 × 10²³ mol⁻¹\nWrite down the equation:\nN = n × Nₐ\nSubstitute in the values, and calculate:\nN = 9.00 × 6.022 × 10²³\nN = 5.4198 × 10²⁴ = 5.42 × 10²⁴ formula units (3 significant figures, set by the 3-significant-figure mole value)\nSanity check: a lab-scale count lands around 10²² to 10²⁵ — 5.42 × 10²⁴ passes.",
 "anticipatedWrong": [
  {
   "value": 1.4945200929923614e-23,
   "misconception": "you divided by Avogadro's number instead of multiplying — each mole contributes 6.022 × 10²³ particles",
   "feedback": "This answer is wrong — you divided by Avogadro's number instead of multiplying — each mole contributes 6.022 × 10²³ particles"
  },
  {
   "value": 6.022e+23,
   "misconception": "you ignored the mole count and answered Nₐ itself",
   "feedback": "This answer is wrong — you ignored the mole count and answered Nₐ itself"
  },
  {
   "value": 5.4198e+23,
   "misconception": "you slipped one power of ten in the exponent",
   "feedback": "This answer is wrong — you slipped one power of ten in the exponent"
  }
 ]
}

[
 {
  "value": 1.99454662e+47,
  "misconception": "you multiplied by Avogadro's number instead of dividing — this direction travels toward moles",
  "feedback": "This answer is wrong — you multiplied by Avogadro's number instead of dividing — this direction travels toward moles"
 },
 {
  "value": 1.8181818181818181,
  "misconception": "you divided Avogadro's number by the particle count instead of the other way around",
  "feedback": "This answer is wrong — you divided Avogadro's number by the particle count instead of the other way around"
 },
 {
  "value": 5.5,
  "misconception": "you slipped one power of ten in the division",
  "feedback": "This answer is wrong — you slipped one power of ten in the division"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nN = 3.3121 × 10²³ atoms\nNₐ = 6.022 × 10²³ mol⁻¹\nWrite down the equation:\nN = n × Nₐ\nMake n the subject:\nn = N/Nₐ\nSubstitute in the values, and calculate:\nn = 3.3121 × 10²³ / (6.022 × 10²³)\nn = 0.550 mol\nSanity check: a count below 6.022 × 10²³ means less than 1 mol, and above it more than 1 mol.",
 "anticipatedWrong": [
  {
   "value": 1.99454662e+47,
   "misconception": "you multiplied by Avogadro's number instead of dividing — this direction travels toward moles",
   "feedback": "This answer is wrong — you multiplied by Avogadro's number instead of dividing — this direction travels toward moles"
  },
  {
   "value": 1.8181818181818181,
   "misconception": "you divided Avogadro's number by the particle count instead of the other way around",
   "feedback": "This answer is wrong — you divided Avogadro's number by the particle count instead of the other way around"
  },
  {
   "value": 5.5,
   "misconception": "you slipped one power of ten in the division",
   "feedback": "This answer is wrong — you slipped one power of ten in the division"
  }
 ]
}

[
 {
  "value": 6.0,
  "misconception": "you ignored the subscript and gave the moles of the compound itself",
  "feedback": "This answer is wrong — you ignored the subscript and gave the moles of the compound itself"
 },
 {
  "value": 3.0,
  "misconception": "you divided the moles by the subscript instead of multiplying",
  "feedback": "This answer is wrong — you divided the moles by the subscript instead of multiplying"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmoles of K₂S = 6.00 mol\nsubscript of potassium in K₂S = 2\nWrite down the equation:\nmoles of potassium atoms = subscript × moles of compound\nSubstitute in the values, and calculate:\nmoles of potassium atoms = 2 × 6.00\nmoles of potassium atoms = 12.0 mol",
 "anticipatedWrong": [
  {
   "value": 6.0,
   "misconception": "you ignored the subscript and gave the moles of the compound itself",
   "feedback": "This answer is wrong — you ignored the subscript and gave the moles of the compound itself"
  },
  {
   "value": 3.0,
   "misconception": "you divided the moles by the subscript instead of multiplying",
   "feedback": "This answer is wrong — you divided the moles by the subscript instead of multiplying"
  }
 ]
}

[
 {
  "value": 3.0,
  "misconception": "you ignored the subscript outside the parentheses — it multiplies everything inside",
  "feedback": "This answer is wrong — you ignored the subscript outside the parentheses — it multiplies everything inside"
 },
 {
  "value": 27.0,
  "misconception": "you applied the outer subscript twice",
  "feedback": "This answer is wrong — you applied the outer subscript twice"
 }
]

{
 "keyExplanation": "The subscript outside the parentheses multiplies everything inside, so each formula unit of Fe(ClO₃)₃ carries 3 × 1 = 3 chlorine atoms.\nWrite down the equation:\nmoles of Cl atoms = subscript × moles of compound\nSubstitute in the values, and calculate:\nmoles of Cl atoms = 3 × 3.00\nmoles of Cl atoms = 9.00 mol",
 "anticipatedWrong": [
  {
   "value": 3.0,
   "misconception": "you ignored the subscript outside the parentheses — it multiplies everything inside",
   "feedback": "This answer is wrong — you ignored the subscript outside the parentheses — it multiplies everything inside"
  },
  {
   "value": 27.0,
   "misconception": "you applied the outer subscript twice",
   "feedback": "This answer is wrong — you applied the outer subscript twice"
  }
 ]
}

[
 {
  "value": 3.1669698e+26,
  "misconception": "you skipped the mass-to-moles step and multiplied the mass by Avogadro's number",
  "feedback": "This answer is wrong — you skipped the mass-to-moles step and multiplied the mass by Avogadro's number"
 },
 {
  "value": 2.0073333333333334e+23,
  "misconception": "you divided the molar mass by the mass in step 1, inverting the mole value",
  "feedback": "This answer is wrong — you divided the molar mass by the mass in step 1, inverting the mole value"
 },
 {
  "value": 4.981733643307871e-24,
  "misconception": "you divided by Avogadro's number instead of multiplying — a count below one fails any sense check",
  "feedback": "This answer is wrong — you divided by Avogadro's number instead of multiplying — a count below one fails any sense check"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nm = 525.9 g\nM = 175.3 g/mol\nNₐ = 6.022 × 10²³ mol⁻¹\nStep 1 — convert mass to moles:\nn = m/M\nn = 525.9 / 175.3\nn = 3.000 mol   (the mole checkpoint — lab-scale values land between about 0.01 and 10 mol)\nStep 2 — convert moles to formula units:\nN = n × Nₐ\nN = 3.000 × 6.022 × 10²³\nN = 1.8066 × 10²⁴ = 1.807 × 10²⁴ formula units (4 significant figures, set by the least-precise given)",
 "anticipatedWrong": [
  {
   "value": 3.1669698e+26,
   "misconception": "you skipped the mass-to-moles step and multiplied the mass by Avogadro's number",
   "feedback": "This answer is wrong — you skipped the mass-to-moles step and multiplied the mass by Avogadro's number"
  },
  {
   "value": 2.0073333333333334e+23,
   "misconception": "you divided the molar mass by the mass in step 1, inverting the mole value",
   "feedback": "This answer is wrong — you divided the molar mass by the mass in step 1, inverting the mole value"
  },
  {
   "value": 4.981733643307871e-24,
   "misconception": "you divided by Avogadro's number instead of multiplying — a count below one fails any sense check",
   "feedback": "This answer is wrong — you divided by Avogadro's number instead of multiplying — a count below one fails any sense check"
  }
 ]
}

[
 {
  "value": 144.9,
  "misconception": "you gave one full mole's mass — the sample is not 1 mol; divide the count by Nₐ first",
  "feedback": "This answer is wrong — you gave one full mole's mass — the sample is not 1 mol; divide the count by Nₐ first"
 },
 {
  "value": 45.28125,
  "misconception": "you divided the molar mass by the moles instead of multiplying them",
  "feedback": "This answer is wrong — you divided the molar mass by the moles instead of multiplying them"
 },
 {
  "value": 2.79228096e+26,
  "misconception": "you skipped the particles-to-moles step and multiplied the particle count by the molar mass",
  "feedback": "This answer is wrong — you skipped the particles-to-moles step and multiplied the particle count by the molar mass"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nN = 1.92704 × 10²⁴ formula units\nM = 144.9 g/mol\nNₐ = 6.022 × 10²³ mol⁻¹\nStep 1 — convert formula units to moles:\nN = n × Nₐ\nMake n the subject:\nn = N/Nₐ\nn = 1.92704 × 10²⁴ / (6.022 × 10²³)\nn = 3.200 mol   (the mole checkpoint)\nStep 2 — convert moles to mass:\nn = m/M\nMake m the subject:\nm = n × M\nm = 3.200 × 144.9\nm = 463.68 g\nReported to 4 significant figures (set by M and Nₐ): m = 463.7 g",
 "anticipatedWrong": [
  {
   "value": 144.9,
   "misconception": "you gave one full mole's mass — the sample is not 1 mol; divide the count by Nₐ first",
   "feedback": "This answer is wrong — you gave one full mole's mass — the sample is not 1 mol; divide the count by Nₐ first"
  },
  {
   "value": 45.28125,
   "misconception": "you divided the molar mass by the moles instead of multiplying them",
   "feedback": "This answer is wrong — you divided the molar mass by the moles instead of multiplying them"
  },
  {
   "value": 2.79228096e+26,
   "misconception": "you skipped the particles-to-moles step and multiplied the particle count by the molar mass",
   "feedback": "This answer is wrong — you skipped the particles-to-moles step and multiplied the particle count by the molar mass"
  }
 ]
}

[
 {
  "value": 164.268,
  "misconception": "you ran a second stage the question never asked for — multiplying by the molar mass gives the mass, not the moles",
  "feedback": "This answer is wrong — you ran a second stage the question never asked for — multiplying by the molar mass gives the mass, not the moles"
 },
 {
  "value": 3.916564272e+47,
  "misconception": "you multiplied by Avogadro's number — moles and particle count are route neighbors, and this direction divides",
  "feedback": "This answer is wrong — you multiplied by Avogadro's number — moles and particle count are route neighbors, and this direction divides"
 },
 {
  "value": 0.9259259259259259,
  "misconception": "you divided Avogadro's number by the particle count instead of the other way around",
  "feedback": "This answer is wrong — you divided Avogadro's number by the particle count instead of the other way around"
 }
]

{
 "keyExplanation": "Ask the two route questions first: the question GIVES a particle count and ASKS for moles.\nCount and moles sit next to each other on the route, so ONE equation finishes the job — the supplied molar mass is never needed.\nN = n × Nₐ\nMake n the subject:\nn = N/Nₐ\nn = 6.50376 × 10²³ / (6.022 × 10²³)\nn = 1.08 mol",
 "anticipatedWrong": [
  {
   "value": 164.268,
   "misconception": "you ran a second stage the question never asked for — multiplying by the molar mass gives the mass, not the moles",
   "feedback": "This answer is wrong — you ran a second stage the question never asked for — multiplying by the molar mass gives the mass, not the moles"
  },
  {
   "value": 3.916564272e+47,
   "misconception": "you multiplied by Avogadro's number — moles and particle count are route neighbors, and this direction divides",
   "feedback": "This answer is wrong — you multiplied by Avogadro's number — moles and particle count are route neighbors, and this direction divides"
  },
  {
   "value": 0.9259259259259259,
   "misconception": "you divided Avogadro's number by the particle count instead of the other way around",
   "feedback": "This answer is wrong — you divided Avogadro's number by the particle count instead of the other way around"
  }
 ]
}

[
 {
  "value": 26.5,
  "misconception": "you forgot to multiply by the subscript — the formula carries 2 Al atoms",
  "feedback": "This answer is wrong — you forgot to multiply by the subscript — the formula carries 2 Al atoms."
 },
 {
  "value": 189.0,
  "misconception": "you inverted the ratio — a percent over 100 is impossible",
  "feedback": "This answer is wrong — you inverted the ratio — a percent over 100 is impossible."
 },
 {
  "value": 0.5294,
  "misconception": "you forgot to multiply by 100",
  "feedback": "This answer is wrong — you forgot to multiply by 100."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of Al in one mole = 2 × 27.0 = 54.0 g\nM = 102.0 g/mol\nWrite down the equation:\n% Al = (mass of Al in one mole ÷ M) × 100\nSubstitute in the values, and calculate:\n% Al = (54.0 ÷ 102.0) × 100\n% Al = 52.9%"
}

[
 {
  "value": 124.0,
  "misconception": "you inverted the ratio — a percent over 100 is impossible",
  "feedback": "This answer is wrong — you inverted the ratio — a percent over 100 is impossible."
 },
 {
  "value": 0.8034,
  "misconception": "you forgot to multiply by 100",
  "feedback": "This answer is wrong — you forgot to multiply by 100."
 },
 {
  "value": 19.7,
  "misconception": "you found the other element's share instead of Zn's",
  "feedback": "This answer is wrong — you found the other element's share instead of Zn's."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of Zn in the sample = 32.7 g\nmass of the sample = 40.7 g\nWrite down the equation:\n% Zn = (mass of Zn in the sample ÷ mass of the sample) × 100\nSubstitute in the values, and calculate:\n% Zn = (32.7 ÷ 40.7) × 100\n% Zn = 80.3%"
}

[
 {
  "value": 232.5,
  "misconception": "you divided the Fe mass by the other element's mass instead of by the whole sample's mass",
  "feedback": "This answer is wrong — you divided the Fe mass by the other element's mass instead of by the whole sample's mass."
 },
 {
  "value": 30.1,
  "misconception": "you computed O's share instead of Fe's",
  "feedback": "This answer is wrong — you computed O's share instead of Fe's."
 },
 {
  "value": 0.6992,
  "misconception": "you forgot to multiply by 100",
  "feedback": "This answer is wrong — you forgot to multiply by 100."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of Fe in the sample = 27.9 g\nmass of the sample = 39.9 g\nWrite down the equation:\n% Fe = (mass of Fe in the sample ÷ mass of the sample) × 100\nSubstitute in the values, and calculate:\n% Fe = (27.9 ÷ 39.9) × 100\n% Fe = 69.9%\nThe divisor is always the whole sample's 39.9 g — dividing by the O mass gives an element-to-element ratio, not a percent of the compound."
}

[
 {
  "value": 9.75,
  "misconception": "you forgot to multiply by the subscript — the formula carries 6 O atoms",
  "feedback": "This answer is wrong — you forgot to multiply by the subscript — the formula carries 6 O atoms."
 },
 {
  "value": 171.0,
  "misconception": "you inverted the ratio — a percent over 100 is impossible",
  "feedback": "This answer is wrong — you inverted the ratio — a percent over 100 is impossible."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of Ca in one mole = 1 × 40.1 = 40.1 g\nmass of N in one mole = 2 × 14.0 = 28.0 g\nmass of O in one mole = 6 × 16.0 = 96.0 g\nM = 164.1 g/mol\nWrite down the equation, and run it once per element:\n% Ca = (40.1 ÷ 164.1) × 100 = 24.4%\n% N = (28.0 ÷ 164.1) × 100 = 17.1%\n% O = (96.0 ÷ 164.1) × 100 = 58.5%\nCheck the total: 100.0 ✓"
}

[
 {
  "value": 100.0,
  "misconception": "you divided by the other elements' combined mass instead of the whole compound's molar mass",
  "feedback": "This answer is wrong — you divided by the other elements' combined mass instead of the whole compound's molar mass."
 },
 {
  "value": 200.0,
  "misconception": "you inverted the ratio — a percent over 100 is impossible",
  "feedback": "This answer is wrong — you inverted the ratio — a percent over 100 is impossible."
 },
 {
  "value": 0.5008,
  "misconception": "you forgot to multiply by 100",
  "feedback": "This answer is wrong — you forgot to multiply by 100."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of S in one mole = 1 × 32.1 = 32.1 g\nM = 64.1 g/mol\nWrite down the equation:\n% S = (mass of S in one mole ÷ M) × 100\nSubstitute in the values, and calculate:\n% S = (32.1 ÷ 64.1) × 100\n% S = 50.1%"
}

[
 {
  "value": 97.8,
  "misconception": "you computed the combined share of Mn and O — the question asks for the H that makes up the rest",
  "feedback": "This answer is wrong — you computed the combined share of Mn and O — the question asks for the H that makes up the rest."
 },
 {
  "value": 61.8,
  "misconception": "you computed Mn's share instead of H's",
  "feedback": "This answer is wrong — you computed Mn's share instead of H's."
 },
 {
  "value": 4.0,
  "misconception": "you gave the H mass in grams as a percent without dividing by the sample's mass",
  "feedback": "This answer is wrong — you gave the H mass in grams as a percent without dividing by the sample's mass."
 }
]

{
 "keyExplanation": "The element masses add up to the sample's mass, so the H is 177.8 − 109.8 − 64.0 = 4.0 g.\nWrite down the equation:\n% H = (mass of H in the sample ÷ mass of the sample) × 100\nSubstitute in the values, and calculate:\n% H = (4.0 ÷ 177.8) × 100\n% H = 2.25%"
}

[
 {
  "value": 22.6,
  "misconception": "you forgot to multiply by the subscript — the formula carries 3 F atoms",
  "feedback": "This answer is wrong — you forgot to multiply by the subscript — the formula carries 3 F atoms."
 },
 {
  "value": 147.0,
  "misconception": "you inverted the ratio — a percent over 100 is impossible",
  "feedback": "This answer is wrong — you inverted the ratio — a percent over 100 is impossible."
 },
 {
  "value": 0.6786,
  "misconception": "you forgot to multiply by 100",
  "feedback": "This answer is wrong — you forgot to multiply by 100."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of F in one mole = 3 × 19.0 = 57.0 g\nM = 84.0 g/mol\nWrite down the equation:\n% F = (mass of F in one mole ÷ M) × 100\nSubstitute in the values, and calculate:\n% F = (57.0 ÷ 84.0) × 100\n% F = 67.9%"
}

