Unit 10 — End of Topic Tests (reviewer copy: all keys and model answers visible)

[
 {
  "value": "LiNO₃(l)",
  "misconception": "you used the pure-liquid symbol — (l) means melted lithium nitrate; dissolved in water is (aq)",
  "feedback": "This answer is wrong — you used the pure-liquid symbol — (l) means melted lithium nitrate; dissolved in water is (aq)"
 },
 {
  "value": "LiNO₃(s)",
  "misconception": "you used the solid symbol — (s) means undissolved solid lithium nitrate; dissolved in water is (aq)",
  "feedback": "This answer is wrong — you used the solid symbol — (s) means undissolved solid lithium nitrate; dissolved in water is (aq)"
 },
 {
  "value": "H₂O(aq)",
  "misconception": "you attached the label to the water — the (aq) follows the solute's formula, not the solvent's",
  "feedback": "This answer is wrong — you attached the label to the water — the (aq) follows the solute's formula, not the solvent's"
 }
]

{
 "keyExplanation": "The solute's formula comes first, and (aq) after it marks the substance as dissolved in water: LiNO₃(aq). The (aq) always belongs to the dissolved substance — the water, as the solvent, never takes the label.",
 "anticipatedWrong": [
  {
   "value": "LiNO₃(l)",
   "misconception": "you used the pure-liquid symbol — (l) means melted lithium nitrate; dissolved in water is (aq)",
   "feedback": "This answer is wrong — you used the pure-liquid symbol — (l) means melted lithium nitrate; dissolved in water is (aq)"
  },
  {
   "value": "LiNO₃(s)",
   "misconception": "you used the solid symbol — (s) means undissolved solid lithium nitrate; dissolved in water is (aq)",
   "feedback": "This answer is wrong — you used the solid symbol — (s) means undissolved solid lithium nitrate; dissolved in water is (aq)"
  },
  {
   "value": "H₂O(aq)",
   "misconception": "you attached the label to the water — the (aq) follows the solute's formula, not the solvent's",
   "feedback": "This answer is wrong — you attached the label to the water — the (aq) follows the solute's formula, not the solvent's"
  }
 ]
}

[
 {
  "value": "Ba(NO₃)₂(l)",
  "misconception": "you used the pure-liquid symbol — (l) means melted barium nitrate; dissolved in water is (aq)",
  "feedback": "This answer is wrong — you used the pure-liquid symbol — (l) means melted barium nitrate; dissolved in water is (aq)"
 },
 {
  "value": "Ba(NO₃)₂(s)",
  "misconception": "you used the solid symbol — (s) means undissolved solid barium nitrate; dissolved in water is (aq)",
  "feedback": "This answer is wrong — you used the solid symbol — (s) means undissolved solid barium nitrate; dissolved in water is (aq)"
 },
 {
  "value": "H₂O(aq)",
  "misconception": "you attached the label to the water — the (aq) follows the solute's formula, not the solvent's",
  "feedback": "This answer is wrong — you attached the label to the water — the (aq) follows the solute's formula, not the solvent's"
 }
]

{
 "keyExplanation": "The solute's formula comes first, and (aq) after it marks the substance as dissolved in water: Ba(NO₃)₂(aq). The (aq) always belongs to the dissolved substance — the water, as the solvent, never takes the label.",
 "anticipatedWrong": [
  {
   "value": "Ba(NO₃)₂(l)",
   "misconception": "you used the pure-liquid symbol — (l) means melted barium nitrate; dissolved in water is (aq)",
   "feedback": "This answer is wrong — you used the pure-liquid symbol — (l) means melted barium nitrate; dissolved in water is (aq)"
  },
  {
   "value": "Ba(NO₃)₂(s)",
   "misconception": "you used the solid symbol — (s) means undissolved solid barium nitrate; dissolved in water is (aq)",
   "feedback": "This answer is wrong — you used the solid symbol — (s) means undissolved solid barium nitrate; dissolved in water is (aq)"
  },
  {
   "value": "H₂O(aq)",
   "misconception": "you attached the label to the water — the (aq) follows the solute's formula, not the solvent's",
   "feedback": "This answer is wrong — you attached the label to the water — the (aq) follows the solute's formula, not the solvent's"
  }
 ]
}

[
 {
  "value": "K₂SO₄(l)",
  "misconception": "you used the pure-liquid symbol — (l) means melted potassium sulfate; dissolved in water is (aq)",
  "feedback": "This answer is wrong — you used the pure-liquid symbol — (l) means melted potassium sulfate; dissolved in water is (aq)"
 },
 {
  "value": "K₂SO₄(s)",
  "misconception": "you used the solid symbol — (s) means undissolved solid potassium sulfate; dissolved in water is (aq)",
  "feedback": "This answer is wrong — you used the solid symbol — (s) means undissolved solid potassium sulfate; dissolved in water is (aq)"
 },
 {
  "value": "H₂O(aq)",
  "misconception": "you attached the label to the water — the (aq) follows the solute's formula, not the solvent's",
  "feedback": "This answer is wrong — you attached the label to the water — the (aq) follows the solute's formula, not the solvent's"
 }
]

{
 "keyExplanation": "The solute's formula comes first, and (aq) after it marks the substance as dissolved in water: K₂SO₄(aq). The (aq) always belongs to the dissolved substance — the water, as the solvent, never takes the label.",
 "anticipatedWrong": [
  {
   "value": "K₂SO₄(l)",
   "misconception": "you used the pure-liquid symbol — (l) means melted potassium sulfate; dissolved in water is (aq)",
   "feedback": "This answer is wrong — you used the pure-liquid symbol — (l) means melted potassium sulfate; dissolved in water is (aq)"
  },
  {
   "value": "K₂SO₄(s)",
   "misconception": "you used the solid symbol — (s) means undissolved solid potassium sulfate; dissolved in water is (aq)",
   "feedback": "This answer is wrong — you used the solid symbol — (s) means undissolved solid potassium sulfate; dissolved in water is (aq)"
  },
  {
   "value": "H₂O(aq)",
   "misconception": "you attached the label to the water — the (aq) follows the solute's formula, not the solvent's",
   "feedback": "This answer is wrong — you attached the label to the water — the (aq) follows the solute's formula, not the solvent's"
  }
 ]
}

[
 {
  "value": "CsNO₃(l)",
  "misconception": "you used the pure-liquid symbol — (l) means melted cesium nitrate; dissolved in water is (aq)",
  "feedback": "This answer is wrong — you used the pure-liquid symbol — (l) means melted cesium nitrate; dissolved in water is (aq)"
 },
 {
  "value": "CsNO₃(s)",
  "misconception": "you used the solid symbol — (s) means undissolved solid cesium nitrate; dissolved in water is (aq)",
  "feedback": "This answer is wrong — you used the solid symbol — (s) means undissolved solid cesium nitrate; dissolved in water is (aq)"
 },
 {
  "value": "H₂O(aq)",
  "misconception": "you attached the label to the water — the (aq) follows the solute's formula, not the solvent's",
  "feedback": "This answer is wrong — you attached the label to the water — the (aq) follows the solute's formula, not the solvent's"
 }
]

{
 "keyExplanation": "The solute's formula comes first, and (aq) after it marks the substance as dissolved in water: CsNO₃(aq). The (aq) always belongs to the dissolved substance — the water, as the solvent, never takes the label.",
 "anticipatedWrong": [
  {
   "value": "CsNO₃(l)",
   "misconception": "you used the pure-liquid symbol — (l) means melted cesium nitrate; dissolved in water is (aq)",
   "feedback": "This answer is wrong — you used the pure-liquid symbol — (l) means melted cesium nitrate; dissolved in water is (aq)"
  },
  {
   "value": "CsNO₃(s)",
   "misconception": "you used the solid symbol — (s) means undissolved solid cesium nitrate; dissolved in water is (aq)",
   "feedback": "This answer is wrong — you used the solid symbol — (s) means undissolved solid cesium nitrate; dissolved in water is (aq)"
  },
  {
   "value": "H₂O(aq)",
   "misconception": "you attached the label to the water — the (aq) follows the solute's formula, not the solvent's",
   "feedback": "This answer is wrong — you attached the label to the water — the (aq) follows the solute's formula, not the solvent's"
  }
 ]
}

[
 {
  "value": "FeCl₃(l)",
  "misconception": "you used the pure-liquid symbol — (l) means melted iron(iii) chloride; dissolved in water is (aq)",
  "feedback": "This answer is wrong — you used the pure-liquid symbol — (l) means melted iron(iii) chloride; dissolved in water is (aq)"
 },
 {
  "value": "FeCl₃(s)",
  "misconception": "you used the solid symbol — (s) means undissolved solid iron(iii) chloride; dissolved in water is (aq)",
  "feedback": "This answer is wrong — you used the solid symbol — (s) means undissolved solid iron(iii) chloride; dissolved in water is (aq)"
 },
 {
  "value": "H₂O(aq)",
  "misconception": "you attached the label to the water — the (aq) follows the solute's formula, not the solvent's",
  "feedback": "This answer is wrong — you attached the label to the water — the (aq) follows the solute's formula, not the solvent's"
 }
]

{
 "keyExplanation": "The solute's formula comes first, and (aq) after it marks the substance as dissolved in water: FeCl₃(aq). The (aq) always belongs to the dissolved substance — the water, as the solvent, never takes the label.",
 "anticipatedWrong": [
  {
   "value": "FeCl₃(l)",
   "misconception": "you used the pure-liquid symbol — (l) means melted iron(iii) chloride; dissolved in water is (aq)",
   "feedback": "This answer is wrong — you used the pure-liquid symbol — (l) means melted iron(iii) chloride; dissolved in water is (aq)"
  },
  {
   "value": "FeCl₃(s)",
   "misconception": "you used the solid symbol — (s) means undissolved solid iron(iii) chloride; dissolved in water is (aq)",
   "feedback": "This answer is wrong — you used the solid symbol — (s) means undissolved solid iron(iii) chloride; dissolved in water is (aq)"
  },
  {
   "value": "H₂O(aq)",
   "misconception": "you attached the label to the water — the (aq) follows the solute's formula, not the solvent's",
   "feedback": "This answer is wrong — you attached the label to the water — the (aq) follows the solute's formula, not the solvent's"
  }
 ]
}

