Unit 1 — End of Topic Tests (reviewer copy: all keys and model answers visible)

[
 {
  "value": 483000,
  "misconception": "you treated milli- as one thousand instead of one thousandth",
  "feedback": "This answer is wrong — you treated milli- as one thousand instead of one thousandth."
 },
 {
  "value": 4.83,
  "misconception": "you moved the decimal point two places instead of three",
  "feedback": "This answer is wrong — you moved the decimal point two places instead of three."
 },
 {
  "value": 0.0483,
  "misconception": "you moved the decimal point four places instead of three",
  "feedback": "This answer is wrong — you moved the decimal point four places instead of three."
 }
]

{
 "keyExplanation": "Write down the value in the question:\nV = 483 mL\nWrite down what the prefix means:\nmilli- means one thousandth, so 1 mL = 0.001 L\nSubstitute in the meaning, and calculate:\nV = 483 × 0.001 L\nV = 0.483 L\nA milliliter is a small unit, so the same volume written in liters must be a smaller number — 0.483 L passes that check; 483,000 L does not (4.83 L is smaller too, but comes from moving the decimal two places, not three)."
}

[
 {
  "value": 0.000735,
  "misconception": "you divided by one thousand instead of multiplying — that direction turns milligrams into grams",
  "feedback": "This answer is wrong — you divided by one thousand instead of multiplying; that direction turns milligrams into grams. One gram holds 1000 mg, so the balance's 0.735 g is 0.735 × 1000 = 735 mg."
 },
 {
  "value": 73.5,
  "misconception": "you multiplied by one hundred instead of one thousand",
  "feedback": "This answer is wrong — you multiplied by one hundred instead of one thousand. milli- means one thousandth, so one gram holds 1000 mg: 0.735 × 1000 = 735 mg."
 },
 {
  "value": 7350,
  "misconception": "you multiplied by ten thousand instead of one thousand",
  "feedback": "This answer is wrong — you multiplied by ten thousand instead of one thousand. One gram holds exactly 1000 mg, so 0.735 g is 0.735 × 1000 = 735 mg."
 }
]

{
 "keyExplanation": "Write down the value in the question:\nm = 0.735 g\nWrite down what the prefix means:\nmilli- means one thousandth, so one gram holds 1000 mg\nSubstitute in the meaning, and calculate:\nm = 0.735 × 1000 mg\nm = 735 mg\nA milligram is a small unit, so the same mass written in milligrams must be a larger number than 0.735 — multiplying by 1000 gives 735 mg.",
 "anticipatedWrong": [
  {
   "value": 0.000735,
   "misconception": "you divided by one thousand instead of multiplying — that direction turns milligrams into grams",
   "feedback": "This answer is wrong — you divided by one thousand instead of multiplying; that direction turns milligrams into grams. One gram holds 1000 mg, so the balance's 0.735 g is 0.735 × 1000 = 735 mg."
  },
  {
   "value": 73.5,
   "misconception": "you multiplied by one hundred instead of one thousand",
   "feedback": "This answer is wrong — you multiplied by one hundred instead of one thousand. milli- means one thousandth, so one gram holds 1000 mg: 0.735 × 1000 = 735 mg."
  },
  {
   "value": 7350,
   "misconception": "you multiplied by ten thousand instead of one thousand",
   "feedback": "This answer is wrong — you multiplied by ten thousand instead of one thousand. One gram holds exactly 1000 mg, so 0.735 g is 0.735 × 1000 = 735 mg."
  }
 ]
}

[
 {
  "value": 2.325,
  "misconception": "you recorded every calculator digit — the calculator does not know which digits the measurements vouch for",
  "feedback": "This answer is wrong — you recorded every calculator digit — the calculator does not know which digits the measurements vouch for."
 },
 {
  "value": 2.33,
  "misconception": "you rounded to the more precise measurement's three significant figures instead of the fewest",
  "feedback": "This answer is wrong — you rounded to the more precise measurement's three significant figures instead of the fewest."
 },
 {
  "value": 2,
  "misconception": "you rounded past the rule — the result keeps as many significant figures as the least precise measurement, no fewer",
  "feedback": "This answer is wrong — you rounded past the rule — the result keeps as many significant figures as the least precise measurement, no fewer."
 }
]

{
 "keyExplanation": "Count the significant figures in each measurement:\n9.30 g — three significant figures\n4.0 cm³ — two significant figures\nDivide, then round to the fewest significant figures:\n9.30 ÷ 4.0 = 2.325\nrecorded result = 2.3 g/cm³\nThe least precise measurement sets the precision — two significant figures, no more and no fewer."
}

[
 {
  "value": 0.004525,
  "misconception": "you treated kilo- as one thousandth instead of one thousand",
  "feedback": "This answer is wrong — you treated kilo- as one thousandth instead of one thousand."
 },
 {
  "value": 452.5,
  "misconception": "you multiplied by one hundred instead of one thousand",
  "feedback": "This answer is wrong — you multiplied by one hundred instead of one thousand."
 },
 {
  "value": 45250,
  "misconception": "you multiplied by ten thousand instead of one thousand",
  "feedback": "This answer is wrong — you multiplied by ten thousand instead of one thousand."
 }
]

{
 "keyExplanation": "Write down the value in the question:\nm = 4.525 kg\nWrite down what the prefix means:\nkilo- means one thousand, so 1 kg = 1000 g\nSubstitute in the meaning, and calculate:\nm = 4.525 × 1000 g\nm = 4525 g\nA kilogram is a large unit, so the same mass written in grams must be a larger number — 4525 g passes that check; 0.004525 g does not."
}

[
 {
  "value": 0.002485,
  "misconception": "you divided by one thousand instead of multiplying — that direction turns milliliters into liters",
  "feedback": "This answer is wrong — you divided by one thousand instead of multiplying; that direction turns milliliters into liters. Each liter holds 1000 mL, so 2.485 L is 2.485 × 1000 = 2485 mL."
 },
 {
  "value": 248.5,
  "misconception": "you multiplied by one hundred instead of one thousand",
  "feedback": "This answer is wrong — you multiplied by one hundred instead of one thousand. milli- means one thousandth, so one liter holds 1000 mL: 2.485 × 1000 = 2485 mL."
 },
 {
  "value": 24850,
  "misconception": "you multiplied by ten thousand instead of one thousand",
  "feedback": "This answer is wrong — you multiplied by ten thousand instead of one thousand. One liter holds exactly 1000 mL, so 2.485 L is 2485 mL."
 }
]

{
 "keyExplanation": "Write down the value in the question:\nV = 2.485 L\nWrite down what the prefix means:\nmilli- means one thousandth, so one liter holds 1000 mL\nSubstitute in the meaning, and calculate:\nV = 2.485 × 1000 mL\nV = 2485 mL\nEach liter is 1000 mL, so 2.485 L must be a little less than two and a half thousand milliliters — 2485 mL fits.",
 "anticipatedWrong": [
  {
   "value": 0.002485,
   "misconception": "you divided by one thousand instead of multiplying — that direction turns milliliters into liters",
   "feedback": "This answer is wrong — you divided by one thousand instead of multiplying; that direction turns milliliters into liters. Each liter holds 1000 mL, so 2.485 L is 2.485 × 1000 = 2485 mL."
  },
  {
   "value": 248.5,
   "misconception": "you multiplied by one hundred instead of one thousand",
   "feedback": "This answer is wrong — you multiplied by one hundred instead of one thousand. milli- means one thousandth, so one liter holds 1000 mL: 2.485 × 1000 = 2485 mL."
  },
  {
   "value": 24850,
   "misconception": "you multiplied by ten thousand instead of one thousand",
   "feedback": "This answer is wrong — you multiplied by ten thousand instead of one thousand. One liter holds exactly 1000 mL, so 2.485 L is 2485 mL."
  }
 ]
}

[
 {
  "value": 6.93,
  "misconception": "you recorded every calculator digit instead of rounding to the fewest significant figures",
  "feedback": "This answer is wrong — you recorded every calculator digit instead of rounding to the fewest significant figures."
 },
 {
  "value": 6.93,
  "misconception": "you padded the result to four digits — extra digits claim precision no measurement vouched for",
  "feedback": "This answer is wrong — you padded the result to four digits — extra digits claim precision no measurement vouched for."
 },
 {
  "value": 7,
  "misconception": "you rounded to one significant figure — the least precise measurements here have two",
  "feedback": "This answer is wrong — you rounded to one significant figure — the least precise measurements here have two."
 }
]

{
 "keyExplanation": "Count the significant figures in each measurement:\n2.0 cm — two, 3.15 cm — three, 1.1 cm — two\nMultiply, then round to the fewest significant figures:\n2.0 × 3.15 × 1.1 = 6.93\nrecorded result = 6.9 cm³\nWith three measurements the rule is unchanged — the fewest significant figures anywhere in the multiplication, two, sets the result."
}

[
 {
  "value": 325000,
  "misconception": "you treated milli- as one thousand instead of one thousandth",
  "feedback": "This answer is wrong — you treated milli- as one thousand instead of one thousandth."
 },
 {
  "value": 3.25,
  "misconception": "you used the centi- meaning, one hundredth, instead of the milli- meaning",
  "feedback": "This answer is wrong — you used the centi- meaning, one hundredth, instead of the milli- meaning."
 },
 {
  "value": 0.0325,
  "misconception": "you moved the decimal point four places instead of three",
  "feedback": "This answer is wrong — you moved the decimal point four places instead of three."
 }
]

{
 "keyExplanation": "Write down the value in the question:\nm = 325 mg\nWrite down what the prefix means:\nmilli- means one thousandth, so 1 mg = 0.001 g\nSubstitute in the meaning, and calculate:\nm = 325 × 0.001 g\nm = 0.325 g\nA milligram is a small unit, so the same mass written in grams must be a smaller number — 0.325 g passes that check; 325,000 g does not (3.25 g is smaller too, but comes from the centi- meaning, not milli-)."
}

[
 {
  "value": 6485000,
  "misconception": "you multiplied by one thousand instead of dividing — that direction turns kilograms into grams",
  "feedback": "This answer is wrong — you multiplied by one thousand instead of dividing; that direction turns kilograms into grams. Only 0.001 kg fits in one gram, so divide: 6485 ÷ 1000 = 6.485 kg."
 },
 {
  "value": 64.85,
  "misconception": "you divided by one hundred instead of one thousand",
  "feedback": "This answer is wrong — you divided by one hundred instead of one thousand. kilo- means one thousand, so 1000 g make one kilogram: 6485 ÷ 1000 = 6.485 kg."
 },
 {
  "value": 0.6485,
  "misconception": "you divided by ten thousand instead of one thousand",
  "feedback": "This answer is wrong — you divided by ten thousand instead of one thousand. 1000 g make one kilogram, so the parcel's 6485 g is 6.485 kg."
 }
]

{
 "keyExplanation": "Write down the value in the question:\nm = 6485 g\nWrite down what the prefix means:\nkilo- means one thousand, so 1000 g make one kilogram\nSubstitute in the meaning, and calculate:\nm = 6485 ÷ 1000 kg\nm = 6.485 kg\nA kilogram is a large unit — 1000 g make one kilogram — so the same mass written in kilograms must be a smaller number than 6485; dividing by 1000 gives 6.485 kg.",
 "anticipatedWrong": [
  {
   "value": 6485000,
   "misconception": "you multiplied by one thousand instead of dividing — that direction turns kilograms into grams",
   "feedback": "This answer is wrong — you multiplied by one thousand instead of dividing; that direction turns kilograms into grams. Only 0.001 kg fits in one gram, so divide: 6485 ÷ 1000 = 6.485 kg."
  },
  {
   "value": 64.85,
   "misconception": "you divided by one hundred instead of one thousand",
   "feedback": "This answer is wrong — you divided by one hundred instead of one thousand. kilo- means one thousand, so 1000 g make one kilogram: 6485 ÷ 1000 = 6.485 kg."
  },
  {
   "value": 0.6485,
   "misconception": "you divided by ten thousand instead of one thousand",
   "feedback": "This answer is wrong — you divided by ten thousand instead of one thousand. 1000 g make one kilogram, so the parcel's 6485 g is 6.485 kg."
  }
 ]
}

[
 {
  "value": 2.7175,
  "misconception": "you recorded every calculator digit — the calculator does not know which digits the measurements vouch for",
  "feedback": "This answer is wrong — you recorded every calculator digit — the calculator does not know which digits the measurements vouch for."
 },
 {
  "value": 2.718,
  "misconception": "you rounded to the more precise measurement's four significant figures instead of the fewest",
  "feedback": "This answer is wrong — you rounded to the more precise measurement's four significant figures instead of the fewest."
 },
 {
  "value": 3,
  "misconception": "you rounded past the rule — the result keeps as many significant figures as the least precise measurement, no fewer",
  "feedback": "This answer is wrong — you rounded past the rule — the result keeps as many significant figures as the least precise measurement, no fewer."
 }
]

{
 "keyExplanation": "Count the significant figures in each measurement:\n9.783 g — four significant figures\n3.6 cm³ — two significant figures\nDivide, then round to the fewest significant figures:\n9.783 ÷ 3.6 = 2.7175\nrecorded result = 2.7 g/cm³\nThe least precise measurement sets the precision — two significant figures, no more and no fewer."
}

[
 {
  "value": 15600,
  "misconception": "you treated centi- as one hundred instead of one hundredth",
  "feedback": "This answer is wrong — you treated centi- as one hundred instead of one hundredth."
 },
 {
  "value": 0.156,
  "misconception": "you used the milli- meaning, one thousandth, instead of the centi- meaning",
  "feedback": "This answer is wrong — you used the milli- meaning, one thousandth, instead of the centi- meaning."
 },
 {
  "value": 15.6,
  "misconception": "you moved the decimal point one place instead of two",
  "feedback": "This answer is wrong — you moved the decimal point one place instead of two."
 }
]