[
 {
  "value": 149.0,
  "misconception": "you inverted the ratio — a percent over 100 is impossible",
  "feedback": "This answer is wrong — you inverted the ratio — a percent over 100 is impossible."
 },
 {
  "value": 0.6708,
  "misconception": "you forgot to multiply by 100",
  "feedback": "This answer is wrong — you forgot to multiply by 100."
 },
 {
  "value": 32.9,
  "misconception": "you found the other element's share instead of Zn's",
  "feedback": "This answer is wrong — you found the other element's share instead of Zn's."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of Zn in the sample = 130.8 g\nmass of the sample = 195.0 g\nWrite down the equation:\n% Zn = (mass of Zn in the sample ÷ mass of the sample) × 100\nSubstitute in the values, and calculate:\n% Zn = (130.8 ÷ 195.0) × 100\n% Zn = 67.1%"
}

[
 {
  "value": 174.0,
  "misconception": "you divided the Fe mass by the other element's mass instead of by the whole sample's mass",
  "feedback": "This answer is wrong — you divided the Fe mass by the other element's mass instead of by the whole sample's mass."
 },
 {
  "value": 36.5,
  "misconception": "you computed S's share instead of Fe's",
  "feedback": "This answer is wrong — you computed S's share instead of Fe's."
 },
 {
  "value": 0.6348,
  "misconception": "you forgot to multiply by 100",
  "feedback": "This answer is wrong — you forgot to multiply by 100."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of Fe in the sample = 111.6 g\nmass of the sample = 175.8 g\nWrite down the equation:\n% Fe = (mass of Fe in the sample ÷ mass of the sample) × 100\nSubstitute in the values, and calculate:\n% Fe = (111.6 ÷ 175.8) × 100\n% Fe = 63.5%\nThe divisor is always the whole sample's 175.8 g — dividing by the S mass gives an element-to-element ratio, not a percent of the compound."
}

[
 {
  "value": 11.7,
  "misconception": "you forgot to multiply by the subscript — the formula carries 4 O atoms",
  "feedback": "This answer is wrong — you forgot to multiply by the subscript — the formula carries 4 O atoms."
 },
 {
  "value": 213.0,
  "misconception": "you inverted the ratio — a percent over 100 is impossible",
  "feedback": "This answer is wrong — you inverted the ratio — a percent over 100 is impossible."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of Ca in one mole = 1 × 40.1 = 40.1 g\nmass of S in one mole = 1 × 32.1 = 32.1 g\nmass of O in one mole = 4 × 16.0 = 64.0 g\nM = 136.2 g/mol\nWrite down the equation, and run it once per element:\n% Ca = (40.1 ÷ 136.2) × 100 = 29.4%\n% S = (32.1 ÷ 136.2) × 100 = 23.6%\n% O = (64.0 ÷ 136.2) × 100 = 47.0%\nCheck the total: 100.0 ✓"
}

[
 {
  "value": 20.0,
  "misconception": "you forgot to multiply by the subscript — the formula carries 3 O atoms",
  "feedback": "This answer is wrong — you forgot to multiply by the subscript — the formula carries 3 O atoms."
 },
 {
  "value": 167.0,
  "misconception": "you inverted the ratio — a percent over 100 is impossible",
  "feedback": "This answer is wrong — you inverted the ratio — a percent over 100 is impossible."
 },
 {
  "value": 0.5993,
  "misconception": "you forgot to multiply by 100",
  "feedback": "This answer is wrong — you forgot to multiply by 100."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of O in one mole = 3 × 16.0 = 48.0 g\nM = 80.1 g/mol\nWrite down the equation:\n% O = (mass of O in one mole ÷ M) × 100\nSubstitute in the values, and calculate:\n% O = (48.0 ÷ 80.1) × 100\n% O = 59.9%"
}

[
 {
  "value": 57.6,
  "misconception": "you computed the combined share of Mn and S — the question asks for the O that makes up the rest",
  "feedback": "This answer is wrong — you computed the combined share of Mn and S — the question asks for the O that makes up the rest."
 },
 {
  "value": 36.4,
  "misconception": "you computed Mn's share instead of O's",
  "feedback": "This answer is wrong — you computed Mn's share instead of O's."
 },
 {
  "value": 192.0,
  "misconception": "you gave the O mass in grams as a percent without dividing by the sample's mass",
  "feedback": "This answer is wrong — you gave the O mass in grams as a percent without dividing by the sample's mass."
 }
]

{
 "keyExplanation": "The element masses add up to the sample's mass, so the O is 453.0 − 164.7 − 96.3 = 192.0 g.\nWrite down the equation:\n% O = (mass of O in the sample ÷ mass of the sample) × 100\nSubstitute in the values, and calculate:\n% O = (192.0 ÷ 453.0) × 100\n% O = 42.4%"
}

[
 {
  "value": 18.0,
  "misconception": "you forgot to multiply by the subscript — the formula carries 2 Al atoms",
  "feedback": "This answer is wrong — you forgot to multiply by the subscript — the formula carries 2 Al atoms."
 },
 {
  "value": 278.0,
  "misconception": "you inverted the ratio — a percent over 100 is impossible",
  "feedback": "This answer is wrong — you inverted the ratio — a percent over 100 is impossible."
 },
 {
  "value": 0.3593,
  "misconception": "you forgot to multiply by 100",
  "feedback": "This answer is wrong — you forgot to multiply by 100."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of Al in one mole = 2 × 27.0 = 54.0 g\nM = 150.3 g/mol\nWrite down the equation:\n% Al = (mass of Al in one mole ÷ M) × 100\nSubstitute in the values, and calculate:\n% Al = (54.0 ÷ 150.3) × 100\n% Al = 35.9%"
}

[
 {
  "value": 158.0,
  "misconception": "you inverted the ratio — a percent over 100 is impossible",
  "feedback": "This answer is wrong — you inverted the ratio — a percent over 100 is impossible."
 },
 {
  "value": 0.6325,
  "misconception": "you forgot to multiply by 100",
  "feedback": "This answer is wrong — you forgot to multiply by 100."
 },
 {
  "value": 36.8,
  "misconception": "you found the other element's share instead of Zn's",
  "feedback": "This answer is wrong — you found the other element's share instead of Zn's."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of Zn in the sample = 163.5 g\nmass of the sample = 258.5 g\nWrite down the equation:\n% Zn = (mass of Zn in the sample ÷ mass of the sample) × 100\nSubstitute in the values, and calculate:\n% Zn = (163.5 ÷ 258.5) × 100\n% Zn = 63.2%"
}

[
 {
  "value": 97.9,
  "misconception": "you divided the Fe mass by the other element's mass instead of by the whole sample's mass",
  "feedback": "This answer is wrong — you divided the Fe mass by the other element's mass instead of by the whole sample's mass."
 },
 {
  "value": 50.5,
  "misconception": "you computed F's share instead of Fe's",
  "feedback": "This answer is wrong — you computed F's share instead of Fe's."
 },
 {
  "value": 0.4947,
  "misconception": "you forgot to multiply by 100",
  "feedback": "This answer is wrong — you forgot to multiply by 100."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of Fe in the sample = 83.7 g\nmass of the sample = 169.2 g\nWrite down the equation:\n% Fe = (mass of Fe in the sample ÷ mass of the sample) × 100\nSubstitute in the values, and calculate:\n% Fe = (83.7 ÷ 169.2) × 100\n% Fe = 49.5%\nThe divisor is always the whole sample's 169.2 g — dividing by the F mass gives an element-to-element ratio, not a percent of the compound."
}

[
 {
  "value": 9.44,
  "misconception": "you forgot to multiply by the subscript — the formula carries 2 N atoms",
  "feedback": "This answer is wrong — you forgot to multiply by the subscript — the formula carries 2 N atoms."
 },
 {
  "value": 530.0,
  "misconception": "you inverted the ratio — a percent over 100 is impossible",
  "feedback": "This answer is wrong — you inverted the ratio — a percent over 100 is impossible."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of Ca in one mole = 3 × 40.1 = 120.3 g\nmass of N in one mole = 2 × 14.0 = 28.0 g\nM = 148.3 g/mol\nWrite down the equation, and run it once per element:\n% Ca = (120.3 ÷ 148.3) × 100 = 81.1%\n% N = (28.0 ÷ 148.3) × 100 = 18.9%\nCheck the total: 100.0 ✓"
}

[
 {
  "value": 48.6,
  "misconception": "you divided by the other elements' combined mass instead of the whole compound's molar mass",
  "feedback": "This answer is wrong — you divided by the other elements' combined mass instead of the whole compound's molar mass."
 },
 {
  "value": 306.0,
  "misconception": "you inverted the ratio — a percent over 100 is impossible",
  "feedback": "This answer is wrong — you inverted the ratio — a percent over 100 is impossible."
 },
 {
  "value": 0.3272,
  "misconception": "you forgot to multiply by 100",
  "feedback": "This answer is wrong — you forgot to multiply by 100."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of S in one mole = 1 × 32.1 = 32.1 g\nM = 98.1 g/mol\nWrite down the equation:\n% S = (mass of S in one mole ÷ M) × 100\nSubstitute in the values, and calculate:\n% S = (32.1 ÷ 98.1) × 100\n% S = 32.7%"
}

[
 {
  "value": 46.3,
  "misconception": "you computed the combined share of Mn and N — the question asks for the O that makes up the rest",
  "feedback": "This answer is wrong — you computed the combined share of Mn and N — the question asks for the O that makes up the rest."
 },
 {
  "value": 30.7,
  "misconception": "you computed Mn's share instead of O's",
  "feedback": "This answer is wrong — you computed Mn's share instead of O's."
 },
 {
  "value": 384.0,
  "misconception": "you gave the O mass in grams as a percent without dividing by the sample's mass",
  "feedback": "This answer is wrong — you gave the O mass in grams as a percent without dividing by the sample's mass."
 }
]

{
 "keyExplanation": "The element masses add up to the sample's mass, so the O is 715.6 − 219.6 − 112.0 = 384.0 g.\nWrite down the equation:\n% O = (mass of O in the sample ÷ mass of the sample) × 100\nSubstitute in the values, and calculate:\n% O = (384.0 ÷ 715.6) × 100\n% O = 53.7%"
}

[
 {
  "value": 26.6,
  "misconception": "you forgot to multiply by the subscript — the formula carries 3 Cl atoms",
  "feedback": "This answer is wrong — you forgot to multiply by the subscript — the formula carries 3 Cl atoms."
 },
 {
  "value": 125.0,
  "misconception": "you inverted the ratio — a percent over 100 is impossible",
  "feedback": "This answer is wrong — you inverted the ratio — a percent over 100 is impossible."
 },
 {
  "value": 0.7978,
  "misconception": "you forgot to multiply by 100",
  "feedback": "This answer is wrong — you forgot to multiply by 100."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of Cl in one mole = 3 × 35.5 = 106.5 g\nM = 133.5 g/mol\nWrite down the equation:\n% Cl = (mass of Cl in one mole ÷ M) × 100\nSubstitute in the values, and calculate:\n% Cl = (106.5 ÷ 133.5) × 100\n% Cl = 79.8%"
}

[
 {
  "value": 344.0,
  "misconception": "you inverted the ratio — a percent over 100 is impossible",
  "feedback": "This answer is wrong — you inverted the ratio — a percent over 100 is impossible."
 },
 {
  "value": 0.2904,
  "misconception": "you forgot to multiply by 100",
  "feedback": "This answer is wrong — you forgot to multiply by 100."
 },
 {
  "value": 71.0,
  "misconception": "you found the other element's share instead of Zn's",
  "feedback": "This answer is wrong — you found the other element's share instead of Zn's."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of Zn in the sample = 196.2 g\nmass of the sample = 675.6 g\nWrite down the equation:\n% Zn = (mass of Zn in the sample ÷ mass of the sample) × 100\nSubstitute in the values, and calculate:\n% Zn = (196.2 ÷ 675.6) × 100\n% Zn = 29.0%"
}

[
 {
  "value": 52.4,
  "misconception": "you divided the Fe mass by the other element's mass instead of by the whole sample's mass",
  "feedback": "This answer is wrong — you divided the Fe mass by the other element's mass instead of by the whole sample's mass."
 },
 {
  "value": 65.6,
  "misconception": "you computed Cl's share instead of Fe's",
  "feedback": "This answer is wrong — you computed Cl's share instead of Fe's."
 },
 {
  "value": 0.3438,
  "misconception": "you forgot to multiply by 100",
  "feedback": "This answer is wrong — you forgot to multiply by 100."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of Fe in the sample = 55.8 g\nmass of the sample = 162.3 g\nWrite down the equation:\n% Fe = (mass of Fe in the sample ÷ mass of the sample) × 100\nSubstitute in the values, and calculate:\n% Fe = (55.8 ÷ 162.3) × 100\n% Fe = 34.4%\nThe divisor is always the whole sample's 162.3 g — dividing by the Cl mass gives an element-to-element ratio, not a percent of the compound."
}

[
 {
  "value": 28.1,
  "misconception": "you gave Si's atomic mass instead of its percent",
  "feedback": "This answer is wrong — you gave Si's atomic mass instead of its percent."
 },
 {
  "value": 414.0,
  "misconception": "you inverted the ratio — a percent over 100 is impossible",
  "feedback": "This answer is wrong — you inverted the ratio — a percent over 100 is impossible."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of Ca in one mole = 1 × 40.1 = 40.1 g\nmass of Si in one mole = 1 × 28.1 = 28.1 g\nmass of O in one mole = 3 × 16.0 = 48.0 g\nM = 116.2 g/mol\nWrite down the equation, and run it once per element:\n% Ca = (40.1 ÷ 116.2) × 100 = 34.5%\n% Si = (28.1 ÷ 116.2) × 100 = 24.2%\n% O = (48.0 ÷ 116.2) × 100 = 41.3%\nCheck the total: 100.0 ✓"
}

[
 {
  "value": 22.6,
  "misconception": "you divided by the other elements' combined mass instead of the whole compound's molar mass",
  "feedback": "This answer is wrong — you divided by the other elements' combined mass instead of the whole compound's molar mass."
 },
 {
  "value": 543.0,
  "misconception": "you inverted the ratio — a percent over 100 is impossible",
  "feedback": "This answer is wrong — you inverted the ratio — a percent over 100 is impossible."
 },
 {
  "value": 0.1842,
  "misconception": "you forgot to multiply by 100",
  "feedback": "This answer is wrong — you forgot to multiply by 100."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of S in one mole = 1 × 32.1 = 32.1 g\nM = 174.3 g/mol\nWrite down the equation:\n% S = (mass of S in one mole ÷ M) × 100\nSubstitute in the values, and calculate:\n% S = (32.1 ÷ 174.3) × 100\n% S = 18.4%"
}

[
 {
  "value": 63.9,
  "misconception": "you computed the combined share of Mn and P — the question asks for the O that makes up the rest",
  "feedback": "This answer is wrong — you computed the combined share of Mn and P — the question asks for the O that makes up the rest."
 },
 {
  "value": 46.4,
  "misconception": "you computed Mn's share instead of O's",
  "feedback": "This answer is wrong — you computed Mn's share instead of O's."
 },
 {
  "value": 256.0,
  "misconception": "you gave the O mass in grams as a percent without dividing by the sample's mass",
  "feedback": "This answer is wrong — you gave the O mass in grams as a percent without dividing by the sample's mass."
 }
]

{
 "keyExplanation": "The element masses add up to the sample's mass, so the O is 709.4 − 329.4 − 124.0 = 256.0 g.\nWrite down the equation:\n% O = (mass of O in the sample ÷ mass of the sample) × 100\nSubstitute in the values, and calculate:\n% O = (256.0 ÷ 709.4) × 100\n% O = 36.1%"
}

[
 {
  "value": 30.0,
  "misconception": "you forgot to multiply by the subscript — the formula carries 3 Br atoms",
  "feedback": "This answer is wrong — you forgot to multiply by the subscript — the formula carries 3 Br atoms."
 },
 {
  "value": 111.0,
  "misconception": "you inverted the ratio — a percent over 100 is impossible",
  "feedback": "This answer is wrong — you inverted the ratio — a percent over 100 is impossible."
 },
 {
  "value": 0.8988,
  "misconception": "you forgot to multiply by 100",
  "feedback": "This answer is wrong — you forgot to multiply by 100."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of Br in one mole = 3 × 79.9 = 239.7 g\nM = 266.7 g/mol\nWrite down the equation:\n% Br = (mass of Br in one mole ÷ M) × 100\nSubstitute in the values, and calculate:\n% Br = (239.7 ÷ 266.7) × 100\n% Br = 89.9%"
}

[
 {
  "value": 488.0,
  "misconception": "you inverted the ratio — a percent over 100 is impossible",
  "feedback": "This answer is wrong — you inverted the ratio — a percent over 100 is impossible."
 },
 {
  "value": 0.2049,
  "misconception": "you forgot to multiply by 100",
  "feedback": "This answer is wrong — you forgot to multiply by 100."
 },
 {
  "value": 79.5,
  "misconception": "you found the other element's share instead of Zn's",
  "feedback": "This answer is wrong — you found the other element's share instead of Zn's."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of Zn in the sample = 228.9 g\nmass of the sample = 1117.2 g\nWrite down the equation:\n% Zn = (mass of Zn in the sample ÷ mass of the sample) × 100\nSubstitute in the values, and calculate:\n% Zn = (228.9 ÷ 1117.2) × 100\n% Zn = 20.5%"
}

[
 {
  "value": 147.0,
  "misconception": "you divided the Fe mass by the other element's mass instead of by the whole sample's mass",
  "feedback": "This answer is wrong — you divided the Fe mass by the other element's mass instead of by the whole sample's mass."
 },
 {
  "value": 40.5,
  "misconception": "you computed F's share instead of Fe's",
  "feedback": "This answer is wrong — you computed F's share instead of Fe's."
 },
 {
  "value": 0.5949,
  "misconception": "you forgot to multiply by 100",
  "feedback": "This answer is wrong — you forgot to multiply by 100."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of Fe in the sample = 139.5 g\nmass of the sample = 234.5 g\nWrite down the equation:\n% Fe = (mass of Fe in the sample ÷ mass of the sample) × 100\nSubstitute in the values, and calculate:\n% Fe = (139.5 ÷ 234.5) × 100\n% Fe = 59.5%\nThe divisor is always the whole sample's 234.5 g — dividing by the F mass gives an element-to-element ratio, not a percent of the compound."
}