[
 {
  "value": 110,
  "misconception": "you read the KNO₃ curve instead of the NaCl curve",
  "feedback": "This answer is wrong — you read the KNO₃ curve instead of the NaCl curve."
 },
 {
  "value": 24,
  "misconception": "you read the KClO₃ curve instead of the NaCl curve",
  "feedback": "This answer is wrong — you read the KClO₃ curve instead of the NaCl curve."
 }
]

{
 "keyExplanation": "Pick the labeled NaCl curve first, then read it: find 60 °C on the bottom axis, go straight up to the NaCl curve, then straight across — the side axis reads 37. The solubility of NaCl at 60 °C is 37 g per 100 g of water. The steep curve belongs to KNO₃ and the low curve to KClO₃; reading either gives a different substance's solubility."
}

[
 {
  "value": 202,
  "misconception": "you added the two curve readings instead of subtracting them",
  "feedback": "This answer is wrong — you added the two curve readings instead of subtracting them."
 },
 {
  "value": 30,
  "misconception": "you subtracted the temperatures instead of the solubilities",
  "feedback": "This answer is wrong — you subtracted the temperatures instead of the solubilities."
 },
 {
  "value": 64,
  "misconception": "you gave the cap at the cooler temperature instead of the difference between the caps",
  "feedback": "This answer is wrong — you gave the cap at the cooler temperature instead of the difference between the caps."
 }
]

{
 "keyExplanation": "A saturated solution holds exactly the cap at its temperature.\nRead the two caps from the curve:\nsolubility at 70 °C = 138 g per 100 g of water\nsolubility at 40 °C = 64 g per 100 g of water\nWrite down the equation:\nmass that crystallizes = solubility at the warmer temperature − solubility at the cooler temperature\nSubstitute in the values, and calculate:\nmass that crystallizes = 138 − 64\nmass that crystallizes = 74 g of KNO₃"
}

[
 {
  "value": 43,
  "misconception": "you read the KCl curve instead of the KBr curve",
  "feedback": "This answer is wrong — you read the KCl curve instead of the KBr curve."
 },
 {
  "value": 76,
  "misconception": "you read the KBr curve at 40 °C instead of 50 °C",
  "feedback": "This answer is wrong — you read the KBr curve at 40 °C instead of 50 °C."
 }
]

{
 "keyExplanation": "Pick the labeled KBr curve — the upper one — then read it: find 50 °C on the bottom axis, go straight up to the KBr curve, then straight across. The side axis reads 81, so the solubility of KBr at 50 °C is 81 g per 100 g of water."
}

[
 {
  "value": 90,
  "misconception": "you read the KBr curve instead of the KNO₃ curve",
  "feedback": "This answer is wrong — you read the KBr curve instead of the KNO₃ curve."
 },
 {
  "value": 64,
  "misconception": "you read the KNO₃ curve at 40 °C instead of 70 °C",
  "feedback": "This answer is wrong — you read the KNO₃ curve at 40 °C instead of 70 °C."
 }
]

{
 "keyExplanation": "Pick the labeled KNO₃ curve — the steeply climbing one — then read it: find 70 °C on the bottom axis, go straight up to the KNO₃ curve, then straight across. The side axis reads 138, so the solubility of KNO₃ at 70 °C is 138 g per 100 g of water."
}

[
 {
  "value": 204,
  "misconception": "you added the two curve readings instead of subtracting them",
  "feedback": "This answer is wrong — you added the two curve readings instead of subtracting them."
 },
 {
  "value": 50,
  "misconception": "you subtracted the temperatures instead of the solubilities",
  "feedback": "This answer is wrong — you subtracted the temperatures instead of the solubilities."
 },
 {
  "value": 124,
  "misconception": "you gave the new cap instead of the extra room the warming opened up",
  "feedback": "This answer is wrong — you gave the new cap instead of the extra room the warming opened up."
 }
]

{
 "keyExplanation": "A saturated solution holds exactly the cap at its temperature, and warming raises the cap.\nRead the two caps from the curve:\nsolubility at 60 °C = 124 g per 100 g of water\nsolubility at 10 °C = 80 g per 100 g of water\nWrite down the equation:\nextra mass that can dissolve = solubility at the warmer temperature − solubility at the cooler temperature\nSubstitute in the values, and calculate:\nextra mass that can dissolve = 124 − 80\nextra mass that can dissolve = 44 g of NaNO₃"
}

[
 {
  "value": 37,
  "misconception": "you read the NaCl curve instead of the NH₄Cl curve",
  "feedback": "This answer is wrong — you read the NaCl curve instead of the NH₄Cl curve."
 },
 {
  "value": 50,
  "misconception": "you read the NH₄Cl curve at 50 °C instead of 40 °C",
  "feedback": "This answer is wrong — you read the NH₄Cl curve at 50 °C instead of 40 °C."
 }
]

{
 "keyExplanation": "Pick the labeled NH₄Cl curve — the climbing one — then read it: find 40 °C on the bottom axis, go straight up to the NH₄Cl curve, then straight across. The side axis reads 46, so the solubility of NH₄Cl at 40 °C is 46 g per 100 g of water."
}

[
 {
  "value": 43,
  "misconception": "you read the KCl curve instead of the NaNO₃ curve",
  "feedback": "This answer is wrong — you read the KCl curve instead of the NaNO₃ curve."
 },
 {
  "value": 104,
  "misconception": "you read the NaNO₃ curve at 40 °C instead of 50 °C",
  "feedback": "This answer is wrong — you read the NaNO₃ curve at 40 °C instead of 50 °C."
 }
]

{
 "keyExplanation": "Pick the labeled NaNO₃ curve — the upper one — then read it: find 50 °C on the bottom axis, go straight up to the NaNO₃ curve, then straight across. The side axis reads 114, so the solubility of NaNO₃ at 50 °C is 114 g per 100 g of water."
}

[
 {
  "value": 85,
  "misconception": "you added the two curve readings instead of subtracting them",
  "feedback": "This answer is wrong — you added the two curve readings instead of subtracting them."
 },
 {
  "value": 40,
  "misconception": "you subtracted the temperatures instead of the solubilities",
  "feedback": "This answer is wrong — you subtracted the temperatures instead of the solubilities."
 },
 {
  "value": 48,
  "misconception": "you gave the new cap instead of the extra room the warming opened up",
  "feedback": "This answer is wrong — you gave the new cap instead of the extra room the warming opened up."
 }
]

{
 "keyExplanation": "A saturated solution holds exactly the cap at its temperature, and warming raises the cap.\nRead the two caps from the curve:\nsolubility at 70 °C = 48 g per 100 g of water\nsolubility at 30 °C = 37 g per 100 g of water\nWrite down the equation:\nextra mass that can dissolve = solubility at the warmer temperature − solubility at the cooler temperature\nSubstitute in the values, and calculate:\nextra mass that can dissolve = 48 − 37\nextra mass that can dissolve = 11 g of KCl"
}

[
 {
  "value": 37,
  "misconception": "you read the NaCl curve instead of the KBr curve",
  "feedback": "This answer is wrong — you read the NaCl curve instead of the KBr curve."
 },
 {
  "value": 81,
  "misconception": "you read the KBr curve at 50 °C instead of 40 °C",
  "feedback": "This answer is wrong — you read the KBr curve at 50 °C instead of 40 °C."
 }
]

{
 "keyExplanation": "Pick the labeled KBr curve — the upper one — then read it: find 40 °C on the bottom axis, go straight up to the KBr curve, then straight across. The side axis reads 76, so the solubility of KBr at 40 °C is 76 g per 100 g of water."
}

[
 {
  "value": 14,
  "misconception": "you read the KClO₃ curve instead of the KCl curve",
  "feedback": "This answer is wrong — you read the KClO₃ curve instead of the KCl curve."
 },
 {
  "value": 43,
  "misconception": "you read the KCl curve at 50 °C instead of 40 °C",
  "feedback": "This answer is wrong — you read the KCl curve at 50 °C instead of 40 °C."
 }
]

{
 "keyExplanation": "Pick the labeled KCl curve — the upper one — then read it: find 40 °C on the bottom axis, go straight up to the KCl curve, then straight across. The side axis reads 40, so the solubility of KCl at 40 °C is 40 g per 100 g of water."
}

[
 {
  "value": 93,
  "misconception": "you added the two curve readings instead of subtracting them",
  "feedback": "This answer is wrong — you added the two curve readings instead of subtracting them."
 },
 {
  "value": 60,
  "misconception": "you reported 60, which matches both the temperature difference (70 − 10) and the cap at 70 °C itself — either way, the answer is the difference between the two caps: 60 − 33 = 27 g",
  "feedback": "This answer is wrong — you reported 60, which matches both the temperature difference (70 − 10) and the cap at 70 °C itself — either way, the answer is the difference between the two caps: 60 − 33 = 27 g."
 },
 {
  "value": 33,
  "misconception": "you gave the cap at the cooler temperature instead of the difference between the caps",
  "feedback": "This answer is wrong — you gave the cap at the cooler temperature instead of the difference between the caps."
 }
]

{
 "keyExplanation": "A saturated solution holds exactly the cap at its temperature.\nRead the two caps from the curve:\nsolubility at 70 °C = 60 g per 100 g of water\nsolubility at 10 °C = 33 g per 100 g of water\nWrite down the equation:\nmass that crystallizes = solubility at the warmer temperature − solubility at the cooler temperature\nSubstitute in the values, and calculate:\nmass that crystallizes = 60 − 33\nmass that crystallizes = 27 g of NH₄Cl"
}