{
 "keyExplanation": "Write down the value in the question:\nl = 156 cm\nWrite down what the prefix means:\ncenti- means one hundredth, so 1 cm = 0.01 m\nSubstitute in the meaning, and calculate:\nl = 156 × 0.01 m\nl = 1.56 m\nA centimeter is a small unit, so the same length written in meters must be a smaller number — 1.56 m passes that check; 15,600 m does not (15.6 m is smaller too, but comes from moving the decimal one place, not two)."
}

[
 {
  "value": 0.0127,
  "misconception": "you divided by one hundred instead of multiplying — that direction turns centimeters into meters",
  "feedback": "This answer is wrong — you divided by one hundred instead of multiplying; that direction turns centimeters into meters. One meter holds 100 cm, so 1.27 m is 1.27 × 100 = 127 cm."
 },
 {
  "value": 1270,
  "misconception": "you multiplied by one thousand, the milli- meaning, instead of one hundred",
  "feedback": "This answer is wrong — you multiplied by one thousand, the milli- meaning, instead of one hundred. centi- means one hundredth, so one meter holds 100 cm: 1.27 × 100 = 127 cm."
 },
 {
  "value": 12.7,
  "misconception": "you multiplied by ten instead of one hundred",
  "feedback": "This answer is wrong — you multiplied by ten instead of one hundred. centi- means one hundredth, so one meter holds 100 cm, and 1.27 × 100 = 127 cm."
 }
]

{
 "keyExplanation": "Write down the value in the question:\nl = 1.27 m\nWrite down what the prefix means:\ncenti- means one hundredth, so one meter holds 100 cm\nSubstitute in the meaning, and calculate:\nl = 1.27 × 100 cm\nl = 127 cm\nA centimeter is a smaller unit than a meter, so the same length written in centimeters must be a larger number than 1.27 — multiplying by 100 gives 127 cm.",
 "anticipatedWrong": [
  {
   "value": 0.0127,
   "misconception": "you divided by one hundred instead of multiplying — that direction turns centimeters into meters",
   "feedback": "This answer is wrong — you divided by one hundred instead of multiplying; that direction turns centimeters into meters. One meter holds 100 cm, so 1.27 m is 1.27 × 100 = 127 cm."
  },
  {
   "value": 1270,
   "misconception": "you multiplied by one thousand, the milli- meaning, instead of one hundred",
   "feedback": "This answer is wrong — you multiplied by one thousand, the milli- meaning, instead of one hundred. centi- means one hundredth, so one meter holds 100 cm: 1.27 × 100 = 127 cm."
  },
  {
   "value": 12.7,
   "misconception": "you multiplied by ten instead of one hundred",
   "feedback": "This answer is wrong — you multiplied by ten instead of one hundred. centi- means one hundredth, so one meter holds 100 cm, and 1.27 × 100 = 127 cm."
  }
 ]
}

[
 {
  "value": 68.714,
  "misconception": "you recorded every calculator digit — the calculator does not know which digits the measurements vouch for",
  "feedback": "This answer is wrong — you recorded every calculator digit — the calculator does not know which digits the measurements vouch for."
 },
 {
  "value": 68.7,
  "misconception": "you rounded to the more precise measurement's three significant figures instead of the fewest",
  "feedback": "This answer is wrong — you rounded to the more precise measurement's three significant figures instead of the fewest."
 },
 {
  "value": 1.3,
  "misconception": "you divided one edge length by the other instead of multiplying — an area multiplies the two lengths",
  "feedback": "This answer is wrong — you divided one edge length by the other instead of multiplying — an area multiplies the two lengths."
 }
]

{
 "keyExplanation": "Count the significant figures in each measurement:\n9.4 cm — two significant figures\n7.31 cm — three significant figures\nMultiply, then round to the fewest significant figures:\n9.4 × 7.31 = 68.714\nrecorded result = 69 cm²\nThe least precise measurement sets the precision — two significant figures, no more and no fewer."
}

[
 {
  "value": 0.002847,
  "misconception": "you treated kilo- as one thousandth instead of one thousand",
  "feedback": "This answer is wrong — you treated kilo- as one thousandth instead of one thousand."
 },
 {
  "value": 284.7,
  "misconception": "you multiplied by one hundred instead of one thousand",
  "feedback": "This answer is wrong — you multiplied by one hundred instead of one thousand."
 },
 {
  "value": 28470,
  "misconception": "you multiplied by ten thousand instead of one thousand",
  "feedback": "This answer is wrong — you multiplied by ten thousand instead of one thousand."
 }
]

{
 "keyExplanation": "Write down the value in the question:\nd = 2.847 km\nWrite down what the prefix means:\nkilo- means one thousand, so 1 km = 1000 m\nSubstitute in the meaning, and calculate:\nd = 2.847 × 1000 m\nd = 2847 m\nA kilometer is a large unit, so the same length written in meters must be a larger number — 2847 m passes that check; 0.002847 m does not."
}

[
 {
  "value": 5275000,
  "misconception": "you multiplied by one thousand instead of dividing — that direction turns kiloliters into liters",
  "feedback": "This answer is wrong — you multiplied by one thousand instead of dividing; that direction turns kiloliters into liters. 1000 L make one kiloliter, so divide: 5275 ÷ 1000 = 5.275 kL."
 },
 {
  "value": 52.75,
  "misconception": "you divided by one hundred instead of one thousand",
  "feedback": "This answer is wrong — you divided by one hundred instead of one thousand. kilo- means one thousand, so 1000 L make one kiloliter: 5275 ÷ 1000 = 5.275 kL."
 },
 {
  "value": 0.5275,
  "misconception": "you divided by ten thousand instead of one thousand",
  "feedback": "This answer is wrong — you divided by ten thousand instead of one thousand. 1000 L make one kiloliter, so the tank's 5275 L is 5.275 kL."
 }
]

{
 "keyExplanation": "Write down the value in the question:\nV = 5275 L\nWrite down what the prefix means:\nkilo- means one thousand, so 1000 L make one kiloliter — a prefix keeps its meaning on any unit\nSubstitute in the meaning, and calculate:\nV = 5275 ÷ 1000 kL\nV = 5.275 kL\nA kiloliter is a large unit, so the same volume written in kiloliters must be a smaller number than 5275 — dividing by 1000 gives 5.275 kL.",
 "anticipatedWrong": [
  {
   "value": 5275000,
   "misconception": "you multiplied by one thousand instead of dividing — that direction turns kiloliters into liters",
   "feedback": "This answer is wrong — you multiplied by one thousand instead of dividing; that direction turns kiloliters into liters. 1000 L make one kiloliter, so divide: 5275 ÷ 1000 = 5.275 kL."
  },
  {
   "value": 52.75,
   "misconception": "you divided by one hundred instead of one thousand",
   "feedback": "This answer is wrong — you divided by one hundred instead of one thousand. kilo- means one thousand, so 1000 L make one kiloliter: 5275 ÷ 1000 = 5.275 kL."
  },
  {
   "value": 0.5275,
   "misconception": "you divided by ten thousand instead of one thousand",
   "feedback": "This answer is wrong — you divided by ten thousand instead of one thousand. 1000 L make one kiloliter, so the tank's 5275 L is 5.275 kL."
  }
 ]
}

[
 {
  "value": 1.39,
  "misconception": "you recorded every calculator digit — the calculator does not know which digits the measurements vouch for",
  "feedback": "This answer is wrong — you recorded every calculator digit — the calculator does not know which digits the measurements vouch for."
 },
 {
  "value": 1.39,
  "misconception": "you rounded to the more precise measurement's four significant figures instead of the fewest",
  "feedback": "This answer is wrong — you rounded to the more precise measurement's four significant figures instead of the fewest."
 },
 {
  "value": 1,
  "misconception": "you rounded past the rule — the result keeps as many significant figures as the least precise measurement, no fewer",
  "feedback": "This answer is wrong — you rounded past the rule — the result keeps as many significant figures as the least precise measurement, no fewer."
 }
]

{
 "keyExplanation": "Count the significant figures in each measurement:\n7.367 g — four significant figures\n5.3 cm³ — two significant figures\nDivide, then round to the fewest significant figures:\n7.367 ÷ 5.3 = 1.39\nrecorded result = 1.4 g/cm³\nThe least precise measurement sets the precision — two significant figures, no more and no fewer."
}

[
 {
  "value": 0.0952,
  "misconception": "you divided the volume by the mass instead of the mass by the volume",
  "feedback": null
 },
 {
  "value": 94.5,
  "misconception": "you multiplied the mass by the volume instead of dividing",
  "feedback": null
 },
 {
  "value": 1.05,
  "misconception": "you slipped the decimal point one place",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nm = 31.5 g\nV = 3.00 cm³\nWrite down the equation:\nD = m / V\nSubstitute in the values, and calculate:\nD = 31.5 / 3.00\nD = 10.5 g/cm³\nMore than 10 g packed into each cubic centimeter fits a dense metal; 0.0952 comes from flipping the division (V/m) — a tenth of water's density, impossible for a solid metal bar, which fails the sense check."
}

[
 {
  "value": 0.333,
  "misconception": "you divided the volume by the density instead of multiplying them",
  "feedback": null
 },
 {
  "value": 3.0,
  "misconception": "you divided the density by the volume instead of multiplying them",
  "feedback": null
 },
 {
  "value": 16.0,
  "misconception": "you added the density to the volume instead of multiplying them",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nD = 12.0 g/cm³\nV = 4.00 cm³\nWrite down the equation:\nD = m / V\nMake m the subject:\nm = D × V\nSubstitute in the values, and calculate:\nm = 12.0 × 4.00\nm = 48.0 g\nEach cubic centimeter of palladium carries 12.0 g, and the casting holds four of them — the mass must exceed 12.0 g, so 0.333 g and 3.00 g fail the sense check."
}

[
 "Write down the values in the question:",
 "D = 12.4 g/cm³",
 "m = 18.6 g",
 "Write down the equation:",
 "D = m / V",
 "Make V the subject:",
 "V = m / D",
 "Substitute in the values, and calculate:",
 "V = 18.6 / 12.4",
 "V = 1.50 cm³"
]

[
 {
  "value": 230.64,
  "misconception": "you multiplied the mass by the density instead of dividing",
  "feedback": "This answer is wrong — you multiplied the mass by the density instead of dividing. Rhodium packs 12.4 g into each cubic centimeter, so divide the mass by the density: V = 18.6 / 12.4 = 1.50 cm³ — a 230.64 cm³ mold — over a hundred and fifty times too large — fails the sense check."
 },
 {
  "value": 0.667,
  "misconception": "you divided the density by the mass instead of the mass by the density",
  "feedback": "This answer is wrong — you divided the density by the mass instead of the mass by the density. Make V the subject of D = m/V: V = m / D = 18.6 / 12.4 = 1.50 cm³."
 },
 {
  "value": 15.0,
  "misconception": "you slipped the decimal point one place",
  "feedback": "This answer is wrong — you slipped the decimal point one place. Each cubic centimeter of rhodium already holds 12.4 g, so 18.6 g needs only 1.50 cm³, not 15.0 cm³."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nD = 12.4 g/cm³\nm = 18.6 g\nWrite down the equation:\nD = m / V\nMake V the subject:\nV = m / D\nSubstitute in the values, and calculate:\nV = 18.6 / 12.4\nV = 1.50 cm³\nRhodium packs 12.4 g into every cubic centimeter, so 18.6 g fills only one and a half of them — 230.64 cm³ would be more than a hundred and fifty times the metal's real volume, which fails the sense check.",
 "anticipatedWrong": [
  {
   "value": 230.64,
   "misconception": "you multiplied the mass by the density instead of dividing",
   "feedback": "This answer is wrong — you multiplied the mass by the density instead of dividing. Rhodium packs 12.4 g into each cubic centimeter, so divide the mass by the density: V = 18.6 / 12.4 = 1.50 cm³ — a 230.64 cm³ mold — over a hundred and fifty times too large — fails the sense check."
  },
  {
   "value": 0.667,
   "misconception": "you divided the density by the mass instead of the mass by the density",
   "feedback": "This answer is wrong — you divided the density by the mass instead of the mass by the density. Make V the subject of D = m/V: V = m / D = 18.6 / 12.4 = 1.50 cm³."
  },
  {
   "value": 15.0,
   "misconception": "you slipped the decimal point one place",
   "feedback": "This answer is wrong — you slipped the decimal point one place. Each cubic centimeter of rhodium already holds 12.4 g, so 18.6 g needs only 1.50 cm³, not 15.0 cm³."
  }
 ]
}

[
 "Check the scale first: the labels step from 50 to 60 across five marks, so each mark is 2 mL.",
 "Read the values from the figure:",
 "starting level = 60 mL",
 "final level = 74 mL",
 "Write down the equation:",
 "V = final level − starting level",
 "Substitute in the values, and calculate:",
 "V = 74 − 60",
 "V = 14 cm³"
]

[
 {
  "value": 7,
  "misconception": "you assumed the marks step by 1 mL — on this cylinder each mark is 2 mL",
  "feedback": "This answer is wrong — you assumed the marks step by 1 mL. Check the scale first: the labels step from 50 to 60 across five marks, so each mark is 2 mL, and V = 74 − 60 = 14 cm³."
 },
 {
  "value": 74,
  "misconception": "you reported the final reading instead of the rise in level",
  "feedback": "This answer is wrong — you reported the final reading instead of the rise in level. The final reading is only where the water now stands; the quartz's volume is the rise: V = 74 − 60 = 14 cm³."
 },
 {
  "value": 134,
  "misconception": "you added the two readings instead of subtracting",
  "feedback": "This answer is wrong — you added the two readings instead of subtracting. The volume is the rise in the level: V = 74 − 60 = 14 cm³."
 }
]