[
 {
  "value": 24.3,
  "misconception": "you forgot to multiply by the subscript — the formula carries 2 F atoms",
  "feedback": "This answer is wrong — you forgot to multiply by the subscript — the formula carries 2 F atoms."
 },
 {
  "value": 206.0,
  "misconception": "you inverted the ratio — a percent over 100 is impossible",
  "feedback": "This answer is wrong — you inverted the ratio — a percent over 100 is impossible."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of Ca in one mole = 1 × 40.1 = 40.1 g\nmass of F in one mole = 2 × 19.0 = 38.0 g\nM = 78.1 g/mol\nWrite down the equation, and run it once per element:\n% Ca = (40.1 ÷ 78.1) × 100 = 51.3%\n% F = (38.0 ÷ 78.1) × 100 = 48.7%\nCheck the total: 100.0 ✓"
}

[
 {
  "value": 64.2,
  "misconception": "you divided by the other elements' combined mass instead of the whole compound's molar mass",
  "feedback": "This answer is wrong — you divided by the other elements' combined mass instead of the whole compound's molar mass."
 },
 {
  "value": 256.0,
  "misconception": "you inverted the ratio — a percent over 100 is impossible",
  "feedback": "This answer is wrong — you inverted the ratio — a percent over 100 is impossible."
 },
 {
  "value": 0.391,
  "misconception": "you forgot to multiply by 100",
  "feedback": "This answer is wrong — you forgot to multiply by 100."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of S in one mole = 1 × 32.1 = 32.1 g\nM = 82.1 g/mol\nWrite down the equation:\n% S = (mass of S in one mole ÷ M) × 100\nSubstitute in the values, and calculate:\n% S = (32.1 ÷ 82.1) × 100\n% S = 39.1%"
}

[
 {
  "value": 63.4,
  "misconception": "you computed the combined share of Mn and Si — the question asks for the O that makes up the rest",
  "feedback": "This answer is wrong — you computed the combined share of Mn and Si — the question asks for the O that makes up the rest."
 },
 {
  "value": 41.9,
  "misconception": "you computed Mn's share instead of O's",
  "feedback": "This answer is wrong — you computed Mn's share instead of O's."
 },
 {
  "value": 240.0,
  "misconception": "you gave the O mass in grams as a percent without dividing by the sample's mass",
  "feedback": "This answer is wrong — you gave the O mass in grams as a percent without dividing by the sample's mass."
 }
]

{
 "keyExplanation": "The element masses add up to the sample's mass, so the O is 655.0 − 274.5 − 140.5 = 240.0 g.\nWrite down the equation:\n% O = (mass of O in the sample ÷ mass of the sample) × 100\nSubstitute in the values, and calculate:\n% O = (240.0 ÷ 655.0) × 100\n% O = 36.6%"
}

[
 {
  "value": 80.0,
  "misconception": "you gave the carbon's mass — the question asks for the hydrogen, the rest of the 100 g",
  "feedback": "This answer is wrong — you gave the carbon's mass — the question asks for the hydrogen, the rest of the 100 g."
 },
 {
  "value": 0.2,
  "misconception": "you divided by 100 — in a 100 g sample the masses are in grams already",
  "feedback": "This answer is wrong — you divided by 100 — in a 100 g sample the masses are in grams already."
 }
]

{
 "keyExplanation": "Assume a sample of exactly 100 g.\nCarbon: 80.0% of the compound → 80.0 g.\nThe element masses in a 100 g sample total 100 g.\nmass of hydrogen = 100 − 80.0 = 20.0 g"
}

[
 {
  "value": "C₂H₄",
  "misconception": "you divided by 2, which is a common factor but not the LARGEST one — 2 and 4 still share the factor 2",
  "feedback": "This answer is wrong — you divided by 2, which is a common factor but not the LARGEST one. The subscripts of C₂H₄ — 2 and 4 — still share the factor 2, so the formula still reduces. Divide C₄H₈'s subscripts by their largest common factor, 4: the empirical formula is CH₂."
 },
 {
  "value": "C₄H₈",
  "misconception": "you left the formula unchanged — the subscripts 4 and 8 share the factor 4, so the formula reduces",
  "feedback": "This answer is wrong — you left the formula unchanged. The subscripts 4 and 8 share the factor 4, so the formula reduces: C: 4 ÷ 4 = 1, H: 8 ÷ 4 = 2, and the empirical formula is CH₂."
 },
 {
  "value": "CH",
  "misconception": "you divided each subscript by its own value, which destroys the ratio",
  "feedback": "This answer is wrong — you divided each subscript by its own value, which destroys the ratio. Every subscript must be divided by the SAME factor — the largest common factor, 4: C: 4 ÷ 4 = 1, H: 8 ÷ 4 = 2, so the empirical formula is CH₂."
 }
]

{
 "keyExplanation": "Subscripts: C 4, H 8. The largest common factor is 4 — dividing by 2 alone leaves C₂H₄, which still reduces. C: 4 ÷ 4 = 1, H: 8 ÷ 4 = 2, and a subscript of 1 is never written, so the empirical formula is CH₂.",
 "anticipatedWrong": [
  {
   "value": "C₂H₄",
   "misconception": "you divided by 2, which is a common factor but not the LARGEST one — 2 and 4 still share the factor 2",
   "feedback": "This answer is wrong — you divided by 2, which is a common factor but not the LARGEST one. The subscripts of C₂H₄ — 2 and 4 — still share the factor 2, so the formula still reduces. Divide C₄H₈'s subscripts by their largest common factor, 4: the empirical formula is CH₂."
  },
  {
   "value": "C₄H₈",
   "misconception": "you left the formula unchanged — the subscripts 4 and 8 share the factor 4, so the formula reduces",
   "feedback": "This answer is wrong — you left the formula unchanged. The subscripts 4 and 8 share the factor 4, so the formula reduces: C: 4 ÷ 4 = 1, H: 8 ÷ 4 = 2, and the empirical formula is CH₂."
  },
  {
   "value": "CH",
   "misconception": "you divided each subscript by its own value, which destroys the ratio",
   "feedback": "This answer is wrong — you divided each subscript by its own value, which destroys the ratio. Every subscript must be divided by the SAME factor — the largest common factor, 4: C: 4 ÷ 4 = 1, H: 8 ÷ 4 = 2, so the empirical formula is CH₂."
  }
 ]
}

[
 {
  "value": "1 : 12",
  "misconception": "you compared the masses instead of the moles — 3.0 : 35.5 is about 1 : 12, but atoms are counted in moles",
  "feedback": "This answer is wrong — you compared the masses instead of the moles. 3.0 : 35.5 is about 1 : 12, but atoms are counted in moles: n(C) = 3.0 / 12.0 = 0.25 mol and n(Cl) = 35.5 / 35.5 = 1.00 mol, and dividing each by 0.25 gives 1 : 4."
 },
 {
  "value": "4 : 1",
  "misconception": "you wrote the ratio backwards — the order follows the elements as named: carbon first, then chlorine",
  "feedback": "This answer is wrong — you wrote the ratio backwards. The ratio order follows the elements as they are named in the question: carbon first, then chlorine, so the answer is 1 : 4."
 }
]

{
 "keyExplanation": "Values from the question:\nm(C) = 3.0 g, m(Cl) = 35.5 g\nEquation:\nn = m/M  (for each element)\nSubstituting the values and calculating:\nn(C) = 3.0 / 12.0 = 0.25 mol\nn(Cl) = 35.5 / 35.5 = 1.00 mol\nDivide each by the smallest (0.25): C gives 1, Cl gives 4.\nMole ratio of carbon to chlorine = 1 : 4",
 "anticipatedWrong": [
  {
   "value": "1 : 12",
   "misconception": "you compared the masses instead of the moles — 3.0 : 35.5 is about 1 : 12, but atoms are counted in moles",
   "feedback": "This answer is wrong — you compared the masses instead of the moles. 3.0 : 35.5 is about 1 : 12, but atoms are counted in moles: n(C) = 3.0 / 12.0 = 0.25 mol and n(Cl) = 35.5 / 35.5 = 1.00 mol, and dividing each by 0.25 gives 1 : 4."
  },
  {
   "value": "4 : 1",
   "misconception": "you wrote the ratio backwards — the order follows the elements as named: carbon first, then chlorine",
   "feedback": "This answer is wrong — you wrote the ratio backwards. The ratio order follows the elements as they are named in the question: carbon first, then chlorine, so the answer is 1 : 4."
  }
 ]
}

[
 {
  "value": "1 : 2",
  "misconception": "you rounded the 2.33 down to 2 — rounding changes the ratio; multiply every number by 3 instead",
  "feedback": "This answer is wrong — you rounded the 2.33 down to 2, and rounding changes the ratio itself. The decimal is near .33, so multiply every number by 3 instead: 1 × 3 = 3 and 2.33 × 3 = 7, giving 3 : 7."
 },
 {
  "value": "1 : 7",
  "misconception": "you multiplied only the decimal number — every number in the ratio must be multiplied by the same amount",
  "feedback": "This answer is wrong — you multiplied only the decimal number. Every number in the ratio must be multiplied by the same amount to keep the ratio unchanged: 1 × 3 = 3 and 2.33 × 3 = 7, giving 3 : 7."
 }
]

{
 "keyExplanation": "The decimal is near .33, so multiply every number by 3: 1 × 3 = 3 and 2.33 × 3 = 7. The whole-number ratio is 3 : 7. Rounding 2.33 down to 2 would change the ratio itself — multiplying never does.",
 "anticipatedWrong": [
  {
   "value": "1 : 2",
   "misconception": "you rounded the 2.33 down to 2 — rounding changes the ratio; multiply every number by 3 instead",
   "feedback": "This answer is wrong — you rounded the 2.33 down to 2, and rounding changes the ratio itself. The decimal is near .33, so multiply every number by 3 instead: 1 × 3 = 3 and 2.33 × 3 = 7, giving 3 : 7."
  },
  {
   "value": "1 : 7",
   "misconception": "you multiplied only the decimal number — every number in the ratio must be multiplied by the same amount",
   "feedback": "This answer is wrong — you multiplied only the decimal number. Every number in the ratio must be multiplied by the same amount to keep the ratio unchanged: 1 × 3 = 3 and 2.33 × 3 = 7, giving 3 : 7."
  }
 ]
}

[
 {
  "value": "B₂H₆",
  "misconception": "you left the formula unchanged — the subscripts 2 and 6 share the factor 2, so the formula reduces",
  "feedback": "This answer is wrong — you left the formula unchanged. The subscripts 2 and 6 share the factor 2, so the formula reduces: B: 2 ÷ 2 = 1, H: 6 ÷ 2 = 3, giving BH₃."
 },
 {
  "value": "BH",
  "misconception": "you divided each subscript by its own value, which destroys the ratio",
  "feedback": "This answer is wrong — you divided each subscript by its own value, which destroys the ratio. Every subscript is divided by the same factor, 2: B: 2 ÷ 2 = 1, H: 6 ÷ 2 = 3, giving BH₃."
 },
 {
  "value": "B₂H₃",
  "misconception": "you divided only the hydrogen's subscript — every subscript must be divided by the same factor",
  "feedback": "This answer is wrong — you divided only the hydrogen's subscript. Every subscript must be divided by the same factor: B: 2 ÷ 2 = 1, H: 6 ÷ 2 = 3, giving BH₃."
 }
]

{
 "keyExplanation": "Subscripts: B 2, H 6. The largest common factor is 2. B: 2 ÷ 2 = 1, H: 6 ÷ 2 = 3. A subscript of 1 is never written, so diborane's empirical formula is BH₃.",
 "anticipatedWrong": [
  {
   "value": "B₂H₆",
   "misconception": "you left the formula unchanged — the subscripts 2 and 6 share the factor 2, so the formula reduces",
   "feedback": "This answer is wrong — you left the formula unchanged. The subscripts 2 and 6 share the factor 2, so the formula reduces: B: 2 ÷ 2 = 1, H: 6 ÷ 2 = 3, giving BH₃."
  },
  {
   "value": "BH",
   "misconception": "you divided each subscript by its own value, which destroys the ratio",
   "feedback": "This answer is wrong — you divided each subscript by its own value, which destroys the ratio. Every subscript is divided by the same factor, 2: B: 2 ÷ 2 = 1, H: 6 ÷ 2 = 3, giving BH₃."
  },
  {
   "value": "B₂H₃",
   "misconception": "you divided only the hydrogen's subscript — every subscript must be divided by the same factor",
   "feedback": "This answer is wrong — you divided only the hydrogen's subscript. Every subscript must be divided by the same factor: B: 2 ÷ 2 = 1, H: 6 ÷ 2 = 3, giving BH₃."
  }
 ]
}

[
 {
  "value": "1.4 : 1 : 2",
  "misconception": "you compared the masses instead of the moles — 138.0 : 96.3 : 192.0 is about 1.4 : 1 : 2, but atoms are counted in moles",
  "feedback": "This answer is wrong — you compared the masses instead of the moles — 138.0 : 96.3 : 192.0 is about 1.4 : 1 : 2, but atoms are counted in moles."
 },
 {
  "value": "0.5 : 0.25 : 1",
  "misconception": "you divided every value by the largest instead of the smallest — divide by the smallest so the smallest becomes 1",
  "feedback": "This answer is wrong — you divided every value by the largest instead of the smallest — divide by the smallest so the smallest becomes 1."
 }
]

{
 "keyExplanation": "Values from the question:\nm(Na) = 138.0 g, m(S) = 96.3 g, m(O) = 192.0 g\nEquation:\nn = m/M  (for each element)\nSubstituting the values and calculating:\nn(Na) = 138.0 / 23.0 = 6.00 mol\nn(S) = 96.3 / 32.1 = 3.00 mol\nn(O) = 192.0 / 16.0 = 12.0 mol\nDivide each by the smallest (3.00): Na gives 2, S gives 1, O gives 4.\nMole ratio of sodium to sulfur to oxygen = 2 : 1 : 4"
}

[
 {
  "value": 6.31,
  "misconception": "you ignored the subscripts in the empirical formula, using 12.0 + 1.0 = 13.0 g/mol — M of C₃H₅ is 3 × 12.0 + 5 × 1.0 = 41.0 g/mol",
  "feedback": "This answer is wrong — you ignored the subscripts in the empirical formula, using 12.0 + 1.0 = 13.0 g/mol. M of C₃H₅ is 3 × 12.0 + 5 × 1.0 = 41.0 g/mol, and a non-whole unit count signals exactly this kind of slip."
 },
 {
  "value": 0.5,
  "misconception": "you divided upside down — the compound's molar mass goes on top, and the unit count is never below 1",
  "feedback": "This answer is wrong — you divided upside down — the compound's molar mass goes on top, and the unit count is never below 1."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmolar mass of the compound = 82.0 g/mol\nM of C₃H₅ = 3 × 12.0 + 5 × 1.0 = 41.0 g/mol\nWrite down the equation:\nnumber of units = molar mass of the compound ÷ molar mass of the empirical formula\nSubstitute in the values, and calculate:\nnumber of units = 82.0 / 41.0\nnumber of units = 2\nThe result is a whole number at least 1, so the division ran the right way up."
}

[
 {
  "value": "FeO₂",
  "misconception": "you rounded the 1.5 up to 2 — rounding changes the ratio; multiply every number by 2 instead",
  "feedback": "This answer is wrong — you rounded the 1.5 up to 2. Rounding changes the ratio; multiply every number by 2 instead: 1 and 1.5 become 2 and 3, so the empirical formula is Fe₂O₃."
 },
 {
  "value": "FeO",
  "misconception": "you dropped the decimal — cutting the .5 off changes the ratio; multiply every number by 2 instead",
  "feedback": "This answer is wrong — you dropped the decimal. Cutting the .5 off changes the ratio; multiply every number by 2 instead: 1 and 1.5 become 2 and 3, so the empirical formula is Fe₂O₃."
 },
 {
  "value": "Fe₃O₂",
  "misconception": "you inverted the ratio — iron has the smaller mole value, so iron takes the 1 before clearing",
  "feedback": "This answer is wrong — you inverted the ratio. Iron has the smaller mole value (0.50 mol against oxygen's 0.75 mol), so iron takes the 1 before clearing: 1 and 1.5 become 2 and 3, giving Fe₂O₃."
 }
]

{
 "keyExplanation": "Values from the question:\nm(Fe) = 27.9 g, m(O) = 12.0 g\nEquation:\nn = m/M  (for each element)\nSubstituting the values and calculating:\nn(Fe) = 27.9 / 55.8 = 0.50 mol\nn(O) = 12.0 / 16.0 = 0.75 mol\nDivide each by the smallest (0.50): Fe gives 1, O gives 1.5.\nThe decimal ends in .5, so multiply every number by 2: 2 and 3.\nEmpirical formula: Fe₂O₃",
 "anticipatedWrong": [
  {
   "value": "FeO₂",
   "misconception": "you rounded the 1.5 up to 2 — rounding changes the ratio; multiply every number by 2 instead",
   "feedback": "This answer is wrong — you rounded the 1.5 up to 2. Rounding changes the ratio; multiply every number by 2 instead: 1 and 1.5 become 2 and 3, so the empirical formula is Fe₂O₃."
  },
  {
   "value": "FeO",
   "misconception": "you dropped the decimal — cutting the .5 off changes the ratio; multiply every number by 2 instead",
   "feedback": "This answer is wrong — you dropped the decimal. Cutting the .5 off changes the ratio; multiply every number by 2 instead: 1 and 1.5 become 2 and 3, so the empirical formula is Fe₂O₃."
  },
  {
   "value": "Fe₃O₂",
   "misconception": "you inverted the ratio — iron has the smaller mole value, so iron takes the 1 before clearing",
   "feedback": "This answer is wrong — you inverted the ratio. Iron has the smaller mole value (0.50 mol against oxygen's 0.75 mol), so iron takes the 1 before clearing: 1 and 1.5 become 2 and 3, giving Fe₂O₃."
  }
 ]
}