[
 {
  "value": 38,
  "misconception": "you read the NaCl curve instead of the KNO₃ curve",
  "feedback": "This answer is wrong — you read the NaCl curve instead of the KNO₃ curve."
 },
 {
  "value": 138,
  "misconception": "you read the KNO₃ curve at 70 °C instead of 80 °C",
  "feedback": "This answer is wrong — you read the KNO₃ curve at 70 °C instead of 80 °C."
 }
]

{
 "keyExplanation": "Pick the labeled KNO₃ curve — the steeply climbing one — then read it: find 80 °C on the bottom axis, go straight up to the KNO₃ curve, then straight across. The side axis reads 169, so the solubility of KNO₃ at 80 °C is 169 g per 100 g of water."
}

[
 {
  "value": 37,
  "misconception": "you read the NaCl curve instead of the NH₄Cl curve",
  "feedback": "This answer is wrong — you read the NaCl curve instead of the NH₄Cl curve."
 },
 {
  "value": 55,
  "misconception": "you read the NH₄Cl curve at 60 °C instead of 50 °C",
  "feedback": "This answer is wrong — you read the NH₄Cl curve at 60 °C instead of 50 °C."
 }
]

{
 "keyExplanation": "Pick the labeled NH₄Cl curve — the middle one — then read it: find 50 °C on the bottom axis, go straight up to the NH₄Cl curve, then straight across. The side axis reads 50, so the solubility of NH₄Cl at 50 °C is 50 g per 100 g of water."
}

[
 {
  "value": 146,
  "misconception": "you added the two curve readings instead of subtracting them",
  "feedback": "This answer is wrong — you added the two curve readings instead of subtracting them."
 },
 {
  "value": 50,
  "misconception": "you subtracted the temperatures instead of the solubilities",
  "feedback": "This answer is wrong — you subtracted the temperatures instead of the solubilities."
 },
 {
  "value": 60,
  "misconception": "you gave the cap at the cooler temperature instead of the difference between the caps",
  "feedback": "This answer is wrong — you gave the cap at the cooler temperature instead of the difference between the caps."
 }
]

{
 "keyExplanation": "A saturated solution holds exactly the cap at its temperature.\nRead the two caps from the curve:\nsolubility at 60 °C = 86 g per 100 g of water\nsolubility at 10 °C = 60 g per 100 g of water\nWrite down the equation:\nmass that crystallizes = solubility at the warmer temperature − solubility at the cooler temperature\nSubstitute in the values, and calculate:\nmass that crystallizes = 86 − 60\nmass that crystallizes = 26 g of KBr"
}

[
 {
  "value": 37,
  "misconception": "you read the KCl curve instead of the NaNO₃ curve",
  "feedback": "This answer is wrong — you read the KCl curve instead of the NaNO₃ curve."
 },
 {
  "value": 104,
  "misconception": "you read the NaNO₃ curve at 40 °C instead of 30 °C",
  "feedback": "This answer is wrong — you read the NaNO₃ curve at 40 °C instead of 30 °C."
 }
]

{
 "keyExplanation": "Pick the labeled NaNO₃ curve — the upper one — then read it: find 30 °C on the bottom axis, go straight up to the NaNO₃ curve, then straight across. The side axis reads 96, so the solubility of NaNO₃ at 30 °C is 96 g per 100 g of water."
}

[
 {
  "value": "NaNO₃",
  "misconception": "you picked the soluble product — sodium and nitrate both guarantee NaNO₃ stays dissolved; the solid is the barium sulfate",
  "feedback": "This answer is wrong — NaNO₃ is the soluble product: sodium and nitrate both guarantee it stays dissolved. The solid is the barium sulfate, BaSO₄."
 },
 {
  "value": "Ba(NO₃)₂",
  "misconception": "you kept the original partners instead of swapping — Ba(NO₃)₂ was already dissolved; the new, insoluble pairing is BaSO₄",
  "feedback": "This answer is wrong — Ba(NO₃)₂ is a reactant, already dissolved. Swap partners: the new pairing BaSO₄ is the insoluble product."
 },
 {
  "value": "Ba₂(SO₄)₂",
  "misconception": "you criss-crossed charges that already balance — Ba²⁺ and SO₄²⁻ pair one-to-one, so the formula is BaSO₄",
  "feedback": "This answer is wrong — Ba²⁺ and SO₄²⁻ have equal-and-opposite charges, so they pair one-to-one. The formula is BaSO₄."
 }
]

{
 "keyExplanation": "Swap partners: the products are BaSO₄ and NaNO₃. Barium is one of the three sulfate exceptions, so BaSO₄ is insoluble and forms the white solid — BaSO₄(s). NaNO₃ stays dissolved as NaNO₃(aq).",
 "anticipatedWrong": [
  {
   "value": "NaNO₃",
   "misconception": "you picked the soluble product — sodium and nitrate both guarantee NaNO₃ stays dissolved; the solid is the barium sulfate",
   "feedback": "This answer is wrong — NaNO₃ is the soluble product: sodium and nitrate both guarantee it stays dissolved. The solid is the barium sulfate, BaSO₄."
  },
  {
   "value": "Ba(NO₃)₂",
   "misconception": "you kept the original partners instead of swapping — Ba(NO₃)₂ was already dissolved; the new, insoluble pairing is BaSO₄",
   "feedback": "This answer is wrong — Ba(NO₃)₂ is a reactant, already dissolved. Swap partners: the new pairing BaSO₄ is the insoluble product."
  },
  {
   "value": "Ba₂(SO₄)₂",
   "misconception": "you criss-crossed charges that already balance — Ba²⁺ and SO₄²⁻ pair one-to-one, so the formula is BaSO₄",
   "feedback": "This answer is wrong — Ba²⁺ and SO₄²⁻ have equal-and-opposite charges, so they pair one-to-one. The formula is BaSO₄."
  }
 ]
}

[
 {
  "value": "NaNO₃",
  "misconception": "you picked the soluble product — sodium and nitrate both guarantee NaNO₃ stays dissolved; the solid is the silver iodide",
  "feedback": "This answer is wrong — NaNO₃ is the soluble product: sodium and nitrate both guarantee it. The solid is the silver iodide, AgI."
 },
 {
  "value": "AgNO₃",
  "misconception": "you kept the original partners instead of swapping — AgNO₃ was already dissolved; the new, insoluble pairing is AgI",
  "feedback": "This answer is wrong — AgNO₃ is a reactant, already dissolved. Swap partners: the new pairing AgI is the insoluble product."
 },
 {
  "value": "Ag₂I",
  "misconception": "you criss-crossed charges that already balance — Ag⁺ and I⁻ pair one-to-one, so the formula is AgI",
  "feedback": "This answer is wrong — Ag⁺ and I⁻ have equal-and-opposite charges, so they pair one-to-one. The formula is AgI."
 }
]

{
 "keyExplanation": "Swap partners: the products are AgI and NaNO₃. Silver is a halide exception, so AgI is insoluble and forms the pale-yellow solid — AgI(s). NaNO₃ stays dissolved as NaNO₃(aq).",
 "anticipatedWrong": [
  {
   "value": "NaNO₃",
   "misconception": "you picked the soluble product — sodium and nitrate both guarantee NaNO₃ stays dissolved; the solid is the silver iodide",
   "feedback": "This answer is wrong — NaNO₃ is the soluble product: sodium and nitrate both guarantee it. The solid is the silver iodide, AgI."
  },
  {
   "value": "AgNO₃",
   "misconception": "you kept the original partners instead of swapping — AgNO₃ was already dissolved; the new, insoluble pairing is AgI",
   "feedback": "This answer is wrong — AgNO₃ is a reactant, already dissolved. Swap partners: the new pairing AgI is the insoluble product."
  },
  {
   "value": "Ag₂I",
   "misconception": "you criss-crossed charges that already balance — Ag⁺ and I⁻ pair one-to-one, so the formula is AgI",
   "feedback": "This answer is wrong — Ag⁺ and I⁻ have equal-and-opposite charges, so they pair one-to-one. The formula is AgI."
  }
 ]
}

[
 {
  "value": "NaNO₃",
  "misconception": "you picked the soluble product — sodium and nitrate both guarantee NaNO₃ stays dissolved; the solid is the cobalt carbonate",
  "feedback": "This answer is wrong — NaNO₃ is the soluble product: sodium and nitrate both guarantee it. The solid is the cobalt carbonate, CoCO₃."
 },
 {
  "value": "Co(NO₃)₂",
  "misconception": "you kept the original partners instead of swapping — Co(NO₃)₂ was already dissolved; the new, insoluble pairing is CoCO₃",
  "feedback": "This answer is wrong — Co(NO₃)₂ is a reactant, already dissolved. Swap partners: the new pairing CoCO₃ is the insoluble product."
 },
 {
  "value": "Co₂(CO₃)₂",
  "misconception": "you criss-crossed charges that already balance — Co²⁺ and CO₃²⁻ pair one-to-one, so the formula is CoCO₃",
  "feedback": "This answer is wrong — Co²⁺ and CO₃²⁻ have equal-and-opposite charges, so they pair one-to-one. The formula is CoCO₃."
 }
]

{
 "keyExplanation": "Swap partners: the products are CoCO₃ and NaNO₃. Carbonates are usually insoluble and cobalt is not a rescue ion, so CoCO₃ forms the pink solid — CoCO₃(s). NaNO₃ stays dissolved as NaNO₃(aq).",
 "anticipatedWrong": [
  {
   "value": "NaNO₃",
   "misconception": "you picked the soluble product — sodium and nitrate both guarantee NaNO₃ stays dissolved; the solid is the cobalt carbonate",
   "feedback": "This answer is wrong — NaNO₃ is the soluble product: sodium and nitrate both guarantee it. The solid is the cobalt carbonate, CoCO₃."
  },
  {
   "value": "Co(NO₃)₂",
   "misconception": "you kept the original partners instead of swapping — Co(NO₃)₂ was already dissolved; the new, insoluble pairing is CoCO₃",
   "feedback": "This answer is wrong — Co(NO₃)₂ is a reactant, already dissolved. Swap partners: the new pairing CoCO₃ is the insoluble product."
  },
  {
   "value": "Co₂(CO₃)₂",
   "misconception": "you criss-crossed charges that already balance — Co²⁺ and CO₃²⁻ pair one-to-one, so the formula is CoCO₃",
   "feedback": "This answer is wrong — Co²⁺ and CO₃²⁻ have equal-and-opposite charges, so they pair one-to-one. The formula is CoCO₃."
  }
 ]
}

