Unit 9 — End of Topic Tests (reviewer copy: all keys and model answers visible)

[
 {
  "value": 288800,
  "misconception": "you multiplied by 760 instead of dividing — going TO atmospheres, divide",
  "feedback": "This answer is wrong — you multiplied by 760 instead of dividing — going TO atmospheres, divide."
 },
 {
  "value": 3.75,
  "misconception": "you divided by 101.3 — a mmHg value converts to atm through the 760 link of the chain",
  "feedback": "This answer is wrong — you divided by 101.3 — a mmHg value converts to atm through the 760 link of the chain."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP = 380 mmHg\nWrite down the equation:\n1 atm = 760 mmHg\nMake P in atm the subject:\nP in atm = P in mmHg ÷ 760\nSubstitute in the values, and calculate:\nP = 380 ÷ 760\nP = 0.500 atm"
}

[
 {
  "value": 469,
  "misconception": "you dropped the minus sign before adding — the −196 must stay negative: K = −196 + 273",
  "feedback": "This answer is wrong — you dropped the minus sign before adding — the −196 must stay negative: K = −196 + 273."
 },
 {
  "value": -469,
  "misconception": "you subtracted 273 instead of adding it — and a kelvin temperature can never be negative",
  "feedback": "This answer is wrong — you subtracted 273 instead of adding it — and a kelvin temperature can never be negative."
 }
]

{
 "keyExplanation": "Write down the values in the question:\n°C = −196 °C\nWrite down the equation:\nK = °C + 273\nSubstitute in the values, and calculate:\nK = −196 + 273\nK = 77 K\nThe answer is small but positive — a kelvin temperature is never negative."
}

[
 {
  "value": 506,
  "misconception": "you added 273 instead of subtracting — going from kelvin to Celsius runs the equation backward: °C = K − 273",
  "feedback": "This answer is wrong — you added 273 instead of subtracting — going from kelvin to Celsius runs the equation backward: °C = K − 273."
 },
 {
  "value": 40,
  "misconception": "you dropped the minus sign — 233 K sits below 273 K, so the Celsius value must be negative",
  "feedback": "This answer is wrong — you dropped the minus sign — 233 K sits below 273 K, so the Celsius value must be negative."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nK = 233 K\nWrite down the equation:\nK = °C + 273\nMake °C the subject:\n°C = K − 273\nSubstitute in the values, and calculate:\n°C = 233 − 273\n°C = −40 °C\n233 K sits below 273 K (0 °C), so the Celsius answer must come out negative."
}

[
 {
  "value": 0.197,
  "misconception": "you divided by 101.3 instead of multiplying — going FROM atmospheres, multiply",
  "feedback": "This answer is wrong — you divided by 101.3 instead of multiplying — going FROM atmospheres, multiply."
 },
 {
  "value": 15200,
  "misconception": "you used the mmHg equivalence — converting to kPa uses the 101.3 link of the chain",
  "feedback": "This answer is wrong — you used the mmHg equivalence — converting to kPa uses the 101.3 link of the chain."
 },
 {
  "value": 121.3,
  "misconception": "you added 101.3 to the atm value — converting multiplies by the equivalence, never adds it",
  "feedback": "This answer is wrong — you added 101.3 to the atm value — converting multiplies by the equivalence, never adds it."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP = 20.0 atm\nWrite down the equation:\n1 atm = 101.3 kPa\nSubstitute in the values, and calculate:\nP = 20.0 × 101.3\nP = 2026 kPa\nThe sanity check agrees: the atm number is always the smallest, so the kPa value must be far larger than 20.0."
}

[
 {
  "value": 318,
  "misconception": "you dropped the minus sign before adding — the −45 must stay negative: K = −45 + 273",
  "feedback": "This answer is wrong — you dropped the minus sign before adding — the −45 must stay negative: K = −45 + 273."
 },
 {
  "value": -318,
  "misconception": "you subtracted 273 instead of adding it — and a kelvin temperature can never be negative",
  "feedback": "This answer is wrong — you subtracted 273 instead of adding it — and a kelvin temperature can never be negative."
 }
]

{
 "keyExplanation": "Write down the values in the question:\n°C = −45 °C\nWrite down the equation:\nK = °C + 273\nSubstitute in the values, and calculate:\nK = −45 + 273\nK = 228 K\nThe −45 stays negative in the sum, yet the result comes out positive — a kelvin temperature is never negative."
}

[
 {
  "value": 584,
  "misconception": "you added 273 instead of subtracting — going from kelvin to Celsius runs the equation backward: °C = K − 273",
  "feedback": "This answer is wrong — you added 273 instead of subtracting — going from kelvin to Celsius runs the equation backward: °C = K − 273."
 },
 {
  "value": 311,
  "misconception": "you copied the kelvin value without converting — the two scales differ by 273",
  "feedback": "This answer is wrong — you copied the kelvin value without converting — the two scales differ by 273."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nK = 311 K\nWrite down the equation:\nK = °C + 273\nMake °C the subject:\n°C = K − 273\nSubstitute in the values, and calculate:\n°C = 311 − 273\n°C = 38 °C\nBecause 311 K is above 273 K, the answer lands above zero — 38 °C passes that check."
}

[
 {
  "value": 0.00151,
  "misconception": "you divided by 760 instead of multiplying — going FROM atmospheres, multiply",
  "feedback": "This answer is wrong — you divided by 760 instead of multiplying — going FROM atmospheres, multiply."
 },
 {
  "value": 116,
  "misconception": "you used the kPa equivalence — converting to mmHg uses the 760 link of the chain",
  "feedback": "This answer is wrong — you used the kPa equivalence — converting to mmHg uses the 760 link of the chain."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP = 1.15 atm\nWrite down the equation:\n1 atm = 760 mmHg\nSubstitute in the values, and calculate:\nP = 1.15 × 760\nP = 874 mmHg\nThe sanity check agrees: the atm number is always the smallest, so the mmHg value must be far larger than 1.15."
}

[
 {
  "value": 301,
  "misconception": "you dropped the minus sign before adding — the −28 must stay negative: K = −28 + 273",
  "feedback": "This answer is wrong — you dropped the minus sign before adding — the −28 must stay negative: K = −28 + 273."
 },
 {
  "value": -301,
  "misconception": "you subtracted 273 instead of adding it — and a kelvin temperature can never be negative",
  "feedback": "This answer is wrong — you subtracted 273 instead of adding it — and a kelvin temperature can never be negative."
 }
]

{
 "keyExplanation": "Write down the values in the question:\n°C = −28 °C\nWrite down the equation:\nK = °C + 273\nSubstitute in the values, and calculate:\nK = −28 + 273\nK = 245 K\n−28 °C sits below 0 °C, so the kelvin answer must land below 273 K — 245 K passes that check."
}

[
 {
  "value": 499,
  "misconception": "you added 273 instead of subtracting — going from kelvin to Celsius runs the equation backward: °C = K − 273",
  "feedback": "This answer is wrong — you added 273 instead of subtracting — going from kelvin to Celsius runs the equation backward: °C = K − 273."
 },
 {
  "value": 47,
  "misconception": "you subtracted the kelvin reading from 273 instead of subtracting 273 from it — the order matters here, and this reading lands below zero on the Celsius scale",
  "feedback": "This answer is wrong — you subtracted the kelvin reading from 273 instead of subtracting 273 from it — the order matters here, and this reading lands below zero on the Celsius scale."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nK = 226 K\nWrite down the equation:\nK = °C + 273\nMake °C the subject:\n°C = K − 273\nSubstitute in the values, and calculate:\n°C = 226 − 273\n°C = −47 °C\nBecause 226 K is below 273 K, the answer lands below zero — a negative Celsius value is expected here, not an error."
}

[
 {
  "value": 61570,
  "misconception": "you multiplied by 101.3 instead of dividing — going TO atmospheres, divide",
  "feedback": "This answer is wrong — you multiplied by 101.3 instead of dividing — going TO atmospheres, divide."
 },
 {
  "value": 0.8,
  "misconception": "you divided by 760 — a kPa value converts to atm through the 101.3 link of the chain",
  "feedback": "This answer is wrong — you divided by 760 — a kPa value converts to atm through the 101.3 link of the chain."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP = 607.8 kPa\nWrite down the equation:\n1 atm = 101.3 kPa\nMake P in atm the subject:\nP in atm = P in kPa ÷ 101.3\nSubstitute in the values, and calculate:\nP = 607.8 ÷ 101.3\nP = 6.00 atm\nThe sanity check agrees: 6.00 is the smallest of the numbers — the atm number is always the smallest."
}

[
 {
  "value": -83,
  "misconception": "you subtracted 273 instead of adding it — and a kelvin temperature can never be negative",
  "feedback": "This answer is wrong — you subtracted 273 instead of adding it — and a kelvin temperature can never be negative."
 },
 {
  "value": 190,
  "misconception": "you copied the Celsius value without converting — the two scales differ by 273",
  "feedback": "This answer is wrong — you copied the Celsius value without converting — the two scales differ by 273."
 },
 {
  "value": 290,
  "misconception": "you added 100 instead of 273",
  "feedback": "This answer is wrong — you added 100 instead of 273."
 }
]

{
 "keyExplanation": "Write down the values in the question:\n°C = 190 °C\nWrite down the equation:\nK = °C + 273\nSubstitute in the values, and calculate:\nK = 190 + 273\nK = 463 K\nA reading hotter than 0 °C must land above 273 K — 463 K passes that check."
}

[
 {
  "value": 611,
  "misconception": "you added 273 instead of subtracting — going from kelvin to Celsius runs the equation backward: °C = K − 273",
  "feedback": "This answer is wrong — you added 273 instead of subtracting — going from kelvin to Celsius runs the equation backward: °C = K − 273."
 },
 {
  "value": 338,
  "misconception": "you copied the kelvin value without converting — the two scales differ by 273",
  "feedback": "This answer is wrong — you copied the kelvin value without converting — the two scales differ by 273."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nK = 338 K\nWrite down the equation:\nK = °C + 273\nMake °C the subject:\n°C = K − 273\nSubstitute in the values, and calculate:\n°C = 338 − 273\n°C = 65 °C\nBecause 338 K is above 273 K, the answer lands above zero — 65 °C passes that check."
}

[
 {
  "value": 490960,
  "misconception": "you multiplied by 760 instead of dividing — going TO atmospheres, divide",
  "feedback": "This answer is wrong — you multiplied by 760 instead of dividing — going TO atmospheres, divide."
 },
 {
  "value": 6.38,
  "misconception": "you divided by 101.3 — a mmHg value converts to atm through the 760 link of the chain; your answer also fails the sanity check, since the atm number must be the smallest",
  "feedback": "This answer is wrong — you divided by 101.3 — a mmHg value converts to atm through the 760 link of the chain; your answer also fails the sanity check, since the atm number must be the smallest."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP = 646 mmHg\nWrite down the equation:\n1 atm = 760 mmHg\nMake P in atm the subject:\nP in atm = P in mmHg ÷ 760\nSubstitute in the values, and calculate:\nP = 646 ÷ 760\nP = 0.850 atm\nThe sanity check agrees: 0.850 is smaller than 646 — the atm number is always the smallest."
}

[
 {
  "value": -191,
  "misconception": "you subtracted 273 instead of adding it — and a kelvin temperature can never be negative",
  "feedback": "This answer is wrong — you subtracted 273 instead of adding it — and a kelvin temperature can never be negative."
 },
 {
  "value": 82,
  "misconception": "you copied the Celsius value without converting — the two scales differ by 273",
  "feedback": "This answer is wrong — you copied the Celsius value without converting — the two scales differ by 273."
 },
 {
  "value": 182,
  "misconception": "you added 100 instead of 273",
  "feedback": "This answer is wrong — you added 100 instead of 273."
 }
]

{
 "keyExplanation": "Write down the values in the question:\n°C = 82 °C\nWrite down the equation:\nK = °C + 273\nSubstitute in the values, and calculate:\nK = 82 + 273\nK = 355 K\n82 °C is warmer than 0 °C, so the kelvin answer must land above 273 K — 355 K passes that check."
}

[
 {
  "value": 578,
  "misconception": "you added 273 instead of subtracting — going from kelvin to Celsius runs the equation backward: °C = K − 273",
  "feedback": "This answer is wrong — you added 273 instead of subtracting — going from kelvin to Celsius runs the equation backward: °C = K − 273."
 },
 {
  "value": 305,
  "misconception": "you copied the kelvin value without converting — the two scales differ by 273",
  "feedback": "This answer is wrong — you copied the kelvin value without converting — the two scales differ by 273."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nK = 305 K\nWrite down the equation:\nK = °C + 273\nMake °C the subject:\n°C = K − 273\nSubstitute in the values, and calculate:\n°C = 305 − 273\n°C = 32 °C\nBecause 305 K is above 273 K, the answer lands above zero — 32 °C passes that check."
}

{
 "keyExplanation": "The cylinder is rigid and sealed — a fixed amount of gas at constant volume — so Gay-Lussac's law applies: P₁/T₁ = P₂/T₂, with both temperatures in kelvin."
}

[
 {
  "value": 2.5,
  "misconception": "you read the curve at 4.0 L instead of 2.0 L — start at the KNOWN value on its own axis",
  "feedback": "This answer is wrong — 2.5 atm is the curve's pressure at 4.0 L. Start at 2.0 L on the volume axis, move up to the curve, then across: 5.0 atm."
 },
 {
  "value": 2.0,
  "misconception": "you echoed the given volume — the question asks for the PAIRED pressure read off the curve",
  "feedback": "This answer is wrong — 2.0 is the given volume, not the pressure. At 2.0 L the curve sits at 5.0 atm."
 }
]

{
 "keyExplanation": "Find 2.0 L on the volume axis, move straight up to the curve, then straight across to the pressure axis: the pressure reads 5.0 atm.",
 "anticipatedWrong": [
  {
   "value": 2.5,
   "misconception": "you read the curve at 4.0 L instead of 2.0 L — start at the KNOWN value on its own axis",
   "feedback": "This answer is wrong — 2.5 atm is the curve's pressure at 4.0 L. Start at 2.0 L on the volume axis, move up to the curve, then across: 5.0 atm."
  },
  {
   "value": 2.0,
   "misconception": "you echoed the given volume — the question asks for the PAIRED pressure read off the curve",
   "feedback": "This answer is wrong — 2.0 is the given volume, not the pressure. At 2.0 L the curve sits at 5.0 atm."
  }
 ]
}

[
 "Write down the values in the question:",
 "P₁ = 760 mmHg",
 "V₁ = 4.0 L",
 "V₂ = 2.0 L",
 "Write down the equation:",
 "P₁V₁ = P₂V₂",
 "Make P₂ the subject:",
 "P₂ = P₁V₁ / V₂",
 "Substitute in the values, and calculate:",
 "P₂ = 760 × 4.0 / 2.0",
 "P₂ = 1520 mmHg"
]

[
 {
  "value": 380,
  "misconception": "you halved the pressure — squeezing the gas into half the space DOUBLES the pressure",
  "feedback": "This answer is wrong — halving the volume doubles the pressure: P₂ = 760 × 4.0 / 2.0 = 1520 mmHg."
 },
 {
  "value": 760,
  "misconception": "you left the pressure unchanged — at constant temperature a volume change must move the pressure",
  "feedback": "This answer is wrong — the volume halved, so the pressure cannot stay at 760 mmHg: P₂ = 760 × 4.0 / 2.0 = 1520 mmHg."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP₁ = 760 mmHg\nV₁ = 4.0 L\nV₂ = 2.0 L\nWrite down the equation:\nP₁V₁ = P₂V₂\nMake P₂ the subject:\nP₂ = P₁V₁ / V₂\nSubstitute in the values, and calculate:\nP₂ = 760 × 4.0 / 2.0\nP₂ = 1520 mmHg\nThe volume halved, so the pressure must exactly double — 1520 mmHg passes that check.",
 "anticipatedWrong": [
  {
   "value": 380,
   "misconception": "you halved the pressure — squeezing the gas into half the space DOUBLES the pressure",
   "feedback": "This answer is wrong — halving the volume doubles the pressure: P₂ = 760 × 4.0 / 2.0 = 1520 mmHg."
  },
  {
   "value": 760,
   "misconception": "you left the pressure unchanged — at constant temperature a volume change must move the pressure",
   "feedback": "This answer is wrong — the volume halved, so the pressure cannot stay at 760 mmHg: P₂ = 760 × 4.0 / 2.0 = 1520 mmHg."
  }
 ]
}

[
 "Write down the values in the question, converting every temperature to kelvin with K = °C + 273:",
 "V₁ = 2.0 L",
 "T₁ = 17 + 273 = 290 K",
 "V₂ = 3.0 L",
 "Write down the equation:",
 "V₁/T₁ = V₂/T₂",
 "Make T₂ the subject:",
 "T₂ = T₁V₂ / V₁",
 "Substitute in the values, and calculate:",
 "T₂ = 290 × 3.0 / 2.0",
 "T₂ = 435 K",
 "Convert back to Celsius: 435 − 273 = 162 °C"
]

[
 {
  "value": 25.5,
  "misconception": "you ran the ratio on the Celsius values — convert to kelvin first, then convert the answer back",
  "feedback": "This answer is wrong — Celsius values cannot ride the ratio. Convert first (17 °C = 290 K), solve T₂ = 290 × 3.0 / 2.0 = 435 K, then convert back: 435 − 273 = 162 °C."
 },
 {
  "value": 435,
  "misconception": "you stopped at the kelvin value — the question asks for the answer in degrees Celsius",
  "feedback": "This answer is wrong as given — 435 K is right but the question asks for Celsius: 435 − 273 = 162 °C."
 }
]

{
 "keyExplanation": "Write down the values in the question, converting every temperature to kelvin with K = °C + 273:\nV₁ = 2.0 L\nT₁ = 17 + 273 = 290 K\nV₂ = 3.0 L\nWrite down the equation:\nV₁/T₁ = V₂/T₂\nMake T₂ the subject:\nT₂ = T₁V₂ / V₁\nSubstitute in the values, and calculate:\nT₂ = 290 × 3.0 / 2.0\nT₂ = 435 K\nConvert back to Celsius: 435 − 273 = 162 °C\nThe pouch grew half again as large, so its kelvin temperature must be half again as high; 435 K = 162 °C passes that check.",
 "anticipatedWrong": [
  {
   "value": 25.5,
   "misconception": "you ran the ratio on the Celsius values — convert to kelvin first, then convert the answer back",
   "feedback": "This answer is wrong — Celsius values cannot ride the ratio. Convert first (17 °C = 290 K), solve T₂ = 290 × 3.0 / 2.0 = 435 K, then convert back: 435 − 273 = 162 °C."
  },
  {
   "value": 435,
   "misconception": "you stopped at the kelvin value — the question asks for the answer in degrees Celsius",
   "feedback": "This answer is wrong as given — 435 K is right but the question asks for Celsius: 435 − 273 = 162 °C."
  }
 ]
}

[
 "Write down the values in the question, converting every temperature to kelvin with K = °C + 273:",
 "P₁ = 2.00 atm",
 "T₁ = 129 + 273 = 402 K",
 "P₂ = 3.00 atm",
 "Write down the equation:",
 "P₁/T₁ = P₂/T₂",
 "Make T₂ the subject:",
 "T₂ = T₁P₂ / P₁",
 "Substitute in the values, and calculate:",
 "T₂ = 402 × 3.00 / 2.00",
 "T₂ = 603 K"
]

[
 {
  "value": 268,
  "misconception": "you flipped the pressure ratio — reaching a HIGHER pressure needs a HIGHER kelvin temperature",
  "feedback": "This answer is wrong — the pressure must climb from 2.00 to 3.00 atm, so the temperature must rise above 402 K: T₂ = 402 × 3.00 / 2.00 = 603 K."
 },
 {
  "value": 193.5,
  "misconception": "you ran the ratio on the Celsius value — convert 129 °C to kelvin before anything else",
  "feedback": "This answer is wrong — convert first: 129 °C = 402 K. Then T₂ = 402 × 3.00 / 2.00 = 603 K."
 }
]

{
 "keyExplanation": "Write down the values in the question, converting every temperature to kelvin with K = °C + 273:\nP₁ = 2.00 atm\nT₁ = 129 + 273 = 402 K\nP₂ = 3.00 atm\nWrite down the equation:\nP₁/T₁ = P₂/T₂\nMake T₂ the subject:\nT₂ = T₁P₂ / P₁\nSubstitute in the values, and calculate:\nT₂ = 402 × 3.00 / 2.00\nT₂ = 603 K\nThe pressure must rise, so T₂ had to come out above 402 K — 603 K passes that check.",
 "anticipatedWrong": [
  {
   "value": 268,
   "misconception": "you flipped the pressure ratio — reaching a HIGHER pressure needs a HIGHER kelvin temperature",
   "feedback": "This answer is wrong — the pressure must climb from 2.00 to 3.00 atm, so the temperature must rise above 402 K: T₂ = 402 × 3.00 / 2.00 = 603 K."
  },
  {
   "value": 193.5,
   "misconception": "you ran the ratio on the Celsius value — convert 129 °C to kelvin before anything else",
   "feedback": "This answer is wrong — convert first: 129 °C = 402 K. Then T₂ = 402 × 3.00 / 2.00 = 603 K."
  }
 ]
}

[
 "Write down the values in the question:",
 "V₂ = 10.0 L",
 "P₂ = 2.4 atm",
 "P₁ = 6.0 atm",
 "Write down the equation:",
 "P₁V₁ = P₂V₂",
 "Make V₁ the subject:",
 "V₁ = P₂V₂ / P₁",
 "Substitute in the values, and calculate:",
 "V₁ = 2.4 × 10.0 / 6.0",
 "V₁ = 4.0 L"
]

[
 {
  "value": 25.0,
  "misconception": "you multiplied by the pressure ratio the wrong way — the gas EXPANDED, so it must have been smaller before",
  "feedback": "This answer is wrong — the sample expanded from its earlier state, so the earlier volume must be SMALLER than 10.0 L: V₁ = 2.4 × 10.0 / 6.0 = 4.0 L."
 },
 {
  "value": 14.4,
  "misconception": "you multiplied the two pressures together (2.4 × 6.0) and left out the 10.0 L volume — make V₁ the subject first",
  "feedback": "This answer is wrong — 14.4 comes from multiplying the two pressures (2.4 × 6.0) and dropping the 10.0 L volume. Make V₁ the subject: V₁ = P₂V₂ / P₁ = 2.4 × 10.0 / 6.0 = 4.0 L."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nV₂ = 10.0 L\nP₂ = 2.4 atm\nP₁ = 6.0 atm\nWrite down the equation:\nP₁V₁ = P₂V₂\nMake V₁ the subject:\nV₁ = P₂V₂ / P₁\nSubstitute in the values, and calculate:\nV₁ = 2.4 × 10.0 / 6.0\nV₁ = 4.0 L\nThe gas ended up expanded at a lower pressure, so it must have started smaller — 4.0 L passes that check.",
 "anticipatedWrong": [
  {
   "value": 25.0,
   "misconception": "you multiplied by the pressure ratio the wrong way — the gas EXPANDED, so it must have been smaller before",
   "feedback": "This answer is wrong — the sample expanded from its earlier state, so the earlier volume must be SMALLER than 10.0 L: V₁ = 2.4 × 10.0 / 6.0 = 4.0 L."
  },
  {
   "value": 14.4,
   "misconception": "you multiplied the two pressures together (2.4 × 6.0) and left out the 10.0 L volume — make V₁ the subject first",
   "feedback": "This answer is wrong — 14.4 comes from multiplying the two pressures (2.4 × 6.0) and dropping the 10.0 L volume. Make V₁ the subject: V₁ = P₂V₂ / P₁ = 2.4 × 10.0 / 6.0 = 4.0 L."
  }
 ]
}