[
 {
  "value": "CH₃O",
  "misconception": "you stopped at the empirical formula — the unit count is 62.0/31.0 = 2, and every subscript must be multiplied by it",
  "feedback": "This answer is wrong — you stopped at the empirical formula. The unit count is 62.0 / 31.0 = 2, and every subscript must be multiplied by it: C: 1 × 2 = 2, H: 3 × 2 = 6, O: 1 × 2 = 2, giving C₂H₆O₂."
 },
 {
  "value": "C₂H₃O",
  "misconception": "you multiplied only carbon's subscript — every subscript in the empirical formula is multiplied by the unit count",
  "feedback": "This answer is wrong — you multiplied only carbon's subscript. Every subscript in the empirical formula is multiplied by the unit count, 2: C: 1 × 2 = 2, H: 3 × 2 = 6, O: 1 × 2 = 2, giving C₂H₆O₂."
 },
 {
  "value": "CH₃O₂",
  "misconception": "you multiplied only oxygen's subscript — every subscript in the empirical formula is multiplied by the unit count",
  "feedback": "This answer is wrong — you multiplied only oxygen's subscript. Every subscript in the empirical formula is multiplied by the unit count, 2: C: 1 × 2 = 2, H: 3 × 2 = 6, O: 1 × 2 = 2, giving C₂H₆O₂."
 }
]

{
 "keyExplanation": "M of CH₃O = 12.0 + 3 × 1.0 + 16.0 = 31.0 g/mol.\nStep 1 — find the number of units:\nnumber of units = molar mass of the compound ÷ molar mass of the empirical formula\nnumber of units = 62.0 / 31.0 = 2\nStep 2 — multiply every subscript by 2:\nC: 1 × 2 = 2,  H: 3 × 2 = 6,  O: 1 × 2 = 2\nMolecular formula: C₂H₆O₂",
 "anticipatedWrong": [
  {
   "value": "CH₃O",
   "misconception": "you stopped at the empirical formula — the unit count is 62.0/31.0 = 2, and every subscript must be multiplied by it",
   "feedback": "This answer is wrong — you stopped at the empirical formula. The unit count is 62.0 / 31.0 = 2, and every subscript must be multiplied by it: C: 1 × 2 = 2, H: 3 × 2 = 6, O: 1 × 2 = 2, giving C₂H₆O₂."
  },
  {
   "value": "C₂H₃O",
   "misconception": "you multiplied only carbon's subscript — every subscript in the empirical formula is multiplied by the unit count",
   "feedback": "This answer is wrong — you multiplied only carbon's subscript. Every subscript in the empirical formula is multiplied by the unit count, 2: C: 1 × 2 = 2, H: 3 × 2 = 6, O: 1 × 2 = 2, giving C₂H₆O₂."
  },
  {
   "value": "CH₃O₂",
   "misconception": "you multiplied only oxygen's subscript — every subscript in the empirical formula is multiplied by the unit count",
   "feedback": "This answer is wrong — you multiplied only oxygen's subscript. Every subscript in the empirical formula is multiplied by the unit count, 2: C: 1 × 2 = 2, H: 3 × 2 = 6, O: 1 × 2 = 2, giving C₂H₆O₂."
  }
 ]
}

[
 {
  "value": "NO₂",
  "misconception": "you rounded the 2.50 down to 2 — rounding changes the ratio; multiply every number by 2 instead",
  "feedback": "This answer is wrong — you rounded the 2.50 down to 2. Rounding changes the ratio; multiply every number by 2 instead: N gives 2 and O gives 5, so the empirical formula is N₂O₅."
 },
 {
  "value": "NO₃",
  "misconception": "you rounded the 2.50 up to 3 — rounding changes the ratio; multiply every number by 2 instead",
  "feedback": "This answer is wrong — you rounded the 2.50 up to 3. Rounding changes the ratio; multiply every number by 2 instead: N gives 2 and O gives 5, so the empirical formula is N₂O₅."
 }
]

{
 "keyExplanation": "Assume a 100 g sample: m(N) = 25.9 g, m(O) = 74.1 g.\nEquation:\nn = m/M  (for each element)\nSubstituting the values and calculating:\nn(N) = 25.9 / 14.0 = 1.85 mol\nn(O) = 74.1 / 16.0 = 4.63 mol\nDivide each by the smallest (1.85): N gives 1, O gives 2.50.\nThe decimal ends in .5, so multiply every number by 2: 2 and 5.\nEmpirical formula: N₂O₅",
 "anticipatedWrong": [
  {
   "value": "NO₂",
   "misconception": "you rounded the 2.50 down to 2 — rounding changes the ratio; multiply every number by 2 instead",
   "feedback": "This answer is wrong — you rounded the 2.50 down to 2. Rounding changes the ratio; multiply every number by 2 instead: N gives 2 and O gives 5, so the empirical formula is N₂O₅."
  },
  {
   "value": "NO₃",
   "misconception": "you rounded the 2.50 up to 3 — rounding changes the ratio; multiply every number by 2 instead",
   "feedback": "This answer is wrong — you rounded the 2.50 up to 3. Rounding changes the ratio; multiply every number by 2 instead: N gives 2 and O gives 5, so the empirical formula is N₂O₅."
  }
 ]
}

[
 {
  "value": 63.6,
  "misconception": "you gave the nitrogen's mass — the question asks for the oxygen, the rest of the 100 g",
  "feedback": "This answer is wrong — you gave the nitrogen's mass — the question asks for the oxygen, the rest of the 100 g."
 },
 {
  "value": 0.364,
  "misconception": "you divided by 100 — in a 100 g sample the masses are in grams already",
  "feedback": "This answer is wrong — you divided by 100 — in a 100 g sample the masses are in grams already."
 }
]

{
 "keyExplanation": "Assume a sample of exactly 100 g.\nNitrogen: 63.6% of the compound → 63.6 g.\nThe element masses in a 100 g sample total 100 g.\nmass of oxygen = 100 − 63.6 = 36.4 g"
}

[
 {
  "value": "C₂F₄",
  "misconception": "you divided by 2, which is a common factor but not the LARGEST one — 2 and 4 still share the factor 2",
  "feedback": "This answer is wrong — you divided by 2, which is a common factor but not the LARGEST one. The subscripts of C₂F₄ — 2 and 4 — still share the factor 2, so the formula still reduces. Divide C₄F₈'s subscripts by their largest common factor, 4: the empirical formula is CF₂."
 },
 {
  "value": "C₄F₈",
  "misconception": "you left the formula unchanged — the subscripts 4 and 8 share the factor 4, so the formula reduces",
  "feedback": "This answer is wrong — you left the formula unchanged. The subscripts 4 and 8 share the factor 4, so the formula reduces: C: 4 ÷ 4 = 1, F: 8 ÷ 4 = 2, and the empirical formula is CF₂."
 },
 {
  "value": "CF",
  "misconception": "you divided each subscript by its own value, which destroys the ratio",
  "feedback": "This answer is wrong — you divided each subscript by its own value, which destroys the ratio. Every subscript must be divided by the SAME factor — the largest common factor, 4: C: 4 ÷ 4 = 1, F: 8 ÷ 4 = 2, so the empirical formula is CF₂."
 }
]

{
 "keyExplanation": "Subscripts: C 4, F 8. The largest common factor is 4 — dividing by 2 alone leaves C₂F₄, which still reduces. C: 4 ÷ 4 = 1, F: 8 ÷ 4 = 2, and a subscript of 1 is never written, so the empirical formula is CF₂.",
 "anticipatedWrong": [
  {
   "value": "C₂F₄",
   "misconception": "you divided by 2, which is a common factor but not the LARGEST one — 2 and 4 still share the factor 2",
   "feedback": "This answer is wrong — you divided by 2, which is a common factor but not the LARGEST one. The subscripts of C₂F₄ — 2 and 4 — still share the factor 2, so the formula still reduces. Divide C₄F₈'s subscripts by their largest common factor, 4: the empirical formula is CF₂."
  },
  {
   "value": "C₄F₈",
   "misconception": "you left the formula unchanged — the subscripts 4 and 8 share the factor 4, so the formula reduces",
   "feedback": "This answer is wrong — you left the formula unchanged. The subscripts 4 and 8 share the factor 4, so the formula reduces: C: 4 ÷ 4 = 1, F: 8 ÷ 4 = 2, and the empirical formula is CF₂."
  },
  {
   "value": "CF",
   "misconception": "you divided each subscript by its own value, which destroys the ratio",
   "feedback": "This answer is wrong — you divided each subscript by its own value, which destroys the ratio. Every subscript must be divided by the SAME factor — the largest common factor, 4: C: 4 ÷ 4 = 1, F: 8 ÷ 4 = 2, so the empirical formula is CF₂."
  }
 ]
}

[
 {
  "value": "1 : 3.1",
  "misconception": "you compared the masses instead of the moles — 21.7 : 66.5 is about 1 : 3.1, but atoms are counted in moles",
  "feedback": "This answer is wrong — you compared the masses instead of the moles. 21.7 : 66.5 is about 1 : 3.1, but atoms are counted in moles: n(P) = 21.7 / 31.0 = 0.70 mol and n(F) = 66.5 / 19.0 = 3.50 mol, and dividing each by 0.70 gives 1 : 5."
 },
 {
  "value": "5 : 1",
  "misconception": "you wrote the ratio backwards — the order follows the elements as named: phosphorus first, then fluorine",
  "feedback": "This answer is wrong — you wrote the ratio backwards. The ratio order follows the elements as they are named in the question: phosphorus first, then fluorine, so the answer is 1 : 5."
 }
]

{
 "keyExplanation": "Values from the question:\nm(P) = 21.7 g, m(F) = 66.5 g\nEquation:\nn = m/M  (for each element)\nSubstituting the values and calculating:\nn(P) = 21.7 / 31.0 = 0.70 mol\nn(F) = 66.5 / 19.0 = 3.50 mol\nDivide each by the smallest (0.70): P gives 1, F gives 5.\nMole ratio of phosphorus to fluorine = 1 : 5",
 "anticipatedWrong": [
  {
   "value": "1 : 3.1",
   "misconception": "you compared the masses instead of the moles — 21.7 : 66.5 is about 1 : 3.1, but atoms are counted in moles",
   "feedback": "This answer is wrong — you compared the masses instead of the moles. 21.7 : 66.5 is about 1 : 3.1, but atoms are counted in moles: n(P) = 21.7 / 31.0 = 0.70 mol and n(F) = 66.5 / 19.0 = 3.50 mol, and dividing each by 0.70 gives 1 : 5."
  },
  {
   "value": "5 : 1",
   "misconception": "you wrote the ratio backwards — the order follows the elements as named: phosphorus first, then fluorine",
   "feedback": "This answer is wrong — you wrote the ratio backwards. The ratio order follows the elements as they are named in the question: phosphorus first, then fluorine, so the answer is 1 : 5."
  }
 ]
}

[
 {
  "value": "1 : 4",
  "misconception": "you rounded the 3.75 up to 4 — rounding changes the ratio; multiply every number by 4 instead",
  "feedback": "This answer is wrong — you rounded the 3.75 up to 4, and rounding changes the ratio itself. The decimal part is .75, so multiply every number by 4 instead: 1 × 4 = 4 and 3.75 × 4 = 15, giving 4 : 15."
 },
 {
  "value": "1 : 15",
  "misconception": "you multiplied only the decimal number — every number in the ratio must be multiplied by the same amount",
  "feedback": "This answer is wrong — you multiplied only the decimal number. Every number in the ratio must be multiplied by the same amount to keep the ratio unchanged: 1 × 4 = 4 and 3.75 × 4 = 15, giving 4 : 15."
 }
]

{
 "keyExplanation": "The decimal part is .75, so multiply every number by 4: 1 × 4 = 4 and 3.75 × 4 = 15. The whole-number ratio is 4 : 15. Rounding 3.75 up to 4 would change the ratio itself — multiplying never does.",
 "anticipatedWrong": [
  {
   "value": "1 : 4",
   "misconception": "you rounded the 3.75 up to 4 — rounding changes the ratio; multiply every number by 4 instead",
   "feedback": "This answer is wrong — you rounded the 3.75 up to 4, and rounding changes the ratio itself. The decimal part is .75, so multiply every number by 4 instead: 1 × 4 = 4 and 3.75 × 4 = 15, giving 4 : 15."
  },
  {
   "value": "1 : 15",
   "misconception": "you multiplied only the decimal number — every number in the ratio must be multiplied by the same amount",
   "feedback": "This answer is wrong — you multiplied only the decimal number. Every number in the ratio must be multiplied by the same amount to keep the ratio unchanged: 1 × 4 = 4 and 3.75 × 4 = 15, giving 4 : 15."
  }
 ]
}

[
 {
  "value": "C₂H₂O₄",
  "misconception": "you left the formula unchanged — the subscripts 2, 2, and 4 share the factor 2, so the formula reduces",
  "feedback": "This answer is wrong — you left the formula unchanged. The subscripts 2, 2, and 4 share the factor 2, so the formula reduces: C: 2 ÷ 2 = 1, H: 2 ÷ 2 = 1, O: 4 ÷ 2 = 2, giving CHO₂."
 },
 {
  "value": "CHO",
  "misconception": "you divided each subscript by its own value, which destroys the ratio",
  "feedback": "This answer is wrong — you divided each subscript by its own value, which destroys the ratio. Every subscript is divided by the same factor, 2: C 1, H 1, O 2, giving CHO₂."
 },
 {
  "value": "CHO₄",
  "misconception": "you left the last subscript undivided — every subscript must be divided by the same factor, including oxygen's",
  "feedback": "This answer is wrong — you left the last subscript undivided. Every subscript must be divided by the same factor, including oxygen's: O: 4 ÷ 2 = 2, giving CHO₂."
 }
]

{
 "keyExplanation": "Subscripts: C 2, H 2, O 4. The largest common factor is 2. C: 2 ÷ 2 = 1, H: 2 ÷ 2 = 1, O: 4 ÷ 2 = 2. A subscript of 1 is never written, so oxalic acid's empirical formula is CHO₂.",
 "anticipatedWrong": [
  {
   "value": "C₂H₂O₄",
   "misconception": "you left the formula unchanged — the subscripts 2, 2, and 4 share the factor 2, so the formula reduces",
   "feedback": "This answer is wrong — you left the formula unchanged. The subscripts 2, 2, and 4 share the factor 2, so the formula reduces: C: 2 ÷ 2 = 1, H: 2 ÷ 2 = 1, O: 4 ÷ 2 = 2, giving CHO₂."
  },
  {
   "value": "CHO",
   "misconception": "you divided each subscript by its own value, which destroys the ratio",
   "feedback": "This answer is wrong — you divided each subscript by its own value, which destroys the ratio. Every subscript is divided by the same factor, 2: C 1, H 1, O 2, giving CHO₂."
  },
  {
   "value": "CHO₄",
   "misconception": "you left the last subscript undivided — every subscript must be divided by the same factor, including oxygen's",
   "feedback": "This answer is wrong — you left the last subscript undivided. Every subscript must be divided by the same factor, including oxygen's: O: 4 ÷ 2 = 2, giving CHO₂."
  }
 ]
}

[
 {
  "value": "1.2 : 1 : 4",
  "misconception": "you compared the masses instead of the moles — 20.7 : 18.0 : 72.0 is about 1.2 : 1 : 4, but atoms are counted in moles",
  "feedback": "This answer is wrong — you compared the masses instead of the moles — 20.7 : 18.0 : 72.0 is about 1.2 : 1 : 4, but atoms are counted in moles."
 },
 {
  "value": "0.67 : 0.33 : 1",
  "misconception": "you divided every value by the largest instead of the smallest — divide by the smallest so the smallest becomes 1",
  "feedback": "This answer is wrong — you divided every value by the largest instead of the smallest — divide by the smallest so the smallest becomes 1."
 }
]

{
 "keyExplanation": "Values from the question:\nm(Li) = 20.7 g, m(C) = 18.0 g, m(O) = 72.0 g\nEquation:\nn = m/M  (for each element)\nSubstituting the values and calculating:\nn(Li) = 20.7 / 6.9 = 3.00 mol\nn(C) = 18.0 / 12.0 = 1.50 mol\nn(O) = 72.0 / 16.0 = 4.50 mol\nDivide each by the smallest (1.50): Li gives 2, C gives 1, O gives 3.\nMole ratio of lithium to carbon to oxygen = 2 : 1 : 3"
}

[
 {
  "value": 3.74,
  "misconception": "you ignored the subscript in the empirical formula, using 12.0 + 1.0 + 35.5 = 48.5 g/mol — M of C₂HCl is 2 × 12.0 + 1.0 + 35.5 = 60.5 g/mol",
  "feedback": "This answer is wrong — you ignored the subscript in the empirical formula, using 12.0 + 1.0 + 35.5 = 48.5 g/mol. M of C₂HCl is 2 × 12.0 + 1.0 + 35.5 = 60.5 g/mol, and a non-whole unit count signals exactly this kind of slip."
 },
 {
  "value": 0.33,
  "misconception": "you divided upside down — the compound's molar mass goes on top, and the unit count is never below 1",
  "feedback": "This answer is wrong — you divided upside down — the compound's molar mass goes on top, and the unit count is never below 1."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmolar mass of the compound = 181.5 g/mol\nM of C₂HCl = 2 × 12.0 + 1.0 + 35.5 = 60.5 g/mol\nWrite down the equation:\nnumber of units = molar mass of the compound ÷ molar mass of the empirical formula\nSubstitute in the values, and calculate:\nnumber of units = 181.5 / 60.5\nnumber of units = 3\nThe result is a whole number at least 1, so the division ran the right way up."
}