{
 "keyExplanation": "Check the scale first: the labels step from 50 to 60 across five marks, so each mark is 2 mL.\nRead the values from the figure:\nstarting level = 60 mL\nfinal level = 74 mL\nWrite down the equation:\nV = final level − starting level\nSubstitute in the values, and calculate:\nV = 74 − 60\nV = 14 cm³",
 "anticipatedWrong": [
  {
   "value": 7,
   "misconception": "you assumed the marks step by 1 mL — on this cylinder each mark is 2 mL",
   "feedback": "This answer is wrong — you assumed the marks step by 1 mL. Check the scale first: the labels step from 50 to 60 across five marks, so each mark is 2 mL, and V = 74 − 60 = 14 cm³."
  },
  {
   "value": 74,
   "misconception": "you reported the final reading instead of the rise in level",
   "feedback": "This answer is wrong — you reported the final reading instead of the rise in level. The final reading is only where the water now stands; the quartz's volume is the rise: V = 74 − 60 = 14 cm³."
  },
  {
   "value": 134,
   "misconception": "you added the two readings instead of subtracting",
   "feedback": "This answer is wrong — you added the two readings instead of subtracting. The volume is the rise in the level: V = 74 − 60 = 14 cm³."
  }
 ]
}

[
 {
  "value": 0.87,
  "misconception": "you divided the volume by the mass instead of the mass by the volume",
  "feedback": null
 },
 {
  "value": 2433.4,
  "misconception": "you multiplied the mass by the volume instead of dividing",
  "feedback": null
 },
 {
  "value": 11.5,
  "misconception": "you slipped the decimal point one place",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nm = 52.9 g\nV = 46.0 mL = 46.0 cm³\nWrite down the equation:\nD = m / V\nSubstitute in the values, and calculate:\nD = 52.9 / 46.0\nD = 1.15 g/cm³\nA density slightly above 1 g/cm³ fits a pourable liquid; the mass 52.9 g and the volume 46.0 cm³ are close in size, so the density must land close to 1 g/cm³ — a value ten times larger flags a slipped decimal point."
}

[
 {
  "value": 24.5,
  "misconception": "you divided the volume by the density instead of multiplying them",
  "feedback": null
 },
 {
  "value": 0.0409,
  "misconception": "you divided the density by the volume instead of multiplying them",
  "feedback": null
 },
 {
  "value": 46.8,
  "misconception": "you added the density to the volume instead of multiplying them",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nD = 1.84 g/cm³\nV = 45.0 mL = 45.0 cm³\nWrite down the equation:\nD = m / V\nMake m the subject:\nm = D × V\nSubstitute in the values, and calculate:\nm = 1.84 × 45.0\nm = 82.8 g\nEach cubic centimeter of the acid carries 1.84 g, and the sample holds forty-five of them — the mass must exceed 1.84 g, so 0.0409 g fails the sense check."
}

[
 "Write down the values in the question:",
 "D = 1.20 g/cm³",
 "m = 23.4 g",
 "Write down the equation:",
 "D = m / V",
 "Make V the subject:",
 "V = m / D",
 "Substitute in the values, and calculate:",
 "V = 23.4 / 1.20",
 "V = 19.5 cm³"
]

[
 {
  "value": 28.08,
  "misconception": "you multiplied the mass by the density instead of dividing",
  "feedback": "This answer is wrong — you multiplied the mass by the density instead of dividing. The saltwater packs 1.20 g into each cubic centimeter, so divide: V = 23.4 / 1.20 = 19.5 cm³ — the volume in cm³ must come out smaller than the mass in grams."
 },
 {
  "value": 0.0513,
  "misconception": "you divided the density by the mass instead of the mass by the density",
  "feedback": "This answer is wrong — you divided the density by the mass instead of the mass by the density. Make V the subject of D = m/V: V = m / D = 23.4 / 1.20 = 19.5 cm³ — a bottle of 0.0513 cm³ is nowhere near the 19.5 cm³ that 23.4 g of saltwater actually needs."
 },
 {
  "value": 195,
  "misconception": "you slipped the decimal point one place",
  "feedback": "This answer is wrong — you slipped the decimal point one place. Dividing 23.4 by 1.20 gives 19.5 cm³, not 195 cm³ — the saltwater is denser than pure water, so its volume in cm³ must be smaller than its 23.4 g mass."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nD = 1.20 g/cm³\nm = 23.4 g\nWrite down the equation:\nD = m / V\nMake V the subject:\nV = m / D\nSubstitute in the values, and calculate:\nV = 23.4 / 1.20\nV = 19.5 cm³\nSaturated saltwater packs 1.20 g into each cubic centimeter, so the volume in cm³ must come out smaller than the mass in grams — 19.5 cm³ passes that check; 28.08 cm³ does not.",
 "anticipatedWrong": [
  {
   "value": 28.08,
   "misconception": "you multiplied the mass by the density instead of dividing",
   "feedback": "This answer is wrong — you multiplied the mass by the density instead of dividing. The saltwater packs 1.20 g into each cubic centimeter, so divide: V = 23.4 / 1.20 = 19.5 cm³ — the volume in cm³ must come out smaller than the mass in grams."
  },
  {
   "value": 0.0513,
   "misconception": "you divided the density by the mass instead of the mass by the density",
   "feedback": "This answer is wrong — you divided the density by the mass instead of the mass by the density. Make V the subject of D = m/V: V = m / D = 23.4 / 1.20 = 19.5 cm³ — a bottle of 0.0513 cm³ is nowhere near the 19.5 cm³ that 23.4 g of saltwater actually needs."
  },
  {
   "value": 195,
   "misconception": "you slipped the decimal point one place",
   "feedback": "This answer is wrong — you slipped the decimal point one place. Dividing 23.4 by 1.20 gives 19.5 cm³, not 195 cm³ — the saltwater is denser than pure water, so its volume in cm³ must be smaller than its 23.4 g mass."
  }
 ]
}

[
 "The mass is extra information — the volume comes from the water levels alone.",
 "Read the values from the figure:",
 "starting level = 18.0 mL",
 "final level = 23.5 mL",
 "Write down the equation:",
 "V = final level − starting level",
 "Substitute in the values, and calculate:",
 "V = 23.5 − 18.0",
 "V = 5.5 cm³"
]

[
 {
  "value": 33.0,
  "misconception": "you brought the padlock's mass into the volume calculation — the volume comes from the two water levels alone",
  "feedback": "This answer is wrong — you brought the padlock's mass into the volume calculation. The mass is extra information; the volume comes from the two water levels alone: V = 23.5 − 18.0 = 5.5 cm³."
 },
 {
  "value": 23.5,
  "misconception": "you reported the final reading instead of the rise in level",
  "feedback": "This answer is wrong — you reported the final reading instead of the rise in level. The final reading is only where the water now stands; the padlock's volume is the rise: V = 23.5 − 18.0 = 5.5 cm³."
 },
 {
  "value": 41.5,
  "misconception": "you added the two readings instead of subtracting",
  "feedback": "This answer is wrong — you added the two readings instead of subtracting. The volume is the rise in the level: V = 23.5 − 18.0 = 5.5 cm³."
 }
]

{
 "keyExplanation": "The mass is extra information — the volume comes from the water levels alone.\nRead the values from the figure:\nstarting level = 18.0 mL\nfinal level = 23.5 mL\nWrite down the equation:\nV = final level − starting level\nSubstitute in the values, and calculate:\nV = 23.5 − 18.0\nV = 5.5 cm³\nThe levels are read in milliliters, and one milliliter is one cubic centimeter, so the volume comes out in cm³.",
 "anticipatedWrong": [
  {
   "value": 33.0,
   "misconception": "you brought the padlock's mass into the volume calculation — the volume comes from the two water levels alone",
   "feedback": "This answer is wrong — you brought the padlock's mass into the volume calculation. The mass is extra information; the volume comes from the two water levels alone: V = 23.5 − 18.0 = 5.5 cm³."
  },
  {
   "value": 23.5,
   "misconception": "you reported the final reading instead of the rise in level",
   "feedback": "This answer is wrong — you reported the final reading instead of the rise in level. The final reading is only where the water now stands; the padlock's volume is the rise: V = 23.5 − 18.0 = 5.5 cm³."
  },
  {
   "value": 41.5,
   "misconception": "you added the two readings instead of subtracting",
   "feedback": "This answer is wrong — you added the two readings instead of subtracting. The volume is the rise in the level: V = 23.5 − 18.0 = 5.5 cm³."
  }
 ]
}

[
 {
  "value": 0.137,
  "misconception": "you divided the volume by the mass instead of the mass by the volume",
  "feedback": null
 },
 {
  "value": 29.24,
  "misconception": "you multiplied the mass by the volume instead of dividing",
  "feedback": null
 },
 {
  "value": 0.731,
  "misconception": "you slipped the decimal point one place",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nm = 14.62 g\nV = 2.00 cm³\nWrite down the equation:\nD = m / V\nSubstitute in the values, and calculate:\nD = 14.62 / 2.00\nD = 7.31 g/cm³\nMore than 7 g packed into each cubic centimeter fits a soft, dense metal; 0.137 g/cm³ would be far too light for any solid metal, which fails the sense check."
}

[
 {
  "value": 1.88,
  "misconception": "you divided the volume by the density instead of multiplying them",
  "feedback": null
 },
 {
  "value": 0.532,
  "misconception": "you divided the density by the volume instead of multiplying them",
  "feedback": null
 },
 {
  "value": 15.3,
  "misconception": "you added the density to the volume instead of multiplying them",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nD = 5.32 g/cm³\nV = 10.0 cm³\nWrite down the equation:\nD = m / V\nMake m the subject:\nm = D × V\nSubstitute in the values, and calculate:\nm = 5.32 × 10.0\nm = 53.2 g\nEach cubic centimeter of germanium carries 5.32 g, and the blank holds ten of them — the mass must exceed 5.32 g, so 1.88 g and 0.532 g fail the sense check."
}

[
 "Write down the values in the question:",
 "D = 5.90 g/cm³",
 "m = 35.4 g",
 "Write down the equation:",
 "D = m / V",
 "Make V the subject:",
 "V = m / D",
 "Substitute in the values, and calculate:",
 "V = 35.4 / 5.90",
 "V = 6.00 cm³"
]

[
 {
  "value": 208.86,
  "misconception": "you multiplied the mass by the density instead of dividing",
  "feedback": "This answer is wrong — you multiplied the mass by the density instead of dividing. Gallium packs 5.90 g into each cubic centimeter, so divide the mass by the density: V = 35.4 / 5.90 = 6.00 cm³ — a 208.86 cm³ bucket of gallium fails the sense check."
 },
 {
  "value": 0.167,
  "misconception": "you divided the density by the mass instead of the mass by the density",
  "feedback": "This answer is wrong — you divided the density by the mass instead of the mass by the density. Make V the subject of D = m/V: V = m / D = 35.4 / 5.90 = 6.00 cm³."
 },
 {
  "value": 60.0,
  "misconception": "you slipped the decimal point one place",
  "feedback": "This answer is wrong — you slipped the decimal point one place. Each cubic centimeter of gallium already holds 5.90 g, so 35.4 g takes up only 6.00 cm³, not 60.0 cm³."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nD = 5.90 g/cm³\nm = 35.4 g\nWrite down the equation:\nD = m / V\nMake V the subject:\nV = m / D\nSubstitute in the values, and calculate:\nV = 35.4 / 5.90\nV = 6.00 cm³\nGallium packs 5.90 g into every cubic centimeter, so 35.4 g needs exactly six of them — 208.86 cm³ would be a bucket of gallium, which fails the sense check.",
 "anticipatedWrong": [
  {
   "value": 208.86,
   "misconception": "you multiplied the mass by the density instead of dividing",
   "feedback": "This answer is wrong — you multiplied the mass by the density instead of dividing. Gallium packs 5.90 g into each cubic centimeter, so divide the mass by the density: V = 35.4 / 5.90 = 6.00 cm³ — a 208.86 cm³ bucket of gallium fails the sense check."
  },
  {
   "value": 0.167,
   "misconception": "you divided the density by the mass instead of the mass by the density",
   "feedback": "This answer is wrong — you divided the density by the mass instead of the mass by the density. Make V the subject of D = m/V: V = m / D = 35.4 / 5.90 = 6.00 cm³."
  },
  {
   "value": 60.0,
   "misconception": "you slipped the decimal point one place",
   "feedback": "This answer is wrong — you slipped the decimal point one place. Each cubic centimeter of gallium already holds 5.90 g, so 35.4 g takes up only 6.00 cm³, not 60.0 cm³."
  }
 ]
}

[
 "Read the values from the figure:",
 "starting level = 34.0 mL",
 "final level = 43.0 mL",
 "Write down the equation:",
 "V = final level − starting level",
 "Substitute in the values, and calculate:",
 "V = 43.0 − 34.0",
 "V = 9 cm³"
]