[
 "Write down the values in the question, converting every temperature to kelvin with K = °C + 273:",
 "P₁ = 1.00 atm",
 "V₁ = 10.0 L",
 "T₁ = 12 + 273 = 285 K",
 "P₂ = 0.500 atm",
 "T₂ = −45 + 273 = 228 K",
 "Write down the equation:",
 "P₁V₁/T₁ = P₂V₂/T₂",
 "Make V₂ the subject:",
 "V₂ = P₁V₁T₂ / (P₂T₁)",
 "Substitute in the values, and calculate:",
 "V₂ = 1.00 × 10.0 × 228 / (0.500 × 285)",
 "V₂ = 16.0 L"
]

[
 {
  "value": -75.0,
  "misconception": "you left the temperatures in Celsius — a negative volume is impossible; convert both with K = °C + 273 first",
  "feedback": "This answer is wrong — a negative volume is impossible, which signals Celsius in the ratio. Convert first (285 K and 228 K), then V₂ = 1.00 × 10.0 × 228 / (0.500 × 285) = 16.0 L."
 },
 {
  "value": 20.0,
  "misconception": "you ignored the temperature drop and solved Boyle's law only — the temperature ratio must multiply in",
  "feedback": "This answer is wrong — pressure alone would double the volume to 20.0 L, but the cooling pulls it back: V₂ = 16.0 L."
 }
]

{
 "keyExplanation": "Write down the values in the question, converting every temperature to kelvin with K = °C + 273:\nP₁ = 1.00 atm\nV₁ = 10.0 L\nT₁ = 12 + 273 = 285 K\nP₂ = 0.500 atm\nT₂ = −45 + 273 = 228 K\nWrite down the equation:\nP₁V₁/T₁ = P₂V₂/T₂\nMake V₂ the subject:\nV₂ = P₁V₁T₂ / (P₂T₁)\nSubstitute in the values, and calculate:\nV₂ = 1.00 × 10.0 × 228 / (0.500 × 285)\nV₂ = 16.0 L\nThe halved pressure roughly doubles the volume, and the cooling pulls it back — 16.0 L fits both effects.",
 "anticipatedWrong": [
  {
   "value": -75.0,
   "misconception": "you left the temperatures in Celsius — a negative volume is impossible; convert both with K = °C + 273 first",
   "feedback": "This answer is wrong — a negative volume is impossible, which signals Celsius in the ratio. Convert first (285 K and 228 K), then V₂ = 1.00 × 10.0 × 228 / (0.500 × 285) = 16.0 L."
  },
  {
   "value": 20.0,
   "misconception": "you ignored the temperature drop and solved Boyle's law only — the temperature ratio must multiply in",
   "feedback": "This answer is wrong — pressure alone would double the volume to 20.0 L, but the cooling pulls it back: V₂ = 16.0 L."
  }
 ]
}

[
 "Write down the values in the question (the rigid tank keeps the volume the same on both sides):",
 "P₁ = 1.80 atm",
 "V₁ = 6.00 L",
 "T₁ = 306 K",
 "P₂ = 2.70 atm",
 "V₂ = 6.00 L",
 "Write down the equation:",
 "P₁V₁/T₁ = P₂V₂/T₂",
 "Make T₂ the subject:",
 "T₂ = T₁P₂V₂ / (P₁V₁)",
 "Substitute in the values, and calculate:",
 "T₂ = 306 × 2.70 × 6.00 / (1.80 × 6.00)",
 "T₂ = 459 K"
]

[
 {
  "value": 204,
  "misconception": "you flipped the pressure ratio — a higher pressure needs a higher kelvin temperature",
  "feedback": "This answer is wrong — the pressure must RISE to 2.70 atm, so the temperature must rise above 306 K: T₂ = 306 × 2.70 × 6.00 / (1.80 × 6.00) = 459 K."
 },
 {
  "value": 76.5,
  "misconception": "you divided by the volume on one side only — the unchanged 6.00 L appears on both sides and cancels",
  "feedback": "This answer is wrong — the rigid tank's 6.00 L sits on BOTH sides and cancels: T₂ = 306 × 2.70 / 1.80 = 459 K."
 }
]

{
 "keyExplanation": "Write down the values in the question (the rigid tank keeps the volume the same on both sides):\nP₁ = 1.80 atm\nV₁ = 6.00 L\nT₁ = 306 K\nP₂ = 2.70 atm\nV₂ = 6.00 L\nWrite down the equation:\nP₁V₁/T₁ = P₂V₂/T₂\nMake T₂ the subject:\nT₂ = T₁P₂V₂ / (P₁V₁)\nSubstitute in the values, and calculate:\nT₂ = 306 × 2.70 × 6.00 / (1.80 × 6.00)\nT₂ = 459 K\nThe pressure must rise, so T₂ had to come out above 306 K — 459 K passes that check.",
 "anticipatedWrong": [
  {
   "value": 204,
   "misconception": "you flipped the pressure ratio — a higher pressure needs a higher kelvin temperature",
   "feedback": "This answer is wrong — the pressure must RISE to 2.70 atm, so the temperature must rise above 306 K: T₂ = 306 × 2.70 × 6.00 / (1.80 × 6.00) = 459 K."
  },
  {
   "value": 76.5,
   "misconception": "you divided by the volume on one side only — the unchanged 6.00 L appears on both sides and cancels",
   "feedback": "This answer is wrong — the rigid tank's 6.00 L sits on BOTH sides and cancels: T₂ = 306 × 2.70 / 1.80 = 459 K."
  }
 ]
}

{
 "keyExplanation": "The cylinder is rigid and sealed, so the volume and the amount of gas are fixed — Gay-Lussac's law applies: P₁/T₁ = P₂/T₂, with both temperatures in kelvin."
}

[
 {
  "value": 5.0,
  "misconception": "you echoed the given pressure — the question asks for the PAIRED volume read off the curve",
  "feedback": "This answer is wrong — 5.0 atm is the given pressure. Start at 5.0 atm on the pressure axis, move across to the curve, then down: 2.0 L."
 },
 {
  "value": 10.0,
  "misconception": "you read the volume where the pressure is 1.0 atm — check which pressure value the question names",
  "feedback": "This answer is wrong — 10.0 L is the volume at 1.0 atm. At 5.0 atm the curve sits at 2.0 L."
 }
]

{
 "keyExplanation": "Find 5.0 atm on the pressure axis, move straight across to the curve, then straight down to the volume axis: the volume reads 2.0 L.",
 "anticipatedWrong": [
  {
   "value": 5.0,
   "misconception": "you echoed the given pressure — the question asks for the PAIRED volume read off the curve",
   "feedback": "This answer is wrong — 5.0 atm is the given pressure. Start at 5.0 atm on the pressure axis, move across to the curve, then down: 2.0 L."
  },
  {
   "value": 10.0,
   "misconception": "you read the volume where the pressure is 1.0 atm — check which pressure value the question names",
   "feedback": "This answer is wrong — 10.0 L is the volume at 1.0 atm. At 5.0 atm the curve sits at 2.0 L."
  }
 ]
}

[
 "Write down the values in the question:",
 "P₁ = 2.0 atm",
 "V₁ = 9.0 L",
 "V₂ = 3.0 L",
 "Write down the equation:",
 "P₁V₁ = P₂V₂",
 "Make P₂ the subject:",
 "P₂ = P₁V₁ / V₂",
 "Substitute in the values, and calculate:",
 "P₂ = 2.0 × 9.0 / 3.0",
 "P₂ = 6.0 atm"
]

[
 {
  "value": 0.67,
  "misconception": "you divided the small volume by the large one and multiplied — the pressure must RISE when the volume shrinks",
  "feedback": "This answer is wrong — squeezing 9.0 L into 3.0 L must RAISE the pressure. Make P₂ the subject: P₂ = P₁V₁ / V₂ = 2.0 × 9.0 / 3.0 = 6.0 atm."
 },
 {
  "value": 8.0,
  "misconception": "you added the volume drop to the pressure — Boyle's law multiplies and divides, it never adds",
  "feedback": "This answer is wrong — Boyle's law is a product rule, not a sum: P₂ = P₁V₁ / V₂ = 2.0 × 9.0 / 3.0 = 6.0 atm."
 },
 {
  "value": 54.0,
  "misconception": "you multiplied all three numbers together — divide P₁V₁ by the NEW volume",
  "feedback": "This answer is wrong — you multiplied by the new volume instead of dividing by it: P₂ = P₁V₁ / V₂ = 2.0 × 9.0 / 3.0 = 6.0 atm."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP₁ = 2.0 atm\nV₁ = 9.0 L\nV₂ = 3.0 L\nWrite down the equation:\nP₁V₁ = P₂V₂\nMake P₂ the subject:\nP₂ = P₁V₁ / V₂\nSubstitute in the values, and calculate:\nP₂ = 2.0 × 9.0 / 3.0\nP₂ = 6.0 atm\nThe gas was squeezed into a third of its space, so the pressure must come out three times higher — 6.0 atm passes that check.",
 "anticipatedWrong": [
  {
   "value": 0.67,
   "misconception": "you divided the small volume by the large one and multiplied — the pressure must RISE when the volume shrinks",
   "feedback": "This answer is wrong — squeezing 9.0 L into 3.0 L must RAISE the pressure. Make P₂ the subject: P₂ = P₁V₁ / V₂ = 2.0 × 9.0 / 3.0 = 6.0 atm."
  },
  {
   "value": 8.0,
   "misconception": "you added the volume drop to the pressure — Boyle's law multiplies and divides, it never adds",
   "feedback": "This answer is wrong — Boyle's law is a product rule, not a sum: P₂ = P₁V₁ / V₂ = 2.0 × 9.0 / 3.0 = 6.0 atm."
  },
  {
   "value": 54.0,
   "misconception": "you multiplied all three numbers together — divide P₁V₁ by the NEW volume",
   "feedback": "This answer is wrong — you multiplied by the new volume instead of dividing by it: P₂ = P₁V₁ / V₂ = 2.0 × 9.0 / 3.0 = 6.0 atm."
  }
 ]
}

[
 "Write down the values in the question:",
 "V₂ = 7.0 L",
 "T₂ = 385 K",
 "T₁ = 275 K",
 "Write down the equation:",
 "V₁/T₁ = V₂/T₂",
 "Make V₁ the subject:",
 "V₁ = V₂T₁ / T₂",
 "Substitute in the values, and calculate:",
 "V₁ = 7.0 × 275 / 385",
 "V₁ = 5.0 L"
]

[
 {
  "value": 9.8,
  "misconception": "you flipped the temperature ratio — the gas was COLDER earlier, so it filled less space",
  "feedback": "This answer is wrong — at 275 K the gas must fill LESS than at 385 K: V₁ = 7.0 × 275 / 385 = 5.0 L."
 },
 {
  "value": 7.0,
  "misconception": "you left the volume unchanged — at constant pressure the volume tracks the kelvin temperature",
  "feedback": "This answer is wrong — the gas was colder at 275 K, so it filled less space then: V₁ = 7.0 × 275 / 385 = 5.0 L."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nV₂ = 7.0 L\nT₂ = 385 K\nT₁ = 275 K\nWrite down the equation:\nV₁/T₁ = V₂/T₂\nMake V₁ the subject:\nV₁ = V₂T₁ / T₂\nSubstitute in the values, and calculate:\nV₁ = 7.0 × 275 / 385\nV₁ = 5.0 L\nThe gas was colder earlier, so it must have filled less space — 5.0 L passes that check.",
 "anticipatedWrong": [
  {
   "value": 9.8,
   "misconception": "you flipped the temperature ratio — the gas was COLDER earlier, so it filled less space",
   "feedback": "This answer is wrong — at 275 K the gas must fill LESS than at 385 K: V₁ = 7.0 × 275 / 385 = 5.0 L."
  },
  {
   "value": 7.0,
   "misconception": "you left the volume unchanged — at constant pressure the volume tracks the kelvin temperature",
   "feedback": "This answer is wrong — the gas was colder at 275 K, so it filled less space then: V₁ = 7.0 × 275 / 385 = 5.0 L."
  }
 ]
}

[
 "Write down the values in the question:",
 "P₂ = 5.00 atm",
 "T₂ = 550 K",
 "T₁ = 330 K",
 "Write down the equation:",
 "P₁/T₁ = P₂/T₂",
 "Make P₁ the subject:",
 "P₁ = P₂T₁ / T₂",
 "Substitute in the values, and calculate:",
 "P₁ = 5.00 × 330 / 550",
 "P₁ = 3.00 atm"
]

[
 {
  "value": 8.33,
  "misconception": "you flipped the temperature ratio — the tank was COOLER earlier, so its pressure was lower",
  "feedback": "This answer is wrong — at 330 K the pressure must be LOWER than at 550 K: P₁ = 5.00 × 330 / 550 = 3.00 atm."
 },
 {
  "value": 5.0,
  "misconception": "you left the pressure unchanged — in a rigid tank the pressure tracks the kelvin temperature",
  "feedback": "This answer is wrong — the temperature fell from 550 K to 330 K, so the pressure fell too: P₁ = 5.00 × 330 / 550 = 3.00 atm."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP₂ = 5.00 atm\nT₂ = 550 K\nT₁ = 330 K\nWrite down the equation:\nP₁/T₁ = P₂/T₂\nMake P₁ the subject:\nP₁ = P₂T₁ / T₂\nSubstitute in the values, and calculate:\nP₁ = 5.00 × 330 / 550\nP₁ = 3.00 atm\nThe tank was cooler earlier, so its pressure had to be lower — 3.00 atm passes that check.",
 "anticipatedWrong": [
  {
   "value": 8.33,
   "misconception": "you flipped the temperature ratio — the tank was COOLER earlier, so its pressure was lower",
   "feedback": "This answer is wrong — at 330 K the pressure must be LOWER than at 550 K: P₁ = 5.00 × 330 / 550 = 3.00 atm."
  },
  {
   "value": 5.0,
   "misconception": "you left the pressure unchanged — in a rigid tank the pressure tracks the kelvin temperature",
   "feedback": "This answer is wrong — the temperature fell from 550 K to 330 K, so the pressure fell too: P₁ = 5.00 × 330 / 550 = 3.00 atm."
  }
 ]
}

[
 "Write down the values in the question:",
 "P₂ = 5.5 atm",
 "V₂ = 4.0 L",
 "V₁ = 11.0 L",
 "Write down the equation:",
 "P₁V₁ = P₂V₂",
 "Make P₁ the subject:",
 "P₁ = P₂V₂ / V₁",
 "Substitute in the values, and calculate:",
 "P₁ = 5.5 × 4.0 / 11.0",
 "P₁ = 2.0 atm"
]

[
 {
  "value": 15.125,
  "misconception": "you flipped the volume ratio — before the squeeze the gas filled MORE space, so its pressure was LOWER",
  "feedback": "This answer is wrong — before the squeeze the gas was at 11.0 L, so its pressure had to be lower than 5.5 atm: P₁ = P₂V₂ / V₁ = 5.5 × 4.0 / 11.0 = 2.0 atm."
 },
 {
  "value": 5.5,
  "misconception": "you echoed the after-pressure — the question asks for the pressure BEFORE the squeeze",
  "feedback": "This answer is wrong — 5.5 atm is the pressure now. Before the squeeze: P₁ = 5.5 × 4.0 / 11.0 = 2.0 atm."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP₂ = 5.5 atm\nV₂ = 4.0 L\nV₁ = 11.0 L\nWrite down the equation:\nP₁V₁ = P₂V₂\nMake P₁ the subject:\nP₁ = P₂V₂ / V₁\nSubstitute in the values, and calculate:\nP₁ = 5.5 × 4.0 / 11.0\nP₁ = 2.0 atm\nThe gas started in more space, so its pressure had to start lower — 2.0 atm passes that check.",
 "anticipatedWrong": [
  {
   "value": 15.125,
   "misconception": "you flipped the volume ratio — before the squeeze the gas filled MORE space, so its pressure was LOWER",
   "feedback": "This answer is wrong — before the squeeze the gas was at 11.0 L, so its pressure had to be lower than 5.5 atm: P₁ = P₂V₂ / V₁ = 5.5 × 4.0 / 11.0 = 2.0 atm."
  },
  {
   "value": 5.5,
   "misconception": "you echoed the after-pressure — the question asks for the pressure BEFORE the squeeze",
   "feedback": "This answer is wrong — 5.5 atm is the pressure now. Before the squeeze: P₁ = 5.5 × 4.0 / 11.0 = 2.0 atm."
  }
 ]
}

[
 "Write down the values in the question, labeling each value condition 1 (before) or condition 2 (after):",
 "P₁ = 1.00 atm",
 "T₁ = 390 K",
 "P₂ = 3.00 atm",
 "V₂ = 4.00 L",
 "T₂ = 260 K",
 "Write down the equation:",
 "P₁V₁/T₁ = P₂V₂/T₂",
 "Make V₁ the subject:",
 "V₁ = P₂V₂T₁ / (P₁T₂)",
 "Substitute in the values, and calculate:",
 "V₁ = 3.00 × 4.00 × 390 / (1.00 × 260)",
 "V₁ = 18.0 L"
]

[
 {
  "value": 8.0,
  "misconception": "you flipped the temperature ratio — label each value as condition 1 or condition 2 before touching the equation",
  "feedback": "This answer is wrong — label the conditions first: the before-values are condition 1. V₁ = P₂V₂T₁ / (P₁T₂) = 3.00 × 4.00 × 390 / (1.00 × 260) = 18.0 L."
 },
 {
  "value": 2.0,
  "misconception": "you flipped the pressure ratio — the sample was at LOWER pressure before, so it filled MORE space",
  "feedback": "This answer is wrong — before the change the gas was at only 1.00 atm, so it must have been LARGER than 4.00 L: V₁ = 3.00 × 4.00 × 390 / (1.00 × 260) = 18.0 L."
 }
]

{
 "keyExplanation": "Write down the values in the question, labeling each value condition 1 (before) or condition 2 (after):\nP₁ = 1.00 atm\nT₁ = 390 K\nP₂ = 3.00 atm\nV₂ = 4.00 L\nT₂ = 260 K\nWrite down the equation:\nP₁V₁/T₁ = P₂V₂/T₂\nMake V₁ the subject:\nV₁ = P₂V₂T₁ / (P₁T₂)\nSubstitute in the values, and calculate:\nV₁ = 3.00 × 4.00 × 390 / (1.00 × 260)\nV₁ = 18.0 L\nThe gas ended up squeezed to a higher pressure, so it must have started larger — 18.0 L passes that check.",
 "anticipatedWrong": [
  {
   "value": 8.0,
   "misconception": "you flipped the temperature ratio — label each value as condition 1 or condition 2 before touching the equation",
   "feedback": "This answer is wrong — label the conditions first: the before-values are condition 1. V₁ = P₂V₂T₁ / (P₁T₂) = 3.00 × 4.00 × 390 / (1.00 × 260) = 18.0 L."
  },
  {
   "value": 2.0,
   "misconception": "you flipped the pressure ratio — the sample was at LOWER pressure before, so it filled MORE space",
   "feedback": "This answer is wrong — before the change the gas was at only 1.00 atm, so it must have been LARGER than 4.00 L: V₁ = 3.00 × 4.00 × 390 / (1.00 × 260) = 18.0 L."
  }
 ]
}

[
 "Write down the values in the question:",
 "P₁ = 3.4 atm",
 "V₁ = 6.0 L",
 "T₁ = 380 K",
 "V₂ = 2.0 L",
 "T₂ = 190 K",
 "Write down the equation:",
 "P₁V₁/T₁ = P₂V₂/T₂",
 "Make P₂ the subject:",
 "P₂ = P₁V₁T₂ / (V₂T₁)",
 "Substitute in the values, and calculate:",
 "P₂ = 3.4 × 6.0 × 190 / (2.0 × 380)",
 "P₂ = 5.1 atm"
]

[
 {
  "value": 10.2,
  "misconception": "you solved Boyle's law only — the halved kelvin temperature must multiply in",
  "feedback": "This answer is wrong — the squeeze alone would triple the pressure to 10.2 atm, but the halved temperature pulls it back: P₂ = 3.4 × 6.0 × 190 / (2.0 × 380) = 5.1 atm."
 },
 {
  "value": 20.4,
  "misconception": "you flipped the temperature ratio — a colder gas pushes less, not more",
  "feedback": "This answer is wrong — the temperature ratio is upside down: P₂ = 3.4 × 6.0 × 190 / (2.0 × 380) = 5.1 atm."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP₁ = 3.4 atm\nV₁ = 6.0 L\nT₁ = 380 K\nV₂ = 2.0 L\nT₂ = 190 K\nWrite down the equation:\nP₁V₁/T₁ = P₂V₂/T₂\nMake P₂ the subject:\nP₂ = P₁V₁T₂ / (V₂T₁)\nSubstitute in the values, and calculate:\nP₂ = 3.4 × 6.0 × 190 / (2.0 × 380)\nP₂ = 5.1 atm\nThe squeeze raises the pressure and the cooling lowers it — 5.1 atm sits between the two pulls, as it should.",
 "anticipatedWrong": [
  {
   "value": 10.2,
   "misconception": "you solved Boyle's law only — the halved kelvin temperature must multiply in",
   "feedback": "This answer is wrong — the squeeze alone would triple the pressure to 10.2 atm, but the halved temperature pulls it back: P₂ = 3.4 × 6.0 × 190 / (2.0 × 380) = 5.1 atm."
  },
  {
   "value": 20.4,
   "misconception": "you flipped the temperature ratio — a colder gas pushes less, not more",
   "feedback": "This answer is wrong — the temperature ratio is upside down: P₂ = 3.4 × 6.0 × 190 / (2.0 × 380) = 5.1 atm."
  }
 ]
}

{
 "keyExplanation": "Rigid walls fix the volume and the seal fixes the amount, so Gay-Lussac's law applies: P₁/T₁ = P₂/T₂, temperatures in kelvin."
}

[
 {
  "value": 4.0,
  "misconception": "you echoed the given volume — the question asks for the PAIRED pressure read off the curve",
  "feedback": "This answer is wrong — 4.0 is the given volume. Start at 4.0 L, move up to the curve, then across: the pressure reads 2.0 atm."
 },
 {
  "value": 1.0,
  "misconception": "you read the curve at 8.0 L instead of 4.0 L — check which volume the question names",
  "feedback": "This answer is wrong — 1.0 atm is the curve's pressure at 8.0 L. At 4.0 L the curve sits at 2.0 atm."
 }
]

{
 "keyExplanation": "Start at 4.0 L on the volume axis, move straight up to the curve, then straight across to the pressure axis — the pressure reads 2.0 atm.",
 "anticipatedWrong": [
  {
   "value": 4.0,
   "misconception": "you echoed the given volume — the question asks for the PAIRED pressure read off the curve",
   "feedback": "This answer is wrong — 4.0 is the given volume. Start at 4.0 L, move up to the curve, then across: the pressure reads 2.0 atm."
  },
  {
   "value": 1.0,
   "misconception": "you read the curve at 8.0 L instead of 4.0 L — check which volume the question names",
   "feedback": "This answer is wrong — 1.0 atm is the curve's pressure at 8.0 L. At 4.0 L the curve sits at 2.0 atm."
  }
 ]
}