[
 {
  "value": "AlO₂",
  "misconception": "you rounded the 1.5 up to 2 — rounding changes the ratio; multiply every number by 2 instead",
  "feedback": "This answer is wrong — you rounded the 1.5 up to 2. Rounding changes the ratio; multiply every number by 2 instead: 1 and 1.5 become 2 and 3, so the empirical formula is Al₂O₃."
 },
 {
  "value": "AlO",
  "misconception": "you dropped the decimal — cutting the .5 off changes the ratio; multiply every number by 2 instead",
  "feedback": "This answer is wrong — you dropped the decimal. Cutting the .5 off changes the ratio; multiply every number by 2 instead: 1 and 1.5 become 2 and 3, so the empirical formula is Al₂O₃."
 },
 {
  "value": "Al₃O₂",
  "misconception": "you inverted the ratio — aluminum has the smaller mole value, so aluminum takes the 1 before clearing",
  "feedback": "This answer is wrong — you inverted the ratio. Aluminum has the smaller mole value (3.50 mol against oxygen's 5.25 mol), so aluminum takes the 1 before clearing: 1 and 1.5 become 2 and 3, giving Al₂O₃."
 }
]

{
 "keyExplanation": "Values from the question:\nm(Al) = 94.5 g, m(O) = 84.0 g\nEquation:\nn = m/M  (for each element)\nSubstituting the values and calculating:\nn(Al) = 94.5 / 27.0 = 3.50 mol\nn(O) = 84.0 / 16.0 = 5.25 mol\nDivide each by the smallest (3.50): Al gives 1, O gives 1.5.\nThe decimal ends in .5, so multiply every number by 2: 2 and 3.\nEmpirical formula: Al₂O₃",
 "anticipatedWrong": [
  {
   "value": "AlO₂",
   "misconception": "you rounded the 1.5 up to 2 — rounding changes the ratio; multiply every number by 2 instead",
   "feedback": "This answer is wrong — you rounded the 1.5 up to 2. Rounding changes the ratio; multiply every number by 2 instead: 1 and 1.5 become 2 and 3, so the empirical formula is Al₂O₃."
  },
  {
   "value": "AlO",
   "misconception": "you dropped the decimal — cutting the .5 off changes the ratio; multiply every number by 2 instead",
   "feedback": "This answer is wrong — you dropped the decimal. Cutting the .5 off changes the ratio; multiply every number by 2 instead: 1 and 1.5 become 2 and 3, so the empirical formula is Al₂O₃."
  },
  {
   "value": "Al₃O₂",
   "misconception": "you inverted the ratio — aluminum has the smaller mole value, so aluminum takes the 1 before clearing",
   "feedback": "This answer is wrong — you inverted the ratio. Aluminum has the smaller mole value (3.50 mol against oxygen's 5.25 mol), so aluminum takes the 1 before clearing: 1 and 1.5 become 2 and 3, giving Al₂O₃."
  }
 ]
}

[
 {
  "value": "C₂H₃O₂",
  "misconception": "you stopped at the empirical formula — the unit count is 118.0/59.0 = 2, and every subscript must be multiplied by it",
  "feedback": "This answer is wrong — you stopped at the empirical formula. The unit count is 118.0 / 59.0 = 2, and every subscript must be multiplied by it: C: 2 × 2 = 4, H: 3 × 2 = 6, O: 2 × 2 = 4, giving C₄H₆O₄."
 },
 {
  "value": "C₄H₃O₂",
  "misconception": "you multiplied only carbon's subscript — every subscript in the empirical formula is multiplied by the unit count",
  "feedback": "This answer is wrong — you multiplied only carbon's subscript. Every subscript in the empirical formula is multiplied by the unit count, 2: C: 2 × 2 = 4, H: 3 × 2 = 6, O: 2 × 2 = 4, giving C₄H₆O₄."
 },
 {
  "value": "C₂H₃O₄",
  "misconception": "you multiplied only oxygen's subscript — every subscript in the empirical formula is multiplied by the unit count",
  "feedback": "This answer is wrong — you multiplied only oxygen's subscript. Every subscript in the empirical formula is multiplied by the unit count, 2: C: 2 × 2 = 4, H: 3 × 2 = 6, O: 2 × 2 = 4, giving C₄H₆O₄."
 }
]

{
 "keyExplanation": "M of C₂H₃O₂ = 2 × 12.0 + 3 × 1.0 + 2 × 16.0 = 59.0 g/mol.\nStep 1 — find the number of units:\nnumber of units = molar mass of the compound ÷ molar mass of the empirical formula\nnumber of units = 118.0 / 59.0 = 2\nStep 2 — multiply every subscript by 2:\nC: 2 × 2 = 4,  H: 3 × 2 = 6,  O: 2 × 2 = 4\nMolecular formula: C₄H₆O₄",
 "anticipatedWrong": [
  {
   "value": "C₂H₃O₂",
   "misconception": "you stopped at the empirical formula — the unit count is 118.0/59.0 = 2, and every subscript must be multiplied by it",
   "feedback": "This answer is wrong — you stopped at the empirical formula. The unit count is 118.0 / 59.0 = 2, and every subscript must be multiplied by it: C: 2 × 2 = 4, H: 3 × 2 = 6, O: 2 × 2 = 4, giving C₄H₆O₄."
  },
  {
   "value": "C₄H₃O₂",
   "misconception": "you multiplied only carbon's subscript — every subscript in the empirical formula is multiplied by the unit count",
   "feedback": "This answer is wrong — you multiplied only carbon's subscript. Every subscript in the empirical formula is multiplied by the unit count, 2: C: 2 × 2 = 4, H: 3 × 2 = 6, O: 2 × 2 = 4, giving C₄H₆O₄."
  },
  {
   "value": "C₂H₃O₄",
   "misconception": "you multiplied only oxygen's subscript — every subscript in the empirical formula is multiplied by the unit count",
   "feedback": "This answer is wrong — you multiplied only oxygen's subscript. Every subscript in the empirical formula is multiplied by the unit count, 2: C: 2 × 2 = 4, H: 3 × 2 = 6, O: 2 × 2 = 4, giving C₄H₆O₄."
  }
 ]
}

[
 {
  "value": "MnO₂",
  "misconception": "you rounded the 1.50 up to 2 — rounding changes the ratio; multiply every number by 2 instead",
  "feedback": "This answer is wrong — you rounded the 1.50 up to 2. Rounding changes the ratio; multiply every number by 2 instead: Mn gives 2 and O gives 3, so the empirical formula is Mn₂O₃."
 },
 {
  "value": "MnO",
  "misconception": "you dropped the decimal — cutting the .50 off changes the ratio; multiply every number by 2 instead",
  "feedback": "This answer is wrong — you dropped the decimal. Cutting the .50 off changes the ratio; multiply every number by 2 instead: Mn gives 2 and O gives 3, so the empirical formula is Mn₂O₃."
 }
]

{
 "keyExplanation": "Assume a 100 g sample: m(Mn) = 69.6 g, m(O) = 30.4 g.\nEquation:\nn = m/M  (for each element)\nSubstituting the values and calculating:\nn(Mn) = 69.6 / 54.9 = 1.27 mol\nn(O) = 30.4 / 16.0 = 1.90 mol\nDivide each by the smallest (1.27): Mn gives 1, O gives 1.50.\nThe decimal ends in .5, so multiply every number by 2: 2 and 3.\nEmpirical formula: Mn₂O₃",
 "anticipatedWrong": [
  {
   "value": "MnO₂",
   "misconception": "you rounded the 1.50 up to 2 — rounding changes the ratio; multiply every number by 2 instead",
   "feedback": "This answer is wrong — you rounded the 1.50 up to 2. Rounding changes the ratio; multiply every number by 2 instead: Mn gives 2 and O gives 3, so the empirical formula is Mn₂O₃."
  },
  {
   "value": "MnO",
   "misconception": "you dropped the decimal — cutting the .50 off changes the ratio; multiply every number by 2 instead",
   "feedback": "This answer is wrong — you dropped the decimal. Cutting the .50 off changes the ratio; multiply every number by 2 instead: Mn gives 2 and O gives 3, so the empirical formula is Mn₂O₃."
  }
 ]
}

[
 {
  "value": 52.4,
  "misconception": "you gave the potassium's mass — the question asks for the chlorine, the rest of the 100 g",
  "feedback": "This answer is wrong — you gave the potassium's mass — the question asks for the chlorine, the rest of the 100 g."
 },
 {
  "value": 0.476,
  "misconception": "you divided by 100 — in a 100 g sample the masses are in grams already",
  "feedback": "This answer is wrong — you divided by 100 — in a 100 g sample the masses are in grams already."
 }
]

{
 "keyExplanation": "Assume a sample of exactly 100 g.\nPotassium: 52.4% of the compound → 52.4 g.\nThe element masses in a 100 g sample total 100 g.\nmass of chlorine = 100 − 52.4 = 47.6 g"
}

[
 {
  "value": "C₆H₄",
  "misconception": "you divided by 2, which is a common factor but not the LARGEST one — 6 and 4 still share the factor 2",
  "feedback": "This answer is wrong — you divided by 2, which is a common factor but not the LARGEST one. The subscripts of C₆H₄ — 6 and 4 — still share the factor 2, so the formula still reduces. Divide C₁₂H₈'s subscripts by their largest common factor, 4: C: 12 ÷ 4 = 3, H: 8 ÷ 4 = 2, and the empirical formula is C₃H₂."
 },
 {
  "value": "C₁₂H₈",
  "misconception": "you left the formula unchanged — the subscripts 12 and 8 share the factor 4, so the formula reduces",
  "feedback": "This answer is wrong — you left the formula unchanged. The subscripts 12 and 8 share the factor 4, so the formula reduces: C: 12 ÷ 4 = 3, H: 8 ÷ 4 = 2, and the empirical formula is C₃H₂."
 },
 {
  "value": "C₁₂H₂",
  "misconception": "you divided only the hydrogen's subscript — every subscript must be divided by the same factor",
  "feedback": "This answer is wrong — you divided only the hydrogen's subscript. Every subscript must be divided by the SAME factor — the largest common factor, 4: C: 12 ÷ 4 = 3, H: 8 ÷ 4 = 2, so the empirical formula is C₃H₂."
 }
]

{
 "keyExplanation": "Subscripts: C 12, H 8. The largest common factor is 4 — dividing by 2 alone leaves C₆H₄, which still reduces. C: 12 ÷ 4 = 3, H: 8 ÷ 4 = 2, so the empirical formula is C₃H₂.",
 "anticipatedWrong": [
  {
   "value": "C₆H₄",
   "misconception": "you divided by 2, which is a common factor but not the LARGEST one — 6 and 4 still share the factor 2",
   "feedback": "This answer is wrong — you divided by 2, which is a common factor but not the LARGEST one. The subscripts of C₆H₄ — 6 and 4 — still share the factor 2, so the formula still reduces. Divide C₁₂H₈'s subscripts by their largest common factor, 4: C: 12 ÷ 4 = 3, H: 8 ÷ 4 = 2, and the empirical formula is C₃H₂."
  },
  {
   "value": "C₁₂H₈",
   "misconception": "you left the formula unchanged — the subscripts 12 and 8 share the factor 4, so the formula reduces",
   "feedback": "This answer is wrong — you left the formula unchanged. The subscripts 12 and 8 share the factor 4, so the formula reduces: C: 12 ÷ 4 = 3, H: 8 ÷ 4 = 2, and the empirical formula is C₃H₂."
  },
  {
   "value": "C₁₂H₂",
   "misconception": "you divided only the hydrogen's subscript — every subscript must be divided by the same factor",
   "feedback": "This answer is wrong — you divided only the hydrogen's subscript. Every subscript must be divided by the SAME factor — the largest common factor, 4: C: 12 ÷ 4 = 3, H: 8 ÷ 4 = 2, so the empirical formula is C₃H₂."
  }
 ]
}

[
 {
  "value": "1 : 3.6",
  "misconception": "you compared the masses instead of the moles — 6.42 : 22.8 is about 1 : 3.6, but atoms are counted in moles",
  "feedback": "This answer is wrong — you compared the masses instead of the moles. 6.42 : 22.8 is about 1 : 3.6, but atoms are counted in moles: n(S) = 6.42 / 32.1 = 0.20 mol and n(F) = 22.8 / 19.0 = 1.20 mol, and dividing each by 0.20 gives 1 : 6."
 },
 {
  "value": "6 : 1",
  "misconception": "you wrote the ratio backwards — the order follows the elements as named: sulfur first, then fluorine",
  "feedback": "This answer is wrong — you wrote the ratio backwards. The ratio order follows the elements as they are named in the question: sulfur first, then fluorine, so the answer is 1 : 6."
 }
]

{
 "keyExplanation": "Values from the question:\nm(S) = 6.42 g, m(F) = 22.8 g\nEquation:\nn = m/M  (for each element)\nSubstituting the values and calculating:\nn(S) = 6.42 / 32.1 = 0.20 mol\nn(F) = 22.8 / 19.0 = 1.20 mol\nDivide each by the smallest (0.20): S gives 1, F gives 6.\nMole ratio of sulfur to fluorine = 1 : 6",
 "anticipatedWrong": [
  {
   "value": "1 : 3.6",
   "misconception": "you compared the masses instead of the moles — 6.42 : 22.8 is about 1 : 3.6, but atoms are counted in moles",
   "feedback": "This answer is wrong — you compared the masses instead of the moles. 6.42 : 22.8 is about 1 : 3.6, but atoms are counted in moles: n(S) = 6.42 / 32.1 = 0.20 mol and n(F) = 22.8 / 19.0 = 1.20 mol, and dividing each by 0.20 gives 1 : 6."
  },
  {
   "value": "6 : 1",
   "misconception": "you wrote the ratio backwards — the order follows the elements as named: sulfur first, then fluorine",
   "feedback": "This answer is wrong — you wrote the ratio backwards. The ratio order follows the elements as they are named in the question: sulfur first, then fluorine, so the answer is 1 : 6."
  }
 ]
}

[
 {
  "value": "1 : 5",
  "misconception": "you rounded the 4.67 up to 5 — rounding changes the ratio; multiply every number by 3 instead",
  "feedback": "This answer is wrong — you rounded the 4.67 up to 5, and rounding changes the ratio itself. The decimal is near .67, so multiply every number by 3 instead: 1 × 3 = 3 and 4.67 × 3 = 14, giving 3 : 14."
 },
 {
  "value": "1 : 14",
  "misconception": "you multiplied only the decimal number — every number in the ratio must be multiplied by the same amount",
  "feedback": "This answer is wrong — you multiplied only the decimal number. Every number in the ratio must be multiplied by the same amount to keep the ratio unchanged: 1 × 3 = 3 and 4.67 × 3 = 14, giving 3 : 14."
 }
]

{
 "keyExplanation": "The decimal is near .67, so multiply every number by 3: 1 × 3 = 3 and 4.67 × 3 = 14. The whole-number ratio is 3 : 14. Rounding 4.67 up to 5 would change the ratio itself — multiplying never does.",
 "anticipatedWrong": [
  {
   "value": "1 : 5",
   "misconception": "you rounded the 4.67 up to 5 — rounding changes the ratio; multiply every number by 3 instead",
   "feedback": "This answer is wrong — you rounded the 4.67 up to 5, and rounding changes the ratio itself. The decimal is near .67, so multiply every number by 3 instead: 1 × 3 = 3 and 4.67 × 3 = 14, giving 3 : 14."
  },
  {
   "value": "1 : 14",
   "misconception": "you multiplied only the decimal number — every number in the ratio must be multiplied by the same amount",
   "feedback": "This answer is wrong — you multiplied only the decimal number. Every number in the ratio must be multiplied by the same amount to keep the ratio unchanged: 1 × 3 = 3 and 4.67 × 3 = 14, giving 3 : 14."
  }
 ]
}

[
 {
  "value": "C₁₂H₂₆",
  "misconception": "you left the formula unchanged — the subscripts 12 and 26 share the factor 2, so the formula reduces",
  "feedback": "This answer is wrong — you left the formula unchanged. The subscripts 12 and 26 share the factor 2, so the formula reduces: C: 12 ÷ 2 = 6, H: 26 ÷ 2 = 13, giving C₆H₁₃."
 },
 {
  "value": "CH",
  "misconception": "you divided each subscript by its own value, which destroys the ratio",
  "feedback": "This answer is wrong — you divided each subscript by its own value, which destroys the ratio. Every subscript is divided by the same factor, 2: C: 12 ÷ 2 = 6, H: 26 ÷ 2 = 13, giving C₆H₁₃."
 },
 {
  "value": "C₁₂H₁₃",
  "misconception": "you divided only the hydrogen's subscript — every subscript must be divided by the same factor",
  "feedback": "This answer is wrong — you divided only the hydrogen's subscript. Every subscript must be divided by the same factor: C: 12 ÷ 2 = 6, H: 26 ÷ 2 = 13, giving C₆H₁₃."
 }
]

{
 "keyExplanation": "Subscripts: C 12, H 26. The largest common factor is 2. C: 12 ÷ 2 = 6, H: 26 ÷ 2 = 13, so dodecane's empirical formula is C₆H₁₃.",
 "anticipatedWrong": [
  {
   "value": "C₁₂H₂₆",
   "misconception": "you left the formula unchanged — the subscripts 12 and 26 share the factor 2, so the formula reduces",
   "feedback": "This answer is wrong — you left the formula unchanged. The subscripts 12 and 26 share the factor 2, so the formula reduces: C: 12 ÷ 2 = 6, H: 26 ÷ 2 = 13, giving C₆H₁₃."
  },
  {
   "value": "CH",
   "misconception": "you divided each subscript by its own value, which destroys the ratio",
   "feedback": "This answer is wrong — you divided each subscript by its own value, which destroys the ratio. Every subscript is divided by the same factor, 2: C: 12 ÷ 2 = 6, H: 26 ÷ 2 = 13, giving C₆H₁₃."
  },
  {
   "value": "C₁₂H₁₃",
   "misconception": "you divided only the hydrogen's subscript — every subscript must be divided by the same factor",
   "feedback": "This answer is wrong — you divided only the hydrogen's subscript. Every subscript must be divided by the same factor: C: 12 ÷ 2 = 6, H: 26 ÷ 2 = 13, giving C₆H₁₃."
  }
 ]
}