[
 {
  "value": "KCl",
  "misconception": "you picked the soluble product — potassium guarantees KCl stays dissolved; the solid is the iron(III) hydroxide",
  "feedback": "This answer is wrong — KCl is the soluble product: potassium guarantees it. The solid is the iron(III) hydroxide, Fe(OH)₃."
 },
 {
  "value": "FeOH",
  "misconception": "you paired the ions one-to-one — iron here is 3+ and hydroxide is 1−, so three hydroxides are needed: Fe(OH)₃",
  "feedback": "This answer is wrong — the charges do not balance one-to-one: Fe³⁺ needs three OH⁻ ions, so the formula is Fe(OH)₃."
 },
 {
  "value": "Fe(OH)₂",
  "misconception": "you used iron(II)'s charge — the reactant FeCl₃ shows iron carrying 3+, so the hydroxide is Fe(OH)₃",
  "feedback": "This answer is wrong — FeCl₃ shows this iron is 3+, so it pairs with three hydroxide ions: Fe(OH)₃."
 }
]

{
 "keyExplanation": "Swap partners: the products are Fe(OH)₃ and KCl. Hydroxides are usually insoluble and iron(III) is not a rescue ion, so Fe(OH)₃ forms the rust-orange solid — Fe(OH)₃(s). KCl stays dissolved as KCl(aq). The 3+ iron pairs with THREE hydroxide ions, so the formula needs the (OH)₃ group.",
 "anticipatedWrong": [
  {
   "value": "KCl",
   "misconception": "you picked the soluble product — potassium guarantees KCl stays dissolved; the solid is the iron(III) hydroxide",
   "feedback": "This answer is wrong — KCl is the soluble product: potassium guarantees it. The solid is the iron(III) hydroxide, Fe(OH)₃."
  },
  {
   "value": "FeOH",
   "misconception": "you paired the ions one-to-one — iron here is 3+ and hydroxide is 1−, so three hydroxides are needed: Fe(OH)₃",
   "feedback": "This answer is wrong — the charges do not balance one-to-one: Fe³⁺ needs three OH⁻ ions, so the formula is Fe(OH)₃."
  },
  {
   "value": "Fe(OH)₂",
   "misconception": "you used iron(II)'s charge — the reactant FeCl₃ shows iron carrying 3+, so the hydroxide is Fe(OH)₃",
   "feedback": "This answer is wrong — FeCl₃ shows this iron is 3+, so it pairs with three hydroxide ions: Fe(OH)₃."
  }
 ]
}

[
 {
  "value": "LiBr",
  "misconception": "you picked the soluble product — lithium's group 1 guarantee keeps LiBr dissolved (and lithium is no bromide exception); the solid is the zinc sulfide",
  "feedback": "This answer is wrong — LiBr is the soluble product: lithium's group 1 guarantee keeps it dissolved. The solid is the zinc sulfide, ZnS."
 },
 {
  "value": "ZnBr₂",
  "misconception": "you kept the original partners instead of swapping — ZnBr₂ was already dissolved; the new, insoluble pairing is ZnS",
  "feedback": "This answer is wrong — ZnBr₂ is a reactant, already dissolved. Swap partners: the new pairing ZnS is the insoluble product."
 },
 {
  "value": "Zn₂S₂",
  "misconception": "you criss-crossed charges that already balance — Zn²⁺ and S²⁻ pair one-to-one, so the formula is ZnS",
  "feedback": "This answer is wrong — Zn²⁺ and S²⁻ have equal-and-opposite charges, so they pair one-to-one. The formula is ZnS."
 }
]

{
 "keyExplanation": "Swap partners: the products are ZnS and LiBr. Sulfides are usually insoluble and zinc is not a rescue ion, so ZnS forms the white solid — ZnS(s). LiBr stays dissolved as LiBr(aq).",
 "anticipatedWrong": [
  {
   "value": "LiBr",
   "misconception": "you picked the soluble product — lithium's group 1 guarantee keeps LiBr dissolved (and lithium is no bromide exception); the solid is the zinc sulfide",
   "feedback": "This answer is wrong — LiBr is the soluble product: lithium's group 1 guarantee keeps it dissolved. The solid is the zinc sulfide, ZnS."
  },
  {
   "value": "ZnBr₂",
   "misconception": "you kept the original partners instead of swapping — ZnBr₂ was already dissolved; the new, insoluble pairing is ZnS",
   "feedback": "This answer is wrong — ZnBr₂ is a reactant, already dissolved. Swap partners: the new pairing ZnS is the insoluble product."
  },
  {
   "value": "Zn₂S₂",
   "misconception": "you criss-crossed charges that already balance — Zn²⁺ and S²⁻ pair one-to-one, so the formula is ZnS",
   "feedback": "This answer is wrong — Zn²⁺ and S²⁻ have equal-and-opposite charges, so they pair one-to-one. The formula is ZnS."
  }
 ]
}

[
 {
  "value": 3.333,
  "misconception": "you divided the volume by the moles — M = n ÷ V puts the moles on top: 0.84 ÷ 2.8",
  "feedback": null
 },
 {
  "value": 2.352,
  "misconception": "you multiplied n by V — molarity DIVIDES the moles by the volume: 0.84 ÷ 2.8",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nn = 0.84 mol\nV = 2.8 L\nWrite down the equation:\nM = n ÷ V\nSubstitute in the values, and calculate:\nM = 0.84 ÷ 2.8\nM = 0.30 M"
}

[
 {
  "value": 0.0002,
  "misconception": "you divided by the milliliters — convert first: 200.0 mL = 0.2000 L, then divide",
  "feedback": null
 },
 {
  "value": 5.0,
  "misconception": "you divided the volume by the moles — M = n ÷ V puts the moles on top: 0.040 ÷ 0.2000",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nn = 0.040 mol\nV = 200.0 mL = 0.2000 L\nWrite down the equation:\nM = n ÷ V\nSubstitute in the values, and calculate:\nM = 0.040 ÷ 0.2000\nM = 0.20 M"
}

[
 {
  "value": 0.21,
  "misconception": "you divided M by V — make n the subject of M = n ÷ V and MULTIPLY: 0.42 × 2.0",
  "feedback": null
 },
 {
  "value": 4.7619,
  "misconception": "you divided V by M — make n the subject of M = n ÷ V and MULTIPLY: 0.42 × 2.0",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nM = 0.42 M\nV = 2.0 L\nWrite down the equation:\nM = n ÷ V\nMake n the subject:\nn = M × V\nSubstitute in the values, and calculate:\nn = 0.42 × 2.0\nn = 0.84 mol"
}

[
 {
  "value": 180.0,
  "misconception": "you multiplied by the milliliters — convert first: 750.0 mL = 0.7500 L, then multiply",
  "feedback": null
 },
 {
  "value": 0.32,
  "misconception": "you divided instead of multiplying — make n the subject of M = n ÷ V: n = M × V = 0.24 × 0.7500",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nM = 0.24 M\nV = 750.0 mL = 0.7500 L\nWrite down the equation:\nM = n ÷ V\nMake n the subject:\nn = M × V\nSubstitute in the values, and calculate:\nn = 0.24 × 0.7500\nn = 0.18 mol"
}

[
 {
  "value": 18.72,
  "misconception": "you divided grams by volume — the mass must first become moles: 46.8 ÷ 58.5 = 0.800 mol, then divide by the liters",
  "feedback": null
 },
 {
  "value": 0.8,
  "misconception": "you stopped at the moles — finish the chain: M = n ÷ V = 0.800 ÷ 2.50",
  "feedback": null
 },
 {
  "value": 0.5,
  "misconception": "you inverted the molar-mass division — the moles are the mass divided by the molar mass: 46.8 ÷ 58.5",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nm = 46.8 g\nmolar mass = 58.5 g/mol\nV = 2.50 L\nFind the moles of solute first:\nn = m ÷ molar mass\nn = 46.8 ÷ 58.5\nn = 0.800 mol\nWrite down the equation:\nM = n ÷ V\nSubstitute in the values, and calculate:\nM = 0.800 ÷ 2.50\nM = 0.320 M"
}

[
 {
  "value": 27.75,
  "misconception": "you divided grams by volume — the mass must first become moles: 13.32 ÷ 111.0 = 0.1200 mol, then divide by the liters",
  "feedback": null
 },
 {
  "value": 0.12,
  "misconception": "you stopped at the moles — finish the chain: M = n ÷ V = 0.1200 ÷ 0.4800",
  "feedback": null
 },
 {
  "value": 17.3611,
  "misconception": "you inverted the molar-mass division — the moles are the mass divided by the molar mass: 13.32 ÷ 111.0",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nm = 13.32 g\nmolar mass = 111.0 g/mol\nV = 480.0 mL = 0.4800 L\nFind the moles of solute first:\nn = m ÷ molar mass\nn = 13.32 ÷ 111.0\nn = 0.1200 mol\nWrite down the equation:\nM = n ÷ V\nSubstitute in the values, and calculate:\nM = 0.1200 ÷ 0.4800\nM = 0.250 M"
}