[
 "Write down the values in the question:",
 "P₁ = 96 kPa",
 "V₁ = 6.0 L",
 "V₂ = 4.0 L",
 "Write down the equation:",
 "P₁V₁ = P₂V₂",
 "Make P₂ the subject:",
 "P₂ = P₁V₁ / V₂",
 "Substitute in the values, and calculate:",
 "P₂ = 96 × 6.0 / 4.0",
 "P₂ = 144 kPa"
]

[
 {
  "value": 64,
  "misconception": "you flipped the volume ratio — squeezing the gas must RAISE the pressure",
  "feedback": "This answer is wrong — the volume shrank, so the pressure must rise above 96 kPa: P₂ = 96 × 6.0 / 4.0 = 144 kPa."
 },
 {
  "value": 98,
  "misconception": "you added the volume drop to the pressure — Boyle's law multiplies and divides, it never adds",
  "feedback": "This answer is wrong — Boyle's law is a product rule: P₂ = P₁V₁ / V₂ = 96 × 6.0 / 4.0 = 144 kPa."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP₁ = 96 kPa\nV₁ = 6.0 L\nV₂ = 4.0 L\nWrite down the equation:\nP₁V₁ = P₂V₂\nMake P₂ the subject:\nP₂ = P₁V₁ / V₂\nSubstitute in the values, and calculate:\nP₂ = 96 × 6.0 / 4.0\nP₂ = 144 kPa\nThe volume went down, so the pressure must come out higher — 144 kPa passes that check.",
 "anticipatedWrong": [
  {
   "value": 64,
   "misconception": "you flipped the volume ratio — squeezing the gas must RAISE the pressure",
   "feedback": "This answer is wrong — the volume shrank, so the pressure must rise above 96 kPa: P₂ = 96 × 6.0 / 4.0 = 144 kPa."
  },
  {
   "value": 98,
   "misconception": "you added the volume drop to the pressure — Boyle's law multiplies and divides, it never adds",
   "feedback": "This answer is wrong — Boyle's law is a product rule: P₂ = P₁V₁ / V₂ = 96 × 6.0 / 4.0 = 144 kPa."
  }
 ]
}

[
 "Write down the values in the question, converting every temperature to kelvin with K = °C + 273:",
 "V₁ = 2.5 L",
 "T₁ = 42 + 273 = 315 K",
 "T₂ = 105 + 273 = 378 K",
 "Write down the equation:",
 "V₁/T₁ = V₂/T₂",
 "Make V₂ the subject:",
 "V₂ = V₁T₂ / T₁",
 "Substitute in the values, and calculate:",
 "V₂ = 2.5 × 378 / 315",
 "V₂ = 3.0 L"
]

[
 {
  "value": 6.25,
  "misconception": "you used the Celsius values directly — convert every temperature to kelvin first",
  "feedback": "This answer is wrong — you ran the ratio on the Celsius numbers. Convert first: 42 °C = 315 K and 105 °C = 378 K, then V₂ = 2.5 × 378 / 315 = 3.0 L."
 },
 {
  "value": 2.08,
  "misconception": "you flipped the temperature ratio — warming at steady pressure must GROW the volume",
  "feedback": "This answer is wrong — the temperature ratio is upside down; warming must grow the volume: V₂ = V₁T₂ / T₁ = 2.5 × 378 / 315 = 3.0 L."
 },
 {
  "value": 2.5,
  "misconception": "you left the volume unchanged — at constant pressure the volume tracks the kelvin temperature",
  "feedback": "This answer is wrong — at constant pressure the volume tracks the kelvin temperature: V₂ = 2.5 × 378 / 315 = 3.0 L."
 }
]

{
 "keyExplanation": "Write down the values in the question, converting every temperature to kelvin with K = °C + 273:\nV₁ = 2.5 L\nT₁ = 42 + 273 = 315 K\nT₂ = 105 + 273 = 378 K\nWrite down the equation:\nV₁/T₁ = V₂/T₂\nMake V₂ the subject:\nV₂ = V₁T₂ / T₁\nSubstitute in the values, and calculate:\nV₂ = 2.5 × 378 / 315\nV₂ = 3.0 L\nThe gas warmed, so at steady pressure it must come out larger than 2.5 L — 3.0 L passes that check.",
 "anticipatedWrong": [
  {
   "value": 6.25,
   "misconception": "you used the Celsius values directly — convert every temperature to kelvin first",
   "feedback": "This answer is wrong — you ran the ratio on the Celsius numbers. Convert first: 42 °C = 315 K and 105 °C = 378 K, then V₂ = 2.5 × 378 / 315 = 3.0 L."
  },
  {
   "value": 2.08,
   "misconception": "you flipped the temperature ratio — warming at steady pressure must GROW the volume",
   "feedback": "This answer is wrong — the temperature ratio is upside down; warming must grow the volume: V₂ = V₁T₂ / T₁ = 2.5 × 378 / 315 = 3.0 L."
  },
  {
   "value": 2.5,
   "misconception": "you left the volume unchanged — at constant pressure the volume tracks the kelvin temperature",
   "feedback": "This answer is wrong — at constant pressure the volume tracks the kelvin temperature: V₂ = 2.5 × 378 / 315 = 3.0 L."
  }
 ]
}

[
 "Write down the values in the question, converting every temperature to kelvin with K = °C + 273:",
 "P₁ = 0.800 atm",
 "T₁ = −73 + 273 = 200 K",
 "T₂ = 32 + 273 = 305 K",
 "Write down the equation:",
 "P₁/T₁ = P₂/T₂",
 "Make P₂ the subject:",
 "P₂ = P₁T₂ / T₁",
 "Substitute in the values, and calculate:",
 "P₂ = 0.800 × 305 / 200",
 "P₂ = 1.22 atm"
]

[
 {
  "value": -0.351,
  "misconception": "you left the temperatures in Celsius — a negative pressure is impossible; convert with K = °C + 273 first",
  "feedback": "This answer is wrong — a negative pressure is impossible, which signals Celsius values in the ratio. Convert first: −73 °C = 200 K, 32 °C = 305 K, then P₂ = 0.800 × 305 / 200 = 1.22 atm."
 },
 {
  "value": 0.525,
  "misconception": "you flipped the temperature ratio — warming a sealed, rigid cylinder must RAISE the pressure",
  "feedback": "This answer is wrong — the cylinder warmed, so the pressure must rise above 0.800 atm: P₂ = 0.800 × 305 / 200 = 1.22 atm."
 }
]

{
 "keyExplanation": "Write down the values in the question, converting every temperature to kelvin with K = °C + 273:\nP₁ = 0.800 atm\nT₁ = −73 + 273 = 200 K\nT₂ = 32 + 273 = 305 K\nWrite down the equation:\nP₁/T₁ = P₂/T₂\nMake P₂ the subject:\nP₂ = P₁T₂ / T₁\nSubstitute in the values, and calculate:\nP₂ = 0.800 × 305 / 200\nP₂ = 1.22 atm\nThe cylinder warmed, so the pressure must come out above 0.800 atm — 1.22 atm passes that check.",
 "anticipatedWrong": [
  {
   "value": -0.351,
   "misconception": "you left the temperatures in Celsius — a negative pressure is impossible; convert with K = °C + 273 first",
   "feedback": "This answer is wrong — a negative pressure is impossible, which signals Celsius values in the ratio. Convert first: −73 °C = 200 K, 32 °C = 305 K, then P₂ = 0.800 × 305 / 200 = 1.22 atm."
  },
  {
   "value": 0.525,
   "misconception": "you flipped the temperature ratio — warming a sealed, rigid cylinder must RAISE the pressure",
   "feedback": "This answer is wrong — the cylinder warmed, so the pressure must rise above 0.800 atm: P₂ = 0.800 × 305 / 200 = 1.22 atm."
  }
 ]
}

[
 "Write down the values in the question:",
 "V₂ = 640 mL",
 "P₂ = 3.75 atm",
 "P₁ = 3.0 atm",
 "Write down the equation:",
 "P₁V₁ = P₂V₂",
 "Make V₁ the subject:",
 "V₁ = P₂V₂ / P₁",
 "Substitute in the values, and calculate:",
 "V₁ = 3.75 × 640 / 3.0",
 "V₁ = 800 mL"
]

[
 {
  "value": 512,
  "misconception": "you flipped the pressure ratio — the earlier pressure was LOWER, so the earlier volume was LARGER",
  "feedback": "This answer is wrong — at the lower earlier pressure the gas filled MORE space: V₁ = P₂V₂ / P₁ = 3.75 × 640 / 3.0 = 800 mL."
 },
 {
  "value": 640,
  "misconception": "you echoed the current volume — the question asks for the volume BEFORE the squeeze",
  "feedback": "This answer is wrong — 640 mL is the volume now. Before: V₁ = 3.75 × 640 / 3.0 = 800 mL."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nV₂ = 640 mL\nP₂ = 3.75 atm\nP₁ = 3.0 atm\nWrite down the equation:\nP₁V₁ = P₂V₂\nMake V₁ the subject:\nV₁ = P₂V₂ / P₁\nSubstitute in the values, and calculate:\nV₁ = 3.75 × 640 / 3.0\nV₁ = 800 mL\nThe gas was at a lower pressure before, so it filled more space — 800 mL passes that check.",
 "anticipatedWrong": [
  {
   "value": 512,
   "misconception": "you flipped the pressure ratio — the earlier pressure was LOWER, so the earlier volume was LARGER",
   "feedback": "This answer is wrong — at the lower earlier pressure the gas filled MORE space: V₁ = P₂V₂ / P₁ = 3.75 × 640 / 3.0 = 800 mL."
  },
  {
   "value": 640,
   "misconception": "you echoed the current volume — the question asks for the volume BEFORE the squeeze",
   "feedback": "This answer is wrong — 640 mL is the volume now. Before: V₁ = 3.75 × 640 / 3.0 = 800 mL."
  }
 ]
}

[
 "Write down the values in the question, converting every temperature to kelvin with K = °C + 273:",
 "P₁ = 1.44 atm",
 "V₁ = 4.4 L",
 "T₁ = 57 + 273 = 330 K",
 "P₂ = 0.72 atm",
 "T₂ = −33 + 273 = 240 K",
 "Write down the equation:",
 "P₁V₁/T₁ = P₂V₂/T₂",
 "Make V₂ the subject:",
 "V₂ = P₁V₁T₂ / (P₂T₁)",
 "Substitute in the values, and calculate:",
 "V₂ = 1.44 × 4.4 × 240 / (0.72 × 330)",
 "V₂ = 6.4 L"
]

[
 {
  "value": -5.1,
  "misconception": "you left the temperatures in Celsius — a negative volume is impossible; convert both with K = °C + 273 first",
  "feedback": "This answer is wrong — a negative volume is impossible, which signals Celsius in the ratio. Convert first: 57 °C = 330 K and −33 °C = 240 K, then V₂ = 1.44 × 4.4 × 240 / (0.72 × 330) = 6.4 L."
 },
 {
  "value": 8.8,
  "misconception": "you solved Boyle's law only — the cooling must pull the volume back below the pressure-only answer",
  "feedback": "This answer is wrong — halving the pressure alone would give 8.8 L, but the temperature ratio must multiply in: V₂ = 1.44 × 4.4 × 240 / (0.72 × 330) = 6.4 L."
 }
]

{
 "keyExplanation": "Write down the values in the question, converting every temperature to kelvin with K = °C + 273:\nP₁ = 1.44 atm\nV₁ = 4.4 L\nT₁ = 57 + 273 = 330 K\nP₂ = 0.72 atm\nT₂ = −33 + 273 = 240 K\nWrite down the equation:\nP₁V₁/T₁ = P₂V₂/T₂\nMake V₂ the subject:\nV₂ = P₁V₁T₂ / (P₂T₁)\nSubstitute in the values, and calculate:\nV₂ = 1.44 × 4.4 × 240 / (0.72 × 330)\nV₂ = 6.4 L\nThe halved pressure would double the volume, and the cooling pulls it back — 6.4 L fits both effects.",
 "anticipatedWrong": [
  {
   "value": -5.1,
   "misconception": "you left the temperatures in Celsius — a negative volume is impossible; convert both with K = °C + 273 first",
   "feedback": "This answer is wrong — a negative volume is impossible, which signals Celsius in the ratio. Convert first: 57 °C = 330 K and −33 °C = 240 K, then V₂ = 1.44 × 4.4 × 240 / (0.72 × 330) = 6.4 L."
  },
  {
   "value": 8.8,
   "misconception": "you solved Boyle's law only — the cooling must pull the volume back below the pressure-only answer",
   "feedback": "This answer is wrong — halving the pressure alone would give 8.8 L, but the temperature ratio must multiply in: V₂ = 1.44 × 4.4 × 240 / (0.72 × 330) = 6.4 L."
  }
 ]
}

[
 "Write down the values in the question, converting every temperature to kelvin with K = °C + 273:",
 "P₁ = 3.8 atm",
 "V₁ = 2.0 L",
 "T₁ = 37 + 273 = 310 K",
 "P₂ = 1.9 atm",
 "V₂ = 6.0 L",
 "Write down the equation:",
 "P₁V₁/T₁ = P₂V₂/T₂",
 "Make T₂ the subject:",
 "T₂ = T₁P₂V₂ / (P₁V₁)",
 "Substitute in the values, and calculate:",
 "T₂ = 310 × 1.9 × 6.0 / (3.8 × 2.0)",
 "T₂ = 465 K"
]

[
 {
  "value": 55.5,
  "misconception": "you ran the ratio on the Celsius value — convert 37 °C to kelvin before anything else",
  "feedback": "This answer is wrong — convert first: 37 °C = 310 K. Then T₂ = T₁P₂V₂ / (P₁V₁) = 310 × 1.9 × 6.0 / (3.8 × 2.0) = 465 K."
 },
 {
  "value": 207,
  "misconception": "you flipped the combined ratio — solve for T₂ by multiplying T₁ by the CONDITION-2 product over the condition-1 product",
  "feedback": "This answer is wrong — T₂ = T₁ × P₂V₂ / (P₁V₁) = 310 × 1.9 × 6.0 / (3.8 × 2.0) = 465 K."
 }
]

{
 "keyExplanation": "Write down the values in the question, converting every temperature to kelvin with K = °C + 273:\nP₁ = 3.8 atm\nV₁ = 2.0 L\nT₁ = 37 + 273 = 310 K\nP₂ = 1.9 atm\nV₂ = 6.0 L\nWrite down the equation:\nP₁V₁/T₁ = P₂V₂/T₂\nMake T₂ the subject:\nT₂ = T₁P₂V₂ / (P₁V₁)\nSubstitute in the values, and calculate:\nT₂ = 310 × 1.9 × 6.0 / (3.8 × 2.0)\nT₂ = 465 K\nThe tripled volume outweighs the halved pressure, so the gas must be hotter — 465 K passes that check.",
 "anticipatedWrong": [
  {
   "value": 55.5,
   "misconception": "you ran the ratio on the Celsius value — convert 37 °C to kelvin before anything else",
   "feedback": "This answer is wrong — convert first: 37 °C = 310 K. Then T₂ = T₁P₂V₂ / (P₁V₁) = 310 × 1.9 × 6.0 / (3.8 × 2.0) = 465 K."
  },
  {
   "value": 207,
   "misconception": "you flipped the combined ratio — solve for T₂ by multiplying T₁ by the CONDITION-2 product over the condition-1 product",
   "feedback": "This answer is wrong — T₂ = T₁ × P₂V₂ / (P₁V₁) = 310 × 1.9 × 6.0 / (3.8 × 2.0) = 465 K."
  }
 ]
}

{
 "keyExplanation": "A sealed, rigid sphere keeps the amount and the volume fixed, so the pressure tracks the kelvin temperature by Gay-Lussac's law: P₁/T₁ = P₂/T₂."
}

[
 {
  "value": 6.0,
  "misconception": "you echoed the given pressure — the question asks for the PAIRED volume read off the curve",
  "feedback": "This answer is wrong — 6.0 atm is the given pressure. Start at 6.0 atm, move across to the curve, then down: the volume reads 2.0 L."
 },
 {
  "value": 3.0,
  "misconception": "you read the volume where the pressure is 4.0 atm — check which pressure value the question names",
  "feedback": "This answer is wrong — 3.0 L pairs with 4.0 atm on this curve. At 6.0 atm the volume reads 2.0 L."
 }
]

{
 "keyExplanation": "Start at 6.0 atm on the pressure axis, move straight across to the curve, then straight down to the volume axis — the volume reads 2.0 L.",
 "anticipatedWrong": [
  {
   "value": 6.0,
   "misconception": "you echoed the given pressure — the question asks for the PAIRED volume read off the curve",
   "feedback": "This answer is wrong — 6.0 atm is the given pressure. Start at 6.0 atm, move across to the curve, then down: the volume reads 2.0 L."
  },
  {
   "value": 3.0,
   "misconception": "you read the volume where the pressure is 4.0 atm — check which pressure value the question names",
   "feedback": "This answer is wrong — 3.0 L pairs with 4.0 atm on this curve. At 6.0 atm the volume reads 2.0 L."
  }
 ]
}

[
 "Write down the values in the question:",
 "P₁ = 0.88 atm",
 "V₁ = 7.5 mL",
 "P₂ = 3.0 atm",
 "Write down the equation:",
 "P₁V₁ = P₂V₂",
 "Make V₂ the subject:",
 "V₂ = P₁V₁ / P₂",
 "Substitute in the values, and calculate:",
 "V₂ = 0.88 × 7.5 / 3.0",
 "V₂ = 2.2 mL"
]

[
 {
  "value": 25.6,
  "misconception": "you flipped the pressure ratio — a higher pressure means the gas was squeezed into LESS space",
  "feedback": "This answer is wrong — the pressure rose, so the volume must shrink below 7.5 mL: V₂ = P₁V₁ / P₂ = 0.88 × 7.5 / 3.0 = 2.2 mL."
 },
 {
  "value": 7.5,
  "misconception": "you left the volume unchanged — at constant temperature a pressure rise must squeeze the gas smaller",
  "feedback": "This answer is wrong — 7.5 mL is the starting volume. After the push: V₂ = 0.88 × 7.5 / 3.0 = 2.2 mL."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP₁ = 0.88 atm\nV₁ = 7.5 mL\nP₂ = 3.0 atm\nWrite down the equation:\nP₁V₁ = P₂V₂\nMake V₂ the subject:\nV₂ = P₁V₁ / P₂\nSubstitute in the values, and calculate:\nV₂ = 0.88 × 7.5 / 3.0\nV₂ = 2.2 mL\nThe pressure went up, so the volume must come out smaller — 2.2 mL passes that check.",
 "anticipatedWrong": [
  {
   "value": 25.6,
   "misconception": "you flipped the pressure ratio — a higher pressure means the gas was squeezed into LESS space",
   "feedback": "This answer is wrong — the pressure rose, so the volume must shrink below 7.5 mL: V₂ = P₁V₁ / P₂ = 0.88 × 7.5 / 3.0 = 2.2 mL."
  },
  {
   "value": 7.5,
   "misconception": "you left the volume unchanged — at constant temperature a pressure rise must squeeze the gas smaller",
   "feedback": "This answer is wrong — 7.5 mL is the starting volume. After the push: V₂ = 0.88 × 7.5 / 3.0 = 2.2 mL."
  }
 ]
}

[
 "Write down the values in the question:",
 "V₁ = 4.5 L",
 "T₁ = 240 K",
 "V₂ = 6.0 L",
 "Write down the equation:",
 "V₁/T₁ = V₂/T₂",
 "Make T₂ the subject:",
 "T₂ = T₁V₂ / V₁",
 "Substitute in the values, and calculate:",
 "T₂ = 240 × 6.0 / 4.5",
 "T₂ = 320 K"
]

[
 {
  "value": 180,
  "misconception": "you flipped the volume ratio — a larger volume at constant pressure needs a HIGHER kelvin temperature",
  "feedback": "This answer is wrong — the pouch grew, so the temperature must rise above 240 K: T₂ = T₁V₂ / V₁ = 240 × 6.0 / 4.5 = 320 K."
 },
 {
  "value": 47,
  "misconception": "you converted a kelvin answer to Celsius — the question asks for kelvin",
  "feedback": "This answer is wrong — no conversion is needed here; the temperatures are already kelvin: T₂ = 240 × 6.0 / 4.5 = 320 K."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nV₁ = 4.5 L\nT₁ = 240 K\nV₂ = 6.0 L\nWrite down the equation:\nV₁/T₁ = V₂/T₂\nMake T₂ the subject:\nT₂ = T₁V₂ / V₁\nSubstitute in the values, and calculate:\nT₂ = 240 × 6.0 / 4.5\nT₂ = 320 K\nThe pouch grew, so the temperature must come out above 240 K — 320 K passes that check.",
 "anticipatedWrong": [
  {
   "value": 180,
   "misconception": "you flipped the volume ratio — a larger volume at constant pressure needs a HIGHER kelvin temperature",
   "feedback": "This answer is wrong — the pouch grew, so the temperature must rise above 240 K: T₂ = T₁V₂ / V₁ = 240 × 6.0 / 4.5 = 320 K."
  },
  {
   "value": 47,
   "misconception": "you converted a kelvin answer to Celsius — the question asks for kelvin",
   "feedback": "This answer is wrong — no conversion is needed here; the temperatures are already kelvin: T₂ = 240 × 6.0 / 4.5 = 320 K."
  }
 ]
}

[
 "Write down the values in the question:",
 "P₁ = 1.15 atm",
 "T₁ = 210 K",
 "T₂ = 630 K",
 "Write down the equation:",
 "P₁/T₁ = P₂/T₂",
 "Make P₂ the subject:",
 "P₂ = P₁T₂ / T₁",
 "Substitute in the values, and calculate:",
 "P₂ = 1.15 × 630 / 210",
 "P₂ = 3.45 atm"
]

[
 {
  "value": 0.383,
  "misconception": "you flipped the temperature ratio — warming a sealed, rigid flask must RAISE the pressure",
  "feedback": "This answer is wrong — the flask warmed, so the pressure must rise above 1.15 atm: P₂ = P₁T₂ / T₁ = 1.15 × 630 / 210 = 3.45 atm."
 },
 {
  "value": 1.15,
  "misconception": "you left the pressure unchanged — in a rigid container the pressure tracks the kelvin temperature",
  "feedback": "This answer is wrong — tripling the kelvin temperature triples the pressure: P₂ = 1.15 × 630 / 210 = 3.45 atm."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP₁ = 1.15 atm\nT₁ = 210 K\nT₂ = 630 K\nWrite down the equation:\nP₁/T₁ = P₂/T₂\nMake P₂ the subject:\nP₂ = P₁T₂ / T₁\nSubstitute in the values, and calculate:\nP₂ = 1.15 × 630 / 210\nP₂ = 3.45 atm\nThe flask warmed, so the pressure must come out higher — 3.45 atm passes that check.",
 "anticipatedWrong": [
  {
   "value": 0.383,
   "misconception": "you flipped the temperature ratio — warming a sealed, rigid flask must RAISE the pressure",
   "feedback": "This answer is wrong — the flask warmed, so the pressure must rise above 1.15 atm: P₂ = P₁T₂ / T₁ = 1.15 × 630 / 210 = 3.45 atm."
  },
  {
   "value": 1.15,
   "misconception": "you left the pressure unchanged — in a rigid container the pressure tracks the kelvin temperature",
   "feedback": "This answer is wrong — tripling the kelvin temperature triples the pressure: P₂ = 1.15 × 630 / 210 = 3.45 atm."
  }
 ]
}