[
 {
  "value": 43.0,
  "misconception": "you reported the final reading instead of the rise in level",
  "feedback": "This answer is wrong — you reported the final reading instead of the rise in level. The final reading is only where the water now stands; the hinge's volume is the rise: V = 43.0 − 34.0 = 9 cm³."
 },
 {
  "value": 34.0,
  "misconception": "you reported the starting reading — that is where the water stood before the hinge went in, not the hinge's volume",
  "feedback": "This answer is wrong — you reported the starting reading; that is only where the water stood before the hinge went in. The hinge's volume is the rise: V = 43.0 − 34.0 = 9 cm³."
 },
 {
  "value": 77.0,
  "misconception": "you added the two readings instead of subtracting",
  "feedback": "This answer is wrong — you added the two readings instead of subtracting. The volume is the rise in the level: V = 43.0 − 34.0 = 9 cm³."
 }
]

{
 "keyExplanation": "Read the values from the figure:\nstarting level = 34.0 mL\nfinal level = 43.0 mL\nWrite down the equation:\nV = final level − starting level\nSubstitute in the values, and calculate:\nV = 43.0 − 34.0\nV = 9 cm³\nThe levels are read in milliliters, and one milliliter is one cubic centimeter, so the volume comes out in cm³.",
 "anticipatedWrong": [
  {
   "value": 43.0,
   "misconception": "you reported the final reading instead of the rise in level",
   "feedback": "This answer is wrong — you reported the final reading instead of the rise in level. The final reading is only where the water now stands; the hinge's volume is the rise: V = 43.0 − 34.0 = 9 cm³."
  },
  {
   "value": 34.0,
   "misconception": "you reported the starting reading — that is where the water stood before the hinge went in, not the hinge's volume",
   "feedback": "This answer is wrong — you reported the starting reading; that is only where the water stood before the hinge went in. The hinge's volume is the rise: V = 43.0 − 34.0 = 9 cm³."
  },
  {
   "value": 77.0,
   "misconception": "you added the two readings instead of subtracting",
   "feedback": "This answer is wrong — you added the two readings instead of subtracting. The volume is the rise in the level: V = 43.0 − 34.0 = 9 cm³."
  }
 ]
}

[
 {
  "value": 0.117,
  "misconception": "you divided the volume by the mass instead of the mass by the volume",
  "feedback": null
 },
 {
  "value": 77.13,
  "misconception": "you multiplied the mass by the volume instead of dividing",
  "feedback": null
 },
 {
  "value": 0.857,
  "misconception": "you slipped the decimal point one place",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nm = 25.71 g\nV = 3.00 cm³\nWrite down the equation:\nD = m / V\nSubstitute in the values, and calculate:\nD = 25.71 / 3.00\nD = 8.57 g/cm³\nMore than 8 g packed into each cubic centimeter fits a dense metal; 0.117 g/cm³ would be far too light for any solid metal, which fails the sense check."
}

[
 {
  "value": 52.6,
  "misconception": "you divided the volume by the density instead of multiplying them",
  "feedback": null
 },
 {
  "value": 0.019,
  "misconception": "you divided the density by the volume instead of multiplying them",
  "feedback": null
 },
 {
  "value": 71.3,
  "misconception": "you added the density to the volume instead of multiplying them",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nD = 1.33 g/cm³\nV = 70.0 mL = 70.0 cm³\nWrite down the equation:\nD = m / V\nMake m the subject:\nm = D × V\nSubstitute in the values, and calculate:\nm = 1.33 × 70.0\nm = 93.1 g\nEach cubic centimeter of dichloromethane carries 1.33 g, and the sample holds seventy of them — the mass must exceed 1.33 g, so 0.019 g fails the sense check."
}

[
 "Write down the values in the question:",
 "D = 6.52 g/cm³",
 "m = 16.3 g",
 "Write down the equation:",
 "D = m / V",
 "Make V the subject:",
 "V = m / D",
 "Substitute in the values, and calculate:",
 "V = 16.3 / 6.52",
 "V = 2.50 cm³"
]

[
 {
  "value": 106.276,
  "misconception": "you multiplied the mass by the density instead of dividing",
  "feedback": "This answer is wrong — you multiplied the mass by the density instead of dividing. Zirconium packs 6.52 g into each cubic centimeter, so divide the mass by the density: V = 16.3 / 6.52 = 2.50 cm³."
 },
 {
  "value": 0.4,
  "misconception": "you divided the density by the mass instead of the mass by the density",
  "feedback": "This answer is wrong — you divided the density by the mass instead of the mass by the density. Make V the subject of D = m/V: V = m / D = 16.3 / 6.52 = 2.50 cm³."
 },
 {
  "value": 25.0,
  "misconception": "you slipped the decimal point one place",
  "feedback": "This answer is wrong — you slipped the decimal point one place. Each cubic centimeter of zirconium already holds 6.52 g, so a 16.3 g blank occupies only 2.50 cm³, not 25.0 cm³."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nD = 6.52 g/cm³\nm = 16.3 g\nWrite down the equation:\nD = m / V\nMake V the subject:\nV = m / D\nSubstitute in the values, and calculate:\nV = 16.3 / 6.52\nV = 2.50 cm³\nZirconium packs 6.52 g into each cubic centimeter, so the blank's volume in cm³ must come out much smaller than its mass in grams — 2.50 cm³ passes that check.",
 "anticipatedWrong": [
  {
   "value": 106.276,
   "misconception": "you multiplied the mass by the density instead of dividing",
   "feedback": "This answer is wrong — you multiplied the mass by the density instead of dividing. Zirconium packs 6.52 g into each cubic centimeter, so divide the mass by the density: V = 16.3 / 6.52 = 2.50 cm³."
  },
  {
   "value": 0.4,
   "misconception": "you divided the density by the mass instead of the mass by the density",
   "feedback": "This answer is wrong — you divided the density by the mass instead of the mass by the density. Make V the subject of D = m/V: V = m / D = 16.3 / 6.52 = 2.50 cm³."
  },
  {
   "value": 25.0,
   "misconception": "you slipped the decimal point one place",
   "feedback": "This answer is wrong — you slipped the decimal point one place. Each cubic centimeter of zirconium already holds 6.52 g, so a 16.3 g blank occupies only 2.50 cm³, not 25.0 cm³."
  }
 ]
}

[
 "Check the scale first: the labels step from 20 to 30 across five marks, so each mark is 2 mL.",
 "Read the values from the figure:",
 "starting level = 28 mL",
 "final level = 44 mL",
 "Write down the equation:",
 "V = final level − starting level",
 "Substitute in the values, and calculate:",
 "V = 44 − 28",
 "V = 16 cm³"
]

[
 {
  "value": 8,
  "misconception": "you assumed the marks step by 1 mL — on this cylinder each mark is 2 mL",
  "feedback": "This answer is wrong — you assumed the marks step by 1 mL. Check the scale first: the labels step from 20 to 30 across five marks, so each mark is 2 mL, and V = 44 − 28 = 16 cm³."
 },
 {
  "value": 44,
  "misconception": "you reported the final reading instead of the rise in level",
  "feedback": "This answer is wrong — you reported the final reading instead of the rise in level. The final reading is only where the water now stands; the spark plug's volume is the rise: V = 44 − 28 = 16 cm³."
 },
 {
  "value": 72,
  "misconception": "you added the two readings instead of subtracting",
  "feedback": "This answer is wrong — you added the two readings instead of subtracting. The volume is the rise in the level: V = 44 − 28 = 16 cm³."
 }
]

{
 "keyExplanation": "Check the scale first: the labels step from 20 to 30 across five marks, so each mark is 2 mL.\nRead the values from the figure:\nstarting level = 28 mL\nfinal level = 44 mL\nWrite down the equation:\nV = final level − starting level\nSubstitute in the values, and calculate:\nV = 44 − 28\nV = 16 cm³\nThe levels are read in milliliters, and one milliliter is one cubic centimeter, so the volume comes out in cm³.",
 "anticipatedWrong": [
  {
   "value": 8,
   "misconception": "you assumed the marks step by 1 mL — on this cylinder each mark is 2 mL",
   "feedback": "This answer is wrong — you assumed the marks step by 1 mL. Check the scale first: the labels step from 20 to 30 across five marks, so each mark is 2 mL, and V = 44 − 28 = 16 cm³."
  },
  {
   "value": 44,
   "misconception": "you reported the final reading instead of the rise in level",
   "feedback": "This answer is wrong — you reported the final reading instead of the rise in level. The final reading is only where the water now stands; the spark plug's volume is the rise: V = 44 − 28 = 16 cm³."
  },
  {
   "value": 72,
   "misconception": "you added the two readings instead of subtracting",
   "feedback": "This answer is wrong — you added the two readings instead of subtracting. The volume is the rise in the level: V = 44 − 28 = 16 cm³."
  }
 ]
}

[
 {
  "value": 0.203,
  "misconception": "you divided the volume by the mass instead of the mass by the volume",
  "feedback": null
 },
 {
  "value": 123.25,
  "misconception": "you multiplied the mass by the volume instead of dividing",
  "feedback": null
 },
 {
  "value": 0.493,
  "misconception": "you slipped the decimal point one place",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nm = 24.65 g\nV = 5.00 cm³\nWrite down the equation:\nD = m / V\nSubstitute in the values, and calculate:\nD = 24.65 / 5.00\nD = 4.93 g/cm³\nAlmost 5 g packed into each cubic centimeter fits a heavy crystalline solid; 0.203 g/cm³ would be lighter than nearly any solid, which fails the sense check."
}

[
 {
  "value": 291,
  "misconception": "you divided the volume by the density instead of multiplying them",
  "feedback": null
 },
 {
  "value": 0.00343,
  "misconception": "you divided the density by the volume instead of multiplying them",
  "feedback": null
 },
 {
  "value": 301,
  "misconception": "you added the density to the volume instead of multiplying them",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nD = 1.03 g/cm³\nV = 300.0 mL = 300.0 cm³\nWrite down the equation:\nD = m / V\nMake m the subject:\nm = D × V\nSubstitute in the values, and calculate:\nm = 1.03 × 300.0\nm = 309 g\nEach cubic centimeter of seawater carries 1.03 g, and the 300.0 cm³ sample holds three hundred of them — the mass must be far above 1.03 g, so 0.00343 g fails the sense check."
}

[
 "Write down the values in the question:",
 "D = 1.14 g/cm³",
 "m = 108.3 g",
 "Write down the equation:",
 "D = m / V",
 "Make V the subject:",
 "V = m / D",
 "Substitute in the values, and calculate:",
 "V = 108.3 / 1.14",
 "V = 95.0 cm³"
]

[
 {
  "value": 123.462,
  "misconception": "you multiplied the mass by the density instead of dividing",
  "feedback": "This answer is wrong — you multiplied the mass by the density instead of dividing. Nylon packs 1.14 g into each cubic centimeter, so divide the mass by the density: V = 108.3 / 1.14 = 95.0 cm³ — slightly smaller than the mass in grams, since nylon is a little denser than water."
 },
 {
  "value": 0.0105,
  "misconception": "you divided the density by the mass instead of the mass by the density",
  "feedback": "This answer is wrong — you divided the density by the mass instead of the mass by the density. Make V the subject of D = m/V: V = m / D = 108.3 / 1.14 = 95.0 cm³ — a 0.0105 cm³ mallet head would be a speck."
 },
 {
  "value": 950,
  "misconception": "you slipped the decimal point one place",
  "feedback": "This answer is wrong — you slipped the decimal point one place. Dividing 108.3 by 1.14 gives 95.0 cm³, not 950 cm³ — nylon is denser than water, so the volume in cm³ must come out smaller than the 108.3 g mass."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nD = 1.14 g/cm³\nm = 108.3 g\nWrite down the equation:\nD = m / V\nMake V the subject:\nV = m / D\nSubstitute in the values, and calculate:\nV = 108.3 / 1.14\nV = 95.0 cm³\nNylon packs just over a gram into each cubic centimeter, so the mallet head's volume in cm³ comes out a little smaller than its 108.3 g mass — 95.0 cm³ passes that check.",
 "anticipatedWrong": [
  {
   "value": 123.462,
   "misconception": "you multiplied the mass by the density instead of dividing",
   "feedback": "This answer is wrong — you multiplied the mass by the density instead of dividing. Nylon packs 1.14 g into each cubic centimeter, so divide the mass by the density: V = 108.3 / 1.14 = 95.0 cm³ — slightly smaller than the mass in grams, since nylon is a little denser than water."
  },
  {
   "value": 0.0105,
   "misconception": "you divided the density by the mass instead of the mass by the density",
   "feedback": "This answer is wrong — you divided the density by the mass instead of the mass by the density. Make V the subject of D = m/V: V = m / D = 108.3 / 1.14 = 95.0 cm³ — a 0.0105 cm³ mallet head would be a speck."
  },
  {
   "value": 950,
   "misconception": "you slipped the decimal point one place",
   "feedback": "This answer is wrong — you slipped the decimal point one place. Dividing 108.3 by 1.14 gives 95.0 cm³, not 950 cm³ — nylon is denser than water, so the volume in cm³ must come out smaller than the 108.3 g mass."
  }
 ]
}

[
 "Read the values from the figure:",
 "starting level = 39.0 mL",
 "final level = 56.5 mL",
 "Write down the equation:",
 "V = final level − starting level",
 "Substitute in the values, and calculate:",
 "V = 56.5 − 39.0",
 "V = 17.5 cm³"
]