[
 {
  "value": 16.2,
  "misconception": "you used the volume ratio upside down — and the sanity check flags it: a diluted solution must come out BELOW 0.90 M",
  "feedback": null
 },
 {
  "value": 0.9,
  "misconception": "you carried the starting molarity across — dilution lowers the molarity; run M₂ = M₁V₁ ÷ V₂",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nM₁ = 0.90 M\nV₁ = 35.0 mL\nV₂ = 630.0 mL\nWrite down the equation:\nM₁V₁ = M₂V₂\nMake M₂ the subject:\nM₂ = M₁V₁ ÷ V₂\nSubstitute in the values, and calculate:\nM₂ = (0.90 × 35.0) ÷ 630.0\nM₂ = 0.050 M\nSanity check: 0.050 M is smaller than the starting 0.90 M, as a dilution demands."
}

[
 {
  "value": 0.6316,
  "misconception": "you divided by the solvent added — V₂ is the TOTAL volume: 60.0 + 190.0 = 250.0 mL",
  "feedback": null
 },
 {
  "value": 8.3333,
  "misconception": "you used the volume ratio upside down — and the sanity check flags it: a diluted solution must come out BELOW 2.0 M",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nM₁ = 2.0 M\nV₁ = 60.0 mL\nV₂ = 60.0 + 190.0 = 250.0 mL — the TOTAL volume, not the solvent added\nWrite down the equation:\nM₁V₁ = M₂V₂\nMake M₂ the subject:\nM₂ = M₁V₁ ÷ V₂\nSubstitute in the values, and calculate:\nM₂ = (2.0 × 60.0) ÷ 250.0\nM₂ = 0.48 M\nSanity check: 0.48 M is smaller than the starting 2.0 M, as a dilution demands."
}

[
 {
  "value": 9846.2,
  "misconception": "you swapped the molarities — and the sanity check flags it: the stock is stronger than the target, so V₁ must come out SMALLER than 640.0 mL",
  "feedback": null
 },
 {
  "value": 208.0,
  "misconception": "you forgot to divide by the stock's molarity M₁ = 5.0 — V₁ = M₂V₂ ÷ M₁",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nM₁ = 5.0 M\nM₂ = 0.325 M\nV₂ = 640.0 mL\nWrite down the equation:\nM₁V₁ = M₂V₂\nMake V₁ the subject:\nV₁ = M₂V₂ ÷ M₁\nSubstitute in the values, and calculate:\nV₁ = (0.325 × 640.0) ÷ 5.0\nV₁ = 41.6 mL ≈ 42 mL (2 significant figures — set by the 5.0 M given)\nSanity check: the stock is stronger than the target, so V₁ (41.6 mL) must come out smaller than V₂ (640.0 mL) — and it does."
}

[
 {
  "value": 0.245,
  "misconception": "you ignored the mole ratio — the equation uses 2 mol of NaOH for every 1 mol of CuCl₂, so multiply by 2",
  "feedback": null
 },
 {
  "value": 0.1225,
  "misconception": "you applied the ratio upside down — NaOH carries the 2 and CuCl₂ the 1, so MULTIPLY the CuCl₂ moles by 2",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nM = 0.70 M\nV = 0.35 L\nFind the moles of the dissolved reactant first:\nM = n ÷ V\nMake n the subject:\nn = M × V\nn(CuCl₂) = 0.70 × 0.35\nn(CuCl₂) = 0.245 mol\nUse the mole ratio from the balanced equation:\n1 mol CuCl₂ → 2 mol NaOH\nn(NaOH) = 0.245 × 2\nn(NaOH) = 0.49 mol"
}

[
 {
  "value": 0.2,
  "misconception": "you stopped at the moles — the question asks for a mass: finish with mass = moles × molar mass = 0.200 × 303.3",
  "feedback": null
 },
 {
  "value": 1516.5,
  "misconception": "you divided by the moles instead of multiplying — mass = moles × molar mass = 0.200 × 303.3",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nM = 1.0 M\nV = 200.0 mL = 0.2000 L\nFind the moles of the dissolved reactant first:\nM = n ÷ V\nMake n the subject:\nn = M × V\nn(lead(II) acetate) = 1.0 × 0.2000\nn(lead(II) acetate) = 0.200 mol\nUse the mole ratio from the balanced equation:\n1 mol lead(II) acetate → 1 mol PbSO₄, so n(PbSO₄) = 0.20 mol\nWrite down the equation for the mass:\nmass = moles × molar mass\nSubstitute in the values, and calculate:\nmass = 0.20 × 303.3\nmass = 60.66 g ≈ 61 g (2 significant figures — set by the 1.0 M given)"
}

[
 {
  "value": 1.6667,
  "misconception": "you divided the volume by the moles — M = n ÷ V puts the moles on top: 0.66 ÷ 1.1",
  "feedback": null
 },
 {
  "value": 0.726,
  "misconception": "you multiplied n by V — molarity DIVIDES the moles by the volume: 0.66 ÷ 1.1",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nn = 0.66 mol\nV = 1.1 L\nWrite down the equation:\nM = n ÷ V\nSubstitute in the values, and calculate:\nM = 0.66 ÷ 1.1\nM = 0.60 M"
}

[
 {
  "value": 0.0002,
  "misconception": "you divided by the milliliters — convert first: 450.0 mL = 0.4500 L, then divide",
  "feedback": null
 },
 {
  "value": 5.0,
  "misconception": "you divided the volume by the moles — M = n ÷ V puts the moles on top: 0.090 ÷ 0.4500",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nn = 0.090 mol\nV = 450.0 mL = 0.4500 L\nWrite down the equation:\nM = n ÷ V\nSubstitute in the values, and calculate:\nM = 0.090 ÷ 0.4500\nM = 0.20 M"
}

[
 {
  "value": 0.575,
  "misconception": "you divided M by V — make n the subject of M = n ÷ V and MULTIPLY: 1.15 × 2.0",
  "feedback": null
 },
 {
  "value": 1.7391,
  "misconception": "you divided V by M — make n the subject of M = n ÷ V and MULTIPLY: 1.15 × 2.0",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nM = 1.15 M\nV = 2.0 L\nWrite down the equation:\nM = n ÷ V\nMake n the subject:\nn = M × V\nSubstitute in the values, and calculate:\nn = 1.15 × 2.0\nn = 2.3 mol"
}

[
 {
  "value": 40.0,
  "misconception": "you multiplied by the milliliters — convert first: 125.0 mL = 0.1250 L, then multiply",
  "feedback": null
 },
 {
  "value": 2.56,
  "misconception": "you divided instead of multiplying — make n the subject of M = n ÷ V: n = M × V = 0.32 × 0.1250",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nM = 0.32 M\nV = 125.0 mL = 0.1250 L\nWrite down the equation:\nM = n ÷ V\nMake n the subject:\nn = M × V\nSubstitute in the values, and calculate:\nn = 0.32 × 0.1250\nn = 0.040 mol"
}

[
 {
  "value": 11.22,
  "misconception": "you divided grams by volume — the mass must first become moles: 16.83 ÷ 56.1 = 0.300 mol, then divide by the liters",
  "feedback": null
 },
 {
  "value": 0.3,
  "misconception": "you stopped at the moles — finish the chain: M = n ÷ V = 0.300 ÷ 1.50",
  "feedback": null
 },
 {
  "value": 2.2222,
  "misconception": "you inverted the molar-mass division — the moles are the mass divided by the molar mass: 16.83 ÷ 56.1",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nm = 16.83 g\nmolar mass = 56.1 g/mol\nV = 1.50 L\nFind the moles of solute first:\nn = m ÷ molar mass\nn = 16.83 ÷ 56.1\nn = 0.300 mol\nWrite down the equation:\nM = n ÷ V\nSubstitute in the values, and calculate:\nM = 0.300 ÷ 1.50\nM = 0.200 M"
}

[
 {
  "value": 47.968,
  "misconception": "you divided grams by volume — the mass must first become moles: 29.98 ÷ 149.9 = 0.2000 mol, then divide by the liters",
  "feedback": null
 },
 {
  "value": 0.2,
  "misconception": "you stopped at the moles — finish the chain: M = n ÷ V = 0.2000 ÷ 0.6250",
  "feedback": null
 },
 {
  "value": 8.0,
  "misconception": "you inverted the molar-mass division — the moles are the mass divided by the molar mass: 29.98 ÷ 149.9",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nm = 29.98 g\nmolar mass = 149.9 g/mol\nV = 625.0 mL = 0.6250 L\nFind the moles of solute first:\nn = m ÷ molar mass\nn = 29.98 ÷ 149.9\nn = 0.2000 mol\nWrite down the equation:\nM = n ÷ V\nSubstitute in the values, and calculate:\nM = 0.2000 ÷ 0.6250\nM = 0.320 M"
}

[
 {
  "value": 30.0,
  "misconception": "you used the volume ratio upside down — and the sanity check flags it: a diluted solution must come out BELOW 3.0 M",
  "feedback": null
 },
 {
  "value": 3.0,
  "misconception": "you carried the starting molarity across — dilution lowers the molarity; run M₂ = M₁V₁ ÷ V₂",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nM₁ = 3.0 M\nV₁ = 44.0 mL\nV₂ = 440.0 mL\nWrite down the equation:\nM₁V₁ = M₂V₂\nMake M₂ the subject:\nM₂ = M₁V₁ ÷ V₂\nSubstitute in the values, and calculate:\nM₂ = (3.0 × 44.0) ÷ 440.0\nM₂ = 0.30 M\nSanity check: 0.30 M is smaller than the starting 3.0 M, as a dilution demands."
}

[
 {
  "value": 0.7059,
  "misconception": "you divided by the solvent added — V₂ is the TOTAL volume: 75.0 + 425.0 = 500.0 mL",
  "feedback": null
 },
 {
  "value": 26.6667,
  "misconception": "you used the volume ratio upside down — and the sanity check flags it: a diluted solution must come out BELOW 4.0 M",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nM₁ = 4.0 M\nV₁ = 75.0 mL\nV₂ = 75.0 + 425.0 = 500.0 mL — the TOTAL volume, not the solvent added\nWrite down the equation:\nM₁V₁ = M₂V₂\nMake M₂ the subject:\nM₂ = M₁V₁ ÷ V₂\nSubstitute in the values, and calculate:\nM₂ = (4.0 × 75.0) ÷ 500.0\nM₂ = 0.60 M\nSanity check: 0.60 M is smaller than the starting 4.0 M, as a dilution demands."
}