[
 "Write down the values in the question:",
 "P₂ = 125 kPa",
 "V₂ = 9.6 L",
 "V₁ = 6.0 L",
 "Write down the equation:",
 "P₁V₁ = P₂V₂",
 "Make P₁ the subject:",
 "P₁ = P₂V₂ / V₁",
 "Substitute in the values, and calculate:",
 "P₁ = 125 × 9.6 / 6.0",
 "P₁ = 200 kPa"
]

[
 {
  "value": 78.125,
  "misconception": "you flipped the volume ratio — before expanding, the gas was squeezed smaller, so its pressure was HIGHER",
  "feedback": "This answer is wrong — before the expansion the gas sat in less space, so its pressure was higher: P₁ = P₂V₂ / V₁ = 125 × 9.6 / 6.0 = 200 kPa."
 },
 {
  "value": 125,
  "misconception": "you echoed the after-pressure — the question asks for the pressure BEFORE the expansion",
  "feedback": "This answer is wrong — 125 kPa is the pressure now. Before: P₁ = 125 × 9.6 / 6.0 = 200 kPa."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP₂ = 125 kPa\nV₂ = 9.6 L\nV₁ = 6.0 L\nWrite down the equation:\nP₁V₁ = P₂V₂\nMake P₁ the subject:\nP₁ = P₂V₂ / V₁\nSubstitute in the values, and calculate:\nP₁ = 125 × 9.6 / 6.0\nP₁ = 200 kPa\nThe gas grew into more space, so its pressure before had to be higher — 200 kPa passes that check.",
 "anticipatedWrong": [
  {
   "value": 78.125,
   "misconception": "you flipped the volume ratio — before expanding, the gas was squeezed smaller, so its pressure was HIGHER",
   "feedback": "This answer is wrong — before the expansion the gas sat in less space, so its pressure was higher: P₁ = P₂V₂ / V₁ = 125 × 9.6 / 6.0 = 200 kPa."
  },
  {
   "value": 125,
   "misconception": "you echoed the after-pressure — the question asks for the pressure BEFORE the expansion",
   "feedback": "This answer is wrong — 125 kPa is the pressure now. Before: P₁ = 125 × 9.6 / 6.0 = 200 kPa."
  }
 ]
}

[
 "Write down the values in the question, labeling each value condition 1 (before) or condition 2 (after):",
 "P₁ = 0.45 atm",
 "T₁ = 480 K",
 "P₂ = 2.7 atm",
 "V₂ = 2.0 L",
 "T₂ = 160 K",
 "Write down the equation:",
 "P₁V₁/T₁ = P₂V₂/T₂",
 "Make V₁ the subject:",
 "V₁ = P₂V₂T₁ / (P₁T₂)",
 "Substitute in the values, and calculate:",
 "V₁ = 2.7 × 2.0 × 480 / (0.45 × 160)",
 "V₁ = 36.0 L"
]

[
 {
  "value": 4.0,
  "misconception": "you flipped the temperature ratio — label each value as condition 1 or condition 2 before touching the equation",
  "feedback": "This answer is wrong — 4.0 L comes from FLIPPING the temperature ratio (multiplying by 160/480 instead of 480/160). Label the before-values condition 1 first: V₁ = P₂V₂T₁ / (P₁T₂) = 2.7 × 2.0 × 480 / (0.45 × 160) = 36.0 L."
 },
 {
  "value": 12.0,
  "misconception": "you solved the pressure ratio only — the temperature ratio must multiply in as well",
  "feedback": "This answer is wrong — pressure alone gives 12.0 L, but the gas was also three times hotter before: V₁ = 2.7 × 2.0 × 480 / (0.45 × 160) = 36.0 L."
 }
]

{
 "keyExplanation": "Write down the values in the question, labeling each value condition 1 (before) or condition 2 (after):\nP₁ = 0.45 atm\nT₁ = 480 K\nP₂ = 2.7 atm\nV₂ = 2.0 L\nT₂ = 160 K\nWrite down the equation:\nP₁V₁/T₁ = P₂V₂/T₂\nMake V₁ the subject:\nV₁ = P₂V₂T₁ / (P₁T₂)\nSubstitute in the values, and calculate:\nV₁ = 2.7 × 2.0 × 480 / (0.45 × 160)\nV₁ = 36.0 L\nThe gas ended up compressed and cold, so it must have started much larger — 36.0 L passes that check.",
 "anticipatedWrong": [
  {
   "value": 4.0,
   "misconception": "you flipped the temperature ratio — label each value as condition 1 or condition 2 before touching the equation",
   "feedback": "This answer is wrong — 4.0 L comes from FLIPPING the temperature ratio (multiplying by 160/480 instead of 480/160). Label the before-values condition 1 first: V₁ = P₂V₂T₁ / (P₁T₂) = 2.7 × 2.0 × 480 / (0.45 × 160) = 36.0 L."
  },
  {
   "value": 12.0,
   "misconception": "you solved the pressure ratio only — the temperature ratio must multiply in as well",
   "feedback": "This answer is wrong — pressure alone gives 12.0 L, but the gas was also three times hotter before: V₁ = 2.7 × 2.0 × 480 / (0.45 × 160) = 36.0 L."
  }
 ]
}

[
 "Write down the values in the question, converting every temperature to kelvin with K = °C + 273 (the steady pressure is entered on both sides):",
 "P₁ = 1.1 atm",
 "V₁ = 5.6 L",
 "T₁ = 7 + 273 = 280 K",
 "P₂ = 1.1 atm",
 "V₂ = 8.4 L",
 "Write down the equation:",
 "P₁V₁/T₁ = P₂V₂/T₂",
 "Make T₂ the subject (the equal pressures cancel):",
 "T₂ = T₁V₂ / V₁",
 "Substitute in the values, and calculate:",
 "T₂ = 280 × 8.4 / 5.6",
 "T₂ = 420 K"
]

[
 {
  "value": 10.5,
  "misconception": "you ran the ratio on the Celsius value — convert 7 °C to kelvin before anything else",
  "feedback": "This answer is wrong — convert first: 7 °C = 280 K. The steady 1.1 atm cancels from both sides, leaving T₂ = 280 × 8.4 / 5.6 = 420 K."
 },
 {
  "value": 187,
  "misconception": "you flipped the volume ratio — a larger volume at steady pressure needs a higher kelvin temperature",
  "feedback": "This answer is wrong — the gas grew, so it must be hotter than 280 K: T₂ = 280 × 8.4 / 5.6 = 420 K."
 }
]

{
 "keyExplanation": "Write down the values in the question, converting every temperature to kelvin with K = °C + 273 (the steady pressure is entered on both sides):\nP₁ = 1.1 atm\nV₁ = 5.6 L\nT₁ = 7 + 273 = 280 K\nP₂ = 1.1 atm\nV₂ = 8.4 L\nWrite down the equation:\nP₁V₁/T₁ = P₂V₂/T₂\nMake T₂ the subject (the equal pressures cancel):\nT₂ = T₁V₂ / V₁\nSubstitute in the values, and calculate:\nT₂ = 280 × 8.4 / 5.6\nT₂ = 420 K\nThe gas grew by half again, so its kelvin temperature must rise by half again — 420 K passes that check.",
 "anticipatedWrong": [
  {
   "value": 10.5,
   "misconception": "you ran the ratio on the Celsius value — convert 7 °C to kelvin before anything else",
   "feedback": "This answer is wrong — convert first: 7 °C = 280 K. The steady 1.1 atm cancels from both sides, leaving T₂ = 280 × 8.4 / 5.6 = 420 K."
  },
  {
   "value": 187,
   "misconception": "you flipped the volume ratio — a larger volume at steady pressure needs a higher kelvin temperature",
   "feedback": "This answer is wrong — the gas grew, so it must be hotter than 280 K: T₂ = 280 × 8.4 / 5.6 = 420 K."
  }
 ]
}

{
 "keyExplanation": "Rigid and sealed means fixed volume and fixed amount — Gay-Lussac's law compares the two states: P₁/T₁ = P₂/T₂, temperatures in kelvin."
}

[
 {
  "value": 2.0,
  "misconception": "you echoed the given pressure — the question asks for the PAIRED volume read off the curve",
  "feedback": "This answer is wrong — 2.0 atm is the given pressure. Start at 2.0 atm, move across to the curve, then down: the volume reads 3.0 L."
 },
 {
  "value": 6.0,
  "misconception": "you read the volume where the pressure is 1.0 atm — check which pressure value the question names",
  "feedback": "This answer is wrong — 6.0 L pairs with 1.0 atm on this curve. At 2.0 atm the volume reads 3.0 L."
 }
]

{
 "keyExplanation": "Start at 2.0 atm on the pressure axis, move straight across to the curve, then straight down — the volume reads 3.0 L.",
 "anticipatedWrong": [
  {
   "value": 2.0,
   "misconception": "you echoed the given pressure — the question asks for the PAIRED volume read off the curve",
   "feedback": "This answer is wrong — 2.0 atm is the given pressure. Start at 2.0 atm, move across to the curve, then down: the volume reads 3.0 L."
  },
  {
   "value": 6.0,
   "misconception": "you read the volume where the pressure is 1.0 atm — check which pressure value the question names",
   "feedback": "This answer is wrong — 6.0 L pairs with 1.0 atm on this curve. At 2.0 atm the volume reads 3.0 L."
  }
 ]
}

[
 "Write down the values in the question:",
 "P₁ = 2.85 atm",
 "V₁ = 5.00 L",
 "P₂ = 0.950 atm",
 "Write down the equation:",
 "P₁V₁ = P₂V₂",
 "Make V₂ the subject:",
 "V₂ = P₁V₁ / P₂",
 "Substitute in the values, and calculate:",
 "V₂ = 2.85 × 5.00 / 0.950",
 "V₂ = 15.0 L"
]

[
 {
  "value": 1.67,
  "misconception": "you INVERTED the pressure ratio (multiplied by 0.950/2.85 instead of 2.85/0.950) — a falling pressure means the gas spreads into MORE space",
  "feedback": "This answer is wrong — 1.67 L comes from inverting the pressure ratio (multiplying 5.00 L by 0.950/2.85 instead of 2.85/0.950). The pressure fell to a third, so the volume must TRIPLE: V₂ = P₁V₁ / P₂ = 2.85 × 5.00 / 0.950 = 15.0 L."
 },
 {
  "value": 13.5,
  "misconception": "you multiplied all three numbers together (2.85 × 5.00 × 0.950) instead of dividing P₁V₁ by the new pressure",
  "feedback": "This answer is wrong — 13.5 comes from multiplying all three given numbers together (2.85 × 5.00 × 0.950). Divide the product P₁V₁ by the NEW pressure instead: V₂ = 2.85 × 5.00 / 0.950 = 15.0 L."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP₁ = 2.85 atm\nV₁ = 5.00 L\nP₂ = 0.950 atm\nWrite down the equation:\nP₁V₁ = P₂V₂\nMake V₂ the subject:\nV₂ = P₁V₁ / P₂\nSubstitute in the values, and calculate:\nV₂ = 2.85 × 5.00 / 0.950\nV₂ = 15.0 L\nThe pressure went down, so the volume must come out larger — 15.0 L passes that check.",
 "anticipatedWrong": [
  {
   "value": 1.67,
   "misconception": "you INVERTED the pressure ratio (multiplied by 0.950/2.85 instead of 2.85/0.950) — a falling pressure means the gas spreads into MORE space",
   "feedback": "This answer is wrong — 1.67 L comes from inverting the pressure ratio (multiplying 5.00 L by 0.950/2.85 instead of 2.85/0.950). The pressure fell to a third, so the volume must TRIPLE: V₂ = P₁V₁ / P₂ = 2.85 × 5.00 / 0.950 = 15.0 L."
  },
  {
   "value": 13.5,
   "misconception": "you multiplied all three numbers together (2.85 × 5.00 × 0.950) instead of dividing P₁V₁ by the new pressure",
   "feedback": "This answer is wrong — 13.5 comes from multiplying all three given numbers together (2.85 × 5.00 × 0.950). Divide the product P₁V₁ by the NEW pressure instead: V₂ = 2.85 × 5.00 / 0.950 = 15.0 L."
  }
 ]
}

[
 "Write down the values in the question, converting every temperature to kelvin with K = °C + 273:",
 "V₁ = 1.8 L",
 "T₁ = 7 + 273 = 280 K",
 "T₂ = 147 + 273 = 420 K",
 "Write down the equation:",
 "V₁/T₁ = V₂/T₂",
 "Make V₂ the subject:",
 "V₂ = V₁T₂ / T₁",
 "Substitute in the values, and calculate:",
 "V₂ = 1.8 × 420 / 280",
 "V₂ = 2.7 L"
]

[
 {
  "value": 37.8,
  "misconception": "you ran the ratio on the Celsius values — convert every temperature to kelvin first",
  "feedback": "This answer is wrong — Celsius values cannot ride the ratio (147/7 is not the real temperature factor). Convert first: 7 °C = 280 K, 147 °C = 420 K, then V₂ = 1.8 × 420 / 280 = 2.7 L."
 },
 {
  "value": 1.2,
  "misconception": "you flipped the temperature ratio — warming at steady pressure must GROW the volume",
  "feedback": "This answer is wrong — the bag warmed, so it must grow beyond 1.8 L: V₂ = V₁T₂ / T₁ = 1.8 × 420 / 280 = 2.7 L."
 }
]

{
 "keyExplanation": "Write down the values in the question, converting every temperature to kelvin with K = °C + 273:\nV₁ = 1.8 L\nT₁ = 7 + 273 = 280 K\nT₂ = 147 + 273 = 420 K\nWrite down the equation:\nV₁/T₁ = V₂/T₂\nMake V₂ the subject:\nV₂ = V₁T₂ / T₁\nSubstitute in the values, and calculate:\nV₂ = 1.8 × 420 / 280\nV₂ = 2.7 L\nThe gas warmed, so the volume must come out larger — 2.7 L passes that check.",
 "anticipatedWrong": [
  {
   "value": 37.8,
   "misconception": "you ran the ratio on the Celsius values — convert every temperature to kelvin first",
   "feedback": "This answer is wrong — Celsius values cannot ride the ratio (147/7 is not the real temperature factor). Convert first: 7 °C = 280 K, 147 °C = 420 K, then V₂ = 1.8 × 420 / 280 = 2.7 L."
  },
  {
   "value": 1.2,
   "misconception": "you flipped the temperature ratio — warming at steady pressure must GROW the volume",
   "feedback": "This answer is wrong — the bag warmed, so it must grow beyond 1.8 L: V₂ = V₁T₂ / T₁ = 1.8 × 420 / 280 = 2.7 L."
  }
 ]
}

[
 "Write down the values in the question, converting every temperature to kelvin with K = °C + 273:",
 "P₁ = 3.60 atm",
 "T₁ = 47 + 273 = 320 K",
 "P₂ = 4.95 atm",
 "Write down the equation:",
 "P₁/T₁ = P₂/T₂",
 "Make T₂ the subject:",
 "T₂ = T₁P₂ / P₁",
 "Substitute in the values, and calculate:",
 "T₂ = 320 × 4.95 / 3.60",
 "T₂ = 440 K"
]

[
 {
  "value": 64.6,
  "misconception": "you ran the ratio on the Celsius value — convert 47 °C to kelvin before anything else",
  "feedback": "This answer is wrong — convert first: 47 °C = 320 K. Then T₂ = T₁P₂ / P₁ = 320 × 4.95 / 3.60 = 440 K."
 },
 {
  "value": 233,
  "misconception": "you flipped the pressure ratio — reaching a HIGHER pressure needs a HIGHER kelvin temperature",
  "feedback": "This answer is wrong — the pressure must climb to 4.95 atm, so the temperature must rise above 320 K: T₂ = 320 × 4.95 / 3.60 = 440 K."
 }
]

{
 "keyExplanation": "Write down the values in the question, converting every temperature to kelvin with K = °C + 273:\nP₁ = 3.60 atm\nT₁ = 47 + 273 = 320 K\nP₂ = 4.95 atm\nWrite down the equation:\nP₁/T₁ = P₂/T₂\nMake T₂ the subject:\nT₂ = T₁P₂ / P₁\nSubstitute in the values, and calculate:\nT₂ = 320 × 4.95 / 3.60\nT₂ = 440 K\nThe pressure must rise, so T₂ had to come out above 320 K — 440 K passes that check.",
 "anticipatedWrong": [
  {
   "value": 64.6,
   "misconception": "you ran the ratio on the Celsius value — convert 47 °C to kelvin before anything else",
   "feedback": "This answer is wrong — convert first: 47 °C = 320 K. Then T₂ = T₁P₂ / P₁ = 320 × 4.95 / 3.60 = 440 K."
  },
  {
   "value": 233,
   "misconception": "you flipped the pressure ratio — reaching a HIGHER pressure needs a HIGHER kelvin temperature",
   "feedback": "This answer is wrong — the pressure must climb to 4.95 atm, so the temperature must rise above 320 K: T₂ = 320 × 4.95 / 3.60 = 440 K."
  }
 ]
}

[
 "Write down the values in the question:",
 "P₂ = 3.5 atm",
 "V₂ = 3.0 L",
 "P₁ = 2.0 atm",
 "Write down the equation:",
 "P₁V₁ = P₂V₂",
 "Make V₁ the subject:",
 "V₁ = P₂V₂ / P₁",
 "Substitute in the values, and calculate:",
 "V₁ = 3.5 × 3.0 / 2.0",
 "V₁ = 5.25 L"
]

[
 {
  "value": 1.71,
  "misconception": "you flipped the pressure ratio — the gas was at a LOWER pressure before, so it filled MORE space",
  "feedback": "This answer is wrong — before the squeeze the pressure was lower, so the volume was larger: V₁ = P₂V₂ / P₁ = 3.5 × 3.0 / 2.0 = 5.25 L."
 },
 {
  "value": 3.0,
  "misconception": "you echoed the current volume — the question asks for the volume BEFORE the squeeze",
  "feedback": "This answer is wrong — 3.0 L is the volume now. Before: V₁ = 3.5 × 3.0 / 2.0 = 5.25 L."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP₂ = 3.5 atm\nV₂ = 3.0 L\nP₁ = 2.0 atm\nWrite down the equation:\nP₁V₁ = P₂V₂\nMake V₁ the subject:\nV₁ = P₂V₂ / P₁\nSubstitute in the values, and calculate:\nV₁ = 3.5 × 3.0 / 2.0\nV₁ = 5.25 L\nThe pressure rose in the squeeze, so the volume had to start larger — 5.25 L passes that check.",
 "anticipatedWrong": [
  {
   "value": 1.71,
   "misconception": "you flipped the pressure ratio — the gas was at a LOWER pressure before, so it filled MORE space",
   "feedback": "This answer is wrong — before the squeeze the pressure was lower, so the volume was larger: V₁ = P₂V₂ / P₁ = 3.5 × 3.0 / 2.0 = 5.25 L."
  },
  {
   "value": 3.0,
   "misconception": "you echoed the current volume — the question asks for the volume BEFORE the squeeze",
   "feedback": "This answer is wrong — 3.0 L is the volume now. Before: V₁ = 3.5 × 3.0 / 2.0 = 5.25 L."
  }
 ]
}

[
 "Write down the values in the question:",
 "P₁ = 0.460 atm",
 "V₁ = 6.30 L",
 "T₁ = 140 K",
 "P₂ = 0.690 atm",
 "T₂ = 420 K",
 "Write down the equation:",
 "P₁V₁/T₁ = P₂V₂/T₂",
 "Make V₂ the subject:",
 "V₂ = P₁V₁T₂ / (P₂T₁)",
 "Substitute in the values, and calculate:",
 "V₂ = 0.460 × 6.30 × 420 / (0.690 × 140)",
 "V₂ = 12.6 L"
]

[
 {
  "value": 4.2,
  "misconception": "you solved the pressure ratio only — the tripled kelvin temperature must multiply in",
  "feedback": "This answer is wrong — pressure alone would shrink the gas to 4.2 L, but the temperature tripled: V₂ = 0.460 × 6.30 × 420 / (0.690 × 140) = 12.6 L."
 },
 {
  "value": 1.4,
  "misconception": "you flipped the temperature ratio — a hotter gas needs MORE room at any given pressure",
  "feedback": "This answer is wrong — the temperature ratio is upside down: V₂ = 0.460 × 6.30 × 420 / (0.690 × 140) = 12.6 L."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP₁ = 0.460 atm\nV₁ = 6.30 L\nT₁ = 140 K\nP₂ = 0.690 atm\nT₂ = 420 K\nWrite down the equation:\nP₁V₁/T₁ = P₂V₂/T₂\nMake V₂ the subject:\nV₂ = P₁V₁T₂ / (P₂T₁)\nSubstitute in the values, and calculate:\nV₂ = 0.460 × 6.30 × 420 / (0.690 × 140)\nV₂ = 12.6 L\nThe pressure rise squeezes the gas but the tripled temperature swells it more — growth to 12.6 L fits the bigger effect.",
 "anticipatedWrong": [
  {
   "value": 4.2,
   "misconception": "you solved the pressure ratio only — the tripled kelvin temperature must multiply in",
   "feedback": "This answer is wrong — pressure alone would shrink the gas to 4.2 L, but the temperature tripled: V₂ = 0.460 × 6.30 × 420 / (0.690 × 140) = 12.6 L."
  },
  {
   "value": 1.4,
   "misconception": "you flipped the temperature ratio — a hotter gas needs MORE room at any given pressure",
   "feedback": "This answer is wrong — the temperature ratio is upside down: V₂ = 0.460 × 6.30 × 420 / (0.690 × 140) = 12.6 L."
  }
 ]
}

[
 "Write down the values in the question, labeling each value condition 1 (before) or condition 2 (after):",
 "P₁ = 4.0 atm",
 "V₁ = 3.0 L",
 "P₂ = 1.0 atm",
 "V₂ = 6.0 L",
 "T₂ = 130 K",
 "Write down the equation:",
 "P₁V₁/T₁ = P₂V₂/T₂",
 "Make T₁ the subject:",
 "T₁ = T₂P₁V₁ / (P₂V₂)",
 "Substitute in the values, and calculate:",
 "T₁ = 130 × 4.0 × 3.0 / (1.0 × 6.0)",
 "T₁ = 260 K"
]

[
 {
  "value": 65,
  "misconception": "you flipped the combined ratio — solve for T₁ by multiplying T₂ by the condition-1 product over the condition-2 product",
  "feedback": "This answer is wrong — T₁ = T₂ × P₁V₁ / (P₂V₂) = 130 × 4.0 × 3.0 / (1.0 × 6.0) = 260 K."
 },
 {
  "value": 130,
  "misconception": "you echoed the after-temperature — the question asks for the temperature BEFORE the change",
  "feedback": "This answer is wrong — 130 K is the temperature now. Before: T₁ = 130 × 4.0 × 3.0 / (1.0 × 6.0) = 260 K."
 }
]

{
 "keyExplanation": "Write down the values in the question, labeling each value condition 1 (before) or condition 2 (after):\nP₁ = 4.0 atm\nV₁ = 3.0 L\nP₂ = 1.0 atm\nV₂ = 6.0 L\nT₂ = 130 K\nWrite down the equation:\nP₁V₁/T₁ = P₂V₂/T₂\nMake T₁ the subject:\nT₁ = T₂P₁V₁ / (P₂V₂)\nSubstitute in the values, and calculate:\nT₁ = 130 × 4.0 × 3.0 / (1.0 × 6.0)\nT₁ = 260 K\nThe before-state packed twice the pressure-volume product, so it had to be twice as hot — 260 K passes that check.",
 "anticipatedWrong": [
  {
   "value": 65,
   "misconception": "you flipped the combined ratio — solve for T₁ by multiplying T₂ by the condition-1 product over the condition-2 product",
   "feedback": "This answer is wrong — T₁ = T₂ × P₁V₁ / (P₂V₂) = 130 × 4.0 × 3.0 / (1.0 × 6.0) = 260 K."
  },
  {
   "value": 130,
   "misconception": "you echoed the after-temperature — the question asks for the temperature BEFORE the change",
   "feedback": "This answer is wrong — 130 K is the temperature now. Before: T₁ = 130 × 4.0 × 3.0 / (1.0 × 6.0) = 260 K."
  }
 ]
}