[
 {
  "value": 56.5,
  "misconception": "you reported the final reading instead of the rise in level",
  "feedback": "This answer is wrong — you reported the final reading instead of the rise in level. The final reading is only where the water now stands; the paperweight's volume is the rise: V = 56.5 − 39.0 = 17.5 cm³."
 },
 {
  "value": 39.0,
  "misconception": "you reported the starting reading — that is where the water stood before the paperweight went in, not the paperweight's volume",
  "feedback": "This answer is wrong — you reported the starting reading; that is only where the water stood before the paperweight went in. The paperweight's volume is the rise: V = 56.5 − 39.0 = 17.5 cm³."
 },
 {
  "value": 95.5,
  "misconception": "you added the two readings instead of subtracting",
  "feedback": "This answer is wrong — you added the two readings instead of subtracting. The volume is the rise in the level: V = 56.5 − 39.0 = 17.5 cm³."
 }
]

{
 "keyExplanation": "Read the values from the figure:\nstarting level = 39.0 mL\nfinal level = 56.5 mL\nWrite down the equation:\nV = final level − starting level\nSubstitute in the values, and calculate:\nV = 56.5 − 39.0\nV = 17.5 cm³\nThe levels are read in milliliters, and one milliliter is one cubic centimeter, so the volume comes out in cm³.",
 "anticipatedWrong": [
  {
   "value": 56.5,
   "misconception": "you reported the final reading instead of the rise in level",
   "feedback": "This answer is wrong — you reported the final reading instead of the rise in level. The final reading is only where the water now stands; the paperweight's volume is the rise: V = 56.5 − 39.0 = 17.5 cm³."
  },
  {
   "value": 39.0,
   "misconception": "you reported the starting reading — that is where the water stood before the paperweight went in, not the paperweight's volume",
   "feedback": "This answer is wrong — you reported the starting reading; that is only where the water stood before the paperweight went in. The paperweight's volume is the rise: V = 56.5 − 39.0 = 17.5 cm³."
  },
  {
   "value": 95.5,
   "misconception": "you added the two readings instead of subtracting",
   "feedback": "This answer is wrong — you added the two readings instead of subtracting. The volume is the rise in the level: V = 56.5 − 39.0 = 17.5 cm³."
  }
 ]
}

[
 "Write down the values in the question:",
 "mass of chalk = 15.7 g",
 "mass of acid solution = 88.9 g",
 "The flask is sealed, so the law of conservation of mass applies:",
 "total mass before = total mass after",
 "In this problem's substances:",
 "mass of chalk + mass of acid solution = total mass after",
 "Substitute in the values, and calculate:",
 "total mass after = 15.7 + 88.9",
 "total mass after = 104.6 g, gas included."
]

[
 {
  "value": 88.9,
  "misconception": "you dropped the solid's mass from the total — everything sealed inside counts",
  "feedback": "This answer is wrong — you dropped the solid's mass from the total; everything sealed inside counts, before and after. The flask holds the chalk's 15.7 g and the acid solution's 88.9 g: 15.7 + 88.9 = 104.6 g."
 },
 {
  "value": 73.2,
  "misconception": "you subtracted the chalk instead of adding it — both starting substances are inside the sealed flask",
  "feedback": "This answer is wrong — you subtracted the chalk instead of adding it; both starting substances are inside the sealed flask. Total mass before = total mass after: 15.7 + 88.9 = 104.6 g."
 },
 {
  "value": 15.7,
  "misconception": "you carried over the solid's mass alone — the total covers everything in the flask",
  "feedback": "This answer is wrong — you carried over the solid's mass alone; the total covers everything in the flask. The acid solution's 88.9 g counts too: 15.7 + 88.9 = 104.6 g."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of chalk = 15.7 g\nmass of acid solution = 88.9 g\nThe flask is sealed, so the law of conservation of mass applies:\ntotal mass before = total mass after\nIn this problem's substances:\nmass of chalk + mass of acid solution = total mass after\nSubstitute in the values, and calculate:\ntotal mass after = 15.7 + 88.9\ntotal mass after = 104.6 g, gas included.",
 "anticipatedWrong": [
  {
   "value": 88.9,
   "misconception": "you dropped the solid's mass from the total — everything sealed inside counts",
   "feedback": "This answer is wrong — you dropped the solid's mass from the total; everything sealed inside counts, before and after. The flask holds the chalk's 15.7 g and the acid solution's 88.9 g: 15.7 + 88.9 = 104.6 g."
  },
  {
   "value": 73.2,
   "misconception": "you subtracted the chalk instead of adding it — both starting substances are inside the sealed flask",
   "feedback": "This answer is wrong — you subtracted the chalk instead of adding it; both starting substances are inside the sealed flask. Total mass before = total mass after: 15.7 + 88.9 = 104.6 g."
  },
  {
   "value": 15.7,
   "misconception": "you carried over the solid's mass alone — the total covers everything in the flask",
   "feedback": "This answer is wrong — you carried over the solid's mass alone; the total covers everything in the flask. The acid solution's 88.9 g counts too: 15.7 + 88.9 = 104.6 g."
  }
 ]
}

[
 {
  "value": 0.5,
  "misconception": "you subtracted the masses — both starting substances end up inside the new substance, so add them",
  "feedback": "This answer is wrong — you subtracted the masses — both starting substances end up inside the new substance, so add them"
 },
 {
  "value": 6.1,
  "misconception": "you carried over the zinc's mass alone — the chlorine's atoms are in the zinc chloride too",
  "feedback": "This answer is wrong — you carried over the zinc's mass alone — the chlorine's atoms are in the zinc chloride too"
 },
 {
  "value": 6.6,
  "misconception": "you carried over the chlorine's mass alone — the zinc's atoms are in the zinc chloride too",
  "feedback": "This answer is wrong — you carried over the chlorine's mass alone — the zinc's atoms are in the zinc chloride too"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of zinc = 6.1 g\nmass of chlorine = 6.6 g\nWrite down the equation:\ntotal mass before = total mass after\nIn this problem's substances:\nmass of zinc before + mass of chlorine before = mass of zinc chloride after\nMake the mass of zinc chloride the subject:\nmass of zinc chloride = mass of zinc + mass of chlorine\nSubstitute in the values, and calculate:\nmass of zinc chloride = 6.1 + 6.6\nmass of zinc chloride = 12.7 g\nSanity check: the answer must exceed each starting mass, and 12.7 g does.",
 "anticipatedWrong": [
  {
   "value": 0.5,
   "misconception": "you subtracted the masses — both starting substances end up inside the new substance, so add them",
   "check": {
    "expr": "6.6-6.1",
    "expected": 0.5
   },
   "feedback": "This answer is wrong — you subtracted the masses — both starting substances end up inside the new substance, so add them"
  },
  {
   "value": 6.1,
   "misconception": "you carried over the zinc's mass alone — the chlorine's atoms are in the zinc chloride too",
   "check": {
    "expr": "6.1",
    "expected": 6.1
   },
   "feedback": "This answer is wrong — you carried over the zinc's mass alone — the chlorine's atoms are in the zinc chloride too"
  },
  {
   "value": 6.6,
   "misconception": "you carried over the chlorine's mass alone — the zinc's atoms are in the zinc chloride too",
   "check": {
    "expr": "6.6",
    "expected": 6.6
   },
   "feedback": "This answer is wrong — you carried over the chlorine's mass alone — the zinc's atoms are in the zinc chloride too"
  }
 ]
}

[
 {
  "value": 3.1,
  "misconception": "you subtracted only the solid — subtract every known substance formed, the condensed liquid included",
  "feedback": "This answer is wrong — you subtracted only the solid — subtract every known substance formed, the condensed liquid included"
 },
 {
  "value": 8.9,
  "misconception": "you added the known masses formed and stopped — subtract that sum from the starting mass",
  "feedback": "This answer is wrong — you added the known masses formed and stopped — subtract that sum from the starting mass"
 },
 {
  "value": 20.0,
  "misconception": "you added everything together — the substances formed must total the starting mass, not exceed it",
  "feedback": "This answer is wrong — you added everything together — the substances formed must total the starting mass, not exceed it"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of malachite = 11.1 g\nmass of black solid = 8.0 g\nmass of condensed liquid = 0.9 g\nWrite down the equation:\ntotal mass before = total mass after\nIn this problem's substances:\nmass of malachite before = mass of black solid after + mass of condensed liquid after + mass of final gas after\nMake the mass of the final gas the subject:\nmass of final gas = mass of malachite − (mass of black solid + mass of condensed liquid)\nSubstitute in the values, and calculate:\nmass of final gas = 11.1 − (8.0 + 0.9)\nmass of final gas = 11.1 − 8.9\nmass of final gas = 2.2 g",
 "anticipatedWrong": [
  {
   "value": 3.1,
   "misconception": "you subtracted only the solid — subtract every known substance formed, the condensed liquid included",
   "check": {
    "expr": "11.1-8.0",
    "expected": 3.1
   },
   "feedback": "This answer is wrong — you subtracted only the solid — subtract every known substance formed, the condensed liquid included"
  },
  {
   "value": 8.9,
   "misconception": "you added the known masses formed and stopped — subtract that sum from the starting mass",
   "check": {
    "expr": "8.0+0.9",
    "expected": 8.9
   },
   "feedback": "This answer is wrong — you added the known masses formed and stopped — subtract that sum from the starting mass"
  },
  {
   "value": 20.0,
   "misconception": "you added everything together — the substances formed must total the starting mass, not exceed it",
   "check": {
    "expr": "11.1+8.0+0.9",
    "expected": 20.0
   },
   "feedback": "This answer is wrong — you added everything together — the substances formed must total the starting mass, not exceed it"
  }
 ]
}

[
 "Write down the values in the question:",
 "mass of aluminum chloride = 34.1 g",
 "mass of aluminum = 6.9 g",
 "Write down the equation:",
 "total mass before = total mass after",
 "In this problem's substances:",
 "mass of aluminum before + mass of chlorine before = mass of aluminum chloride after",
 "Make the mass of chlorine the subject:",
 "mass of chlorine = mass of aluminum chloride − mass of aluminum",
 "Substitute in the values, and calculate:",
 "mass of chlorine = 34.1 − 6.9",
 "mass of chlorine = 27.2 g"
]

[
 {
  "value": 41.0,
  "misconception": "you added instead of subtracting — the 34.1 g of aluminum chloride is the total after, so the chlorine is that total minus the aluminum",
  "feedback": "This answer is wrong — you added instead of subtracting; the 34.1 g of aluminum chloride is the total after, so the chlorine is that total minus the aluminum. 34.1 − 6.9 = 27.2 g."
 },
 {
  "value": 34.1,
  "misconception": "you gave the mass of the new substance as the answer — the chlorine is only part of it",
  "feedback": "This answer is wrong — you gave the mass of the new substance as the answer; the chlorine is only part of it. The aluminum's 6.9 g is in there too: 34.1 − 6.9 = 27.2 g."
 },
 {
  "value": 6.9,
  "misconception": "you repeated the aluminum's mass — the chlorine's mass is what remains of the total",
  "feedback": "This answer is wrong — you repeated the aluminum's mass; the chlorine's mass is what remains of the total. 34.1 − 6.9 = 27.2 g."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of aluminum chloride = 34.1 g\nmass of aluminum = 6.9 g\nWrite down the equation:\ntotal mass before = total mass after\nIn this problem's substances:\nmass of aluminum before + mass of chlorine before = mass of aluminum chloride after\nMake the mass of chlorine the subject:\nmass of chlorine = mass of aluminum chloride − mass of aluminum\nSubstitute in the values, and calculate:\nmass of chlorine = 34.1 − 6.9\nmass of chlorine = 27.2 g",
 "anticipatedWrong": [
  {
   "value": 41.0,
   "misconception": "you added instead of subtracting — the 34.1 g of aluminum chloride is the total after, so the chlorine is that total minus the aluminum",
   "feedback": "This answer is wrong — you added instead of subtracting; the 34.1 g of aluminum chloride is the total after, so the chlorine is that total minus the aluminum. 34.1 − 6.9 = 27.2 g."
  },
  {
   "value": 34.1,
   "misconception": "you gave the mass of the new substance as the answer — the chlorine is only part of it",
   "feedback": "This answer is wrong — you gave the mass of the new substance as the answer; the chlorine is only part of it. The aluminum's 6.9 g is in there too: 34.1 − 6.9 = 27.2 g."
  },
  {
   "value": 6.9,
   "misconception": "you repeated the aluminum's mass — the chlorine's mass is what remains of the total",
   "feedback": "This answer is wrong — you repeated the aluminum's mass; the chlorine's mass is what remains of the total. 34.1 − 6.9 = 27.2 g."
  }
 ]
}

[
 "Write down the values in the question:",
 "mass of oil = 46.2 g",
 "mass of lemon juice = 39.1 g",
 "The bottle is sealed, so the law of conservation of mass applies:",
 "total mass before = total mass after",
 "In this problem's substances:",
 "mass of oil + mass of lemon juice = total mass after",
 "Substitute in the values, and calculate:",
 "total mass after = 46.2 + 39.1",
 "total mass after = 85.3 g"
]