[
 {
  "value": "1 : 10.3 : 21.3",
  "misconception": "you compared the masses instead of the moles — 3.0 : 31.0 : 64.0 is about 1 : 10.3 : 21.3, but atoms are counted in moles",
  "feedback": "This answer is wrong — you compared the masses instead of the moles — 3.0 : 31.0 : 64.0 is about 1 : 10.3 : 21.3, but atoms are counted in moles."
 },
 {
  "value": "4 : 1 : 3",
  "misconception": "you wrote the ratio backwards — the order follows the elements as named: hydrogen first, then phosphorus, then oxygen",
  "feedback": "This answer is wrong — you wrote the ratio backwards — the order follows the elements as named: hydrogen first, then phosphorus, then oxygen."
 }
]

{
 "keyExplanation": "Values from the question:\nm(H) = 3.0 g, m(P) = 31.0 g, m(O) = 64.0 g\nEquation:\nn = m/M  (for each element)\nSubstituting the values and calculating:\nn(H) = 3.0 / 1.0 = 3.00 mol\nn(P) = 31.0 / 31.0 = 1.00 mol\nn(O) = 64.0 / 16.0 = 4.00 mol\nDivide each by the smallest (1.00): H gives 3, P gives 1, O gives 4.\nMole ratio of hydrogen to phosphorus to oxygen = 3 : 1 : 4"
}

[
 {
  "value": 3.07,
  "misconception": "you ignored the subscripts in the empirical formula, using 12.0 + 1.0 + 32.1 = 45.1 g/mol — M of CH₂S is 12.0 + 2 × 1.0 + 32.1 = 46.1 g/mol",
  "feedback": "This answer is wrong — you ignored the subscripts in the empirical formula, using 12.0 + 1.0 + 32.1 = 45.1 g/mol. M of CH₂S is 12.0 + 2 × 1.0 + 32.1 = 46.1 g/mol — the unit count always lands exactly on a whole number, so a close-but-not-whole result signals this slip."
 },
 {
  "value": 0.33,
  "misconception": "you divided upside down — the compound's molar mass goes on top, and the unit count is never below 1",
  "feedback": "This answer is wrong — you divided upside down — the compound's molar mass goes on top, and the unit count is never below 1."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmolar mass of the compound = 138.3 g/mol\nM of CH₂S = 12.0 + 2 × 1.0 + 32.1 = 46.1 g/mol\nWrite down the equation:\nnumber of units = molar mass of the compound ÷ molar mass of the empirical formula\nSubstitute in the values, and calculate:\nnumber of units = 138.3 / 46.1\nnumber of units = 3\nThe result is a whole number at least 1, so the division ran the right way up."
}

[
 {
  "value": "CrO₂",
  "misconception": "you rounded the 1.5 up to 2 — rounding changes the ratio; multiply every number by 2 instead",
  "feedback": "This answer is wrong — you rounded the 1.5 up to 2. Rounding changes the ratio; multiply every number by 2 instead: 1 and 1.5 become 2 and 3, so the empirical formula is Cr₂O₃."
 },
 {
  "value": "CrO",
  "misconception": "you dropped the decimal — cutting the .5 off changes the ratio; multiply every number by 2 instead",
  "feedback": "This answer is wrong — you dropped the decimal. Cutting the .5 off changes the ratio; multiply every number by 2 instead: 1 and 1.5 become 2 and 3, so the empirical formula is Cr₂O₃."
 },
 {
  "value": "Cr₃O₂",
  "misconception": "you inverted the ratio — chromium has the smaller mole value, so chromium takes the 1 before clearing",
  "feedback": "This answer is wrong — you inverted the ratio. Chromium has the smaller mole value (0.60 mol against oxygen's 0.90 mol), so chromium takes the 1 before clearing: 1 and 1.5 become 2 and 3, giving Cr₂O₃."
 }
]

{
 "keyExplanation": "Values from the question:\nm(Cr) = 31.2 g, m(O) = 14.4 g\nEquation:\nn = m/M  (for each element)\nSubstituting the values and calculating:\nn(Cr) = 31.2 / 52.0 = 0.60 mol\nn(O) = 14.4 / 16.0 = 0.90 mol\nDivide each by the smallest (0.60): Cr gives 1, O gives 1.5.\nThe decimal ends in .5, so multiply every number by 2: 2 and 3.\nEmpirical formula: Cr₂O₃",
 "anticipatedWrong": [
  {
   "value": "CrO₂",
   "misconception": "you rounded the 1.5 up to 2 — rounding changes the ratio; multiply every number by 2 instead",
   "feedback": "This answer is wrong — you rounded the 1.5 up to 2. Rounding changes the ratio; multiply every number by 2 instead: 1 and 1.5 become 2 and 3, so the empirical formula is Cr₂O₃."
  },
  {
   "value": "CrO",
   "misconception": "you dropped the decimal — cutting the .5 off changes the ratio; multiply every number by 2 instead",
   "feedback": "This answer is wrong — you dropped the decimal. Cutting the .5 off changes the ratio; multiply every number by 2 instead: 1 and 1.5 become 2 and 3, so the empirical formula is Cr₂O₃."
  },
  {
   "value": "Cr₃O₂",
   "misconception": "you inverted the ratio — chromium has the smaller mole value, so chromium takes the 1 before clearing",
   "feedback": "This answer is wrong — you inverted the ratio. Chromium has the smaller mole value (0.60 mol against oxygen's 0.90 mol), so chromium takes the 1 before clearing: 1 and 1.5 become 2 and 3, giving Cr₂O₃."
  }
 ]
}

[
 {
  "value": "CHNO",
  "misconception": "you stopped at the empirical formula — the unit count is 129.0/43.0 = 3, and every subscript must be multiplied by it",
  "feedback": "This answer is wrong — you stopped at the empirical formula. The unit count is 129.0 / 43.0 = 3, and every subscript must be multiplied by it: C: 1 × 3 = 3, H: 1 × 3 = 3, N: 1 × 3 = 3, O: 1 × 3 = 3, giving C₃H₃N₃O₃."
 },
 {
  "value": "C₃HNO",
  "misconception": "you multiplied only carbon's subscript — every subscript in the empirical formula is multiplied by the unit count, including every unwritten 1",
  "feedback": "This answer is wrong — you multiplied only carbon's subscript. Every subscript in the empirical formula is multiplied by the unit count, 3 — including every unwritten 1: C: 1 × 3 = 3, H: 1 × 3 = 3, N: 1 × 3 = 3, O: 1 × 3 = 3, giving C₃H₃N₃O₃."
 },
 {
  "value": "CHNO₃",
  "misconception": "you multiplied only oxygen's subscript — every subscript in the empirical formula is multiplied by the unit count, including every unwritten 1",
  "feedback": "This answer is wrong — you multiplied only oxygen's subscript. Every subscript in the empirical formula is multiplied by the unit count, 3 — including every unwritten 1: C: 1 × 3 = 3, H: 1 × 3 = 3, N: 1 × 3 = 3, O: 1 × 3 = 3, giving C₃H₃N₃O₃."
 }
]

{
 "keyExplanation": "M of CHNO = 12.0 + 1.0 + 14.0 + 16.0 = 43.0 g/mol.\nStep 1 — find the number of units:\nnumber of units = molar mass of the compound ÷ molar mass of the empirical formula\nnumber of units = 129.0 / 43.0 = 3\nStep 2 — multiply every subscript by 3 (an unwritten subscript is 1):\nC: 1 × 3 = 3,  H: 1 × 3 = 3,  N: 1 × 3 = 3,  O: 1 × 3 = 3\nMolecular formula: C₃H₃N₃O₃",
 "anticipatedWrong": [
  {
   "value": "CHNO",
   "misconception": "you stopped at the empirical formula — the unit count is 129.0/43.0 = 3, and every subscript must be multiplied by it",
   "feedback": "This answer is wrong — you stopped at the empirical formula. The unit count is 129.0 / 43.0 = 3, and every subscript must be multiplied by it: C: 1 × 3 = 3, H: 1 × 3 = 3, N: 1 × 3 = 3, O: 1 × 3 = 3, giving C₃H₃N₃O₃."
  },
  {
   "value": "C₃HNO",
   "misconception": "you multiplied only carbon's subscript — every subscript in the empirical formula is multiplied by the unit count, including every unwritten 1",
   "feedback": "This answer is wrong — you multiplied only carbon's subscript. Every subscript in the empirical formula is multiplied by the unit count, 3 — including every unwritten 1: C: 1 × 3 = 3, H: 1 × 3 = 3, N: 1 × 3 = 3, O: 1 × 3 = 3, giving C₃H₃N₃O₃."
  },
  {
   "value": "CHNO₃",
   "misconception": "you multiplied only oxygen's subscript — every subscript in the empirical formula is multiplied by the unit count, including every unwritten 1",
   "feedback": "This answer is wrong — you multiplied only oxygen's subscript. Every subscript in the empirical formula is multiplied by the unit count, 3 — including every unwritten 1: C: 1 × 3 = 3, H: 1 × 3 = 3, N: 1 × 3 = 3, O: 1 × 3 = 3, giving C₃H₃N₃O₃."
  }
 ]
}

[
 {
  "value": "SiN",
  "misconception": "you dropped the decimal — cutting the .33 off changes the ratio; multiply every number by 3 instead",
  "feedback": "This answer is wrong — you dropped the decimal. Cutting the .33 off changes the ratio; multiply every number by 3 instead: Si gives 3 and N gives 4, so the empirical formula is Si₃N₄."
 },
 {
  "value": "SiN₄",
  "misconception": "you multiplied only the number with the decimal — multiplying just one number changes the ratio; multiply EVERY number by 3",
  "feedback": "This answer is wrong — you multiplied only the number with the decimal. Multiplying just one number changes the ratio; multiply EVERY number by 3: Si gives 3 and N gives 4, so the empirical formula is Si₃N₄."
 }
]

{
 "keyExplanation": "Assume a 100 g sample: m(Si) = 60.1 g, m(N) = 39.9 g.\nEquation:\nn = m/M  (for each element)\nSubstituting the values and calculating:\nn(Si) = 60.1 / 28.1 = 2.14 mol\nn(N) = 39.9 / 14.0 = 2.85 mol\nDivide each by the smallest (2.14): Si gives 1, N gives 1.33.\nThe decimal is near .33, so multiply every number by 3: 3 and 4.\nEmpirical formula: Si₃N₄",
 "anticipatedWrong": [
  {
   "value": "SiN",
   "misconception": "you dropped the decimal — cutting the .33 off changes the ratio; multiply every number by 3 instead",
   "feedback": "This answer is wrong — you dropped the decimal. Cutting the .33 off changes the ratio; multiply every number by 3 instead: Si gives 3 and N gives 4, so the empirical formula is Si₃N₄."
  },
  {
   "value": "SiN₄",
   "misconception": "you multiplied only the number with the decimal — multiplying just one number changes the ratio; multiply EVERY number by 3",
   "feedback": "This answer is wrong — you multiplied only the number with the decimal. Multiplying just one number changes the ratio; multiply EVERY number by 3: Si gives 3 and N gives 4, so the empirical formula is Si₃N₄."
  }
 ]
}

[
 {
  "value": 55.5,
  "misconception": "you gave the calcium's mass — the question asks for the sulfur, the rest of the 100 g",
  "feedback": "This answer is wrong — you gave the calcium's mass — the question asks for the sulfur, the rest of the 100 g."
 },
 {
  "value": 0.445,
  "misconception": "you divided by 100 — in a 100 g sample the masses are in grams already",
  "feedback": "This answer is wrong — you divided by 100 — in a 100 g sample the masses are in grams already."
 }
]

{
 "keyExplanation": "Assume a sample of exactly 100 g.\nCalcium: 55.5% of the compound → 55.5 g.\nThe element masses in a 100 g sample total 100 g.\nmass of sulfur = 100 − 55.5 = 44.5 g"
}

[
 {
  "value": "C₄H₈O₂",
  "misconception": "you divided by 2, which is a common factor but not the LARGEST one — 4, 8, and 2 still share the factor 2",
  "feedback": "This answer is wrong — you divided by 2, which is a common factor but not the LARGEST one. The subscripts of C₄H₈O₂ — 4, 8, and 2 — still share the factor 2, so the formula still reduces. Divide C₈H₁₆O₄'s subscripts by their largest common factor, 4: C: 8 ÷ 4 = 2, H: 16 ÷ 4 = 4, O: 4 ÷ 4 = 1, and the empirical formula is C₂H₄O."
 },
 {
  "value": "C₈H₁₆O₄",
  "misconception": "you left the formula unchanged — the subscripts 8, 16, and 4 share the factor 4, so the formula reduces",
  "feedback": "This answer is wrong — you left the formula unchanged. The subscripts 8, 16, and 4 share the factor 4, so the formula reduces: C: 8 ÷ 4 = 2, H: 16 ÷ 4 = 4, O: 4 ÷ 4 = 1, and the empirical formula is C₂H₄O."
 },
 {
  "value": "CHO",
  "misconception": "you divided each subscript by its own value, which destroys the ratio",
  "feedback": "This answer is wrong — you divided each subscript by its own value, which destroys the ratio. Every subscript must be divided by the SAME factor — the largest common factor, 4: C: 8 ÷ 4 = 2, H: 16 ÷ 4 = 4, O: 4 ÷ 4 = 1, so the empirical formula is C₂H₄O."
 }
]

{
 "keyExplanation": "Subscripts: C 8, H 16, O 4. The largest common factor is 4 — dividing by 2 alone leaves C₄H₈O₂, which still reduces. C: 8 ÷ 4 = 2, H: 16 ÷ 4 = 4, O: 4 ÷ 4 = 1, and a subscript of 1 is never written, so the empirical formula is C₂H₄O.",
 "anticipatedWrong": [
  {
   "value": "C₄H₈O₂",
   "misconception": "you divided by 2, which is a common factor but not the LARGEST one — 4, 8, and 2 still share the factor 2",
   "feedback": "This answer is wrong — you divided by 2, which is a common factor but not the LARGEST one. The subscripts of C₄H₈O₂ — 4, 8, and 2 — still share the factor 2, so the formula still reduces. Divide C₈H₁₆O₄'s subscripts by their largest common factor, 4: C: 8 ÷ 4 = 2, H: 16 ÷ 4 = 4, O: 4 ÷ 4 = 1, and the empirical formula is C₂H₄O."
  },
  {
   "value": "C₈H₁₆O₄",
   "misconception": "you left the formula unchanged — the subscripts 8, 16, and 4 share the factor 4, so the formula reduces",
   "feedback": "This answer is wrong — you left the formula unchanged. The subscripts 8, 16, and 4 share the factor 4, so the formula reduces: C: 8 ÷ 4 = 2, H: 16 ÷ 4 = 4, O: 4 ÷ 4 = 1, and the empirical formula is C₂H₄O."
  },
  {
   "value": "CHO",
   "misconception": "you divided each subscript by its own value, which destroys the ratio",
   "feedback": "This answer is wrong — you divided each subscript by its own value, which destroys the ratio. Every subscript must be divided by the SAME factor — the largest common factor, 4: C: 8 ÷ 4 = 2, H: 16 ÷ 4 = 4, O: 4 ÷ 4 = 1, so the empirical formula is C₂H₄O."
  }
 ]
}

[
 {
  "value": "5.7 : 1",
  "misconception": "you compared the masses instead of the moles — 71.0 : 12.4 is about 5.7 : 1, but atoms are counted in moles",
  "feedback": "This answer is wrong — you compared the masses instead of the moles. 71.0 : 12.4 is about 5.7 : 1, but atoms are counted in moles: n(Cl) = 71.0 / 35.5 = 2.00 mol and n(P) = 12.4 / 31.0 = 0.40 mol, and dividing each by 0.40 gives 5 : 1."
 },
 {
  "value": "1 : 5",
  "misconception": "you wrote the ratio backwards — the order follows the elements as named: chlorine first, then phosphorus, so the larger number comes first here",
  "feedback": "This answer is wrong — you wrote the ratio backwards. The ratio order follows the elements as they are named in the question: chlorine first, then phosphorus. Chlorine has the larger mole value, so the answer is 5 : 1 — the ratio is not automatically written smallest-first."
 }
]

{
 "keyExplanation": "Values from the question:\nm(Cl) = 71.0 g, m(P) = 12.4 g\nEquation:\nn = m/M  (for each element)\nSubstituting the values and calculating:\nn(Cl) = 71.0 / 35.5 = 2.00 mol\nn(P) = 12.4 / 31.0 = 0.40 mol\nDivide each by the smallest (0.40): Cl gives 5, P gives 1.\nMole ratio of chlorine to phosphorus = 5 : 1",
 "anticipatedWrong": [
  {
   "value": "5.7 : 1",
   "misconception": "you compared the masses instead of the moles — 71.0 : 12.4 is about 5.7 : 1, but atoms are counted in moles",
   "feedback": "This answer is wrong — you compared the masses instead of the moles. 71.0 : 12.4 is about 5.7 : 1, but atoms are counted in moles: n(Cl) = 71.0 / 35.5 = 2.00 mol and n(P) = 12.4 / 31.0 = 0.40 mol, and dividing each by 0.40 gives 5 : 1."
  },
  {
   "value": "1 : 5",
   "misconception": "you wrote the ratio backwards — the order follows the elements as named: chlorine first, then phosphorus, so the larger number comes first here",
   "feedback": "This answer is wrong — you wrote the ratio backwards. The ratio order follows the elements as they are named in the question: chlorine first, then phosphorus. Chlorine has the larger mole value, so the answer is 5 : 1 — the ratio is not automatically written smallest-first."
  }
 ]
}