[
 {
  "value": 273,
  "misconception": "you gave the kelvin value — 273 K is standard temperature in kelvin; in Celsius it is 0 °C",
  "feedback": "This answer is wrong — you gave the kelvin value — 273 K is standard temperature in kelvin; in Celsius it is 0 °C."
 },
 {
  "value": 25,
  "misconception": "you gave room temperature — standard temperature is 0 °C",
  "feedback": "This answer is wrong — you gave room temperature — standard temperature is 0 °C."
 }
]

{
 "keyExplanation": "Standard temperature is 273 K, which is 0 °C."
}

[
 {
  "value": 273,
  "misconception": "you gave standard temperature — 273 is the kelvin value at STP; the molar volume is 22.4 L",
  "feedback": "This answer is wrong — you gave standard temperature — 273 is the kelvin value at STP; the molar volume is 22.4 L."
 },
 {
  "value": 11.2,
  "misconception": "you halved the molar volume — one full mole of any gas fills the full 22.4 L at STP",
  "feedback": "This answer is wrong — you halved the molar volume — one full mole of any gas fills the full 22.4 L at STP."
 }
]

{
 "keyExplanation": "One mole of any gas occupies 22.4 L at STP — ethane included."
}

[
 {
  "value": 752.64,
  "misconception": "you multiplied by the molar volume instead of dividing",
  "feedback": "This answer is wrong — you multiplied by the molar volume instead of dividing."
 },
 {
  "value": 0.667,
  "misconception": "you divided the molar volume by the volume — the gas volume goes on top",
  "feedback": "This answer is wrong — you divided the molar volume by the volume — the gas volume goes on top."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nV = 33.6 L\nWrite down the equation:\nn = V ÷ 22.4 L/mol\nSubstitute in the values, and calculate:\nn = 33.6 / 22.4\nn = 1.50 mol\n33.6 L is more than 22.4 L, so the answer had to exceed one mole — 1.50 mol passes that check."
}

[
 {
  "value": 2508.8,
  "misconception": "you multiplied by the molar volume instead of dividing",
  "feedback": "This answer is wrong — you multiplied by the molar volume instead of dividing."
 },
 {
  "value": 0.2,
  "misconception": "you divided the molar volume by the volume — the gas volume goes on top",
  "feedback": "This answer is wrong — you divided the molar volume by the volume — the gas volume goes on top."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nV = 112 L\nWrite down the equation:\nn = V ÷ 22.4 L/mol\nSubstitute in the values, and calculate:\nn = 112 / 22.4\nn = 5.00 mol\n112 L is five times 22.4 L, so the answer had to land at five moles — 5.00 mol passes that check."
}

[
 {
  "value": 100.35,
  "misconception": "you multiplied by the molar volume instead of dividing",
  "feedback": "This answer is wrong — you multiplied by the molar volume instead of dividing."
 },
 {
  "value": 5.0,
  "misconception": "you divided the molar volume by the volume — the gas volume goes on top",
  "feedback": "This answer is wrong — you divided the molar volume by the volume — the gas volume goes on top."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nV = 4.48 L\nWrite down the equation:\nn = V ÷ 22.4 L/mol\nSubstitute in the values, and calculate:\nn = 4.48 / 22.4\nn = 0.200 mol\n4.48 L is less than 22.4 L, so the answer had to come out below one mole — 0.200 mol passes that check."
}

[
 {
  "value": 0.223,
  "misconception": "you divided by the molar volume instead of multiplying",
  "feedback": "This answer is wrong — you divided by the molar volume instead of multiplying."
 },
 {
  "value": 4.48,
  "misconception": "you divided the molar volume by the moles instead of multiplying them",
  "feedback": "This answer is wrong — you divided the molar volume by the moles instead of multiplying them."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nn = 5.00 mol\nWrite down the equation:\nV = n × 22.4 L/mol\nSubstitute in the values, and calculate:\nV = 5.00 × 22.4\nV = 112 L\nFive moles must fill five times 22.4 L — 112 L passes that check."
}

[
 {
  "value": 0.00223,
  "misconception": "you divided by the molar volume instead of multiplying",
  "feedback": "This answer is wrong — you divided by the molar volume instead of multiplying."
 },
 {
  "value": 448,
  "misconception": "you divided the molar volume by the moles instead of multiplying them",
  "feedback": "This answer is wrong — you divided the molar volume by the moles instead of multiplying them."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nn = 0.0500 mol\nWrite down the equation:\nV = n × 22.4 L/mol\nSubstitute in the values, and calculate:\nV = 0.0500 × 22.4\nV = 1.12 L\nWell under one mole must fill well under 22.4 L — 1.12 L passes that check; 448 L fails it."
}

[
 {
  "value": 0.0123,
  "misconception": "you divided by the molar volume instead of multiplying",
  "feedback": "This answer is wrong — you divided by the molar volume instead of multiplying."
 },
 {
  "value": 81.5,
  "misconception": "you divided the molar volume by the moles instead of multiplying them",
  "feedback": "This answer is wrong — you divided the molar volume by the moles instead of multiplying them."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nn = 0.275 mol\nWrite down the equation:\nV = n × 22.4 L/mol\nSubstitute in the values, and calculate:\nV = 0.275 × 22.4\nV = 6.16 L\nA bit more than a quarter of a mole must fill a bit more than a quarter of 22.4 L — 6.16 L passes that check."
}

[
 {
  "value": 5.72,
  "misconception": "you multiplied PV by nR instead of dividing PV by nR",
  "feedback": "This answer is wrong — you multiplied PV by nR instead of dividing PV by nR."
 },
 {
  "value": 0.00472,
  "misconception": "you divided nR by PV instead of PV by nR",
  "feedback": "This answer is wrong — you divided nR by PV instead of PV by nR."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP = 1.06 atm\nV = 32.84 L\nn = 2.00 mol\nWrite down the equation:\nPV = nRT\nMake T the subject:\nT = PV ÷ (nR)\nSubstitute in the values, and calculate:\nT = (1.06 × 32.84) ÷ (2.00 × 0.0821)\nT = 212 K"
}

[
 {
  "value": 0.826,
  "misconception": "you substituted the Celsius temperature — convert first: 127 + 273 = 400 K",
  "feedback": "This answer is wrong — you substituted the Celsius temperature — convert first: 127 + 273 = 400 K."
 },
 {
  "value": 0.385,
  "misconception": "you divided V by nRT — P is nRT divided by V",
  "feedback": "This answer is wrong — you divided V by nRT — P is nRT divided by V."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nn = 0.650 mol\nV = 8.21 L\nConvert the temperature to kelvin:\nT = 127 + 273 = 400 K\nWrite down the equation:\nPV = nRT\nMake P the subject:\nP = nRT ÷ V\nSubstitute in the values, and calculate:\nP = 0.650 × 0.0821 × 400 ÷ 8.21\nP = 2.60 atm"
}

[
 {
  "value": 0.0378,
  "misconception": "you substituted 760 without converting — 760 mmHg is exactly 1.00 atm",
  "feedback": "This answer is wrong — you substituted 760 without converting — 760 mmHg is exactly 1.00 atm."
 },
 {
  "value": 3.78,
  "misconception": "you converted 760 mmHg to 7.60 atm — 760 mmHg is 1.00 atm, not 7.60",
  "feedback": "This answer is wrong — you converted 760 mmHg to 7.60 atm — 760 mmHg is 1.00 atm, not 7.60."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nn = 1.00 mol\nT = 350 K\nConvert the pressure to atm:\nP = 760 mmHg = 1.00 atm\nWrite down the equation:\nPV = nRT\nMake V the subject:\nV = nRT ÷ P\nSubstitute in the values, and calculate:\nV = 1.00 × 0.0821 × 350 ÷ 1.00\nV = 28.7 L"
}

[
 {
  "value": 0,
  "misconception": "you gave the Celsius value — standard temperature is 0 °C, which is 273 K",
  "feedback": "This answer is wrong — you gave the Celsius value — standard temperature is 0 °C, which is 273 K."
 },
 {
  "value": 298,
  "misconception": "you gave room temperature in kelvin — standard temperature is 273 K, colder than a typical room",
  "feedback": "This answer is wrong — you gave room temperature in kelvin — standard temperature is 273 K, colder than a typical room."
 }
]

{
 "keyExplanation": "'At STP' fixes the temperature at standard temperature, which is 273 K (0 °C)."
}

[
 {
  "value": 273,
  "misconception": "you gave standard temperature — 273 is the kelvin value at STP; the molar volume is 22.4 L",
  "feedback": "This answer is wrong — you gave standard temperature — 273 is the kelvin value at STP; the molar volume is 22.4 L."
 },
 {
  "value": 44.8,
  "misconception": "you doubled the molar volume — ONE mole of any gas fills 22.4 L at STP",
  "feedback": "This answer is wrong — you doubled the molar volume — ONE mole of any gas fills 22.4 L at STP."
 }
]

{
 "keyExplanation": "One mole of any gas occupies 22.4 L at STP — krypton included."
}

[
 {
  "value": 1756.16,
  "misconception": "you multiplied by the molar volume instead of dividing",
  "feedback": "This answer is wrong — you multiplied by the molar volume instead of dividing."
 },
 {
  "value": 0.286,
  "misconception": "you divided the molar volume by the volume — the gas volume goes on top",
  "feedback": "This answer is wrong — you divided the molar volume by the volume — the gas volume goes on top."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nV = 78.4 L\nWrite down the equation:\nn = V ÷ 22.4 L/mol\nSubstitute in the values, and calculate:\nn = 78.4 / 22.4\nn = 3.50 mol\n78.4 L is more than 22.4 L, so the answer had to exceed one mole — 3.50 mol passes that check."
}

[
 {
  "value": 1128.96,
  "misconception": "you multiplied by the molar volume instead of dividing",
  "feedback": "This answer is wrong — you multiplied by the molar volume instead of dividing."
 },
 {
  "value": 0.444,
  "misconception": "you divided the molar volume by the volume — the gas volume goes on top",
  "feedback": "This answer is wrong — you divided the molar volume by the volume — the gas volume goes on top."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nV = 50.4 L\nWrite down the equation:\nn = V ÷ 22.4 L/mol\nSubstitute in the values, and calculate:\nn = 50.4 / 22.4\nn = 2.25 mol\n50.4 L is more than 22.4 L, so the answer had to exceed one mole — 2.25 mol passes that check."
}

[
 {
  "value": 301.06,
  "misconception": "you multiplied by the molar volume instead of dividing",
  "feedback": "This answer is wrong — you multiplied by the molar volume instead of dividing."
 },
 {
  "value": 1.67,
  "misconception": "you divided the molar volume by the volume — the gas volume goes on top",
  "feedback": "This answer is wrong — you divided the molar volume by the volume — the gas volume goes on top."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nV = 13.44 L\nWrite down the equation:\nn = V ÷ 22.4 L/mol\nSubstitute in the values, and calculate:\nn = 13.44 / 22.4\nn = 0.600 mol\n13.44 L is less than 22.4 L, so the answer had to come out below one mole — 0.600 mol passes that check."
}

[
 {
  "value": 0.335,
  "misconception": "you divided by the molar volume instead of multiplying",
  "feedback": "This answer is wrong — you divided by the molar volume instead of multiplying."
 },
 {
  "value": 2.99,
  "misconception": "you divided the molar volume by the moles instead of multiplying them",
  "feedback": "This answer is wrong — you divided the molar volume by the moles instead of multiplying them."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nn = 7.50 mol\nWrite down the equation:\nV = n × 22.4 L/mol\nSubstitute in the values, and calculate:\nV = 7.50 × 22.4\nV = 168 L\nMore than one mole must fill more than 22.4 L — 168 L passes that check."
}

[
 {
  "value": 0.00391,
  "misconception": "you divided by the molar volume instead of multiplying",
  "feedback": "This answer is wrong — you divided by the molar volume instead of multiplying."
 },
 {
  "value": 256,
  "misconception": "you divided the molar volume by the moles instead of multiplying them",
  "feedback": "This answer is wrong — you divided the molar volume by the moles instead of multiplying them."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nn = 0.0875 mol\nWrite down the equation:\nV = n × 22.4 L/mol\nSubstitute in the values, and calculate:\nV = 0.0875 × 22.4\nV = 1.96 L\nLess than one mole must fill less than 22.4 L — 1.96 L passes that check."
}

[
 {
  "value": 0.0167,
  "misconception": "you divided by the molar volume instead of multiplying",
  "feedback": "This answer is wrong — you divided by the molar volume instead of multiplying."
 },
 {
  "value": 59.7,
  "misconception": "you divided the molar volume by the moles instead of multiplying them",
  "feedback": "This answer is wrong — you divided the molar volume by the moles instead of multiplying them."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nn = 0.375 mol\nWrite down the equation:\nV = n × 22.4 L/mol\nSubstitute in the values, and calculate:\nV = 0.375 × 22.4\nV = 8.40 L\nLess than one mole must fill less than 22.4 L — 8.40 L passes that check."
}

[
 {
  "value": 0.417,
  "misconception": "you divided RT by PV instead of PV by RT",
  "feedback": "This answer is wrong — you divided RT by PV instead of PV by RT."
 },
 {
  "value": 0.197,
  "misconception": "you left R out — the bottom of the fraction is RT, not T alone",
  "feedback": "This answer is wrong — you left R out — the bottom of the fraction is RT, not T alone."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP = 3.00 atm\nV = 16.42 L\nT = 250 K\nWrite down the equation:\nPV = nRT\nMake n the subject:\nn = PV ÷ (RT)\nSubstitute in the values, and calculate:\nn = (3.00 × 16.42) ÷ (0.0821 × 250)\nn = 2.40 mol"
}

[
 {
  "value": 0.854,
  "misconception": "you substituted the Celsius temperature — convert first: 52 + 273 = 325 K",
  "feedback": "This answer is wrong — you substituted the Celsius temperature — convert first: 52 + 273 = 325 K."
 },
 {
  "value": 0.187,
  "misconception": "you divided P by nRT — V is nRT divided by P",
  "feedback": "This answer is wrong — you divided P by nRT — V is nRT divided by P."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nn = 0.200 mol\nP = 1.00 atm\nConvert the temperature to kelvin:\nT = 52 + 273 = 325 K\nWrite down the equation:\nPV = nRT\nMake V the subject:\nV = nRT ÷ P\nSubstitute in the values, and calculate:\nV = 0.200 × 0.0821 × 325 ÷ 1.00\nV = 5.34 L"
}

[
 {
  "value": 307800,
  "misconception": "you substituted 1026 without converting — 1026 mmHg is 1.35 atm",
  "feedback": "This answer is wrong — you substituted 1026 without converting — 1026 mmHg is 1.35 atm."
 },
 {
  "value": 3078,
  "misconception": "you converted 1026 mmHg to 10.26 atm — dividing by 760 gives 1.35 atm",
  "feedback": "This answer is wrong — you converted 1026 mmHg to 10.26 atm — dividing by 760 gives 1.35 atm."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nV = 24.63 L\nn = 1.00 mol\nConvert the pressure to atm:\nP = 1026 mmHg = 1.35 atm\nWrite down the equation:\nPV = nRT\nMake T the subject:\nT = PV ÷ (nR)\nSubstitute in the values, and calculate:\nT = (1.35 × 24.63) ÷ (1.00 × 0.0821)\nT = 405 K"
}

[
 {
  "value": 273,
  "misconception": "you gave the kelvin value — 273 K is standard temperature in kelvin; in Celsius it is 0 °C",
  "feedback": "This answer is wrong — you gave the kelvin value — 273 K is standard temperature in kelvin; in Celsius it is 0 °C."
 },
 {
  "value": 100,
  "misconception": "you gave water's boiling point — standard temperature is 0 °C, the freezing mark",
  "feedback": "This answer is wrong — you gave water's boiling point — standard temperature is 0 °C, the freezing mark."
 }
]

{
 "keyExplanation": "'At STP' means 273 K and 1 atm — and 273 K is 0 °C, so the syringe sits at 0 °C."
}

[
 {
  "value": 6.022,
  "misconception": "you gave Avogadro's number's leading digits — 6.022 × 10²³ counts particles in a mole; the molar volume is 22.4 L",
  "feedback": "This answer is wrong — you gave Avogadro's number's leading digits — 6.022 × 10²³ counts particles in a mole; the molar volume is 22.4 L."
 },
 {
  "value": 11.2,
  "misconception": "you halved the molar volume — one full mole fills the full 22.4 L at STP",
  "feedback": "This answer is wrong — you halved the molar volume — one full mole fills the full 22.4 L at STP."
 }
]

{
 "keyExplanation": "One mole of any gas occupies 22.4 L at STP, so the bag holds 22.4 L of nitrous oxide."
}

[
 {
  "value": 878.08,
  "misconception": "you multiplied by the molar volume instead of dividing",
  "feedback": "This answer is wrong — you multiplied by the molar volume instead of dividing."
 },
 {
  "value": 0.571,
  "misconception": "you divided the molar volume by the volume — the gas volume goes on top",
  "feedback": "This answer is wrong — you divided the molar volume by the volume — the gas volume goes on top."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nV = 39.2 L\nWrite down the equation:\nn = V ÷ 22.4 L/mol\nSubstitute in the values, and calculate:\nn = 39.2 / 22.4\nn = 1.75 mol\n39.2 L is more than 22.4 L, so the answer had to exceed one mole — 1.75 mol passes that check."
}

[
 {
  "value": 1881.6,
  "misconception": "you multiplied by the molar volume instead of dividing",
  "feedback": "This answer is wrong — you multiplied by the molar volume instead of dividing."
 },
 {
  "value": 0.267,
  "misconception": "you divided the molar volume by the volume — the gas volume goes on top",
  "feedback": "This answer is wrong — you divided the molar volume by the volume — the gas volume goes on top."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nV = 84.0 L\nWrite down the equation:\nn = V ÷ 22.4 L/mol\nSubstitute in the values, and calculate:\nn = 84.0 / 22.4\nn = 3.75 mol\n84.0 L is more than 22.4 L, so the answer had to exceed one mole — 3.75 mol passes that check."
}

[
 {
  "value": 75.26,
  "misconception": "you multiplied by the molar volume instead of dividing",
  "feedback": "This answer is wrong — you multiplied by the molar volume instead of dividing."
 },
 {
  "value": 6.67,
  "misconception": "you divided the molar volume by the volume — the gas volume goes on top",
  "feedback": "This answer is wrong — you divided the molar volume by the volume — the gas volume goes on top."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nV = 3.36 L\nWrite down the equation:\nn = V ÷ 22.4 L/mol\nSubstitute in the values, and calculate:\nn = 3.36 / 22.4\nn = 0.150 mol\n3.36 L is less than 22.4 L, so the answer had to come out below one mole — 0.150 mol passes that check."
}

[
 {
  "value": 0.391,
  "misconception": "you divided by the molar volume instead of multiplying",
  "feedback": "This answer is wrong — you divided by the molar volume instead of multiplying."
 },
 {
  "value": 2.56,
  "misconception": "you divided the molar volume by the moles instead of multiplying them",
  "feedback": "This answer is wrong — you divided the molar volume by the moles instead of multiplying them."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nn = 8.75 mol\nWrite down the equation:\nV = n × 22.4 L/mol\nSubstitute in the values, and calculate:\nV = 8.75 × 22.4\nV = 196 L\nMore than one mole must fill more than 22.4 L — 196 L passes that check."
}

[
 {
  "value": 0.00781,
  "misconception": "you divided by the molar volume instead of multiplying",
  "feedback": "This answer is wrong — you divided by the molar volume instead of multiplying."
 },
 {
  "value": 128,
  "misconception": "you divided the molar volume by the moles instead of multiplying them",
  "feedback": "This answer is wrong — you divided the molar volume by the moles instead of multiplying them."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nn = 0.175 mol\nWrite down the equation:\nV = n × 22.4 L/mol\nSubstitute in the values, and calculate:\nV = 0.175 × 22.4\nV = 3.92 L\nLess than one mole must fill less than 22.4 L — 3.92 L passes that check."
}

[
 {
  "value": 0.01,
  "misconception": "you divided by the molar volume instead of multiplying",
  "feedback": "This answer is wrong — you divided by the molar volume instead of multiplying."
 },
 {
  "value": 99.6,
  "misconception": "you divided the molar volume by the moles instead of multiplying them",
  "feedback": "This answer is wrong — you divided the molar volume by the moles instead of multiplying them."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nn = 0.225 mol\nWrite down the equation:\nV = n × 22.4 L/mol\nSubstitute in the values, and calculate:\nV = 0.225 × 22.4\nV = 5.04 L\nLess than one mole must fill less than 22.4 L — 5.04 L passes that check."
}

[
 {
  "value": 0.417,
  "misconception": "you divided the volume by nRT instead of dividing nRT by the volume",
  "feedback": "This answer is wrong — you divided the volume by nRT instead of dividing nRT by the volume."
 },
 {
  "value": 29.2,
  "misconception": "you left R out — the top of the fraction is nRT, not nT",
  "feedback": "This answer is wrong — you left R out — the top of the fraction is nRT, not nT."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nn = 1.80 mol\nT = 400 K\nV = 24.63 L\nWrite down the equation:\nPV = nRT\nMake P the subject:\nP = nRT ÷ V\nSubstitute in the values, and calculate:\nP = 1.80 × 0.0821 × 400 ÷ 24.63\nP = 2.40 atm"
}

[
 {
  "value": 7.35,
  "misconception": "you substituted the Celsius temperature — convert first: 102 + 273 = 375 K",
  "feedback": "This answer is wrong — you substituted the Celsius temperature — convert first: 102 + 273 = 375 K."
 },
 {
  "value": 0.5,
  "misconception": "you divided RT by PV instead of PV by RT",
  "feedback": "This answer is wrong — you divided RT by PV instead of PV by RT."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP = 3.75 atm\nV = 16.42 L\nConvert the temperature to kelvin:\nT = 102 + 273 = 375 K\nWrite down the equation:\nPV = nRT\nMake n the subject:\nn = PV ÷ (RT)\nSubstitute in the values, and calculate:\nn = (3.75 × 16.42) ÷ (0.0821 × 375)\nn = 2.00 mol"
}

[
 {
  "value": 0.0356,
  "misconception": "you substituted 380 without converting — 380 mmHg is 0.500 atm",
  "feedback": "This answer is wrong — you substituted 380 without converting — 380 mmHg is 0.500 atm."
 },
 {
  "value": 3.56,
  "misconception": "you converted 380 mmHg to 3.80 atm — dividing by 760 gives 0.500 atm",
  "feedback": "This answer is wrong — you converted 380 mmHg to 3.80 atm — dividing by 760 gives 0.500 atm."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nn = 0.300 mol\nT = 550 K\nConvert the pressure to atm:\nP = 380 mmHg = 0.500 atm\nWrite down the equation:\nPV = nRT\nMake V the subject:\nV = nRT ÷ P\nSubstitute in the values, and calculate:\nV = 0.300 × 0.0821 × 550 ÷ 0.500\nV = 27.1 L"
}