[
 {
  "value": 39.1,
  "misconception": "you dropped the oil's mass from the total — everything sealed inside counts",
  "feedback": "This answer is wrong — you dropped the oil's mass from the total; everything sealed inside counts, before and after. The bottle holds the oil's 46.2 g and the lemon juice's 39.1 g: 46.2 + 39.1 = 85.3 g."
 },
 {
  "value": 7.1,
  "misconception": "you subtracted the lemon juice instead of adding it — both liquids are inside the sealed bottle",
  "feedback": "This answer is wrong — you subtracted the lemon juice instead of adding it; both liquids are inside the sealed bottle. Total mass before = total mass after: 46.2 + 39.1 = 85.3 g."
 },
 {
  "value": 46.2,
  "misconception": "you carried over the oil's mass alone — the total covers everything in the bottle",
  "feedback": "This answer is wrong — you carried over the oil's mass alone; the total covers everything in the bottle. The lemon juice's 39.1 g counts too: 46.2 + 39.1 = 85.3 g."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of oil = 46.2 g\nmass of lemon juice = 39.1 g\nThe bottle is sealed, so the law of conservation of mass applies:\ntotal mass before = total mass after\nIn this problem's substances:\nmass of oil + mass of lemon juice = total mass after\nSubstitute in the values, and calculate:\ntotal mass after = 46.2 + 39.1\ntotal mass after = 85.3 g\nShaking the liquids together is a physical change, and the law covers any physical or chemical change — sealed in, the total cannot change.",
 "anticipatedWrong": [
  {
   "value": 39.1,
   "misconception": "you dropped the oil's mass from the total — everything sealed inside counts",
   "feedback": "This answer is wrong — you dropped the oil's mass from the total; everything sealed inside counts, before and after. The bottle holds the oil's 46.2 g and the lemon juice's 39.1 g: 46.2 + 39.1 = 85.3 g."
  },
  {
   "value": 7.1,
   "misconception": "you subtracted the lemon juice instead of adding it — both liquids are inside the sealed bottle",
   "feedback": "This answer is wrong — you subtracted the lemon juice instead of adding it; both liquids are inside the sealed bottle. Total mass before = total mass after: 46.2 + 39.1 = 85.3 g."
  },
  {
   "value": 46.2,
   "misconception": "you carried over the oil's mass alone — the total covers everything in the bottle",
   "feedback": "This answer is wrong — you carried over the oil's mass alone; the total covers everything in the bottle. The lemon juice's 39.1 g counts too: 46.2 + 39.1 = 85.3 g."
  }
 ]
}

[
 {
  "value": 4.8,
  "misconception": "you subtracted the masses — both starting substances end up inside the new substance, so add them",
  "feedback": "This answer is wrong — you subtracted the masses — both starting substances end up inside the new substance, so add them"
 },
 {
  "value": 7.8,
  "misconception": "you carried over the magnesium's mass alone — the nitrogen's atoms are in the magnesium nitride too",
  "feedback": "This answer is wrong — you carried over the magnesium's mass alone — the nitrogen's atoms are in the magnesium nitride too"
 },
 {
  "value": 3.0,
  "misconception": "you carried over the nitrogen's mass alone — the magnesium's atoms are in the magnesium nitride too",
  "feedback": "This answer is wrong — you carried over the nitrogen's mass alone — the magnesium's atoms are in the magnesium nitride too"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of magnesium = 7.8 g\nmass of nitrogen = 3.0 g\nWrite down the equation:\ntotal mass before = total mass after\nIn this problem's substances:\nmass of magnesium before + mass of nitrogen before = mass of magnesium nitride after\nMake the mass of magnesium nitride the subject:\nmass of magnesium nitride = mass of magnesium + mass of nitrogen\nSubstitute in the values, and calculate:\nmass of magnesium nitride = 7.8 + 3.0\nmass of magnesium nitride = 10.8 g\nSanity check: the answer must exceed each starting mass, and 10.8 g does.",
 "anticipatedWrong": [
  {
   "value": 4.8,
   "misconception": "you subtracted the masses — both starting substances end up inside the new substance, so add them",
   "check": {
    "expr": "7.8-3.0",
    "expected": 4.8
   },
   "feedback": "This answer is wrong — you subtracted the masses — both starting substances end up inside the new substance, so add them"
  },
  {
   "value": 7.8,
   "misconception": "you carried over the magnesium's mass alone — the nitrogen's atoms are in the magnesium nitride too",
   "check": {
    "expr": "7.8",
    "expected": 7.8
   },
   "feedback": "This answer is wrong — you carried over the magnesium's mass alone — the nitrogen's atoms are in the magnesium nitride too"
  },
  {
   "value": 3.0,
   "misconception": "you carried over the nitrogen's mass alone — the magnesium's atoms are in the magnesium nitride too",
   "check": {
    "expr": "3.0",
    "expected": 3.0
   },
   "feedback": "This answer is wrong — you carried over the nitrogen's mass alone — the magnesium's atoms are in the magnesium nitride too"
  }
 ]
}

[
 {
  "value": 10.5,
  "misconception": "you subtracted only the gas that stayed a gas — subtract every known substance formed, the condensed one included",
  "feedback": "This answer is wrong — you subtracted only the gas that stayed a gas — subtract every known substance formed, the condensed one included"
 },
 {
  "value": 18.6,
  "misconception": "you added the known masses formed and stopped — subtract that sum from the starting mass",
  "feedback": "This answer is wrong — you added the known masses formed and stopped — subtract that sum from the starting mass"
 },
 {
  "value": 42.3,
  "misconception": "you added everything together — the substances formed must total the starting mass, not exceed it",
  "feedback": "This answer is wrong — you added everything together — the substances formed must total the starting mass, not exceed it"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of ammonium bicarbonate = 23.7 g\nmass of condensed gas = 5.4 g\nmass of uncondensed gas = 13.2 g\nWrite down the equation:\ntotal mass before = total mass after\nIn this problem's substances:\nmass of ammonium bicarbonate before = mass of ammonia after + mass of condensed gas after + mass of uncondensed gas after\nMake the mass of ammonia the subject:\nmass of ammonia = mass of ammonium bicarbonate − (mass of condensed gas + mass of uncondensed gas)\nSubstitute in the values, and calculate:\nmass of ammonia = 23.7 − (5.4 + 13.2)\nmass of ammonia = 23.7 − 18.6\nmass of ammonia = 5.1 g",
 "anticipatedWrong": [
  {
   "value": 10.5,
   "misconception": "you subtracted only the gas that stayed a gas — subtract every known substance formed, the condensed one included",
   "check": {
    "expr": "23.7-13.2",
    "expected": 10.5
   },
   "feedback": "This answer is wrong — you subtracted only the gas that stayed a gas — subtract every known substance formed, the condensed one included"
  },
  {
   "value": 18.6,
   "misconception": "you added the known masses formed and stopped — subtract that sum from the starting mass",
   "check": {
    "expr": "5.4+13.2",
    "expected": 18.6
   },
   "feedback": "This answer is wrong — you added the known masses formed and stopped — subtract that sum from the starting mass"
  },
  {
   "value": 42.3,
   "misconception": "you added everything together — the substances formed must total the starting mass, not exceed it",
   "check": {
    "expr": "23.7+5.4+13.2",
    "expected": 42.3
   },
   "feedback": "This answer is wrong — you added everything together — the substances formed must total the starting mass, not exceed it"
  }
 ]
}

[
 "Write down the values in the question:",
 "mass of golden solid = 18.6 g",
 "mass of metal = 14.4 g",
 "Write down the equation:",
 "total mass before = total mass after",
 "In this problem's substances:",
 "mass of metal before + mass of gas before = mass of golden solid after",
 "Make the mass of gas the subject:",
 "mass of gas = mass of golden solid − mass of metal",
 "Substitute in the values, and calculate:",
 "mass of gas = 18.6 − 14.4",
 "mass of gas = 4.2 g"
]

[
 {
  "value": 33.0,
  "misconception": "you added instead of subtracting — the 18.6 g of golden solid is the total after, so the gas is that total minus the metal",
  "feedback": "This answer is wrong — you added instead of subtracting; the 18.6 g of golden solid is the total after, so the gas is that total minus the metal. 18.6 − 14.4 = 4.2 g."
 },
 {
  "value": 18.6,
  "misconception": "you gave the mass of the new substance as the answer — the gas is only part of it",
  "feedback": "This answer is wrong — you gave the mass of the new substance as the answer; the gas is only part of it. The metal's 14.4 g is in there too: 18.6 − 14.4 = 4.2 g."
 },
 {
  "value": 14.4,
  "misconception": "you repeated the metal's mass — the gas's mass is what remains of the total",
  "feedback": "This answer is wrong — you repeated the metal's mass; the gas's mass is what remains of the total. 18.6 − 14.4 = 4.2 g."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of golden solid = 18.6 g\nmass of metal = 14.4 g\nWrite down the equation:\ntotal mass before = total mass after\nIn this problem's substances:\nmass of metal before + mass of gas before = mass of golden solid after\nMake the mass of gas the subject:\nmass of gas = mass of golden solid − mass of metal\nSubstitute in the values, and calculate:\nmass of gas = 18.6 − 14.4\nmass of gas = 4.2 g",
 "anticipatedWrong": [
  {
   "value": 33.0,
   "misconception": "you added instead of subtracting — the 18.6 g of golden solid is the total after, so the gas is that total minus the metal",
   "feedback": "This answer is wrong — you added instead of subtracting; the 18.6 g of golden solid is the total after, so the gas is that total minus the metal. 18.6 − 14.4 = 4.2 g."
  },
  {
   "value": 18.6,
   "misconception": "you gave the mass of the new substance as the answer — the gas is only part of it",
   "feedback": "This answer is wrong — you gave the mass of the new substance as the answer; the gas is only part of it. The metal's 14.4 g is in there too: 18.6 − 14.4 = 4.2 g."
  },
  {
   "value": 14.4,
   "misconception": "you repeated the metal's mass — the gas's mass is what remains of the total",
   "feedback": "This answer is wrong — you repeated the metal's mass; the gas's mass is what remains of the total. 18.6 − 14.4 = 4.2 g."
  }
 ]
}

[
 "Write down the values in the question:",
 "mass of first liquid = 13.6 g",
 "mass of second liquid = 4.9 g",
 "The glow stick is sealed, so the law of conservation of mass applies:",
 "total mass before = total mass after",
 "In this problem's substances:",
 "mass of first liquid + mass of second liquid = total mass after",
 "Substitute in the values, and calculate:",
 "total mass after = 13.6 + 4.9",
 "total mass after = 18.5 g"
]

[
 {
  "value": 4.9,
  "misconception": "you dropped the first liquid's mass from the total — everything sealed inside counts",
  "feedback": "This answer is wrong — you dropped the first liquid's mass from the total; everything sealed inside counts, before and after. The stick holds 13.6 g of one liquid and 4.9 g of the other: 13.6 + 4.9 = 18.5 g."
 },
 {
  "value": 8.7,
  "misconception": "you subtracted the second liquid instead of adding it — both liquids are inside the sealed stick",
  "feedback": "This answer is wrong — you subtracted the second liquid instead of adding it; both liquids are inside the sealed stick. Total mass before = total mass after: 13.6 + 4.9 = 18.5 g."
 },
 {
  "value": 13.6,
  "misconception": "you carried over the first liquid's mass alone — the total covers everything in the stick",
  "feedback": "This answer is wrong — you carried over the first liquid's mass alone; the total covers everything in the stick. The second liquid's 4.9 g counts too: 13.6 + 4.9 = 18.5 g."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of first liquid = 13.6 g\nmass of second liquid = 4.9 g\nThe glow stick is sealed, so the law of conservation of mass applies:\ntotal mass before = total mass after\nIn this problem's substances:\nmass of first liquid + mass of second liquid = total mass after\nSubstitute in the values, and calculate:\ntotal mass after = 13.6 + 4.9\ntotal mass after = 18.5 g\nThe stick gives off light, but light is not matter — the law is about matter, and no matter gets in or out of the sealed stick.",
 "anticipatedWrong": [
  {
   "value": 4.9,
   "misconception": "you dropped the first liquid's mass from the total — everything sealed inside counts",
   "feedback": "This answer is wrong — you dropped the first liquid's mass from the total; everything sealed inside counts, before and after. The stick holds 13.6 g of one liquid and 4.9 g of the other: 13.6 + 4.9 = 18.5 g."
  },
  {
   "value": 8.7,
   "misconception": "you subtracted the second liquid instead of adding it — both liquids are inside the sealed stick",
   "feedback": "This answer is wrong — you subtracted the second liquid instead of adding it; both liquids are inside the sealed stick. Total mass before = total mass after: 13.6 + 4.9 = 18.5 g."
  },
  {
   "value": 13.6,
   "misconception": "you carried over the first liquid's mass alone — the total covers everything in the stick",
   "feedback": "This answer is wrong — you carried over the first liquid's mass alone; the total covers everything in the stick. The second liquid's 4.9 g counts too: 13.6 + 4.9 = 18.5 g."
  }
 ]
}

[
 {
  "value": 5.7,
  "misconception": "you subtracted the masses — both starting substances end up inside the new substance, so add them",
  "feedback": "This answer is wrong — you subtracted the masses — both starting substances end up inside the new substance, so add them"
 },
 {
  "value": 2.3,
  "misconception": "you carried over the sodium's mass alone — the bromine's atoms are in the sodium bromide too",
  "feedback": "This answer is wrong — you carried over the sodium's mass alone — the bromine's atoms are in the sodium bromide too"
 },
 {
  "value": 8.0,
  "misconception": "you carried over the bromine's mass alone — the sodium's atoms are in the sodium bromide too",
  "feedback": "This answer is wrong — you carried over the bromine's mass alone — the sodium's atoms are in the sodium bromide too"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of sodium = 2.3 g\nmass of bromine = 8.0 g\nWrite down the equation:\ntotal mass before = total mass after\nIn this problem's substances:\nmass of sodium before + mass of bromine before = mass of sodium bromide after\nMake the mass of sodium bromide the subject:\nmass of sodium bromide = mass of sodium + mass of bromine\nSubstitute in the values, and calculate:\nmass of sodium bromide = 2.3 + 8.0\nmass of sodium bromide = 10.3 g\nSanity check: the answer must exceed each starting mass, and 10.3 g does.",
 "anticipatedWrong": [
  {
   "value": 5.7,
   "misconception": "you subtracted the masses — both starting substances end up inside the new substance, so add them",
   "check": {
    "expr": "8.0-2.3",
    "expected": 5.7
   },
   "feedback": "This answer is wrong — you subtracted the masses — both starting substances end up inside the new substance, so add them"
  },
  {
   "value": 2.3,
   "misconception": "you carried over the sodium's mass alone — the bromine's atoms are in the sodium bromide too",
   "check": {
    "expr": "2.3",
    "expected": 2.3
   },
   "feedback": "This answer is wrong — you carried over the sodium's mass alone — the bromine's atoms are in the sodium bromide too"
  },
  {
   "value": 8.0,
   "misconception": "you carried over the bromine's mass alone — the sodium's atoms are in the sodium bromide too",
   "check": {
    "expr": "8.0",
    "expected": 8.0
   },
   "feedback": "This answer is wrong — you carried over the bromine's mass alone — the sodium's atoms are in the sodium bromide too"
  }
 ]
}