[
 {
  "value": 5939.4,
  "misconception": "you swapped the molarities — and the sanity check flags it: the stock is stronger than the target, so V₁ must come out SMALLER than 560.0 mL",
  "feedback": null
 },
 {
  "value": 369.6,
  "misconception": "you forgot to divide by the stock's molarity M₁ = 7.0 — V₁ = M₂V₂ ÷ M₁",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nM₁ = 7.0 M\nM₂ = 0.66 M\nV₂ = 560.0 mL\nWrite down the equation:\nM₁V₁ = M₂V₂\nMake V₁ the subject:\nV₁ = M₂V₂ ÷ M₁\nSubstitute in the values, and calculate:\nV₁ = (0.66 × 560.0) ÷ 7.0\nV₁ = 52.8 mL ≈ 53 mL (2 significant figures — set by the 7.0 M given)\nSanity check: the stock is stronger than the target, so V₁ (52.8 mL) must come out smaller than V₂ (560.0 mL) — and it does."
}

[
 {
  "value": 0.28,
  "misconception": "you ignored the mole ratio — the equation uses 2 mol of NaOH for every 1 mol of Cu(NO₃)₂, so multiply by 2",
  "feedback": null
 },
 {
  "value": 0.14,
  "misconception": "you applied the ratio upside down — NaOH carries the 2 and Cu(NO₃)₂ the 1, so MULTIPLY the Cu(NO₃)₂ moles by 2",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nM = 2.0 M\nV = 140.0 mL = 0.1400 L\nFind the moles of the dissolved reactant first:\nM = n ÷ V\nMake n the subject:\nn = M × V\nn(Cu(NO₃)₂) = 2.0 × 0.1400\nn(Cu(NO₃)₂) = 0.280 mol\nUse the mole ratio from the balanced equation:\n1 mol Cu(NO₃)₂ → 2 mol NaOH\nn(NaOH) = 0.280 × 2\nn(NaOH) = 0.56 mol"
}

[
 {
  "value": 0.4,
  "misconception": "you stopped at the moles — the question asks for a mass: finish with mass = moles × molar mass = 0.400 × 143.3",
  "feedback": null
 },
 {
  "value": 358.25,
  "misconception": "you divided by the moles instead of multiplying — mass = moles × molar mass = 0.400 × 143.3",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nM = 5.0 M\nV = 80.0 mL = 0.0800 L\nFind the moles of the dissolved reactant first:\nM = n ÷ V\nMake n the subject:\nn = M × V\nn(AgNO₃) = 5.0 × 0.0800\nn(AgNO₃) = 0.400 mol\nUse the mole ratio from the balanced equation:\n1 mol AgNO₃ → 1 mol AgCl, so n(AgCl) = 0.40 mol\nWrite down the equation for the mass:\nmass = moles × molar mass\nSubstitute in the values, and calculate:\nmass = 0.40 × 143.3\nmass = 57.32 g ≈ 57 g (2 significant figures — set by the 5.0 M given)"
}

[
 {
  "value": 1.4286,
  "misconception": "you divided the volume by the moles — M = n ÷ V puts the moles on top: 0.98 ÷ 1.4",
  "feedback": null
 },
 {
  "value": 1.372,
  "misconception": "you multiplied n by V — molarity DIVIDES the moles by the volume: 0.98 ÷ 1.4",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nn = 0.98 mol\nV = 1.4 L\nWrite down the equation:\nM = n ÷ V\nSubstitute in the values, and calculate:\nM = 0.98 ÷ 1.4\nM = 0.70 M"
}

[
 {
  "value": 0.00025,
  "misconception": "you divided by the milliliters — convert first: 280.0 mL = 0.2800 L, then divide",
  "feedback": null
 },
 {
  "value": 4.0,
  "misconception": "you divided the volume by the moles — M = n ÷ V puts the moles on top: 0.070 ÷ 0.2800",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nn = 0.070 mol\nV = 280.0 mL = 0.2800 L\nWrite down the equation:\nM = n ÷ V\nSubstitute in the values, and calculate:\nM = 0.070 ÷ 0.2800\nM = 0.25 M"
}

[
 {
  "value": 0.2125,
  "misconception": "you divided M by V — make n the subject of M = n ÷ V and MULTIPLY: 0.85 × 4.0",
  "feedback": null
 },
 {
  "value": 4.7059,
  "misconception": "you divided V by M — make n the subject of M = n ÷ V and MULTIPLY: 0.85 × 4.0",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nM = 0.85 M\nV = 4.0 L\nWrite down the equation:\nM = n ÷ V\nMake n the subject:\nn = M × V\nSubstitute in the values, and calculate:\nn = 0.85 × 4.0\nn = 3.4 mol"
}

[
 {
  "value": 279.0,
  "misconception": "you multiplied by the milliliters — convert first: 620.0 mL = 0.6200 L, then multiply",
  "feedback": null
 },
 {
  "value": 0.7258,
  "misconception": "you divided instead of multiplying — make n the subject of M = n ÷ V: n = M × V = 0.45 × 0.6200",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nM = 0.45 M\nV = 620.0 mL = 0.6200 L\nWrite down the equation:\nM = n ÷ V\nMake n the subject:\nn = M × V\nSubstitute in the values, and calculate:\nn = 0.45 × 0.6200\nn = 0.279 mol ≈ 0.28 mol (2 significant figures — set by the 0.45 M given)"
}

[
 {
  "value": 26.45,
  "misconception": "you divided grams by volume — the mass must first become moles: 42.32 ÷ 211.6 = 0.2000 mol, then divide by the liters",
  "feedback": null
 },
 {
  "value": 0.2,
  "misconception": "you stopped at the moles — finish the chain: M = n ÷ V = 0.2000 ÷ 1.60",
  "feedback": null
 },
 {
  "value": 3.125,
  "misconception": "you inverted the molar-mass division — the moles are the mass divided by the molar mass: 42.32 ÷ 211.6",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nm = 42.32 g\nmolar mass = 211.6 g/mol\nV = 1.60 L\nFind the moles of solute first:\nn = m ÷ molar mass\nn = 42.32 ÷ 211.6\nn = 0.2000 mol\nWrite down the equation:\nM = n ÷ V\nSubstitute in the values, and calculate:\nM = 0.2000 ÷ 1.60\nM = 0.125 M"
}

[
 {
  "value": 83.3125,
  "misconception": "you divided grams by volume — the mass must first become moles: 13.33 ÷ 133.3 = 0.1000 mol, then divide by the liters",
  "feedback": null
 },
 {
  "value": 0.1,
  "misconception": "you stopped at the moles — finish the chain: M = n ÷ V = 0.1000 ÷ 0.1600",
  "feedback": null
 },
 {
  "value": 62.5,
  "misconception": "you inverted the molar-mass division — the moles are the mass divided by the molar mass: 13.33 ÷ 133.3",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nm = 13.33 g\nmolar mass = 133.3 g/mol\nV = 160.0 mL = 0.1600 L\nFind the moles of solute first:\nn = m ÷ molar mass\nn = 13.33 ÷ 133.3\nn = 0.1000 mol\nWrite down the equation:\nM = n ÷ V\nSubstitute in the values, and calculate:\nM = 0.1000 ÷ 0.1600\nM = 0.625 M"
}

[
 {
  "value": 22.5,
  "misconception": "you used the volume ratio upside down — and the sanity check flags it: a diluted solution must come out BELOW 3.0 M",
  "feedback": null
 },
 {
  "value": 3.0,
  "misconception": "you carried the starting molarity across — dilution lowers the molarity; run M₂ = M₁V₁ ÷ V₂",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nM₁ = 3.0 M\nV₁ = 52.0 mL\nV₂ = 390.0 mL\nWrite down the equation:\nM₁V₁ = M₂V₂\nMake M₂ the subject:\nM₂ = M₁V₁ ÷ V₂\nSubstitute in the values, and calculate:\nM₂ = (3.0 × 52.0) ÷ 390.0\nM₂ = 0.40 M\nSanity check: 0.40 M is smaller than the starting 3.0 M, as a dilution demands."
}

[
 {
  "value": 0.4364,
  "misconception": "you divided by the solvent added — V₂ is the TOTAL volume: 55.0 + 605.0 = 660.0 mL",
  "feedback": null
 },
 {
  "value": 57.6,
  "misconception": "you used the volume ratio upside down — and the sanity check flags it: a diluted solution must come out BELOW 4.8 M",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nM₁ = 4.8 M\nV₁ = 55.0 mL\nV₂ = 55.0 + 605.0 = 660.0 mL — the TOTAL volume, not the solvent added\nWrite down the equation:\nM₁V₁ = M₂V₂\nMake M₂ the subject:\nM₂ = M₁V₁ ÷ V₂\nSubstitute in the values, and calculate:\nM₂ = (4.8 × 55.0) ÷ 660.0\nM₂ = 0.40 M\nSanity check: 0.40 M is smaller than the starting 4.8 M, as a dilution demands."
}

[
 {
  "value": 4470.6,
  "misconception": "you swapped the molarities — and the sanity check flags it: the stock is stronger than the target, so V₁ must come out SMALLER than 380.0 mL",
  "feedback": null
 },
 {
  "value": 129.2,
  "misconception": "you forgot to divide by the stock's molarity M₁ = 4.0 — V₁ = M₂V₂ ÷ M₁",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nM₁ = 4.0 M\nM₂ = 0.34 M\nV₂ = 380.0 mL\nWrite down the equation:\nM₁V₁ = M₂V₂\nMake V₁ the subject:\nV₁ = M₂V₂ ÷ M₁\nSubstitute in the values, and calculate:\nV₁ = (0.34 × 380.0) ÷ 4.0\nV₁ = 32.3 mL ≈ 32 mL (2 significant figures — set by the 4.0 M and 0.34 M givens)\nSanity check: the stock is stronger than the target, so V₁ (32.3 mL) must come out smaller than V₂ (380.0 mL) — and it does."
}