[
 {
  "value": 0,
  "misconception": "you gave the Celsius value — standard temperature is 0 °C, which is 273 K",
  "feedback": "This answer is wrong — you gave the Celsius value — standard temperature is 0 °C, which is 273 K."
 },
 {
  "value": 373,
  "misconception": "you gave water's boiling point in kelvin — standard temperature is 273 K, the 0 °C mark",
  "feedback": "This answer is wrong — you gave water's boiling point in kelvin — standard temperature is 273 K, the 0 °C mark."
 }
]

{
 "keyExplanation": "Standard temperature is 273 K, which is 0 °C — that is the temperature 'at STP' names."
}

[
 {
  "value": 273,
  "misconception": "you gave standard temperature — 273 is the kelvin value at STP; the molar volume is 22.4 L",
  "feedback": "This answer is wrong — you gave standard temperature — 273 is the kelvin value at STP; the molar volume is 22.4 L."
 },
 {
  "value": 0.0821,
  "misconception": "you gave the gas constant — R is 0.0821 L·atm/(mol·K); the molar volume at STP is 22.4 L",
  "feedback": "This answer is wrong — you gave the gas constant — R is 0.0821 L·atm/(mol·K); the molar volume at STP is 22.4 L."
 }
]

{
 "keyExplanation": "One mole of any gas occupies 22.4 L at STP — the kind of gas makes no difference, so the ethene fills 22.4 L."
}

[
 {
  "value": 1379.84,
  "misconception": "you multiplied by the molar volume instead of dividing",
  "feedback": "This answer is wrong — you multiplied by the molar volume instead of dividing."
 },
 {
  "value": 0.364,
  "misconception": "you divided the molar volume by the volume — the gas volume goes on top",
  "feedback": "This answer is wrong — you divided the molar volume by the volume — the gas volume goes on top."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nV = 61.6 L\nWrite down the equation:\nn = V ÷ 22.4 L/mol\nSubstitute in the values, and calculate:\nn = 61.6 / 22.4\nn = 2.75 mol\n61.6 L is more than 22.4 L, so the answer had to exceed one mole — 2.75 mol passes that check."
}

[
 {
  "value": 1630.72,
  "misconception": "you multiplied by the molar volume instead of dividing",
  "feedback": "This answer is wrong — you multiplied by the molar volume instead of dividing."
 },
 {
  "value": 0.308,
  "misconception": "you divided the molar volume by the volume — the gas volume goes on top",
  "feedback": "This answer is wrong — you divided the molar volume by the volume — the gas volume goes on top."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nV = 72.8 L\nWrite down the equation:\nn = V ÷ 22.4 L/mol\nSubstitute in the values, and calculate:\nn = 72.8 / 22.4\nn = 3.25 mol\n72.8 L is more than 22.4 L, so the answer had to exceed one mole — 3.25 mol passes that check."
}

[
 {
  "value": 175.62,
  "misconception": "you multiplied by the molar volume instead of dividing",
  "feedback": "This answer is wrong — you multiplied by the molar volume instead of dividing."
 },
 {
  "value": 2.86,
  "misconception": "you divided the molar volume by the volume — the gas volume goes on top",
  "feedback": "This answer is wrong — you divided the molar volume by the volume — the gas volume goes on top."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nV = 7.84 L\nWrite down the equation:\nn = V ÷ 22.4 L/mol\nSubstitute in the values, and calculate:\nn = 7.84 / 22.4\nn = 0.350 mol\n7.84 L is less than 22.4 L, so the answer had to come out below one mole — 0.350 mol passes that check."
}

[
 {
  "value": 0.446,
  "misconception": "you divided by the molar volume instead of multiplying",
  "feedback": "This answer is wrong — you divided by the molar volume instead of multiplying."
 },
 {
  "value": 2.24,
  "misconception": "you divided the molar volume by the moles instead of multiplying them",
  "feedback": "This answer is wrong — you divided the molar volume by the moles instead of multiplying them."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nn = 10.0 mol\nWrite down the equation:\nV = n × 22.4 L/mol\nSubstitute in the values, and calculate:\nV = 10.0 × 22.4\nV = 224 L\nMore than one mole must fill more than 22.4 L — 224 L passes that check."
}

[
 {
  "value": 0.0145,
  "misconception": "you divided by the molar volume instead of multiplying",
  "feedback": "This answer is wrong — you divided by the molar volume instead of multiplying."
 },
 {
  "value": 68.9,
  "misconception": "you divided the molar volume by the moles instead of multiplying them",
  "feedback": "This answer is wrong — you divided the molar volume by the moles instead of multiplying them."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nn = 0.325 mol\nWrite down the equation:\nV = n × 22.4 L/mol\nSubstitute in the values, and calculate:\nV = 0.325 × 22.4\nV = 7.28 L\nLess than one mole must fill less than 22.4 L — 7.28 L passes that check."
}

[
 {
  "value": 0.019,
  "misconception": "you divided by the molar volume instead of multiplying",
  "feedback": "This answer is wrong — you divided by the molar volume instead of multiplying."
 },
 {
  "value": 52.7,
  "misconception": "you divided the molar volume by the moles instead of multiplying them",
  "feedback": "This answer is wrong — you divided the molar volume by the moles instead of multiplying them."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nn = 0.425 mol\nWrite down the equation:\nV = n × 22.4 L/mol\nSubstitute in the values, and calculate:\nV = 0.425 × 22.4\nV = 9.52 L\nLess than one mole must fill less than 22.4 L — 9.52 L passes that check."
}

[
 {
  "value": 0.122,
  "misconception": "you divided P by nRT — V is nRT divided by P",
  "feedback": "This answer is wrong — you divided P by nRT — V is nRT divided by P."
 },
 {
  "value": 14.4,
  "misconception": "you forgot to divide by the pressure — V is nRT ÷ P",
  "feedback": "This answer is wrong — you forgot to divide by the pressure — V is nRT ÷ P."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nn = 0.625 mol\nT = 280 K\nP = 1.75 atm\nWrite down the equation:\nPV = nRT\nMake V the subject:\nV = nRT ÷ P\nSubstitute in the values, and calculate:\nV = 0.625 × 0.0821 × 280 ÷ 1.75\nV = 8.21 L"
}

[
 {
  "value": 0.304,
  "misconception": "you substituted the Celsius temperature — convert first: 152 + 273 = 425 K",
  "feedback": "This answer is wrong — you substituted the Celsius temperature — convert first: 152 + 273 = 425 K."
 },
 {
  "value": 1.18,
  "misconception": "you divided V by nRT — P is nRT divided by V",
  "feedback": "This answer is wrong — you divided V by nRT — P is nRT divided by V."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nn = 0.600 mol\nV = 24.63 L\nConvert the temperature to kelvin:\nT = 152 + 273 = 425 K\nWrite down the equation:\nPV = nRT\nMake P the subject:\nP = nRT ÷ V\nSubstitute in the values, and calculate:\nP = 0.600 × 0.0821 × 425 ÷ 24.63\nP = 0.850 atm"
}

[
 {
  "value": 95000,
  "misconception": "you substituted 2280 without converting — 2280 mmHg is 3.00 atm",
  "feedback": "This answer is wrong — you substituted 2280 without converting — 2280 mmHg is 3.00 atm."
 },
 {
  "value": 10.3,
  "misconception": "you left R out — the bottom of the fraction is nR, not n alone",
  "feedback": "This answer is wrong — you left R out — the bottom of the fraction is nR, not n alone."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nV = 16.42 L\nn = 4.80 mol\nConvert the pressure to atm:\nP = 2280 mmHg = 3.00 atm\nWrite down the equation:\nPV = nRT\nMake T the subject:\nT = PV ÷ (nR)\nSubstitute in the values, and calculate:\nT = (3.00 × 16.42) ÷ (4.80 × 0.0821)\nT = 125 K"
}

[
 {
  "value": 273,
  "misconception": "you gave the kelvin value — 273 K is standard temperature in kelvin; in Celsius it is 0 °C",
  "feedback": "This answer is wrong — you gave the kelvin value — 273 K is standard temperature in kelvin; in Celsius it is 0 °C."
 },
 {
  "value": -273,
  "misconception": "you flipped the conversion — 0 °C equals 273 K; absolute zero, −273 °C, is not standard temperature",
  "feedback": "This answer is wrong — you flipped the conversion — 0 °C equals 273 K; absolute zero, −273 °C, is not standard temperature."
 }
]

{
 "keyExplanation": "Standard temperature is 273 K, which is 0 °C — so a flask at STP reads 0 °C."
}

[
 {
  "value": 44.8,
  "misconception": "you doubled the molar volume — ONE mole of any gas fills 22.4 L at STP",
  "feedback": "This answer is wrong — you doubled the molar volume — ONE mole of any gas fills 22.4 L at STP."
 },
 {
  "value": 6.022,
  "misconception": "you gave Avogadro's number's leading digits — 6.022 × 10²³ counts particles in a mole; the molar volume is 22.4 L",
  "feedback": "This answer is wrong — you gave Avogadro's number's leading digits — 6.022 × 10²³ counts particles in a mole; the molar volume is 22.4 L."
 }
]

{
 "keyExplanation": "One mole of any gas occupies 22.4 L at STP — xenon included, whatever its atoms weigh."
}

[
 {
  "value": 2132.48,
  "misconception": "you multiplied by the molar volume instead of dividing",
  "feedback": "This answer is wrong — you multiplied by the molar volume instead of dividing."
 },
 {
  "value": 0.235,
  "misconception": "you divided the molar volume by the volume — the gas volume goes on top",
  "feedback": "This answer is wrong — you divided the molar volume by the volume — the gas volume goes on top."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nV = 95.2 L\nWrite down the equation:\nn = V ÷ 22.4 L/mol\nSubstitute in the values, and calculate:\nn = 95.2 / 22.4\nn = 4.25 mol\n95.2 L is more than 22.4 L, so the answer had to exceed one mole — 4.25 mol passes that check."
}

[
 {
  "value": 2257.92,
  "misconception": "you multiplied by the molar volume instead of dividing",
  "feedback": "This answer is wrong — you multiplied by the molar volume instead of dividing."
 },
 {
  "value": 0.222,
  "misconception": "you divided the molar volume by the volume — the gas volume goes on top",
  "feedback": "This answer is wrong — you divided the molar volume by the volume — the gas volume goes on top."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nV = 100.8 L\nWrite down the equation:\nn = V ÷ 22.4 L/mol\nSubstitute in the values, and calculate:\nn = 100.8 / 22.4\nn = 4.50 mol\n100.8 L is four and a half times 22.4 L, so the answer had to exceed one mole — 4.50 mol passes that check."
}

[
 {
  "value": 62.72,
  "misconception": "you multiplied by the molar volume instead of dividing",
  "feedback": "This answer is wrong — you multiplied by the molar volume instead of dividing."
 },
 {
  "value": 8.0,
  "misconception": "you divided the molar volume by the volume — the gas volume goes on top",
  "feedback": "This answer is wrong — you divided the molar volume by the volume — the gas volume goes on top."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nV = 2.80 L\nWrite down the equation:\nn = V ÷ 22.4 L/mol\nSubstitute in the values, and calculate:\nn = 2.80 / 22.4\nn = 0.125 mol\n2.80 L is less than 22.4 L, so the answer had to come out below one mole — 0.125 mol passes that check."
}

[
 {
  "value": 0.67,
  "misconception": "you divided by the molar volume instead of multiplying",
  "feedback": "This answer is wrong — you divided by the molar volume instead of multiplying."
 },
 {
  "value": 1.49,
  "misconception": "you divided the molar volume by the moles instead of multiplying them",
  "feedback": "This answer is wrong — you divided the molar volume by the moles instead of multiplying them."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nn = 15.0 mol\nWrite down the equation:\nV = n × 22.4 L/mol\nSubstitute in the values, and calculate:\nV = 15.0 × 22.4\nV = 336 L\nMore than one mole must fill more than 22.4 L — 336 L passes that check."
}

[
 {
  "value": 0.00112,
  "misconception": "you divided by the molar volume instead of multiplying",
  "feedback": "This answer is wrong — you divided by the molar volume instead of multiplying."
 },
 {
  "value": 896,
  "misconception": "you divided the molar volume by the moles instead of multiplying them",
  "feedback": "This answer is wrong — you divided the molar volume by the moles instead of multiplying them."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nn = 0.0250 mol\nWrite down the equation:\nV = n × 22.4 L/mol\nSubstitute in the values, and calculate:\nV = 0.0250 × 22.4\nV = 0.560 L\nLess than one mole must fill less than 22.4 L — 0.560 L passes that check."
}

[
 {
  "value": 0.00279,
  "misconception": "you divided by the molar volume instead of multiplying",
  "feedback": "This answer is wrong — you divided by the molar volume instead of multiplying."
 },
 {
  "value": 358,
  "misconception": "you divided the molar volume by the moles instead of multiplying them",
  "feedback": "This answer is wrong — you divided the molar volume by the moles instead of multiplying them."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nn = 0.0625 mol\nWrite down the equation:\nV = n × 22.4 L/mol\nSubstitute in the values, and calculate:\nV = 0.0625 × 22.4\nV = 1.40 L\nLess than one mole must fill less than 22.4 L — 1.40 L passes that check."
}

[
 {
  "value": 12.5,
  "misconception": "you multiplied PV by nR instead of dividing PV by nR",
  "feedback": "This answer is wrong — you multiplied PV by nR instead of dividing PV by nR."
 },
 {
  "value": 0.00216,
  "misconception": "you divided nR by PV instead of PV by nR",
  "feedback": "This answer is wrong — you divided nR by PV instead of PV by nR."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP = 2.31 atm\nV = 32.84 L\nn = 2.00 mol\nWrite down the equation:\nPV = nRT\nMake T the subject:\nT = PV ÷ (nR)\nSubstitute in the values, and calculate:\nT = (2.31 × 32.84) ÷ (2.00 × 0.0821)\nT = 462 K"
}

[
 {
  "value": 13.3,
  "misconception": "you substituted the Celsius temperature — convert first: 202 + 273 = 475 K",
  "feedback": "This answer is wrong — you substituted the Celsius temperature — convert first: 202 + 273 = 475 K."
 },
 {
  "value": 0.0321,
  "misconception": "you divided P by nRT — V is nRT divided by P",
  "feedback": "This answer is wrong — you divided P by nRT — V is nRT divided by P."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nn = 1.60 mol\nP = 2.00 atm\nConvert the temperature to kelvin:\nT = 202 + 273 = 475 K\nWrite down the equation:\nPV = nRT\nMake V the subject:\nV = nRT ÷ P\nSubstitute in the values, and calculate:\nV = 1.60 × 0.0821 × 475 ÷ 2.00\nV = 31.2 L"
}

[
 {
  "value": 570,
  "misconception": "you substituted 1520 without converting — 1520 mmHg is 2.00 atm",
  "feedback": "This answer is wrong — you substituted 1520 without converting — 1520 mmHg is 2.00 atm."
 },
 {
  "value": 5.7,
  "misconception": "you converted 1520 mmHg to 15.2 atm — dividing by 760 gives 2.00 atm",
  "feedback": "This answer is wrong — you converted 1520 mmHg to 15.2 atm — dividing by 760 gives 2.00 atm."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nV = 24.63 L\nT = 800 K\nConvert the pressure to atm:\nP = 1520 mmHg = 2.00 atm\nWrite down the equation:\nPV = nRT\nMake n the subject:\nn = PV ÷ (RT)\nSubstitute in the values, and calculate:\nn = (2.00 × 24.63) ÷ (0.0821 × 800)\nn = 0.750 mol"
}

[
 {
  "value": 3.0,
  "misconception": "you inverted the coefficient ratio — CO₂ carries the 4 and C₂H₂ the 2, so multiply by 4 ÷ 2",
  "feedback": null
 },
 {
  "value": 6.0,
  "misconception": "you ignored the coefficients and assumed a 1 : 1 ratio",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nV(given) = 6.0 L of C₂H₂\ncoefficient of CO₂ = 4, coefficient of C₂H₂ = 2\nWrite down the equation:\nV(wanted) = V(given) × (coefficient of wanted ÷ coefficient of given)\nSubstitute in the values, and calculate:\nV(CO₂) = 6.0 × (4 ÷ 2)\nV(CO₂) = 12 L"
}

[
 {
  "value": 16.0,
  "misconception": "you multiplied by 2 instead of dividing — NO carries the 2, so it goes on the bottom of the ratio",
  "feedback": null
 },
 {
  "value": 8.0,
  "misconception": "you ignored the coefficients and assumed a 1 : 1 ratio",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nV(given) = 8.0 L of NO\ncoefficient of N₂ = 1, coefficient of NO = 2\nWrite down the equation:\nV(wanted) = V(given) × (coefficient of wanted ÷ coefficient of given)\nSubstitute in the values, and calculate:\nV(N₂) = 8.0 × (1 ÷ 2)\nV(N₂) = 4.0 L"
}

[
 {
  "value": 16.0,
  "misconception": "you inverted the coefficient ratio — O₂ carries the 5 and NH₃ the 4, so multiply by 5 ÷ 4",
  "feedback": null
 },
 {
  "value": 20.0,
  "misconception": "you ignored the coefficients and assumed a 1 : 1 ratio",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nV(given) = 20.0 L of NH₃\ncoefficient of O₂ = 5, coefficient of NH₃ = 4\nWrite down the equation:\nV(wanted) = V(given) × (coefficient of wanted ÷ coefficient of given)\nSubstitute in the values, and calculate:\nV(O₂) = 20.0 × (5 ÷ 4)\nV(O₂) = 25.0 L"
}

[
 {
  "value": 8.96,
  "misconception": "you used HCl's coefficient — the metal and H₂ both carry coefficient 1",
  "feedback": null
 },
 {
  "value": 0.2,
  "misconception": "you stopped at moles — the question asks for a volume, so multiply by 22.4 L/mol",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of manganese: n = 10.98 ÷ 54.9 = 0.200 mol\nStage 2 — mole ratio: Mn and H₂ both carry coefficient 1, so n(H₂) = 0.200 mol\nStage 3 — write down the equation:\nV = n × 22.4\nSubstitute in the values, and calculate:\nV = 0.200 × 22.4\nV = 4.48 L at STP"
}

[
 {
  "value": 5.6,
  "misconception": "you skipped the mole ratio — each fuel particle makes more than one CO₂ here",
  "feedback": null
 },
 {
  "value": 0.75,
  "misconception": "you stopped at moles — the question asks for a volume, so multiply by 22.4 L/mol",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of C₃H₈: M(C₃H₈) = 3 × 12.0 + 8 × 1.0 = 44.0 g/mol; n = 11.0 ÷ 44.0 = 0.250 mol\nStage 2 — mole ratio: 1C₃H₈ make 3CO₂, so n(CO₂) = 0.250 × (3 ÷ 1) = 0.750 mol\nStage 3 — write down the equation:\nV = n × 22.4\nSubstitute in the values, and calculate:\nV = 0.750 × 22.4\nV = 16.8 L at STP"
}

[
 {
  "value": 11.9,
  "misconception": "you inverted the mole ratio — O₂ carries the 3 and Fe the 4, so multiply the moles of iron by 3 ÷ 4",
  "feedback": null
 },
 {
  "value": 8.96,
  "misconception": "you skipped the mole ratio — four Fe use three O₂",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of iron: n = 22.32 ÷ 55.8 = 0.400 mol\nStage 2 — mole ratio: 4Fe use 3O₂, so n(O₂) = 0.400 × (3 ÷ 4) = 0.300 mol\nStage 3 — write down the equation:\nV = n × 22.4\nSubstitute in the values, and calculate:\nV = 0.300 × 22.4\nV = 6.72 L at STP"
}

[
 {
  "value": 461.8,
  "misconception": "you multiplied the volume itself by the molar mass — convert the volume to moles first",
  "feedback": null
 },
 {
  "value": 0.35,
  "misconception": "you stopped at moles — the question asks for a mass, so multiply by M",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of gas: n = 7.84 ÷ 22.4 = 0.350 mol\nStage 2 — mole ratio: Co and H₂ both carry coefficient 1, so n(Co) = 0.350 mol\nStage 3 — write down the equation:\nm = n × M\nSubstitute in the values, and calculate:\nm = 0.350 × 58.9\nm = 20.6 g"
}

[
 {
  "value": 126.0,
  "misconception": "you skipped the mole ratio — each fuel particle makes several CO₂, so fewer fuel moles are needed",
  "feedback": null
 },
 {
  "value": 0.35,
  "misconception": "you stopped at moles — the question asks for a mass, so multiply by M",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of CO₂: n = 39.2 ÷ 22.4 = 1.75 mol\nStage 2 — mole ratio: 1C₅H₁₂ make 5CO₂, so n(C₅H₁₂) = 1.75 × (1 ÷ 5) = 0.350 mol\nStage 3 — build the molar mass, then write down the equation:\nM = 5 × 12.0 + 12 × 1.0 = 72.0 g/mol\nm = n × M\nSubstitute in the values, and calculate:\nm = 0.350 × 72.0\nm = 25.2 g"
}

[
 {
  "value": 287.6,
  "misconception": "you multiplied the volume itself by the molar mass — convert the volume to moles first",
  "feedback": null
 },
 {
  "value": 0.4,
  "misconception": "you stopped at moles — the question asks for a mass, so multiply by M",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of SO₂: n = 8.96 ÷ 22.4 = 0.400 mol\nStage 2 — mole ratio: S and SO₂ both carry coefficient 1, so n(S) = 0.400 mol\nStage 3 — write down the equation:\nm = n × M\nSubstitute in the values, and calculate:\nm = 0.400 × 32.1\nm = 12.8 g"
}

[
 {
  "value": 26.88,
  "misconception": "you multiplied the volume itself by the molar mass route — convert the volume to moles first",
  "feedback": null
 },
 {
  "value": 0.9,
  "misconception": "you stopped at moles — the question asks for a mass, so multiply by M(H₂) = 2.0 g/mol",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of NH₃: n = 13.44 ÷ 22.4 = 0.600 mol\nStage 2 — mole ratio: 3H₂ make 2NH₃, so n(H₂) = 0.600 × (3 ÷ 2) = 0.900 mol\nStage 3 — build the molar mass, then write down the equation:\nM = 2 × 1.0 = 2.0 g/mol\nm = n × M\nSubstitute in the values, and calculate:\nm = 0.900 × 2.0\nm = 1.80 g, which is reported as 1.8 g (M(H₂) = 2.0 g/mol carries 2 significant figures, so the answer is reported to 2)"
}

[
 {
  "value": 17.9,
  "misconception": "you divided by the ATOMIC molar mass — bromine gas is Br₂, so M = 2 × 79.9 = 159.8 g/mol",
  "feedback": null
 },
 {
  "value": 4.48,
  "misconception": "you skipped the mole ratio — one Br₂ makes two HBr",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of Br₂: M(Br₂) = 2 × 79.9 = 159.8 g/mol; n = 31.96 ÷ 159.8 = 0.200 mol\nStage 2 — mole ratio: 1Br₂ makes 2HBr, so n(HBr) = 0.200 × 2 = 0.400 mol\nStage 3 — write down the equation:\nV = n × 22.4\nSubstitute in the values, and calculate:\nV = 0.400 × 22.4\nV = 8.96 L at STP"
}