[
 {
  "value": 2.5,
  "misconception": "you subtracted only the solid — subtract every known substance formed, the condensed liquid included",
  "feedback": "This answer is wrong — you subtracted only the solid — subtract every known substance formed, the condensed liquid included"
 },
 {
  "value": 5.6,
  "misconception": "you added the known masses formed and stopped — subtract that sum from the starting mass",
  "feedback": "This answer is wrong — you added the known masses formed and stopped — subtract that sum from the starting mass"
 },
 {
  "value": 11.9,
  "misconception": "you added everything together — the substances formed must total the starting mass, not exceed it",
  "feedback": "This answer is wrong — you added everything together — the substances formed must total the starting mass, not exceed it"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of ammonium dichromate = 6.3 g\nmass of dark-green solid = 3.8 g\nmass of condensed liquid = 1.8 g\nWrite down the equation:\ntotal mass before = total mass after\nIn this problem's substances:\nmass of ammonium dichromate before = mass of dark-green solid after + mass of condensed liquid after + mass of last gas after\nMake the mass of the last gas the subject:\nmass of last gas = mass of ammonium dichromate − (mass of dark-green solid + mass of condensed liquid)\nSubstitute in the values, and calculate:\nmass of last gas = 6.3 − (3.8 + 1.8)\nmass of last gas = 6.3 − 5.6\nmass of last gas = 0.7 g",
 "anticipatedWrong": [
  {
   "value": 2.5,
   "misconception": "you subtracted only the solid — subtract every known substance formed, the condensed liquid included",
   "check": {
    "expr": "6.3-3.8",
    "expected": 2.5
   },
   "feedback": "This answer is wrong — you subtracted only the solid — subtract every known substance formed, the condensed liquid included"
  },
  {
   "value": 5.6,
   "misconception": "you added the known masses formed and stopped — subtract that sum from the starting mass",
   "check": {
    "expr": "3.8+1.8",
    "expected": 5.6
   },
   "feedback": "This answer is wrong — you added the known masses formed and stopped — subtract that sum from the starting mass"
  },
  {
   "value": 11.9,
   "misconception": "you added everything together — the substances formed must total the starting mass, not exceed it",
   "check": {
    "expr": "6.3+3.8+1.8",
    "expected": 11.9
   },
   "feedback": "This answer is wrong — you added everything together — the substances formed must total the starting mass, not exceed it"
  }
 ]
}

[
 "Write down the values in the question:",
 "mass of red powder = 21.7 g",
 "mass of gas = 1.6 g",
 "Write down the equation:",
 "total mass before = total mass after",
 "In this problem's substances:",
 "mass of metal before + mass of gas before = mass of red powder after",
 "Make the mass of metal the subject:",
 "mass of metal = mass of red powder − mass of gas",
 "Substitute in the values, and calculate:",
 "mass of metal = 21.7 − 1.6",
 "mass of metal = 20.1 g"
]

[
 {
  "value": 23.3,
  "misconception": "you added instead of subtracting — the 21.7 g of red powder is the total after, so the metal is that total minus the gas",
  "feedback": "This answer is wrong — you added instead of subtracting; the 21.7 g of red powder is the total after, so the metal is that total minus the gas. 21.7 − 1.6 = 20.1 g."
 },
 {
  "value": 21.7,
  "misconception": "you gave the mass of the new substance as the answer — the metal is only part of it",
  "feedback": "This answer is wrong — you gave the mass of the new substance as the answer; the metal is only part of it. The gas's 1.6 g is in there too: 21.7 − 1.6 = 20.1 g."
 },
 {
  "value": 1.6,
  "misconception": "you repeated the gas's mass — the metal's mass is what remains of the total",
  "feedback": "This answer is wrong — you repeated the gas's mass; the metal's mass is what remains of the total. 21.7 − 1.6 = 20.1 g."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of red powder = 21.7 g\nmass of gas = 1.6 g\nWrite down the equation:\ntotal mass before = total mass after\nIn this problem's substances:\nmass of metal before + mass of gas before = mass of red powder after\nMake the mass of metal the subject:\nmass of metal = mass of red powder − mass of gas\nSubstitute in the values, and calculate:\nmass of metal = 21.7 − 1.6\nmass of metal = 20.1 g",
 "anticipatedWrong": [
  {
   "value": 23.3,
   "misconception": "you added instead of subtracting — the 21.7 g of red powder is the total after, so the metal is that total minus the gas",
   "feedback": "This answer is wrong — you added instead of subtracting; the 21.7 g of red powder is the total after, so the metal is that total minus the gas. 21.7 − 1.6 = 20.1 g."
  },
  {
   "value": 21.7,
   "misconception": "you gave the mass of the new substance as the answer — the metal is only part of it",
   "feedback": "This answer is wrong — you gave the mass of the new substance as the answer; the metal is only part of it. The gas's 1.6 g is in there too: 21.7 − 1.6 = 20.1 g."
  },
  {
   "value": 1.6,
   "misconception": "you repeated the gas's mass — the metal's mass is what remains of the total",
   "feedback": "This answer is wrong — you repeated the gas's mass; the metal's mass is what remains of the total. 21.7 − 1.6 = 20.1 g."
  }
 ]
}

[
 "Write down the values in the question:",
 "mass of mango pulp = 32.4 g",
 "mass of smoothie = 45.9 g",
 "The pouch is sealed, so the law of conservation of mass applies:",
 "total mass before = total mass after",
 "In this problem's substances:",
 "mass of mango pulp + mass of smoothie = total mass after",
 "Substitute in the values, and calculate:",
 "total mass after = 32.4 + 45.9",
 "total mass after = 78.3 g"
]

[
 {
  "value": 45.9,
  "misconception": "you dropped the frozen pulp's mass from the total — everything sealed inside counts, solid or melted",
  "feedback": "This answer is wrong — you dropped the frozen pulp's mass from the total; everything sealed inside counts, solid or melted. The pouch holds the pulp's 32.4 g and the smoothie's 45.9 g: 32.4 + 45.9 = 78.3 g."
 },
 {
  "value": 13.5,
  "misconception": "you subtracted the pulp's mass instead of adding it — both foods are inside the sealed pouch",
  "feedback": "This answer is wrong — you subtracted the pulp's mass instead of adding it; both foods are inside the sealed pouch. Total mass before = total mass after: 32.4 + 45.9 = 78.3 g."
 },
 {
  "value": 32.4,
  "misconception": "you carried over the pulp's mass alone — the total covers everything in the pouch",
  "feedback": "This answer is wrong — you carried over the pulp's mass alone; the total covers everything in the pouch. The smoothie's 45.9 g counts too: 32.4 + 45.9 = 78.3 g."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of mango pulp = 32.4 g\nmass of smoothie = 45.9 g\nThe pouch is sealed, so the law of conservation of mass applies:\ntotal mass before = total mass after\nIn this problem's substances:\nmass of mango pulp + mass of smoothie = total mass after\nSubstitute in the values, and calculate:\ntotal mass after = 32.4 + 45.9\ntotal mass after = 78.3 g\nMelting is a physical change, and the law covers any physical or chemical change — sealed in, the total cannot change.",
 "anticipatedWrong": [
  {
   "value": 45.9,
   "misconception": "you dropped the frozen pulp's mass from the total — everything sealed inside counts, solid or melted",
   "feedback": "This answer is wrong — you dropped the frozen pulp's mass from the total; everything sealed inside counts, solid or melted. The pouch holds the pulp's 32.4 g and the smoothie's 45.9 g: 32.4 + 45.9 = 78.3 g."
  },
  {
   "value": 13.5,
   "misconception": "you subtracted the pulp's mass instead of adding it — both foods are inside the sealed pouch",
   "feedback": "This answer is wrong — you subtracted the pulp's mass instead of adding it; both foods are inside the sealed pouch. Total mass before = total mass after: 32.4 + 45.9 = 78.3 g."
  },
  {
   "value": 32.4,
   "misconception": "you carried over the pulp's mass alone — the total covers everything in the pouch",
   "feedback": "This answer is wrong — you carried over the pulp's mass alone; the total covers everything in the pouch. The smoothie's 45.9 g counts too: 32.4 + 45.9 = 78.3 g."
  }
 ]
}

[
 {
  "value": 9.5,
  "misconception": "you subtracted the masses — both starting substances end up inside the new substance, so add them",
  "feedback": "This answer is wrong — you subtracted the masses — both starting substances end up inside the new substance, so add them"
 },
 {
  "value": 2.9,
  "misconception": "you carried over the tin's mass alone — the iodine's atoms are in the tin iodide too",
  "feedback": "This answer is wrong — you carried over the tin's mass alone — the iodine's atoms are in the tin iodide too"
 },
 {
  "value": 12.4,
  "misconception": "you carried over the iodine's mass alone — the tin's atoms are in the tin iodide too",
  "feedback": "This answer is wrong — you carried over the iodine's mass alone — the tin's atoms are in the tin iodide too"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of tin = 2.9 g\nmass of iodine = 12.4 g\nWrite down the equation:\ntotal mass before = total mass after\nIn this problem's substances:\nmass of tin before + mass of iodine before = mass of tin iodide after\nMake the mass of tin iodide the subject:\nmass of tin iodide = mass of tin + mass of iodine\nSubstitute in the values, and calculate:\nmass of tin iodide = 2.9 + 12.4\nmass of tin iodide = 15.3 g\nSanity check: the answer must exceed each starting mass, and 15.3 g does.",
 "anticipatedWrong": [
  {
   "value": 9.5,
   "misconception": "you subtracted the masses — both starting substances end up inside the new substance, so add them",
   "check": {
    "expr": "12.4-2.9",
    "expected": 9.5
   },
   "feedback": "This answer is wrong — you subtracted the masses — both starting substances end up inside the new substance, so add them"
  },
  {
   "value": 2.9,
   "misconception": "you carried over the tin's mass alone — the iodine's atoms are in the tin iodide too",
   "check": {
    "expr": "2.9",
    "expected": 2.9
   },
   "feedback": "This answer is wrong — you carried over the tin's mass alone — the iodine's atoms are in the tin iodide too"
  },
  {
   "value": 12.4,
   "misconception": "you carried over the iodine's mass alone — the tin's atoms are in the tin iodide too",
   "check": {
    "expr": "12.4",
    "expected": 12.4
   },
   "feedback": "This answer is wrong — you carried over the iodine's mass alone — the tin's atoms are in the tin iodide too"
  }
 ]
}

[
 {
  "value": 15.2,
  "misconception": "you subtracted only the lighter gas — subtract every known substance formed, the heavier gas included",
  "feedback": "This answer is wrong — you subtracted only the lighter gas — subtract every known substance formed, the heavier gas included"
 },
 {
  "value": 9.5,
  "misconception": "you added the two known masses and stopped — subtract that sum from the starting mass",
  "feedback": "This answer is wrong — you added the two known masses and stopped — subtract that sum from the starting mass"
 },
 {
  "value": 28.4,
  "misconception": "you added everything together — the substances formed must total the starting mass, not exceed it",
  "feedback": "This answer is wrong — you added everything together — the substances formed must total the starting mass, not exceed it"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of manganese oxalate = 18.9 g\nmass of first gas = 3.7 g\nmass of second gas = 5.8 g\nWrite down the equation:\ntotal mass before = total mass after\nIn this problem's substances:\nmass of manganese oxalate before = mass of pale-green solid after + mass of first gas after + mass of second gas after\nMake the mass of the pale-green solid the subject:\nmass of pale-green solid = mass of manganese oxalate − (mass of first gas + mass of second gas)\nSubstitute in the values, and calculate:\nmass of pale-green solid = 18.9 − (3.7 + 5.8)\nmass of pale-green solid = 18.9 − 9.5\nmass of pale-green solid = 9.4 g",
 "anticipatedWrong": [
  {
   "value": 15.2,
   "misconception": "you subtracted only the lighter gas — subtract every known substance formed, the heavier gas included",
   "check": {
    "expr": "18.9-3.7",
    "expected": 15.2
   },
   "feedback": "This answer is wrong — you subtracted only the lighter gas — subtract every known substance formed, the heavier gas included"
  },
  {
   "value": 9.5,
   "misconception": "you added the two known masses and stopped — subtract that sum from the starting mass",
   "check": {
    "expr": "3.7+5.8",
    "expected": 9.5
   },
   "feedback": "This answer is wrong — you added the two known masses and stopped — subtract that sum from the starting mass"
  },
  {
   "value": 28.4,
   "misconception": "you added everything together — the substances formed must total the starting mass, not exceed it",
   "check": {
    "expr": "18.9+3.7+5.8",
    "expected": 28.4
   },
   "feedback": "This answer is wrong — you added everything together — the substances formed must total the starting mass, not exceed it"
  }
 ]
}