[
 {
  "value": 0.23,
  "misconception": "you ignored the mole ratio — the equation uses 2 mol of NaOH for every 1 mol of CuBr₂, so multiply by 2",
  "feedback": null
 },
 {
  "value": 0.115,
  "misconception": "you applied the ratio upside down — NaOH carries the 2 and CuBr₂ the 1, so MULTIPLY the CuBr₂ moles by 2",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nM = 1.0 M\nV = 230.0 mL = 0.2300 L\nFind the moles of the dissolved reactant first:\nM = n ÷ V\nMake n the subject:\nn = M × V\nn(CuBr₂) = 1.0 × 0.2300\nn(CuBr₂) = 0.230 mol\nUse the mole ratio from the balanced equation:\n1 mol CuBr₂ → 2 mol NaOH\nn(NaOH) = 0.230 × 2\nn(NaOH) = 0.46 mol"
}

[
 {
  "value": 0.34,
  "misconception": "you ignored the mole ratio — the equation makes 2 mol of AgCl for every 1 mol of MgCl₂, so multiply by 2",
  "feedback": null
 },
 {
  "value": 680.0,
  "misconception": "you skipped the mL → L conversion — divide the milliliters by 1000 first: 340.0 mL = 0.3400 L",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nM = 1.0 M\nV = 340.0 mL = 0.3400 L\nFind the moles of the dissolved reactant first:\nM = n ÷ V\nMake n the subject:\nn = M × V\nn(MgCl₂) = 1.0 × 0.3400\nn(MgCl₂) = 0.340 mol\nUse the mole ratio from the balanced equation:\n1 mol MgCl₂ → 2 mol AgCl\nn(AgCl) = 0.340 × 2\nn(AgCl) = 0.68 mol"
}

[
 {
  "value": 1.3333,
  "misconception": "you divided the volume by the moles — M = n ÷ V puts the moles on top: 0.72 ÷ 0.96",
  "feedback": null
 },
 {
  "value": 0.6912,
  "misconception": "you multiplied n by V — molarity DIVIDES the moles by the volume: 0.72 ÷ 0.96",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nn = 0.72 mol\nV = 0.96 L\nWrite down the equation:\nM = n ÷ V\nSubstitute in the values, and calculate:\nM = 0.72 ÷ 0.96\nM = 0.75 M"
}

[
 {
  "value": 0.0004,
  "misconception": "you divided by the milliliters — convert first: 360.0 mL = 0.3600 L, then divide",
  "feedback": null
 },
 {
  "value": 2.5,
  "misconception": "you divided the volume by the moles — M = n ÷ V puts the moles on top: 0.144 ÷ 0.3600",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nn = 0.144 mol\nV = 360.0 mL = 0.3600 L\nWrite down the equation:\nM = n ÷ V\nSubstitute in the values, and calculate:\nM = 0.144 ÷ 0.3600\nM = 0.400 M (3 significant figures — set by the 0.144 mol given)"
}

[
 {
  "value": 0.475,
  "misconception": "you divided M by V — make n the subject of M = n ÷ V and MULTIPLY: 0.95 × 2.0",
  "feedback": null
 },
 {
  "value": 2.1053,
  "misconception": "you divided V by M — make n the subject of M = n ÷ V and MULTIPLY: 0.95 × 2.0",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nM = 0.95 M\nV = 2.0 L\nWrite down the equation:\nM = n ÷ V\nMake n the subject:\nn = M × V\nSubstitute in the values, and calculate:\nn = 0.95 × 2.0\nn = 1.9 mol"
}

[
 {
  "value": 195.0,
  "misconception": "you multiplied by the milliliters — convert first: 375.0 mL = 0.3750 L, then multiply",
  "feedback": null
 },
 {
  "value": 1.3867,
  "misconception": "you divided instead of multiplying — make n the subject of M = n ÷ V: n = M × V = 0.52 × 0.3750",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nM = 0.52 M\nV = 375.0 mL = 0.3750 L\nWrite down the equation:\nM = n ÷ V\nMake n the subject:\nn = M × V\nSubstitute in the values, and calculate:\nn = 0.52 × 0.3750\nn = 0.195 mol ≈ 0.20 mol (2 significant figures — set by the 0.52 M given)"
}

[
 {
  "value": 27.475,
  "misconception": "you divided grams by volume — the mass must first become moles: 21.98 ÷ 109.9 = 0.2000 mol, then divide by the liters",
  "feedback": null
 },
 {
  "value": 0.2,
  "misconception": "you stopped at the moles — finish the chain: M = n ÷ V = 0.2000 ÷ 0.800",
  "feedback": null
 },
 {
  "value": 6.25,
  "misconception": "you inverted the molar-mass division — the moles are the mass divided by the molar mass: 21.98 ÷ 109.9",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nm = 21.98 g\nmolar mass = 109.9 g/mol\nV = 0.800 L\nFind the moles of solute first:\nn = m ÷ molar mass\nn = 21.98 ÷ 109.9\nn = 0.2000 mol\nWrite down the equation:\nM = n ÷ V\nSubstitute in the values, and calculate:\nM = 0.2000 ÷ 0.800\nM = 0.250 M"
}

[
 {
  "value": 86.125,
  "misconception": "you divided grams by volume — the mass must first become moles: 20.67 ÷ 68.9 = 0.300 mol, then divide by the liters",
  "feedback": null
 },
 {
  "value": 0.3,
  "misconception": "you stopped at the moles — finish the chain: M = n ÷ V = 0.300 ÷ 0.2400",
  "feedback": null
 },
 {
  "value": 13.8889,
  "misconception": "you inverted the molar-mass division — the moles are the mass divided by the molar mass: 20.67 ÷ 68.9",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nm = 20.67 g\nmolar mass = 68.9 g/mol\nV = 240.0 mL = 0.2400 L\nFind the moles of solute first:\nn = m ÷ molar mass\nn = 20.67 ÷ 68.9\nn = 0.300 mol\nWrite down the equation:\nM = n ÷ V\nSubstitute in the values, and calculate:\nM = 0.300 ÷ 0.2400\nM = 1.25 M"
}

[
 {
  "value": 22.8571,
  "misconception": "you used the volume ratio upside down — and the sanity check flags it: a diluted solution must come out BELOW 2.0 M",
  "feedback": null
 },
 {
  "value": 2.0,
  "misconception": "you carried the starting molarity across — dilution lowers the molarity; run M₂ = M₁V₁ ÷ V₂",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nM₁ = 2.0 M\nV₁ = 28.0 mL\nV₂ = 320.0 mL\nWrite down the equation:\nM₁V₁ = M₂V₂\nMake M₂ the subject:\nM₂ = M₁V₁ ÷ V₂\nSubstitute in the values, and calculate:\nM₂ = (2.0 × 28.0) ÷ 320.0\nM₂ = 0.175 M ≈ 0.18 M (2 significant figures — set by the 2.0 M given)\nSanity check: 0.175 M is smaller than the starting 2.0 M, as a dilution demands."
}

[
 {
  "value": 1.0667,
  "misconception": "you divided by the solvent added — V₂ is the TOTAL volume: 65.0 + 195.0 = 260.0 mL",
  "feedback": null
 },
 {
  "value": 12.8,
  "misconception": "you used the volume ratio upside down — and the sanity check flags it: a diluted solution must come out BELOW 3.2 M",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nM₁ = 3.2 M\nV₁ = 65.0 mL\nV₂ = 65.0 + 195.0 = 260.0 mL — the TOTAL volume, not the solvent added\nWrite down the equation:\nM₁V₁ = M₂V₂\nMake M₂ the subject:\nM₂ = M₁V₁ ÷ V₂\nSubstitute in the values, and calculate:\nM₂ = (3.2 × 65.0) ÷ 260.0\nM₂ = 0.80 M\nSanity check: 0.80 M is smaller than the starting 3.2 M, as a dilution demands."
}

[
 {
  "value": 6080.0,
  "misconception": "you swapped the molarities — and the sanity check flags it: the stock is stronger than the target, so V₁ must come out SMALLER than 760.0 mL",
  "feedback": null
 },
 {
  "value": 285.0,
  "misconception": "you forgot to divide by the stock's molarity M₁ = 3.0 — V₁ = M₂V₂ ÷ M₁",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nM₁ = 3.0 M\nM₂ = 0.375 M\nV₂ = 760.0 mL\nWrite down the equation:\nM₁V₁ = M₂V₂\nMake V₁ the subject:\nV₁ = M₂V₂ ÷ M₁\nSubstitute in the values, and calculate:\nV₁ = (0.375 × 760.0) ÷ 3.0\nV₁ = 95 mL (2 significant figures — set by the 3.0 M given)\nSanity check: the stock is stronger than the target, so V₁ (95.0 mL) must come out smaller than V₂ (760.0 mL) — and it does."
}

[
 {
  "value": 0.21,
  "misconception": "you ignored the mole ratio — the equation uses 2 mol of KOH for every 1 mol of CuCl₂, so multiply by 2",
  "feedback": null
 },
 {
  "value": 0.105,
  "misconception": "you applied the ratio upside down — KOH carries the 2 and CuCl₂ the 1, so MULTIPLY the CuCl₂ moles by 2",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nM = 3.0 M\nV = 70.0 mL = 0.0700 L\nFind the moles of the dissolved reactant first:\nM = n ÷ V\nMake n the subject:\nn = M × V\nn(CuCl₂) = 3.0 × 0.0700\nn(CuCl₂) = 0.210 mol\nUse the mole ratio from the balanced equation:\n1 mol CuCl₂ → 2 mol KOH\nn(KOH) = 0.210 × 2\nn(KOH) = 0.42 mol"
}