[
 {
  "value": "1 : 3",
  "misconception": "you rounded the 3.25 down to 3 — rounding changes the ratio; multiply every number by 4 instead",
  "feedback": "This answer is wrong — you rounded the 3.25 down to 3, and rounding changes the ratio itself. The decimal part is .25, so multiply every number by 4 instead: 1 × 4 = 4 and 3.25 × 4 = 13, giving 4 : 13."
 },
 {
  "value": "1 : 13",
  "misconception": "you multiplied only the decimal number — every number in the ratio must be multiplied by the same amount",
  "feedback": "This answer is wrong — you multiplied only the decimal number. Every number in the ratio must be multiplied by the same amount to keep the ratio unchanged: 1 × 4 = 4 and 3.25 × 4 = 13, giving 4 : 13."
 }
]

{
 "keyExplanation": "The decimal part is .25, so multiply every number by 4: 1 × 4 = 4 and 3.25 × 4 = 13. The whole-number ratio is 4 : 13. Rounding 3.25 down to 3 would change the ratio itself — multiplying never does.",
 "anticipatedWrong": [
  {
   "value": "1 : 3",
   "misconception": "you rounded the 3.25 down to 3 — rounding changes the ratio; multiply every number by 4 instead",
   "feedback": "This answer is wrong — you rounded the 3.25 down to 3, and rounding changes the ratio itself. The decimal part is .25, so multiply every number by 4 instead: 1 × 4 = 4 and 3.25 × 4 = 13, giving 4 : 13."
  },
  {
   "value": "1 : 13",
   "misconception": "you multiplied only the decimal number — every number in the ratio must be multiplied by the same amount",
   "feedback": "This answer is wrong — you multiplied only the decimal number. Every number in the ratio must be multiplied by the same amount to keep the ratio unchanged: 1 × 4 = 4 and 3.25 × 4 = 13, giving 4 : 13."
  }
 ]
}

[
 {
  "value": "S₂Cl₂",
  "misconception": "you left the formula unchanged — the subscripts 2 and 2 share the factor 2, so the formula reduces",
  "feedback": "This answer is wrong — you left the formula unchanged. The subscripts 2 and 2 share the factor 2, so the formula reduces: S: 2 ÷ 2 = 1, Cl: 2 ÷ 2 = 1, and a subscript of 1 is never written, giving SCl."
 },
 {
  "value": "SCl₂",
  "misconception": "you divided only the sulfur's subscript — every subscript must be divided by the same factor",
  "feedback": "This answer is wrong — you divided only the sulfur's subscript. Every subscript must be divided by the same factor: S: 2 ÷ 2 = 1, Cl: 2 ÷ 2 = 1, giving SCl."
 },
 {
  "value": "S₂Cl",
  "misconception": "you divided only the chlorine's subscript — every subscript must be divided by the same factor",
  "feedback": "This answer is wrong — you divided only the chlorine's subscript. Every subscript must be divided by the same factor: S: 2 ÷ 2 = 1, Cl: 2 ÷ 2 = 1, giving SCl."
 }
]

{
 "keyExplanation": "Subscripts: S 2, Cl 2. The largest common factor is 2. S: 2 ÷ 2 = 1, Cl: 2 ÷ 2 = 1. A subscript of 1 is never written, so disulfur dichloride's empirical formula is SCl.",
 "anticipatedWrong": [
  {
   "value": "S₂Cl₂",
   "misconception": "you left the formula unchanged — the subscripts 2 and 2 share the factor 2, so the formula reduces",
   "feedback": "This answer is wrong — you left the formula unchanged. The subscripts 2 and 2 share the factor 2, so the formula reduces: S: 2 ÷ 2 = 1, Cl: 2 ÷ 2 = 1, and a subscript of 1 is never written, giving SCl."
  },
  {
   "value": "SCl₂",
   "misconception": "you divided only the sulfur's subscript — every subscript must be divided by the same factor",
   "feedback": "This answer is wrong — you divided only the sulfur's subscript. Every subscript must be divided by the same factor: S: 2 ÷ 2 = 1, Cl: 2 ÷ 2 = 1, giving SCl."
  },
  {
   "value": "S₂Cl",
   "misconception": "you divided only the chlorine's subscript — every subscript must be divided by the same factor",
   "feedback": "This answer is wrong — you divided only the chlorine's subscript. Every subscript must be divided by the same factor: S: 2 ÷ 2 = 1, Cl: 2 ÷ 2 = 1, giving SCl."
  }
 ]
}

[
 {
  "value": "3.4 : 1 : 2",
  "misconception": "you compared the masses instead of the moles — 36.0 : 10.5 : 21.0 is about 3.4 : 1 : 2, but atoms are counted in moles",
  "feedback": "This answer is wrong — you compared the masses instead of the moles — 36.0 : 10.5 : 21.0 is about 3.4 : 1 : 2, but atoms are counted in moles."
 },
 {
  "value": "1 : 7 : 2",
  "misconception": "you wrote the ratio backwards — the order follows the elements as named: carbon first, then hydrogen, then nitrogen",
  "feedback": "This answer is wrong — you wrote the ratio backwards — the order follows the elements as named: carbon first, then hydrogen, then nitrogen."
 }
]

{
 "keyExplanation": "Values from the question:\nm(C) = 36.0 g, m(H) = 10.5 g, m(N) = 21.0 g\nEquation:\nn = m/M  (for each element)\nSubstituting the values and calculating:\nn(C) = 36.0 / 12.0 = 3.00 mol\nn(H) = 10.5 / 1.0 = 10.5 mol\nn(N) = 21.0 / 14.0 = 1.50 mol\nDivide each by the smallest (1.50): C gives 2, H gives 7, N gives 1.\nMole ratio of carbon to hydrogen to nitrogen = 2 : 7 : 1"
}

[
 {
  "value": 6.74,
  "misconception": "you ignored the subscripts in the empirical formula, using 12.0 + 1.0 + 14.0 = 27.0 g/mol — M of C₆H₅N is 6 × 12.0 + 5 × 1.0 + 14.0 = 91.0 g/mol",
  "feedback": "This answer is wrong — you ignored the subscripts in the empirical formula, using 12.0 + 1.0 + 14.0 = 27.0 g/mol. M of C₆H₅N is 6 × 12.0 + 5 × 1.0 + 14.0 = 91.0 g/mol, and a non-whole unit count signals exactly this kind of slip."
 },
 {
  "value": 0.5,
  "misconception": "you divided upside down — the compound's molar mass goes on top, and the unit count is never below 1",
  "feedback": "This answer is wrong — you divided upside down — the compound's molar mass goes on top, and the unit count is never below 1."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmolar mass of the compound = 182.0 g/mol\nM of C₆H₅N = 6 × 12.0 + 5 × 1.0 + 14.0 = 91.0 g/mol\nWrite down the equation:\nnumber of units = molar mass of the compound ÷ molar mass of the empirical formula\nSubstitute in the values, and calculate:\nnumber of units = 182.0 / 91.0\nnumber of units = 2\nThe result is a whole number at least 1, so the division ran the right way up."
}

[
 {
  "value": "BO₂",
  "misconception": "you rounded the 1.5 up to 2 — rounding changes the ratio; multiply every number by 2 instead",
  "feedback": "This answer is wrong — you rounded the 1.5 up to 2. Rounding changes the ratio; multiply every number by 2 instead: 1 and 1.5 become 2 and 3, so the empirical formula is B₂O₃."
 },
 {
  "value": "BO",
  "misconception": "you dropped the decimal — cutting the .5 off changes the ratio; multiply every number by 2 instead",
  "feedback": "This answer is wrong — you dropped the decimal. Cutting the .5 off changes the ratio; multiply every number by 2 instead: 1 and 1.5 become 2 and 3, so the empirical formula is B₂O₃."
 },
 {
  "value": "B₃O₂",
  "misconception": "you inverted the ratio — boron has the smaller mole value, so boron takes the 1 before clearing",
  "feedback": "This answer is wrong — you inverted the ratio. Boron has the smaller mole value (2.00 mol against oxygen's 3.00 mol), so boron takes the 1 before clearing: 1 and 1.5 become 2 and 3, giving B₂O₃."
 }
]

{
 "keyExplanation": "Values from the question:\nm(B) = 21.6 g, m(O) = 48.0 g\nEquation:\nn = m/M  (for each element)\nSubstituting the values and calculating:\nn(B) = 21.6 / 10.8 = 2.00 mol\nn(O) = 48.0 / 16.0 = 3.00 mol\nDivide each by the smallest (2.00): B gives 1, O gives 1.5.\nThe decimal ends in .5, so multiply every number by 2: 2 and 3.\nEmpirical formula: B₂O₃",
 "anticipatedWrong": [
  {
   "value": "BO₂",
   "misconception": "you rounded the 1.5 up to 2 — rounding changes the ratio; multiply every number by 2 instead",
   "feedback": "This answer is wrong — you rounded the 1.5 up to 2. Rounding changes the ratio; multiply every number by 2 instead: 1 and 1.5 become 2 and 3, so the empirical formula is B₂O₃."
  },
  {
   "value": "BO",
   "misconception": "you dropped the decimal — cutting the .5 off changes the ratio; multiply every number by 2 instead",
   "feedback": "This answer is wrong — you dropped the decimal. Cutting the .5 off changes the ratio; multiply every number by 2 instead: 1 and 1.5 become 2 and 3, so the empirical formula is B₂O₃."
  },
  {
   "value": "B₃O₂",
   "misconception": "you inverted the ratio — boron has the smaller mole value, so boron takes the 1 before clearing",
   "feedback": "This answer is wrong — you inverted the ratio. Boron has the smaller mole value (2.00 mol against oxygen's 3.00 mol), so boron takes the 1 before clearing: 1 and 1.5 become 2 and 3, giving B₂O₃."
  }
 ]
}

[
 {
  "value": "CF₂",
  "misconception": "you stopped at the empirical formula — the unit count is 200.0/50.0 = 4, and every subscript must be multiplied by it",
  "feedback": "This answer is wrong — you stopped at the empirical formula. The unit count is 200.0 / 50.0 = 4, and every subscript must be multiplied by it: C: 1 × 4 = 4, F: 2 × 4 = 8, giving C₄F₈."
 },
 {
  "value": "C₄F₂",
  "misconception": "you multiplied only carbon's subscript — every subscript in the empirical formula is multiplied by the unit count",
  "feedback": "This answer is wrong — you multiplied only carbon's subscript. Every subscript in the empirical formula is multiplied by the unit count, 4: C: 1 × 4 = 4, F: 2 × 4 = 8, giving C₄F₈."
 },
 {
  "value": "CF₈",
  "misconception": "you multiplied only fluorine's subscript — every subscript in the empirical formula is multiplied by the unit count",
  "feedback": "This answer is wrong — you multiplied only fluorine's subscript. Every subscript in the empirical formula is multiplied by the unit count, 4: C: 1 × 4 = 4, F: 2 × 4 = 8, giving C₄F₈."
 }
]

{
 "keyExplanation": "M of CF₂ = 12.0 + 2 × 19.0 = 50.0 g/mol.\nStep 1 — find the number of units:\nnumber of units = molar mass of the compound ÷ molar mass of the empirical formula\nnumber of units = 200.0 / 50.0 = 4\nStep 2 — multiply every subscript by 4:\nC: 1 × 4 = 4,  F: 2 × 4 = 8\nMolecular formula: C₄F₈",
 "anticipatedWrong": [
  {
   "value": "CF₂",
   "misconception": "you stopped at the empirical formula — the unit count is 200.0/50.0 = 4, and every subscript must be multiplied by it",
   "feedback": "This answer is wrong — you stopped at the empirical formula. The unit count is 200.0 / 50.0 = 4, and every subscript must be multiplied by it: C: 1 × 4 = 4, F: 2 × 4 = 8, giving C₄F₈."
  },
  {
   "value": "C₄F₂",
   "misconception": "you multiplied only carbon's subscript — every subscript in the empirical formula is multiplied by the unit count",
   "feedback": "This answer is wrong — you multiplied only carbon's subscript. Every subscript in the empirical formula is multiplied by the unit count, 4: C: 1 × 4 = 4, F: 2 × 4 = 8, giving C₄F₈."
  },
  {
   "value": "CF₈",
   "misconception": "you multiplied only fluorine's subscript — every subscript in the empirical formula is multiplied by the unit count",
   "feedback": "This answer is wrong — you multiplied only fluorine's subscript. Every subscript in the empirical formula is multiplied by the unit count, 4: C: 1 × 4 = 4, F: 2 × 4 = 8, giving C₄F₈."
  }
 ]
}

[
 {
  "value": "AlO₂",
  "misconception": "you rounded the 1.50 up to 2 — rounding changes the ratio; multiply every number by 2 instead",
  "feedback": "This answer is wrong — you rounded the 1.50 up to 2. Rounding changes the ratio; multiply every number by 2 instead: Al gives 2 and O gives 3, so the empirical formula is Al₂O₃."
 },
 {
  "value": "AlO",
  "misconception": "you dropped the decimal — cutting the .50 off changes the ratio; multiply every number by 2 instead",
  "feedback": "This answer is wrong — you dropped the decimal. Cutting the .50 off changes the ratio; multiply every number by 2 instead: Al gives 2 and O gives 3, so the empirical formula is Al₂O₃."
 }
]

{
 "keyExplanation": "Assume a 100 g sample: m(Al) = 52.9 g, m(O) = 47.1 g.\nEquation:\nn = m/M  (for each element)\nSubstituting the values and calculating:\nn(Al) = 52.9 / 27.0 = 1.96 mol\nn(O) = 47.1 / 16.0 = 2.94 mol\nDivide each by the smallest (1.96): Al gives 1, O gives 1.50.\nThe decimal ends in .5, so multiply every number by 2: 2 and 3.\nEmpirical formula: Al₂O₃",
 "anticipatedWrong": [
  {
   "value": "AlO₂",
   "misconception": "you rounded the 1.50 up to 2 — rounding changes the ratio; multiply every number by 2 instead",
   "feedback": "This answer is wrong — you rounded the 1.50 up to 2. Rounding changes the ratio; multiply every number by 2 instead: Al gives 2 and O gives 3, so the empirical formula is Al₂O₃."
  },
  {
   "value": "AlO",
   "misconception": "you dropped the decimal — cutting the .50 off changes the ratio; multiply every number by 2 instead",
   "feedback": "This answer is wrong — you dropped the decimal. Cutting the .50 off changes the ratio; multiply every number by 2 instead: Al gives 2 and O gives 3, so the empirical formula is Al₂O₃."
  }
 ]
}

[
 {
  "value": 39.0,
  "misconception": "you gave the magnesium's mass — the question asks for the fluorine, the rest of the 100 g",
  "feedback": "This answer is wrong — you gave the magnesium's mass — the question asks for the fluorine, the rest of the 100 g."
 },
 {
  "value": 0.61,
  "misconception": "you divided by 100 — in a 100 g sample the masses are in grams already",
  "feedback": "This answer is wrong — you divided by 100 — in a 100 g sample the masses are in grams already."
 }
]

{
 "keyExplanation": "Assume a sample of exactly 100 g.\nMagnesium: 39.0% of the compound → 39.0 g.\nThe element masses in a 100 g sample total 100 g.\nmass of fluorine = 100 − 39.0 = 61.0 g"
}

[
 {
  "value": "C₂H₂O₂",
  "misconception": "you divided by 2, which is a common factor but not the LARGEST one — 2, 2, and 2 still share the factor 2",
  "feedback": "This answer is wrong — you divided by 2, which is a common factor but not the LARGEST one. The subscripts of C₂H₂O₂ — 2, 2, and 2 — still share the factor 2, so the formula still reduces. Divide C₄H₄O₄'s subscripts by their largest common factor, 4: every subscript becomes 1, and the empirical formula is CHO."
 },
 {
  "value": "C₄H₄O₄",
  "misconception": "you left the formula unchanged — the subscripts 4, 4, and 4 share the factor 4, so the formula reduces",
  "feedback": "This answer is wrong — you left the formula unchanged. The subscripts 4, 4, and 4 share the factor 4, so the formula reduces: every subscript divides by 4 to give 1, a subscript of 1 is never written, and the empirical formula is CHO."
 },
 {
  "value": "C₄H₄O",
  "misconception": "you divided only the oxygen's subscript — every subscript must be divided by the same factor",
  "feedback": "This answer is wrong — you divided only the oxygen's subscript. Every subscript must be divided by the SAME factor — the largest common factor, 4: C: 4 ÷ 4 = 1, H: 4 ÷ 4 = 1, O: 4 ÷ 4 = 1, so the empirical formula is CHO."
 }
]

{
 "keyExplanation": "Subscripts: C 4, H 4, O 4. The largest common factor is 4 — dividing by 2 alone leaves C₂H₂O₂, which still reduces. C: 4 ÷ 4 = 1, H: 4 ÷ 4 = 1, O: 4 ÷ 4 = 1, and a subscript of 1 is never written, so the empirical formula is CHO.",
 "anticipatedWrong": [
  {
   "value": "C₂H₂O₂",
   "misconception": "you divided by 2, which is a common factor but not the LARGEST one — 2, 2, and 2 still share the factor 2",
   "feedback": "This answer is wrong — you divided by 2, which is a common factor but not the LARGEST one. The subscripts of C₂H₂O₂ — 2, 2, and 2 — still share the factor 2, so the formula still reduces. Divide C₄H₄O₄'s subscripts by their largest common factor, 4: every subscript becomes 1, and the empirical formula is CHO."
  },
  {
   "value": "C₄H₄O₄",
   "misconception": "you left the formula unchanged — the subscripts 4, 4, and 4 share the factor 4, so the formula reduces",
   "feedback": "This answer is wrong — you left the formula unchanged. The subscripts 4, 4, and 4 share the factor 4, so the formula reduces: every subscript divides by 4 to give 1, a subscript of 1 is never written, and the empirical formula is CHO."
  },
  {
   "value": "C₄H₄O",
   "misconception": "you divided only the oxygen's subscript — every subscript must be divided by the same factor",
   "feedback": "This answer is wrong — you divided only the oxygen's subscript. Every subscript must be divided by the SAME factor — the largest common factor, 4: C: 4 ÷ 4 = 1, H: 4 ÷ 4 = 1, O: 4 ÷ 4 = 1, so the empirical formula is CHO."
  }
 ]
}