[
 {
  "value": 213.0,
  "misconception": "you skipped the mole ratio — two decane particles make twenty CO₂, so scale the CO₂ moles by 2 ÷ 20",
  "feedback": null
 },
 {
  "value": 0.15,
  "misconception": "you stopped at moles — the question asks for a mass, so multiply by M(C₁₀H₂₂) = 142.0 g/mol",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of CO₂: n = 33.6 ÷ 22.4 = 1.50 mol\nStage 2 — mole ratio: 2C₁₀H₂₂ make 20CO₂, so n(C₁₀H₂₂) = 1.50 × (2 ÷ 20) = 0.150 mol\nStage 3 — build the molar mass, then write down the equation:\nM = 10 × 12.0 + 22 × 1.0 = 142.0 g/mol\nm = n × M\nSubstitute in the values, and calculate:\nm = 0.150 × 142.0\nm = 21.3 g"
}

[
 {
  "value": 3.5,
  "misconception": "you inverted the coefficient ratio — NO₂ carries the 2 and O₂ the 1, so multiply by 2 ÷ 1",
  "feedback": null
 },
 {
  "value": 7.0,
  "misconception": "you ignored the coefficients and assumed a 1 : 1 ratio",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nV(given) = 7.0 L of O₂\ncoefficient of NO₂ = 2, coefficient of O₂ = 1\nWrite down the equation:\nV(wanted) = V(given) × (coefficient of wanted ÷ coefficient of given)\nSubstitute in the values, and calculate:\nV(NO₂) = 7.0 × (2 ÷ 1)\nV(NO₂) = 14 L"
}

[
 {
  "value": 12.0,
  "misconception": "you multiplied by 2 instead of dividing — NO₂ carries the 2, so it goes on the bottom of the ratio",
  "feedback": null
 },
 {
  "value": 6.0,
  "misconception": "you ignored the coefficients and assumed a 1 : 1 ratio",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nV(given) = 6.0 L of NO₂\ncoefficient of N₂O₄ = 1, coefficient of NO₂ = 2\nWrite down the equation:\nV(wanted) = V(given) × (coefficient of wanted ÷ coefficient of given)\nSubstitute in the values, and calculate:\nV(N₂O₄) = 6.0 × (1 ÷ 2)\nV(N₂O₄) = 3.0 L"
}

[
 {
  "value": 0.444,
  "misconception": "you inverted the coefficient ratio — O₂ carries the 9 and C₇H₈ the 1, so multiply by 9 ÷ 1",
  "feedback": null
 },
 {
  "value": 4.0,
  "misconception": "you ignored the coefficients and assumed a 1 : 1 ratio",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nV(given) = 4.00 L of C₇H₈\ncoefficient of O₂ = 9, coefficient of C₇H₈ = 1\nWrite down the equation:\nV(wanted) = V(given) × (coefficient of wanted ÷ coefficient of given)\nSubstitute in the values, and calculate:\nV(O₂) = 4.00 × (9 ÷ 1)\nV(O₂) = 36.0 L"
}

[
 {
  "value": 13.44,
  "misconception": "you used HCl's coefficient — the metal and H₂ both carry coefficient 1",
  "feedback": null
 },
 {
  "value": 0.3,
  "misconception": "you stopped at moles — the question asks for a volume, so multiply by 22.4 L/mol",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of nickel: n = 17.61 ÷ 58.7 = 0.300 mol\nStage 2 — mole ratio: Ni and H₂ both carry coefficient 1, so n(H₂) = 0.300 mol\nStage 3 — write down the equation:\nV = n × 22.4\nSubstitute in the values, and calculate:\nV = 0.300 × 22.4\nV = 6.72 L at STP"
}

[
 {
  "value": 5.6,
  "misconception": "you skipped the mole ratio — each fuel particle makes more than one CO₂ here",
  "feedback": null
 },
 {
  "value": 0.5,
  "misconception": "you stopped at moles — the question asks for a volume, so multiply by 22.4 L/mol",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of C₂H₆: M(C₂H₆) = 2 × 12.0 + 6 × 1.0 = 30.0 g/mol; n = 7.50 ÷ 30.0 = 0.250 mol\nStage 2 — mole ratio: 2C₂H₆ make 4CO₂, so n(CO₂) = 0.250 × (4 ÷ 2) = 0.500 mol\nStage 3 — write down the equation:\nV = n × 22.4\nSubstitute in the values, and calculate:\nV = 0.500 × 22.4\nV = 11.2 L at STP"
}

[
 {
  "value": 17.9,
  "misconception": "you inverted the mole ratio — O₂ carries the 1 and Cu the 2, so multiply the moles of copper by 1 ÷ 2",
  "feedback": null
 },
 {
  "value": 8.96,
  "misconception": "you skipped the mole ratio — two Cu use one O₂",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of copper: n = 25.40 ÷ 63.5 = 0.400 mol\nStage 2 — mole ratio: 2Cu use 1O₂, so n(O₂) = 0.400 × (1 ÷ 2) = 0.200 mol\nStage 3 — write down the equation:\nV = n × 22.4\nSubstitute in the values, and calculate:\nV = 0.200 × 22.4\nV = 4.48 L at STP"
}

[
 {
  "value": 332.4,
  "misconception": "you multiplied the volume itself by the molar mass — convert the volume to moles first",
  "feedback": null
 },
 {
  "value": 0.125,
  "misconception": "you stopped at moles — the question asks for a mass, so multiply by M",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of gas: n = 2.80 ÷ 22.4 = 0.125 mol\nStage 2 — mole ratio: Sn and O₂ both carry coefficient 1, so n(Sn) = 0.125 mol\nStage 3 — write down the equation:\nm = n × M\nSubstitute in the values, and calculate:\nm = 0.125 × 118.7\nm = 14.8 g"
}

[
 {
  "value": 140.0,
  "misconception": "you skipped the mole ratio — each fuel particle makes several CO₂, so fewer fuel moles are needed",
  "feedback": null
 },
 {
  "value": 0.2,
  "misconception": "you stopped at moles — the question asks for a mass, so multiply by M",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of CO₂: n = 31.36 ÷ 22.4 = 1.40 mol\nStage 2 — mole ratio: 1C₇H₁₆ make 7CO₂, so n(C₇H₁₆) = 1.40 × (1 ÷ 7) = 0.200 mol\nStage 3 — build the molar mass, then write down the equation:\nM = 7 × 12.0 + 16 × 1.0 = 100.0 g/mol\nm = n × M\nSubstitute in the values, and calculate:\nm = 0.200 × 100.0\nm = 20.0 g"
}

[
 {
  "value": 440.6,
  "misconception": "you multiplied the volume itself by the molar mass — convert the volume to moles first",
  "feedback": null
 },
 {
  "value": 0.7,
  "misconception": "you stopped at moles — the question asks for a mass, so multiply by M",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of O₂: n = 15.68 ÷ 22.4 = 0.700 mol\nStage 2 — mole ratio: Si and O₂ both carry coefficient 1, so n(Si) = 0.700 mol\nStage 3 — write down the equation:\nm = n × M\nSubstitute in the values, and calculate:\nm = 0.700 × 28.1\nm = 19.7 g"
}

[
 {
  "value": 208.7,
  "misconception": "you multiplied the volume itself by the molar mass — convert the volume to moles first",
  "feedback": null
 },
 {
  "value": 1.35,
  "misconception": "you stopped at moles of H₂ and skipped the ratio — 2Li make 1H₂, so double the moles before using M",
  "feedback": null
 },
 {
  "value": 18.6,
  "misconception": "you calculated 18.63 g correctly but skipped the final step — the answer is asked to 2 significant figures, so report 19 g",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of H₂: n = 30.24 ÷ 22.4 = 1.35 mol\nStage 2 — mole ratio: 2Li make 1H₂, so n(Li) = 1.35 × 2 = 2.70 mol\nStage 3 — write down the equation:\nm = n × M\nSubstitute in the values, and calculate:\nm = 2.70 × 6.9\nm = 18.63 g, which rounds to 19 g (the lithium molar mass 6.9 carries 2 significant figures, so the answer is reported to 2)"
}

[
 {
  "value": 8.96,
  "misconception": "you divided by the ATOMIC molar mass — iodine vapor is I₂, so M = 2 × 126.9 = 253.8 g/mol",
  "feedback": null
 },
 {
  "value": 2.24,
  "misconception": "you skipped the mole ratio — one I₂ makes two HI",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of I₂: M(I₂) = 2 × 126.9 = 253.8 g/mol; n = 25.38 ÷ 253.8 = 0.100 mol\nStage 2 — mole ratio: 1I₂ makes 2HI, so n(HI) = 0.100 × 2 = 0.200 mol\nStage 3 — write down the equation:\nV = n × 22.4\nSubstitute in the values, and calculate:\nV = 0.200 × 22.4\nV = 4.48 L at STP"
}

[
 {
  "value": 1405.2,
  "misconception": "you multiplied the volume itself by the molar mass — convert the volume to moles first",
  "feedback": null
 },
 {
  "value": 0.9,
  "misconception": "you stopped at moles of H₂ and skipped the ratio — 2Ga make 3H₂, so scale by 2 ÷ 3 before using M",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of H₂: n = 20.16 ÷ 22.4 = 0.900 mol\nStage 2 — mole ratio: 2Ga make 3H₂, so n(Ga) = 0.900 × (2 ÷ 3) = 0.600 mol\nStage 3 — write down the equation:\nm = n × M\nSubstitute in the values, and calculate:\nm = 0.600 × 69.7\nm = 41.8 g"
}

[
 {
  "value": 4.5,
  "misconception": "you inverted the coefficient ratio — HCl carries the 2 and Cl₂ the 1, so multiply by 2 ÷ 1",
  "feedback": null
 },
 {
  "value": 9.0,
  "misconception": "you ignored the coefficients and assumed a 1 : 1 ratio",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nV(given) = 9.0 L of Cl₂\ncoefficient of HCl = 2, coefficient of Cl₂ = 1\nWrite down the equation:\nV(wanted) = V(given) × (coefficient of wanted ÷ coefficient of given)\nSubstitute in the values, and calculate:\nV(HCl) = 9.0 × (2 ÷ 1)\nV(HCl) = 18 L"
}

[
 {
  "value": 13.5,
  "misconception": "you inverted the coefficient ratio — NH₃ carries the 2 and H₂ the 3, so multiply by 2 ÷ 3",
  "feedback": null
 },
 {
  "value": 9.0,
  "misconception": "you ignored the coefficients and assumed a 1 : 1 ratio",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nV(given) = 9.0 L of H₂\ncoefficient of NH₃ = 2, coefficient of H₂ = 3\nWrite down the equation:\nV(wanted) = V(given) × (coefficient of wanted ÷ coefficient of given)\nSubstitute in the values, and calculate:\nV(NH₃) = 9.0 × (2 ÷ 3)\nV(NH₃) = 6.0 L"
}

[
 {
  "value": 48.0,
  "misconception": "you inverted the coefficient ratio — O₂ carries the 1 and HCl the 4, so multiply by 1 ÷ 4",
  "feedback": null
 },
 {
  "value": 12.0,
  "misconception": "you ignored the coefficients and assumed a 1 : 1 ratio",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nV(given) = 12.0 L of HCl\ncoefficient of O₂ = 1, coefficient of HCl = 4\nWrite down the equation:\nV(wanted) = V(given) × (coefficient of wanted ÷ coefficient of given)\nSubstitute in the values, and calculate:\nV(O₂) = 12.0 × (1 ÷ 4)\nV(O₂) = 3.00 L"
}

[
 {
  "value": 13.44,
  "misconception": "you used HCl's coefficient — the metal and H₂ both carry coefficient 1",
  "feedback": null
 },
 {
  "value": 0.3,
  "misconception": "you stopped at moles — the question asks for a volume, so multiply by 22.4 L/mol",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of strontium: n = 26.28 ÷ 87.6 = 0.300 mol\nStage 2 — mole ratio: Sr and H₂ both carry coefficient 1, so n(H₂) = 0.300 mol\nStage 3 — write down the equation:\nV = n × 22.4\nSubstitute in the values, and calculate:\nV = 0.300 × 22.4\nV = 6.72 L at STP"
}

[
 {
  "value": 5.6,
  "misconception": "you skipped the mole ratio — each fuel particle makes more than one CO₂ here",
  "feedback": null
 },
 {
  "value": 1.0,
  "misconception": "you stopped at moles — the question asks for a volume, so multiply by 22.4 L/mol",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of C₄H₁₀: M(C₄H₁₀) = 4 × 12.0 + 10 × 1.0 = 58.0 g/mol; n = 14.50 ÷ 58.0 = 0.250 mol\nStage 2 — mole ratio: 2C₄H₁₀ make 8CO₂, so n(CO₂) = 0.250 × (8 ÷ 2) = 1.00 mol\nStage 3 — write down the equation:\nV = n × 22.4\nSubstitute in the values, and calculate:\nV = 1.00 × 22.4\nV = 22.4 L at STP"
}

[
 {
  "value": 1.49,
  "misconception": "you inverted the mole ratio — O₂ carries the 3 and W the 2, so multiply the moles of tungsten by 3 ÷ 2",
  "feedback": null
 },
 {
  "value": 2.24,
  "misconception": "you skipped the mole ratio — two W use three O₂",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of tungsten: n = 18.38 ÷ 183.8 = 0.100 mol\nStage 2 — mole ratio: 2W use 3O₂, so n(O₂) = 0.100 × (3 ÷ 2) = 0.150 mol\nStage 3 — write down the equation:\nV = n × 22.4\nSubstitute in the values, and calculate:\nV = 0.150 × 22.4\nV = 3.36 L at STP"
}

[
 {
  "value": 187.8,
  "misconception": "you multiplied the volume itself by the molar mass — convert the volume to moles first",
  "feedback": null
 },
 {
  "value": 0.175,
  "misconception": "you stopped at moles — the question asks for a mass, so multiply by M",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of gas: n = 3.92 ÷ 22.4 = 0.175 mol\nStage 2 — mole ratio: Ti and O₂ both carry coefficient 1, so n(Ti) = 0.175 mol\nStage 3 — write down the equation:\nm = n × M\nSubstitute in the values, and calculate:\nm = 0.175 × 47.9\nm = 8.38 g"
}

[
 {
  "value": 352.8,
  "misconception": "you skipped the mole ratio — each fuel particle makes several CO₂, so fewer fuel moles are needed",
  "feedback": null
 },
 {
  "value": 0.7,
  "misconception": "you stopped at moles — the question asks for a mass, so multiply by M",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of CO₂: n = 94.08 ÷ 22.4 = 4.20 mol\nStage 2 — mole ratio: 1C₆H₁₂ make 6CO₂, so n(C₆H₁₂) = 4.20 × (1 ÷ 6) = 0.700 mol\nStage 3 — build the molar mass, then write down the equation:\nM = 6 × 12.0 + 12 × 1.0 = 84.0 g/mol\nm = n × M\nSubstitute in the values, and calculate:\nm = 0.700 × 84.0\nm = 58.8 g"
}

[
 {
  "value": 815.4,
  "misconception": "you multiplied the volume itself by the molar mass — convert the volume to moles first",
  "feedback": null
 },
 {
  "value": 0.65,
  "misconception": "you stopped at moles — the question asks for a mass, so multiply by M",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of C₄H₁₀: n = 14.56 ÷ 22.4 = 0.650 mol\nStage 2 — mole ratio: C₄H₈ and C₄H₁₀ both carry coefficient 1, so n(C₄H₈) = 0.650 mol\nStage 3 — build the molar mass, then write down the equation:\nM = 4 × 12.0 + 8 × 1.0 = 56.0 g/mol\nm = n × M\nSubstitute in the values, and calculate:\nm = 0.650 × 56.0\nm = 36.4 g"
}

[
 {
  "value": 272.2,
  "misconception": "you multiplied the volume itself by the molar mass — convert the volume to moles first",
  "feedback": null
 },
 {
  "value": 0.45,
  "misconception": "you stopped at moles of H₂ and skipped the ratio — 2Al make 3H₂, so scale by 2 ÷ 3 before using M",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of H₂: n = 10.08 ÷ 22.4 = 0.450 mol\nStage 2 — mole ratio: 2Al make 3H₂, so n(Al) = 0.450 × (2 ÷ 3) = 0.300 mol\nStage 3 — write down the equation:\nm = n × M\nSubstitute in the values, and calculate:\nm = 0.300 × 27.0\nm = 8.10 g"
}

[
 {
  "value": 53.8,
  "misconception": "you divided by the ATOMIC molar mass — the gas is H₂, so M = 2 × 1.0 = 2.0 g/mol",
  "feedback": null
 },
 {
  "value": 40.3,
  "misconception": "you skipped the mole ratio — three H₂ make two NH₃, so multiply the hydrogen moles by 2 ÷ 3",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of H₂: M(H₂) = 2 × 1.0 = 2.0 g/mol; n = 3.60 ÷ 2.0 = 1.80 mol\nStage 2 — mole ratio: 3H₂ make 2NH₃, so n(NH₃) = 1.80 × (2 ÷ 3) = 1.20 mol\nStage 3 — write down the equation:\nV = n × 22.4\nSubstitute in the values, and calculate:\nV = 1.20 × 22.4\nV = 26.9 L at STP"
}

[
 {
  "value": 52.8,
  "misconception": "you skipped the mole ratio — one C₃H₈ makes three CO₂, so divide the CO₂ moles by 3",
  "feedback": null
 },
 {
  "value": 0.4,
  "misconception": "you stopped at moles — the question asks for a mass, so multiply by M(C₃H₈) = 44.0 g/mol",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of CO₂: n = 26.88 ÷ 22.4 = 1.20 mol\nStage 2 — mole ratio: 1C₃H₈ makes 3CO₂, so n(C₃H₈) = 1.20 × (1 ÷ 3) = 0.400 mol\nStage 3 — build the molar mass, then write down the equation:\nM = 3 × 12.0 + 8 × 1.0 = 44.0 g/mol\nm = n × M\nSubstitute in the values, and calculate:\nm = 0.400 × 44.0\nm = 17.6 g"
}

[
 {
  "value": 6.7,
  "misconception": "you inverted the coefficient ratio — O₂ carries the 3 and O₃ the 2, so multiply by 3 ÷ 2",
  "feedback": null
 },
 {
  "value": 10.0,
  "misconception": "you ignored the coefficients and assumed a 1 : 1 ratio",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nV(given) = 10.0 L of O₃\ncoefficient of O₂ = 3, coefficient of O₃ = 2\nWrite down the equation:\nV(wanted) = V(given) × (coefficient of wanted ÷ coefficient of given)\nSubstitute in the values, and calculate:\nV(O₂) = 10.0 × (3 ÷ 2)\nV(O₂) = 15 L"
}

[
 {
  "value": 2.0,
  "misconception": "you inverted the coefficient ratio — H₂ carries the 2 and CH₃OH the 1, so multiply by 2 ÷ 1",
  "feedback": null
 },
 {
  "value": 4.0,
  "misconception": "you ignored the coefficients and assumed a 1 : 1 ratio",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nV(given) = 4.0 L of CH₃OH\ncoefficient of H₂ = 2, coefficient of CH₃OH = 1\nWrite down the equation:\nV(wanted) = V(given) × (coefficient of wanted ÷ coefficient of given)\nSubstitute in the values, and calculate:\nV(H₂) = 4.0 × (2 ÷ 1)\nV(H₂) = 8.0 L"
}

[
 {
  "value": 5.5,
  "misconception": "you inverted the coefficient ratio — O₂ carries the 2 and CH₄ the 1, so multiply by 2 ÷ 1",
  "feedback": null
 },
 {
  "value": 11.0,
  "misconception": "you ignored the coefficients and assumed a 1 : 1 ratio",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nV(given) = 11.0 L of CH₄\ncoefficient of O₂ = 2, coefficient of CH₄ = 1\nWrite down the equation:\nV(wanted) = V(given) × (coefficient of wanted ÷ coefficient of given)\nSubstitute in the values, and calculate:\nV(O₂) = 11.0 × (2 ÷ 1)\nV(O₂) = 22.0 L"
}

[
 {
  "value": 8.96,
  "misconception": "you used HCl's coefficient — the metal and H₂ both carry coefficient 1",
  "feedback": null
 },
 {
  "value": 0.2,
  "misconception": "you stopped at moles — the question asks for a volume, so multiply by 22.4 L/mol",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of barium: n = 27.46 ÷ 137.3 = 0.200 mol\nStage 2 — mole ratio: Ba and H₂ both carry coefficient 1, so n(H₂) = 0.200 mol\nStage 3 — write down the equation:\nV = n × 22.4\nSubstitute in the values, and calculate:\nV = 0.200 × 22.4\nV = 4.48 L at STP"
}

[
 {
  "value": 5.6,
  "misconception": "you skipped the mole ratio — each fuel particle makes more than one CO₂ here",
  "feedback": null
 },
 {
  "value": 0.75,
  "misconception": "you stopped at moles — the question asks for a volume, so multiply by 22.4 L/mol",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of C₃H₆: M(C₃H₆) = 3 × 12.0 + 6 × 1.0 = 42.0 g/mol; n = 10.50 ÷ 42.0 = 0.250 mol\nStage 2 — mole ratio: 2C₃H₆ make 6CO₂, so n(CO₂) = 0.250 × (6 ÷ 2) = 0.750 mol\nStage 3 — write down the equation:\nV = n × 22.4\nSubstitute in the values, and calculate:\nV = 0.750 × 22.4\nV = 16.8 L at STP"
}

[
 {
  "value": 7.17,
  "misconception": "you inverted the mole ratio — O₂ carries the 5 and V the 4, so multiply the moles of vanadium by 5 ÷ 4",
  "feedback": null
 },
 {
  "value": 8.96,
  "misconception": "you skipped the mole ratio — four V use five O₂",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of vanadium: n = 20.36 ÷ 50.9 = 0.400 mol\nStage 2 — mole ratio: 4V use 5O₂, so n(O₂) = 0.400 × (5 ÷ 4) = 0.500 mol\nStage 3 — write down the equation:\nV = n × 22.4\nSubstitute in the values, and calculate:\nV = 0.500 × 22.4\nV = 11.2 L at STP"
}

[
 {
  "value": 609.8,
  "misconception": "you multiplied the volume itself by the molar mass — convert the volume to moles first",
  "feedback": null
 },
 {
  "value": 0.375,
  "misconception": "you stopped at moles — the question asks for a mass, so multiply by M",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of gas: n = 8.40 ÷ 22.4 = 0.375 mol\nStage 2 — mole ratio: Ge and O₂ both carry coefficient 1, so n(Ge) = 0.375 mol\nStage 3 — write down the equation:\nm = n × M\nSubstitute in the values, and calculate:\nm = 0.375 × 72.6\nm = 27.2 g"
}

[
 {
  "value": 246.0,
  "misconception": "you skipped the mole ratio — each fuel particle makes several CO₂, so fewer fuel moles are needed",
  "feedback": null
 },
 {
  "value": 0.5,
  "misconception": "you stopped at moles — the question asks for a mass, so multiply by M",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of CO₂: n = 67.2 ÷ 22.4 = 3.00 mol\nStage 2 — mole ratio: 2C₆H₁₀ make 12CO₂, so n(C₆H₁₀) = 3.00 × (2 ÷ 12) = 0.500 mol\nStage 3 — build the molar mass, then write down the equation:\nM = 6 × 12.0 + 10 × 1.0 = 82.0 g/mol\nm = n × M\nSubstitute in the values, and calculate:\nm = 0.500 × 82.0\nm = 41.0 g"
}