[
 "Write down the values in the question:",
 "mass of white solid = 10.7 g",
 "mass of the known gas = 3.4 g",
 "Write down the equation:",
 "total mass before = total mass after",
 "In this problem's substances:",
 "mass of the known gas before + mass of the other gas before = mass of white solid after",
 "Make the mass of the other gas the subject:",
 "mass of the other gas = mass of white solid − mass of the known gas",
 "Substitute in the values, and calculate:",
 "mass of the other gas = 10.7 − 3.4",
 "mass of the other gas = 7.3 g"
]

[
 {
  "value": 14.1,
  "misconception": "you added instead of subtracting — the 10.7 g of white solid is the total after, so the other gas is that total minus the known gas",
  "feedback": "This answer is wrong — you added instead of subtracting; the 10.7 g of white solid is the total after, so the other gas is that total minus the known gas. 10.7 − 3.4 = 7.3 g."
 },
 {
  "value": 10.7,
  "misconception": "you gave the mass of the new substance as the answer — the other gas is only part of it",
  "feedback": "This answer is wrong — you gave the mass of the new substance as the answer; the other gas is only part of it. The known gas's 3.4 g is in there too: 10.7 − 3.4 = 7.3 g."
 },
 {
  "value": 3.4,
  "misconception": "you repeated the known gas's mass — the other gas's mass is what remains of the total",
  "feedback": "This answer is wrong — you repeated the known gas's mass; the other gas's mass is what remains of the total. 10.7 − 3.4 = 7.3 g."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of white solid = 10.7 g\nmass of the known gas = 3.4 g\nWrite down the equation:\ntotal mass before = total mass after\nIn this problem's substances:\nmass of the known gas before + mass of the other gas before = mass of white solid after\nMake the mass of the other gas the subject:\nmass of the other gas = mass of white solid − mass of the known gas\nSubstitute in the values, and calculate:\nmass of the other gas = 10.7 − 3.4\nmass of the other gas = 7.3 g",
 "anticipatedWrong": [
  {
   "value": 14.1,
   "misconception": "you added instead of subtracting — the 10.7 g of white solid is the total after, so the other gas is that total minus the known gas",
   "feedback": "This answer is wrong — you added instead of subtracting; the 10.7 g of white solid is the total after, so the other gas is that total minus the known gas. 10.7 − 3.4 = 7.3 g."
  },
  {
   "value": 10.7,
   "misconception": "you gave the mass of the new substance as the answer — the other gas is only part of it",
   "feedback": "This answer is wrong — you gave the mass of the new substance as the answer; the other gas is only part of it. The known gas's 3.4 g is in there too: 10.7 − 3.4 = 7.3 g."
  },
  {
   "value": 3.4,
   "misconception": "you repeated the known gas's mass — the other gas's mass is what remains of the total",
   "feedback": "This answer is wrong — you repeated the known gas's mass; the other gas's mass is what remains of the total. 10.7 − 3.4 = 7.3 g."
  }
 ]
}

[
 "Write down the values in the question:",
 "mass of base paste = 28.4 g",
 "mass of hardener = 13.1 g",
 "The bag is sealed, so the law of conservation of mass applies:",
 "total mass before = total mass after",
 "In this problem's substances:",
 "mass of base paste + mass of hardener = total mass after",
 "Substitute in the values, and calculate:",
 "total mass after = 28.4 + 13.1",
 "total mass after = 41.5 g"
]

[
 {
  "value": 13.1,
  "misconception": "you dropped the base paste's mass from the total — everything sealed inside counts",
  "feedback": "This answer is wrong — you dropped the base paste's mass from the total; everything sealed inside counts, before and after. The bag holds the base paste's 28.4 g and the hardener's 13.1 g: 28.4 + 13.1 = 41.5 g."
 },
 {
  "value": 15.3,
  "misconception": "you subtracted the hardener instead of adding it — both pastes are inside the sealed bag",
  "feedback": "This answer is wrong — you subtracted the hardener instead of adding it; both pastes are inside the sealed bag. Total mass before = total mass after: 28.4 + 13.1 = 41.5 g."
 },
 {
  "value": 28.4,
  "misconception": "you carried over the base paste's mass alone — the total covers everything in the bag",
  "feedback": "This answer is wrong — you carried over the base paste's mass alone; the total covers everything in the bag. The hardener's 13.1 g counts too: 28.4 + 13.1 = 41.5 g."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of base paste = 28.4 g\nmass of hardener = 13.1 g\nThe bag is sealed, so the law of conservation of mass applies:\ntotal mass before = total mass after\nIn this problem's substances:\nmass of base paste + mass of hardener = total mass after\nSubstitute in the values, and calculate:\ntotal mass after = 28.4 + 13.1\ntotal mass after = 41.5 g\nSetting hard is a chemical change — the new substance is made entirely from the matter already sealed inside, so the total cannot change.",
 "anticipatedWrong": [
  {
   "value": 13.1,
   "misconception": "you dropped the base paste's mass from the total — everything sealed inside counts",
   "feedback": "This answer is wrong — you dropped the base paste's mass from the total; everything sealed inside counts, before and after. The bag holds the base paste's 28.4 g and the hardener's 13.1 g: 28.4 + 13.1 = 41.5 g."
  },
  {
   "value": 15.3,
   "misconception": "you subtracted the hardener instead of adding it — both pastes are inside the sealed bag",
   "feedback": "This answer is wrong — you subtracted the hardener instead of adding it; both pastes are inside the sealed bag. Total mass before = total mass after: 28.4 + 13.1 = 41.5 g."
  },
  {
   "value": 28.4,
   "misconception": "you carried over the base paste's mass alone — the total covers everything in the bag",
   "feedback": "This answer is wrong — you carried over the base paste's mass alone; the total covers everything in the bag. The hardener's 13.1 g counts too: 28.4 + 13.1 = 41.5 g."
  }
 ]
}

[
 {
  "value": 2.5,
  "misconception": "you subtracted the masses — both starting substances end up inside the new substance, so add them",
  "feedback": "This answer is wrong — you subtracted the masses — both starting substances end up inside the new substance, so add them"
 },
 {
  "value": 1.4,
  "misconception": "you carried over the lithium's mass alone — the fluorine's atoms are in the lithium fluoride too",
  "feedback": "This answer is wrong — you carried over the lithium's mass alone — the fluorine's atoms are in the lithium fluoride too"
 },
 {
  "value": 3.9,
  "misconception": "you carried over the fluorine's mass alone — the lithium's atoms are in the lithium fluoride too",
  "feedback": "This answer is wrong — you carried over the fluorine's mass alone — the lithium's atoms are in the lithium fluoride too"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of lithium = 1.4 g\nmass of fluorine = 3.9 g\nWrite down the equation:\ntotal mass before = total mass after\nIn this problem's substances:\nmass of lithium before + mass of fluorine before = mass of lithium fluoride after\nMake the mass of lithium fluoride the subject:\nmass of lithium fluoride = mass of lithium + mass of fluorine\nSubstitute in the values, and calculate:\nmass of lithium fluoride = 1.4 + 3.9\nmass of lithium fluoride = 5.3 g\nSanity check: the answer must exceed each starting mass, and 5.3 g does.",
 "anticipatedWrong": [
  {
   "value": 2.5,
   "misconception": "you subtracted the masses — both starting substances end up inside the new substance, so add them",
   "check": {
    "expr": "3.9-1.4",
    "expected": 2.5
   },
   "feedback": "This answer is wrong — you subtracted the masses — both starting substances end up inside the new substance, so add them"
  },
  {
   "value": 1.4,
   "misconception": "you carried over the lithium's mass alone — the fluorine's atoms are in the lithium fluoride too",
   "check": {
    "expr": "1.4",
    "expected": 1.4
   },
   "feedback": "This answer is wrong — you carried over the lithium's mass alone — the fluorine's atoms are in the lithium fluoride too"
  },
  {
   "value": 3.9,
   "misconception": "you carried over the fluorine's mass alone — the lithium's atoms are in the lithium fluoride too",
   "check": {
    "expr": "3.9",
    "expected": 3.9
   },
   "feedback": "This answer is wrong — you carried over the fluorine's mass alone — the lithium's atoms are in the lithium fluoride too"
  }
 ]
}

[
 {
  "value": 13.0,
  "misconception": "you subtracted only the lighter gas — subtract every known substance formed, the heavier gas included",
  "feedback": "This answer is wrong — you subtracted only the lighter gas — subtract every known substance formed, the heavier gas included"
 },
 {
  "value": 7.9,
  "misconception": "you added the two known masses and stopped — subtract that sum from the starting mass",
  "feedback": "This answer is wrong — you added the two known masses and stopped — subtract that sum from the starting mass"
 },
 {
  "value": 24.0,
  "misconception": "you added everything together — the substances formed must total the starting mass, not exceed it",
  "feedback": "This answer is wrong — you added everything together — the substances formed must total the starting mass, not exceed it"
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of cobalt oxalate = 16.1 g\nmass of first gas = 3.1 g\nmass of second gas = 4.8 g\nWrite down the equation:\ntotal mass before = total mass after\nIn this problem's substances:\nmass of cobalt oxalate before = mass of gray solid after + mass of first gas after + mass of second gas after\nMake the mass of the gray solid the subject:\nmass of gray solid = mass of cobalt oxalate − (mass of first gas + mass of second gas)\nSubstitute in the values, and calculate:\nmass of gray solid = 16.1 − (3.1 + 4.8)\nmass of gray solid = 16.1 − 7.9\nmass of gray solid = 8.2 g",
 "anticipatedWrong": [
  {
   "value": 13.0,
   "misconception": "you subtracted only the lighter gas — subtract every known substance formed, the heavier gas included",
   "check": {
    "expr": "16.1-3.1",
    "expected": 13.0
   },
   "feedback": "This answer is wrong — you subtracted only the lighter gas — subtract every known substance formed, the heavier gas included"
  },
  {
   "value": 7.9,
   "misconception": "you added the two known masses and stopped — subtract that sum from the starting mass",
   "check": {
    "expr": "3.1+4.8",
    "expected": 7.9
   },
   "feedback": "This answer is wrong — you added the two known masses and stopped — subtract that sum from the starting mass"
  },
  {
   "value": 24.0,
   "misconception": "you added everything together — the substances formed must total the starting mass, not exceed it",
   "check": {
    "expr": "16.1+3.1+4.8",
    "expected": 24.0
   },
   "feedback": "This answer is wrong — you added everything together — the substances formed must total the starting mass, not exceed it"
  }
 ]
}

[
 "Write down the values in the question:",
 "mass of oily liquid = 17.3 g",
 "mass of gas = 2.6 g",
 "Write down the equation:",
 "total mass before = total mass after",
 "In this problem's substances:",
 "mass of red-brown liquid before + mass of gas before = mass of oily liquid after",
 "Make the mass of red-brown liquid the subject:",
 "mass of red-brown liquid = mass of oily liquid − mass of gas",
 "Substitute in the values, and calculate:",
 "mass of red-brown liquid = 17.3 − 2.6",
 "mass of red-brown liquid = 14.7 g"
]

[
 {
  "value": 19.9,
  "misconception": "you added instead of subtracting — the 17.3 g of oily liquid is the total after, so the red-brown liquid is that total minus the gas",
  "feedback": "This answer is wrong — you added instead of subtracting; the 17.3 g of oily liquid is the total after, so the red-brown liquid is that total minus the gas. 17.3 − 2.6 = 14.7 g."
 },
 {
  "value": 17.3,
  "misconception": "you gave the mass of the new substance as the answer — the red-brown liquid is only part of it",
  "feedback": "This answer is wrong — you gave the mass of the new substance as the answer; the red-brown liquid is only part of it. The gas's 2.6 g is in there too: 17.3 − 2.6 = 14.7 g."
 },
 {
  "value": 2.6,
  "misconception": "you repeated the gas's mass — the red-brown liquid's mass is what remains of the total",
  "feedback": "This answer is wrong — you repeated the gas's mass; the red-brown liquid's mass is what remains of the total. 17.3 − 2.6 = 14.7 g."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass of oily liquid = 17.3 g\nmass of gas = 2.6 g\nWrite down the equation:\ntotal mass before = total mass after\nIn this problem's substances:\nmass of red-brown liquid before + mass of gas before = mass of oily liquid after\nMake the mass of red-brown liquid the subject:\nmass of red-brown liquid = mass of oily liquid − mass of gas\nSubstitute in the values, and calculate:\nmass of red-brown liquid = 17.3 − 2.6\nmass of red-brown liquid = 14.7 g",
 "anticipatedWrong": [
  {
   "value": 19.9,
   "misconception": "you added instead of subtracting — the 17.3 g of oily liquid is the total after, so the red-brown liquid is that total minus the gas",
   "feedback": "This answer is wrong — you added instead of subtracting; the 17.3 g of oily liquid is the total after, so the red-brown liquid is that total minus the gas. 17.3 − 2.6 = 14.7 g."
  },
  {
   "value": 17.3,
   "misconception": "you gave the mass of the new substance as the answer — the red-brown liquid is only part of it",
   "feedback": "This answer is wrong — you gave the mass of the new substance as the answer; the red-brown liquid is only part of it. The gas's 2.6 g is in there too: 17.3 − 2.6 = 14.7 g."
  },
  {
   "value": 2.6,
   "misconception": "you repeated the gas's mass — the red-brown liquid's mass is what remains of the total",
   "feedback": "This answer is wrong — you repeated the gas's mass; the red-brown liquid's mass is what remains of the total. 17.3 − 2.6 = 14.7 g."
  }
 ]
}