[
 {
  "value": "1 : 1.6",
  "misconception": "you compared the masses instead of the moles — 5.7 : 9.19 is about 1 : 1.6, but atoms are counted in moles, and one tungsten atom far outweighs one fluorine atom",
  "feedback": "This answer is wrong — you compared the masses instead of the moles. 5.7 : 9.19 is about 1 : 1.6, but atoms are counted in moles, and one tungsten atom far outweighs one fluorine atom: n(F) = 5.7 / 19.0 = 0.30 mol and n(W) = 9.19 / 183.8 = 0.050 mol, and dividing each by 0.050 gives 6 : 1."
 },
 {
  "value": "1 : 6",
  "misconception": "you wrote the ratio backwards — the order follows the elements as named: fluorine first, then tungsten, so the larger number comes first here",
  "feedback": "This answer is wrong — you wrote the ratio backwards. The ratio order follows the elements as they are named in the question: fluorine first, then tungsten. Fluorine has the larger mole value, so the answer is 6 : 1 — the ratio is not automatically written smallest-first."
 }
]

{
 "keyExplanation": "Values from the question:\nm(F) = 5.7 g, m(W) = 9.19 g\nEquation:\nn = m/M  (for each element)\nSubstituting the values and calculating:\nn(F) = 5.7 / 19.0 = 0.30 mol\nn(W) = 9.19 / 183.8 = 0.050 mol\nDivide each by the smallest (0.050): F gives 6, W gives 1.\nMole ratio of fluorine to tungsten = 6 : 1",
 "anticipatedWrong": [
  {
   "value": "1 : 1.6",
   "misconception": "you compared the masses instead of the moles — 5.7 : 9.19 is about 1 : 1.6, but atoms are counted in moles, and one tungsten atom far outweighs one fluorine atom",
   "feedback": "This answer is wrong — you compared the masses instead of the moles. 5.7 : 9.19 is about 1 : 1.6, but atoms are counted in moles, and one tungsten atom far outweighs one fluorine atom: n(F) = 5.7 / 19.0 = 0.30 mol and n(W) = 9.19 / 183.8 = 0.050 mol, and dividing each by 0.050 gives 6 : 1."
  },
  {
   "value": "1 : 6",
   "misconception": "you wrote the ratio backwards — the order follows the elements as named: fluorine first, then tungsten, so the larger number comes first here",
   "feedback": "This answer is wrong — you wrote the ratio backwards. The ratio order follows the elements as they are named in the question: fluorine first, then tungsten. Fluorine has the larger mole value, so the answer is 6 : 1 — the ratio is not automatically written smallest-first."
  }
 ]
}

[
 {
  "value": "1 : 2 : 5",
  "misconception": "you rounded the 4.5 up to 5 — rounding changes the ratio; multiply every number by 2 instead",
  "feedback": "This answer is wrong — you rounded the 4.5 up to 5, and rounding changes the ratio itself. The decimal ends in .5, so multiply every number by 2 instead: 1 × 2 = 2, 2 × 2 = 4, and 4.5 × 2 = 9, giving 2 : 4 : 9."
 },
 {
  "value": "1 : 2 : 9",
  "misconception": "you multiplied only the decimal number — every number in the ratio must be multiplied by the same amount",
  "feedback": "This answer is wrong — you multiplied only the decimal number. Every number in the ratio must be multiplied by the same amount to keep the ratio unchanged: 1 × 2 = 2, 2 × 2 = 4, and 4.5 × 2 = 9, giving 2 : 4 : 9."
 }
]

{
 "keyExplanation": "The decimal ends in .5, so multiply every number by 2: 1 × 2 = 2, 2 × 2 = 4, and 4.5 × 2 = 9. The whole-number ratio is 2 : 4 : 9 — the multiplication covers all three numbers, not just the one carrying the decimal.",
 "anticipatedWrong": [
  {
   "value": "1 : 2 : 5",
   "misconception": "you rounded the 4.5 up to 5 — rounding changes the ratio; multiply every number by 2 instead",
   "feedback": "This answer is wrong — you rounded the 4.5 up to 5, and rounding changes the ratio itself. The decimal ends in .5, so multiply every number by 2 instead: 1 × 2 = 2, 2 × 2 = 4, and 4.5 × 2 = 9, giving 2 : 4 : 9."
  },
  {
   "value": "1 : 2 : 9",
   "misconception": "you multiplied only the decimal number — every number in the ratio must be multiplied by the same amount",
   "feedback": "This answer is wrong — you multiplied only the decimal number. Every number in the ratio must be multiplied by the same amount to keep the ratio unchanged: 1 × 2 = 2, 2 × 2 = 4, and 4.5 × 2 = 9, giving 2 : 4 : 9."
  }
 ]
}

[
 {
  "value": "B₃N₃H₆",
  "misconception": "you left the formula unchanged — the subscripts 3, 3, and 6 share the factor 3, so the formula reduces",
  "feedback": "This answer is wrong — you left the formula unchanged. The subscripts 3, 3, and 6 share the factor 3, so the formula reduces: B: 3 ÷ 3 = 1, N: 3 ÷ 3 = 1, H: 6 ÷ 3 = 2, giving BNH₂."
 },
 {
  "value": "BNH",
  "misconception": "you divided each subscript by its own value, which destroys the ratio",
  "feedback": "This answer is wrong — you divided each subscript by its own value, which destroys the ratio. Every subscript is divided by the same factor, 3: B 1, N 1, H 2, giving BNH₂."
 },
 {
  "value": "BNH₆",
  "misconception": "you left the last subscript undivided — every subscript must be divided by the same factor, including hydrogen's",
  "feedback": "This answer is wrong — you left the last subscript undivided. Every subscript must be divided by the same factor, including hydrogen's: H: 6 ÷ 3 = 2, giving BNH₂."
 }
]

{
 "keyExplanation": "Subscripts: B 3, N 3, H 6. The largest common factor is 3. B: 3 ÷ 3 = 1, N: 3 ÷ 3 = 1, H: 6 ÷ 3 = 2. A subscript of 1 is never written, so borazine's empirical formula is BNH₂.",
 "anticipatedWrong": [
  {
   "value": "B₃N₃H₆",
   "misconception": "you left the formula unchanged — the subscripts 3, 3, and 6 share the factor 3, so the formula reduces",
   "feedback": "This answer is wrong — you left the formula unchanged. The subscripts 3, 3, and 6 share the factor 3, so the formula reduces: B: 3 ÷ 3 = 1, N: 3 ÷ 3 = 1, H: 6 ÷ 3 = 2, giving BNH₂."
  },
  {
   "value": "BNH",
   "misconception": "you divided each subscript by its own value, which destroys the ratio",
   "feedback": "This answer is wrong — you divided each subscript by its own value, which destroys the ratio. Every subscript is divided by the same factor, 3: B 1, N 1, H 2, giving BNH₂."
  },
  {
   "value": "BNH₆",
   "misconception": "you left the last subscript undivided — every subscript must be divided by the same factor, including hydrogen's",
   "feedback": "This answer is wrong — you left the last subscript undivided. Every subscript must be divided by the same factor, including hydrogen's: H: 6 ÷ 3 = 2, giving BNH₂."
  }
 ]
}

[
 {
  "value": "1 : 3.6 : 16",
  "misconception": "you compared the masses instead of the moles — 9.0 : 32.4 : 144.0 is about 1 : 3.6 : 16, but atoms are counted in moles",
  "feedback": "This answer is wrong — you compared the masses instead of the moles — 9.0 : 32.4 : 144.0 is about 1 : 3.6 : 16, but atoms are counted in moles."
 },
 {
  "value": "1 : 0.33 : 1",
  "misconception": "you divided every value by the largest instead of the smallest — divide by the smallest so the smallest becomes 1",
  "feedback": "This answer is wrong — you divided every value by the largest instead of the smallest — divide by the smallest so the smallest becomes 1."
 }
]

{
 "keyExplanation": "Values from the question:\nm(H) = 9.0 g, m(B) = 32.4 g, m(O) = 144.0 g\nEquation:\nn = m/M  (for each element)\nSubstituting the values and calculating:\nn(H) = 9.0 / 1.0 = 9.00 mol\nn(B) = 32.4 / 10.8 = 3.00 mol\nn(O) = 144.0 / 16.0 = 9.00 mol\nDivide each by the smallest (3.00): H gives 3, B gives 1, O gives 3.\nMole ratio of hydrogen to boron to oxygen = 3 : 1 : 3"
}

[
 {
  "value": 8.46,
  "misconception": "you ignored the subscripts in the empirical formula, using 12.0 + 1.0 = 13.0 g/mol — M of C₄H₇ is 4 × 12.0 + 7 × 1.0 = 55.0 g/mol",
  "feedback": "This answer is wrong — you ignored the subscripts in the empirical formula, using 12.0 + 1.0 = 13.0 g/mol. M of C₄H₇ is 4 × 12.0 + 7 × 1.0 = 55.0 g/mol, and a non-whole unit count signals exactly this kind of slip."
 },
 {
  "value": 0.5,
  "misconception": "you divided upside down — the compound's molar mass goes on top, and the unit count is never below 1",
  "feedback": "This answer is wrong — you divided upside down — the compound's molar mass goes on top, and the unit count is never below 1."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmolar mass of the compound = 110.0 g/mol\nM of C₄H₇ = 4 × 12.0 + 7 × 1.0 = 55.0 g/mol\nWrite down the equation:\nnumber of units = molar mass of the compound ÷ molar mass of the empirical formula\nSubstitute in the values, and calculate:\nnumber of units = 110.0 / 55.0\nnumber of units = 2\nThe result is a whole number at least 1, so the division ran the right way up."
}

[
 {
  "value": "TiO₂",
  "misconception": "you rounded the 1.5 up to 2 — rounding changes the ratio; multiply every number by 2 instead",
  "feedback": "This answer is wrong — you rounded the 1.5 up to 2. Rounding changes the ratio; multiply every number by 2 instead: 1 and 1.5 become 2 and 3, so this sample's empirical formula is Ti₂O₃ — the data decide the formula, not the titanium compound you have heard of most often."
 },
 {
  "value": "TiO",
  "misconception": "you dropped the decimal — cutting the .5 off changes the ratio; multiply every number by 2 instead",
  "feedback": "This answer is wrong — you dropped the decimal. Cutting the .5 off changes the ratio; multiply every number by 2 instead: 1 and 1.5 become 2 and 3, so the empirical formula is Ti₂O₃."
 },
 {
  "value": "Ti₃O₂",
  "misconception": "you inverted the ratio — titanium has the smaller mole value, so titanium takes the 1 before clearing",
  "feedback": "This answer is wrong — you inverted the ratio. Titanium has the smaller mole value (5.00 mol against oxygen's 7.50 mol), so titanium takes the 1 before clearing: 1 and 1.5 become 2 and 3, giving Ti₂O₃."
 }
]

{
 "keyExplanation": "Values from the question:\nm(Ti) = 239.5 g, m(O) = 120.0 g\nEquation:\nn = m/M  (for each element)\nSubstituting the values and calculating:\nn(Ti) = 239.5 / 47.9 = 5.00 mol\nn(O) = 120.0 / 16.0 = 7.50 mol\nDivide each by the smallest (5.00): Ti gives 1, O gives 1.50.\nThe decimal ends in .5, so multiply every number by 2: 2 and 3.\nEmpirical formula: Ti₂O₃",
 "anticipatedWrong": [
  {
   "value": "TiO₂",
   "misconception": "you rounded the 1.5 up to 2 — rounding changes the ratio; multiply every number by 2 instead",
   "feedback": "This answer is wrong — you rounded the 1.5 up to 2. Rounding changes the ratio; multiply every number by 2 instead: 1 and 1.5 become 2 and 3, so this sample's empirical formula is Ti₂O₃ — the data decide the formula, not the titanium compound you have heard of most often."
  },
  {
   "value": "TiO",
   "misconception": "you dropped the decimal — cutting the .5 off changes the ratio; multiply every number by 2 instead",
   "feedback": "This answer is wrong — you dropped the decimal. Cutting the .5 off changes the ratio; multiply every number by 2 instead: 1 and 1.5 become 2 and 3, so the empirical formula is Ti₂O₃."
  },
  {
   "value": "Ti₃O₂",
   "misconception": "you inverted the ratio — titanium has the smaller mole value, so titanium takes the 1 before clearing",
   "feedback": "This answer is wrong — you inverted the ratio. Titanium has the smaller mole value (5.00 mol against oxygen's 7.50 mol), so titanium takes the 1 before clearing: 1 and 1.5 become 2 and 3, giving Ti₂O₃."
  }
 ]
}

[
 {
  "value": "CHN",
  "misconception": "you stopped at the empirical formula — the unit count is 135.0/27.0 = 5, and every subscript must be multiplied by it",
  "feedback": "This answer is wrong — you stopped at the empirical formula. The unit count is 135.0 / 27.0 = 5, and every subscript must be multiplied by it: C: 1 × 5 = 5, H: 1 × 5 = 5, N: 1 × 5 = 5, giving C₅H₅N₅."
 },
 {
  "value": "C₅HN",
  "misconception": "you multiplied only carbon's subscript — every subscript in the empirical formula is multiplied by the unit count, including every unwritten 1",
  "feedback": "This answer is wrong — you multiplied only carbon's subscript. Every subscript in the empirical formula is multiplied by the unit count, 5 — including every unwritten 1: C: 1 × 5 = 5, H: 1 × 5 = 5, N: 1 × 5 = 5, giving C₅H₅N₅."
 },
 {
  "value": "CHN₅",
  "misconception": "you multiplied only nitrogen's subscript — every subscript in the empirical formula is multiplied by the unit count, including every unwritten 1",
  "feedback": "This answer is wrong — you multiplied only nitrogen's subscript. Every subscript in the empirical formula is multiplied by the unit count, 5 — including every unwritten 1: C: 1 × 5 = 5, H: 1 × 5 = 5, N: 1 × 5 = 5, giving C₅H₅N₅."
 }
]

{
 "keyExplanation": "M of CHN = 12.0 + 1.0 + 14.0 = 27.0 g/mol.\nStep 1 — find the number of units:\nnumber of units = molar mass of the compound ÷ molar mass of the empirical formula\nnumber of units = 135.0 / 27.0 = 5\nStep 2 — multiply every subscript by 5 (an unwritten subscript is 1):\nC: 1 × 5 = 5,  H: 1 × 5 = 5,  N: 1 × 5 = 5\nMolecular formula: C₅H₅N₅",
 "anticipatedWrong": [
  {
   "value": "CHN",
   "misconception": "you stopped at the empirical formula — the unit count is 135.0/27.0 = 5, and every subscript must be multiplied by it",
   "feedback": "This answer is wrong — you stopped at the empirical formula. The unit count is 135.0 / 27.0 = 5, and every subscript must be multiplied by it: C: 1 × 5 = 5, H: 1 × 5 = 5, N: 1 × 5 = 5, giving C₅H₅N₅."
  },
  {
   "value": "C₅HN",
   "misconception": "you multiplied only carbon's subscript — every subscript in the empirical formula is multiplied by the unit count, including every unwritten 1",
   "feedback": "This answer is wrong — you multiplied only carbon's subscript. Every subscript in the empirical formula is multiplied by the unit count, 5 — including every unwritten 1: C: 1 × 5 = 5, H: 1 × 5 = 5, N: 1 × 5 = 5, giving C₅H₅N₅."
  },
  {
   "value": "CHN₅",
   "misconception": "you multiplied only nitrogen's subscript — every subscript in the empirical formula is multiplied by the unit count, including every unwritten 1",
   "feedback": "This answer is wrong — you multiplied only nitrogen's subscript. Every subscript in the empirical formula is multiplied by the unit count, 5 — including every unwritten 1: C: 1 × 5 = 5, H: 1 × 5 = 5, N: 1 × 5 = 5, giving C₅H₅N₅."
  }
 ]
}

[
 {
  "value": "PN₂",
  "misconception": "you rounded the 1.66 up to 2 — rounding changes the ratio; multiply every number by 3 instead",
  "feedback": "This answer is wrong — you rounded the 1.66 up to 2. Rounding changes the ratio; multiply every number by 3 instead: P gives 3 and N gives 5, so the empirical formula is P₃N₅."
 },
 {
  "value": "PN₅",
  "misconception": "you multiplied only the number with the decimal — multiplying just one number changes the ratio; multiply EVERY number by 3",
  "feedback": "This answer is wrong — you multiplied only the number with the decimal. Multiplying just one number changes the ratio; multiply EVERY number by 3: P gives 3 and N gives 5, so the empirical formula is P₃N₅."
 }
]

{
 "keyExplanation": "Assume a 100 g sample: m(P) = 57.1 g, m(N) = 42.9 g.\nEquation:\nn = m/M  (for each element)\nSubstituting the values and calculating:\nn(P) = 57.1 / 31.0 = 1.84 mol\nn(N) = 42.9 / 14.0 = 3.06 mol\nDivide each by the smallest (1.84): P gives 1, N gives 1.66.\nThe decimal is near .67, so multiply every number by 3: 3 and 5.\nEmpirical formula: P₃N₅",
 "anticipatedWrong": [
  {
   "value": "PN₂",
   "misconception": "you rounded the 1.66 up to 2 — rounding changes the ratio; multiply every number by 3 instead",
   "feedback": "This answer is wrong — you rounded the 1.66 up to 2. Rounding changes the ratio; multiply every number by 3 instead: P gives 3 and N gives 5, so the empirical formula is P₃N₅."
  },
  {
   "value": "PN₅",
   "misconception": "you multiplied only the number with the decimal — multiplying just one number changes the ratio; multiply EVERY number by 3",
   "feedback": "This answer is wrong — you multiplied only the number with the decimal. Multiplying just one number changes the ratio; multiply EVERY number by 3: P gives 3 and N gives 5, so the empirical formula is P₃N₅."
  }
 ]
}