[
 {
  "value": 0.46,
  "misconception": "you ignored the mole ratio — the equation makes 2 mol of AgCl for every 1 mol of MgCl₂, so multiply by 2",
  "feedback": null
 },
 {
  "value": 920.0,
  "misconception": "you skipped the mL → L conversion — divide the milliliters by 1000 first: 460.0 mL = 0.4600 L",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nM = 1.0 M\nV = 460.0 mL = 0.4600 L\nFind the moles of the dissolved reactant first:\nM = n ÷ V\nMake n the subject:\nn = M × V\nn(MgCl₂) = 1.0 × 0.4600\nn(MgCl₂) = 0.460 mol\nUse the mole ratio from the balanced equation:\n1 mol MgCl₂ → 2 mol AgCl\nn(AgCl) = 0.460 × 2\nn(AgCl) = 0.92 mol"
}

[
 {
  "value": 0.4444,
  "misconception": "you divided the volume by the moles — M = n ÷ V puts the moles on top: 0.63 ÷ 0.28",
  "feedback": null
 },
 {
  "value": 0.1764,
  "misconception": "you multiplied n by V — molarity DIVIDES the moles by the volume: 0.63 ÷ 0.28",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nn = 0.63 mol\nV = 0.28 L\nWrite down the equation:\nM = n ÷ V\nSubstitute in the values, and calculate:\nM = 0.63 ÷ 0.28\nM = 2.25 M ≈ 2.3 M (2 significant figures — set by the 0.63 mol and 0.28 L givens)"
}

[
 {
  "value": 0.00025,
  "misconception": "you divided by the milliliters — convert first: 920.0 mL = 0.9200 L, then divide",
  "feedback": null
 },
 {
  "value": 4.0,
  "misconception": "you divided the volume by the moles — M = n ÷ V puts the moles on top: 0.230 ÷ 0.9200",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nn = 0.230 mol\nV = 920.0 mL = 0.9200 L\nWrite down the equation:\nM = n ÷ V\nSubstitute in the values, and calculate:\nM = 0.230 ÷ 0.9200\nM = 0.250 M (3 significant figures — set by the 0.230 mol given)"
}

[
 {
  "value": 0.136,
  "misconception": "you divided M by V — make n the subject of M = n ÷ V and MULTIPLY: 0.68 × 5.0",
  "feedback": null
 },
 {
  "value": 7.3529,
  "misconception": "you divided V by M — make n the subject of M = n ÷ V and MULTIPLY: 0.68 × 5.0",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nM = 0.68 M\nV = 5.0 L\nWrite down the equation:\nM = n ÷ V\nMake n the subject:\nn = M × V\nSubstitute in the values, and calculate:\nn = 0.68 × 5.0\nn = 3.4 mol"
}

[
 {
  "value": 490.0,
  "misconception": "you multiplied by the milliliters — convert first: 875.0 mL = 0.8750 L, then multiply",
  "feedback": null
 },
 {
  "value": 0.64,
  "misconception": "you divided instead of multiplying — make n the subject of M = n ÷ V: n = M × V = 0.56 × 0.8750",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nM = 0.56 M\nV = 875.0 mL = 0.8750 L\nWrite down the equation:\nM = n ÷ V\nMake n the subject:\nn = M × V\nSubstitute in the values, and calculate:\nn = 0.56 × 0.8750\nn = 0.49 mol"
}

[
 {
  "value": 7.925,
  "misconception": "you divided grams by volume — the mass must first become moles: 15.85 ÷ 158.5 = 0.1000 mol, then divide by the liters",
  "feedback": null
 },
 {
  "value": 0.1,
  "misconception": "you stopped at the moles — finish the chain: M = n ÷ V = 0.1000 ÷ 2.00",
  "feedback": null
 },
 {
  "value": 5.0,
  "misconception": "you inverted the molar-mass division — the moles are the mass divided by the molar mass: 15.85 ÷ 158.5",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nm = 15.85 g\nmolar mass = 158.5 g/mol\nV = 2.00 L\nFind the moles of solute first:\nn = m ÷ molar mass\nn = 15.85 ÷ 158.5\nn = 0.1000 mol\nWrite down the equation:\nM = n ÷ V\nSubstitute in the values, and calculate:\nM = 0.1000 ÷ 2.00\nM = 0.0500 M"
}

[
 {
  "value": 56.3,
  "misconception": "you divided grams by volume — the mass must first become moles: 45.04 ÷ 225.2 = 0.2000 mol, then divide by the liters",
  "feedback": null
 },
 {
  "value": 0.2,
  "misconception": "you stopped at the moles — finish the chain: M = n ÷ V = 0.2000 ÷ 0.8000",
  "feedback": null
 },
 {
  "value": 6.25,
  "misconception": "you inverted the molar-mass division — the moles are the mass divided by the molar mass: 45.04 ÷ 225.2",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nm = 45.04 g\nmolar mass = 225.2 g/mol\nV = 800.0 mL = 0.8000 L\nFind the moles of solute first:\nn = m ÷ molar mass\nn = 45.04 ÷ 225.2\nn = 0.2000 mol\nWrite down the equation:\nM = n ÷ V\nSubstitute in the values, and calculate:\nM = 0.2000 ÷ 0.8000\nM = 0.250 M"
}

[
 {
  "value": 16.0,
  "misconception": "you used the volume ratio upside down — and the sanity check flags it: a diluted solution must come out BELOW 2.0 M",
  "feedback": null
 },
 {
  "value": 2.0,
  "misconception": "you carried the starting molarity across — dilution lowers the molarity; run M₂ = M₁V₁ ÷ V₂",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nM₁ = 2.0 M\nV₁ = 64.0 mL\nV₂ = 512.0 mL\nWrite down the equation:\nM₁V₁ = M₂V₂\nMake M₂ the subject:\nM₂ = M₁V₁ ÷ V₂\nSubstitute in the values, and calculate:\nM₂ = (2.0 × 64.0) ÷ 512.0\nM₂ = 0.25 M\nSanity check: 0.25 M is smaller than the starting 2.0 M, as a dilution demands."
}

[
 {
  "value": 0.8815,
  "misconception": "you divided by the solvent added — V₂ is the TOTAL volume: 105.0 + 405.0 = 510.0 mL",
  "feedback": null
 },
 {
  "value": 16.5143,
  "misconception": "you used the volume ratio upside down — and the sanity check flags it: a diluted solution must come out BELOW 3.4 M",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nM₁ = 3.4 M\nV₁ = 105.0 mL\nV₂ = 105.0 + 405.0 = 510.0 mL — the TOTAL volume, not the solvent added\nWrite down the equation:\nM₁V₁ = M₂V₂\nMake M₂ the subject:\nM₂ = M₁V₁ ÷ V₂\nSubstitute in the values, and calculate:\nM₂ = (3.4 × 105.0) ÷ 510.0\nM₂ = 0.70 M\nSanity check: 0.70 M is smaller than the starting 3.4 M, as a dilution demands."
}

[
 {
  "value": 13571.4,
  "misconception": "you swapped the molarities — and the sanity check flags it: the stock is stronger than the target, so V₁ must come out SMALLER than 950.0 mL",
  "feedback": null
 },
 {
  "value": 133.0,
  "misconception": "you forgot to divide by the stock's molarity M₁ = 2.0 — V₁ = M₂V₂ ÷ M₁",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nM₁ = 2.0 M\nM₂ = 0.14 M\nV₂ = 950.0 mL\nWrite down the equation:\nM₁V₁ = M₂V₂\nMake V₁ the subject:\nV₁ = M₂V₂ ÷ M₁\nSubstitute in the values, and calculate:\nV₁ = (0.14 × 950.0) ÷ 2.0\nV₁ = 66.5 mL ≈ 67 mL (2 significant figures — set by the 2.0 M and 0.14 M givens)\nSanity check: the stock is stronger than the target, so V₁ (66.5 mL) must come out smaller than V₂ (950.0 mL) — and it does."
}

[
 {
  "value": 0.37,
  "misconception": "you ignored the mole ratio — the equation uses 2 mol of KOH for every 1 mol of CuBr₂, so multiply by 2",
  "feedback": null
 },
 {
  "value": 0.185,
  "misconception": "you applied the ratio upside down — KOH carries the 2 and CuBr₂ the 1, so MULTIPLY the CuBr₂ moles by 2",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nM = 2.0 M\nV = 185.0 mL = 0.1850 L\nFind the moles of the dissolved reactant first:\nM = n ÷ V\nMake n the subject:\nn = M × V\nn(CuBr₂) = 2.0 × 0.1850\nn(CuBr₂) = 0.370 mol\nUse the mole ratio from the balanced equation:\n1 mol CuBr₂ → 2 mol KOH\nn(KOH) = 0.370 × 2\nn(KOH) = 0.74 mol"
}

[
 {
  "value": 0.54,
  "misconception": "you ignored the mole ratio — the equation makes 2 mol of AgCl for every 1 mol of MgCl₂, so multiply by 2",
  "feedback": null
 },
 {
  "value": 1080.0,
  "misconception": "you skipped the mL → L conversion — divide the milliliters by 1000 first: 540.0 mL = 0.5400 L",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nM = 1.0 M\nV = 540.0 mL = 0.5400 L\nFind the moles of the dissolved reactant first:\nM = n ÷ V\nMake n the subject:\nn = M × V\nn(MgCl₂) = 1.0 × 0.5400\nn(MgCl₂) = 0.540 mol\nUse the mole ratio from the balanced equation:\n1 mol MgCl₂ → 2 mol AgCl\nn(AgCl) = 0.540 × 2\nn(AgCl) = 1.08 mol ≈ 1.1 mol (2 significant figures — set by the 1.0 M given)"
}