[
 {
  "value": 799.7,
  "misconception": "you multiplied the volume itself by the molar mass — convert the volume to moles first",
  "feedback": null
 },
 {
  "value": 0.85,
  "misconception": "you stopped at moles — the question asks for a mass, so multiply by M",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of C₃H₈: n = 19.04 ÷ 22.4 = 0.850 mol\nStage 2 — mole ratio: C₃H₆ and C₃H₈ both carry coefficient 1, so n(C₃H₆) = 0.850 mol\nStage 3 — build the molar mass, then write down the equation:\nM = 3 × 12.0 + 6 × 1.0 = 42.0 g/mol\nm = n × M\nSubstitute in the values, and calculate:\nm = 0.850 × 42.0\nm = 35.7 g"
}

[
 {
  "value": 283.4,
  "misconception": "you multiplied the volume itself by the molar mass — convert the volume to moles first",
  "feedback": null
 },
 {
  "value": 0.55,
  "misconception": "you stopped at moles of H₂ and skipped the ratio — 2Na make 1H₂, so double the moles before using M",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of H₂: n = 12.32 ÷ 22.4 = 0.550 mol\nStage 2 — mole ratio: 2Na make 1H₂, so n(Na) = 0.550 × 2 = 1.10 mol\nStage 3 — write down the equation:\nm = n × M\nSubstitute in the values, and calculate:\nm = 1.10 × 23.0\nm = 25.3 g"
}

[
 {
  "value": 17.9,
  "misconception": "you divided by the ATOMIC molar mass — fluorine gas is F₂, so M = 2 × 19.0 = 38.0 g/mol",
  "feedback": null
 },
 {
  "value": 4.48,
  "misconception": "you skipped the mole ratio — one F₂ makes two HF",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of F₂: M(F₂) = 2 × 19.0 = 38.0 g/mol; n = 7.60 ÷ 38.0 = 0.200 mol\nStage 2 — mole ratio: 1F₂ makes 2HF, so n(HF) = 0.200 × 2 = 0.400 mol\nStage 3 — write down the equation:\nV = n × 22.4\nSubstitute in the values, and calculate:\nV = 0.400 × 22.4\nV = 8.96 L at STP"
}

[
 {
  "value": 74.8,
  "misconception": "you skipped the mole ratio — one C₅H₈ makes five CO₂, so divide the CO₂ moles by 5",
  "feedback": null
 },
 {
  "value": 0.22,
  "misconception": "you stopped at moles — the question asks for a mass, so multiply by M(C₅H₈) = 68.0 g/mol",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of CO₂: n = 24.64 ÷ 22.4 = 1.10 mol\nStage 2 — mole ratio: 1C₅H₈ makes 5CO₂, so n(C₅H₈) = 1.10 × (1 ÷ 5) = 0.220 mol\nStage 3 — build the molar mass, then write down the equation:\nM = 5 × 12.0 + 8 × 1.0 = 68.0 g/mol\nm = n × M\nSubstitute in the values, and calculate:\nm = 0.220 × 68.0\nm = 15.0 g"
}

[
 {
  "value": 2.0,
  "misconception": "you inverted the coefficient ratio — CO₂ carries the 2 and C₂H₄ the 1, so multiply by 2 ÷ 1",
  "feedback": null
 },
 {
  "value": 4.0,
  "misconception": "you ignored the coefficients and assumed a 1 : 1 ratio",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nV(given) = 4.0 L of C₂H₄\ncoefficient of CO₂ = 2, coefficient of C₂H₄ = 1\nWrite down the equation:\nV(wanted) = V(given) × (coefficient of wanted ÷ coefficient of given)\nSubstitute in the values, and calculate:\nV(CO₂) = 4.0 × (2 ÷ 1)\nV(CO₂) = 8.0 L"
}

[
 {
  "value": 1.5,
  "misconception": "you inverted the coefficient ratio — N₂O carries the 2 and O₂ the 1, so multiply by 2 ÷ 1",
  "feedback": null
 },
 {
  "value": 3.0,
  "misconception": "you ignored the coefficients and assumed a 1 : 1 ratio",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nV(given) = 3.0 L of O₂\ncoefficient of N₂O = 2, coefficient of O₂ = 1\nWrite down the equation:\nV(wanted) = V(given) × (coefficient of wanted ÷ coefficient of given)\nSubstitute in the values, and calculate:\nV(N₂O) = 3.0 × (2 ÷ 1)\nV(N₂O) = 6.0 L"
}

[
 {
  "value": 4.57,
  "misconception": "you inverted the coefficient ratio — O₂ carries the 7 and NH₃ the 4, so multiply by 7 ÷ 4",
  "feedback": null
 },
 {
  "value": 8.0,
  "misconception": "you ignored the coefficients and assumed a 1 : 1 ratio",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nV(given) = 8.00 L of NH₃\ncoefficient of O₂ = 7, coefficient of NH₃ = 4\nWrite down the equation:\nV(wanted) = V(given) × (coefficient of wanted ÷ coefficient of given)\nSubstitute in the values, and calculate:\nV(O₂) = 8.00 × (7 ÷ 4)\nV(O₂) = 14.0 L"
}

[
 {
  "value": 8.96,
  "misconception": "you used HCl's coefficient — the metal and H₂ both carry coefficient 1",
  "feedback": null
 },
 {
  "value": 0.2,
  "misconception": "you stopped at moles — the question asks for a volume, so multiply by 22.4 L/mol",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of calcium: n = 8.02 ÷ 40.1 = 0.200 mol\nStage 2 — mole ratio: Ca and H₂ both carry coefficient 1, so n(H₂) = 0.200 mol\nStage 3 — write down the equation:\nV = n × 22.4\nSubstitute in the values, and calculate:\nV = 0.200 × 22.4\nV = 4.48 L at STP"
}

[
 {
  "value": 1.12,
  "misconception": "you skipped the mole ratio — each fuel particle makes more than one CO₂ here",
  "feedback": null
 },
 {
  "value": 0.4,
  "misconception": "you stopped at moles — the question asks for a volume, so multiply by 22.4 L/mol",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of C₈H₈: M(C₈H₈) = 8 × 12.0 + 8 × 1.0 = 104.0 g/mol; n = 5.20 ÷ 104.0 = 0.0500 mol\nStage 2 — mole ratio: 1C₈H₈ make 8CO₂, so n(CO₂) = 0.0500 × (8 ÷ 1) = 0.400 mol\nStage 3 — write down the equation:\nV = n × 22.4\nSubstitute in the values, and calculate:\nV = 0.400 × 22.4\nV = 8.96 L at STP"
}

[
 {
  "value": 4.48,
  "misconception": "you skipped the mole ratio — every two butadiene particles use eleven O₂",
  "feedback": null
 },
 {
  "value": 1.1,
  "misconception": "you stopped at moles — the question asks for a volume, so multiply by 22.4 L/mol",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of butadiene: M(C₄H₆) = 4 × 12.0 + 6 × 1.0 = 54.0 g/mol; n = 10.80 ÷ 54.0 = 0.200 mol\nStage 2 — mole ratio: 2C₄H₆ use 11O₂, so n(O₂) = 0.200 × (11 ÷ 2) = 1.10 mol\nStage 3 — write down the equation:\nV = n × 22.4\nSubstitute in the values, and calculate:\nV = 1.10 × 22.4\nV = 24.6 L at STP"
}

[
 {
  "value": 320.3,
  "misconception": "you multiplied the volume itself by the molar mass — convert the volume to moles first",
  "feedback": null
 },
 {
  "value": 0.275,
  "misconception": "you stopped at moles — the question asks for a mass, so multiply by M",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of gas: n = 6.16 ÷ 22.4 = 0.275 mol\nStage 2 — mole ratio: Cr and H₂ both carry coefficient 1, so n(Cr) = 0.275 mol\nStage 3 — write down the equation:\nm = n × M\nSubstitute in the values, and calculate:\nm = 0.275 × 52.0\nm = 14.3 g"
}

[
 {
  "value": 84.0,
  "misconception": "you skipped the mole ratio — each fuel particle makes several CO₂, so fewer fuel moles are needed",
  "feedback": null
 },
 {
  "value": 0.7,
  "misconception": "you stopped at moles — the question asks for a mass, so multiply by M",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of CO₂: n = 47.04 ÷ 22.4 = 2.10 mol\nStage 2 — mole ratio: 1C₃H₄ make 3CO₂, so n(C₃H₄) = 2.10 × (1 ÷ 3) = 0.700 mol\nStage 3 — build the molar mass, then write down the equation:\nM = 3 × 12.0 + 4 × 1.0 = 40.0 g/mol\nm = n × M\nSubstitute in the values, and calculate:\nm = 0.700 × 40.0\nm = 28.0 g"
}

[
 {
  "value": 64.4,
  "misconception": "you skipped the mole ratio — one C₂H₄ makes two CO₂, so divide the CO₂ moles by 2",
  "feedback": null
 },
 {
  "value": 1.15,
  "misconception": "you stopped at moles — the question asks for a mass, so multiply by M(C₂H₄) = 28.0 g/mol",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of CO₂: n = 51.52 ÷ 22.4 = 2.30 mol\nStage 2 — mole ratio: 1C₂H₄ makes 2CO₂, so n(C₂H₄) = 2.30 × (1 ÷ 2) = 1.15 mol\nStage 3 — build the molar mass, then write down the equation:\nM(C₂H₄) = 2 × 12.0 + 4 × 1.0 = 28.0 g/mol\nm = n × M\nSubstitute in the values, and calculate:\nm = 1.15 × 28.0\nm = 32.2 g"
}

[
 {
  "value": 85.8,
  "misconception": "you skipped the mole ratio — one C₃H₈ makes three CO₂, so divide the CO₂ moles by 3",
  "feedback": null
 },
 {
  "value": 0.65,
  "misconception": "you stopped at moles — the question asks for a mass, so multiply by M(C₃H₈) = 44.0 g/mol",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of CO₂: n = 43.68 ÷ 22.4 = 1.95 mol\nStage 2 — mole ratio: 1C₃H₈ makes 3CO₂, so n(C₃H₈) = 1.95 × (1 ÷ 3) = 0.650 mol\nStage 3 — build the molar mass, then write down the equation:\nM(C₃H₈) = 3 × 12.0 + 8 × 1.0 = 44.0 g/mol\nm = n × M\nSubstitute in the values, and calculate:\nm = 0.650 × 44.0\nm = 28.6 g"
}

[
 {
  "value": 44.8,
  "misconception": "you divided by the ATOMIC molar mass — phosphorus vapor is P₄, so M = 4 × 31.0 = 124.0 g/mol",
  "feedback": null
 },
 {
  "value": 2.24,
  "misconception": "you skipped the mole ratio — one P₄ uses five O₂",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of P₄: M(P₄) = 4 × 31.0 = 124.0 g/mol; n = 12.40 ÷ 124.0 = 0.100 mol\nStage 2 — mole ratio: 1P₄ uses 5O₂, so n(O₂) = 0.100 × 5 = 0.500 mol\nStage 3 — write down the equation:\nV = n × 22.4\nSubstitute in the values, and calculate:\nV = 0.500 × 22.4\nV = 11.2 L at STP"
}

[
 {
  "value": 181.3,
  "misconception": "you multiplied the volume itself by the molar mass — convert the volume to moles first",
  "feedback": null
 },
 {
  "value": 0.075,
  "misconception": "you stopped at moles of O₂ and skipped the ratio — 4Ag come with every O₂, so multiply by 4 before using M",
  "feedback": null
 }
]

{
 "keyExplanation": "Stage 1 — moles of O₂: n = 1.68 ÷ 22.4 = 0.0750 mol\nStage 2 — mole ratio: 4Ag form with 1O₂, so n(Ag) = 0.0750 × 4 = 0.300 mol\nStage 3 — write down the equation:\nm = n × M\nSubstitute in the values, and calculate:\nm = 0.300 × 107.9\nm = 32.4 g"
}

[
 {
  "value": 0.98,
  "misconception": "you left the smallest gas out of the sum — one term per gas, all of them",
  "feedback": null
 },
 {
  "value": 0.29,
  "misconception": "you averaged the partial pressures instead of adding them",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP(gas 1) = 0.46 atm\nP(gas 2) = 0.28 atm\nP(gas 3) = 0.24 atm\nP(gas 4) = 0.18 atm\nCheck the units: every partial pressure is in atm.\nWrite down the equation, one term per gas:\nP(total) = P₁ + P₂ + P₃ + P₄\nSubstitute in the values, and calculate:\nP(total) = 0.46 + 0.28 + 0.24 + 0.18\nP(total) = 1.16 atm"
}

[
 {
  "value": 12.7,
  "misconception": "you subtracted the partial pressures — every gas adds its share to the total",
  "feedback": null
 },
 {
  "value": 47.55,
  "misconception": "you averaged the partial pressures instead of adding them",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP(gas 1) = 41.2 kPa\nP(gas 2) = 53.9 kPa\nCheck the units: every partial pressure is in kPa.\nWrite down the equation, one term per gas:\nP(total) = P₁ + P₂\nSubstitute in the values, and calculate:\nP(total) = 41.2 + 53.9\nP(total) = 95.1 kPa"
}

[
 {
  "value": 1.7,
  "misconception": "you subtracted only the H₂ — the N₂'s share comes off too",
  "feedback": null
 },
 {
  "value": 6.45,
  "misconception": "you added everything together — the unknown share is the total MINUS the known shares",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP(total) = 3.55 atm\nP(H₂) = 1.85 atm\nP(N₂) = 1.05 atm\nWrite down the equation, one term per gas:\nP(total) = P₁ + P₂ + P₃\nExpand it in this problem's own gases:\nP(total) = P(H₂) + P(N₂) + P(NH₃)\nMake P(NH₃) the subject:\nP(NH₃) = P(total) − P(H₂) − P(N₂)\nSubstitute in the values, and calculate:\nP(NH₃) = 3.55 − 1.85 − 1.05\nP(NH₃) = 0.65 atm"
}

[
 {
  "value": 56.7,
  "misconception": "you subtracted only the methane — the ethane's share comes off too",
  "feedback": null
 },
 {
  "value": 104.3,
  "misconception": "you found the sum of the known gases — now subtract it from the total to get the unknown",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP(total) = 118.4 kPa\nP(methane) = 61.7 kPa\nP(ethane) = 42.6 kPa\nWrite down the equation, one term per gas:\nP(total) = P₁ + P₂ + P₃\nExpand it in this problem's own gases:\nP(total) = P(methane) + P(ethane) + P(propane)\nMake P(propane) the subject:\nP(propane) = P(total) − P(methane) − P(ethane)\nSubstitute in the values, and calculate:\nP(propane) = 118.4 − 61.7 − 42.6\nP(propane) = 14.1 kPa"
}

[
 {
  "value": 1.4,
  "misconception": "you left one known gas in the total — all three known shares come off",
  "feedback": null
 },
 {
  "value": 4.45,
  "misconception": "you found the sum of the known gases — now subtract it from the total to get the unknown",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP(total) = 5.00 atm\nP₁ = 2.15 atm\nP₂ = 1.45 atm\nP₃ = 0.85 atm\nWrite down the equation, one term per gas:\nP(total) = P₁ + P₂ + P₃ + P₄\nExpand it in this problem's own gases:\nP(total) = P₁ + P₂ + P₃ + P₄\nMake P₄ the subject:\nP₄ = P(total) − P₁ − P₂ − P₃\nSubstitute in the values, and calculate:\nP₄ = 5.00 − 2.15 − 1.45 − 0.85\nP₄ = 0.55 atm"
}

[
 {
  "value": 456.36,
  "misconception": "you added the raw numbers without converting — 456 mmHg is 0.60 atm",
  "feedback": null
 },
 {
  "value": 4.92,
  "misconception": "you shifted the decimal instead of dividing by 760 — converting mmHg to atm divides by 760, so 456 mmHg is 0.60 atm",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP(gas 1) = 0.36 atm\nP(gas 2) = 456 mmHg\nCheck the units — they differ, so convert first (1 atm = 760 mmHg):\nP(gas 2) = 456 ÷ 760 = 0.60 atm\nWrite down the equation, one term per gas:\nP(total) = P₁ + P₂\nSubstitute in the values, and calculate:\nP(total) = 0.36 + 0.60\nP(total) = 0.96 atm"
}

[
 {
  "value": 0.89,
  "misconception": "you left the smallest gas out of the sum — one term per gas, all of them",
  "feedback": null
 },
 {
  "value": 0.36,
  "misconception": "you averaged the partial pressures instead of adding them",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP(gas 1) = 0.52 atm\nP(gas 2) = 0.37 atm\nP(gas 3) = 0.19 atm\nCheck the units: every partial pressure is in atm.\nWrite down the equation, one term per gas:\nP(total) = P₁ + P₂ + P₃\nSubstitute in the values, and calculate:\nP(total) = 0.52 + 0.37 + 0.19\nP(total) = 1.08 atm"
}

[
 {
  "value": 63.4,
  "misconception": "you left the last gas out of the sum — one term per gas, all of them",
  "feedback": null
 },
 {
  "value": 27.4,
  "misconception": "you averaged the partial pressures instead of adding them",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP(gas 1) = 37.8 kPa\nP(gas 2) = 25.6 kPa\nP(gas 3) = 18.8 kPa\nCheck the units: every partial pressure is in kPa.\nWrite down the equation, one term per gas:\nP(total) = P₁ + P₂ + P₃\nSubstitute in the values, and calculate:\nP(total) = 37.8 + 25.6 + 18.8\nP(total) = 82.2 kPa"
}

[
 {
  "value": 2.05,
  "misconception": "you subtracted only the H₂ — the N₂'s share comes off too",
  "feedback": null
 },
 {
  "value": 7.85,
  "misconception": "you added everything together — the unknown share is the total MINUS the known shares",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP(total) = 4.35 atm\nP(H₂) = 2.30 atm\nP(N₂) = 1.20 atm\nWrite down the equation, one term per gas:\nP(total) = P₁ + P₂ + P₃\nExpand it in this problem's own gases:\nP(total) = P(H₂) + P(N₂) + P(NH₃)\nMake P(NH₃) the subject:\nP(NH₃) = P(total) − P(H₂) − P(N₂)\nSubstitute in the values, and calculate:\nP(NH₃) = 4.35 − 2.30 − 1.20\nP(NH₃) = 0.85 atm"
}

[
 {
  "value": 47.5,
  "misconception": "you subtracted only the CH₄ — the C₂H₆'s share comes off too",
  "feedback": null
 },
 {
  "value": 78.0,
  "misconception": "you found the sum of the known gases — now subtract it from the total to get the unknown",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP(total) = 96.8 kPa\nP(CH₄) = 49.3 kPa\nP(C₂H₆) = 28.7 kPa\nWrite down the equation, one term per gas:\nP(total) = P₁ + P₂ + P₃\nExpand it in this problem's own gases:\nP(total) = P(CH₄) + P(C₂H₆) + P(C₃H₈)\nMake P(C₃H₈) the subject:\nP(C₃H₈) = P(total) − P(CH₄) − P(C₂H₆)\nSubstitute in the values, and calculate:\nP(C₃H₈) = 96.8 − 49.3 − 28.7\nP(C₃H₈) = 18.8 kPa"
}

[
 {
  "value": 1.6,
  "misconception": "you left one known gas in the total — all three known shares come off",
  "feedback": null
 },
 {
  "value": 5.35,
  "misconception": "you found the sum of the known gases — now subtract it from the total to get the unknown",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP(total) = 6.00 atm\nP₁ = 2.75 atm\nP₂ = 1.65 atm\nP₃ = 0.95 atm\nWrite down the equation, one term per gas:\nP(total) = P₁ + P₂ + P₃ + P₄\nExpand it in this problem's own gases:\nP(total) = P₁ + P₂ + P₃ + P₄\nMake P₄ the subject:\nP₄ = P(total) − P₁ − P₂ − P₃\nSubstitute in the values, and calculate:\nP₄ = 6.00 − 2.75 − 1.65 − 0.95\nP₄ = 0.65 atm"
}

[
 {
  "value": 494.26,
  "misconception": "you added the raw numbers without converting — 494 mmHg is 0.65 atm",
  "feedback": null
 },
 {
  "value": 5.2,
  "misconception": "you shifted the decimal instead of dividing by 760 — converting mmHg to atm divides by 760, so 494 mmHg is 0.65 atm",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP(gas 1) = 0.26 atm\nP(gas 2) = 494 mmHg\nCheck the units — they differ, so convert first (1 atm = 760 mmHg):\nP(gas 2) = 494 ÷ 760 = 0.65 atm\nWrite down the equation, one term per gas:\nP(total) = P₁ + P₂\nSubstitute in the values, and calculate:\nP(total) = 0.26 + 0.65\nP(total) = 0.91 atm"
}

[
 {
  "value": 1.06,
  "misconception": "you left the smallest gas out of the sum — one term per gas, all of them",
  "feedback": null
 },
 {
  "value": 0.3,
  "misconception": "you averaged the partial pressures instead of adding them",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP(gas 1) = 0.51 atm\nP(gas 2) = 0.38 atm\nP(gas 3) = 0.17 atm\nP(gas 4) = 0.14 atm\nCheck the units: every partial pressure is in atm.\nWrite down the equation, one term per gas:\nP(total) = P₁ + P₂ + P₃ + P₄\nSubstitute in the values, and calculate:\nP(total) = 0.51 + 0.38 + 0.17 + 0.14\nP(total) = 1.20 atm"
}

[
 {
  "value": 32.6,
  "misconception": "you subtracted the partial pressures — every gas adds its share to the total",
  "feedback": null
 },
 {
  "value": 46.1,
  "misconception": "you averaged the partial pressures instead of adding them",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP(gas 1) = 62.4 kPa\nP(gas 2) = 29.8 kPa\nCheck the units: every partial pressure is in kPa.\nWrite down the equation, one term per gas:\nP(total) = P₁ + P₂\nSubstitute in the values, and calculate:\nP(total) = 62.4 + 29.8\nP(total) = 92.2 kPa"
}

[
 {
  "value": 2.05,
  "misconception": "you subtracted only the H₂ — the N₂'s share comes off too",
  "feedback": null
 },
 {
  "value": 6.95,
  "misconception": "you added everything together — the unknown share is the total MINUS the known shares",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP(total) = 3.95 atm\nP(H₂) = 1.90 atm\nP(N₂) = 1.10 atm\nWrite down the equation, one term per gas:\nP(total) = P₁ + P₂ + P₃\nExpand it in this problem's own gases:\nP(total) = P(H₂) + P(N₂) + P(NH₃)\nMake P(NH₃) the subject:\nP(NH₃) = P(total) − P(H₂) − P(N₂)\nSubstitute in the values, and calculate:\nP(NH₃) = 3.95 − 1.90 − 1.10\nP(NH₃) = 0.95 atm"
}

[
 {
  "value": 60.7,
  "misconception": "you subtracted only the CH₄ — the C₂H₆'s share comes off too",
  "feedback": null
 },
 {
  "value": 110.3,
  "misconception": "you found the sum of the known gases — now subtract it from the total to get the unknown",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP(total) = 132.6 kPa\nP(CH₄) = 71.9 kPa\nP(C₂H₆) = 38.4 kPa\nWrite down the equation, one term per gas:\nP(total) = P₁ + P₂ + P₃\nExpand it in this problem's own gases:\nP(total) = P(CH₄) + P(C₂H₆) + P(C₃H₈)\nMake P(C₃H₈) the subject:\nP(C₃H₈) = P(total) − P(CH₄) − P(C₂H₆)\nSubstitute in the values, and calculate:\nP(C₃H₈) = 132.6 − 71.9 − 38.4\nP(C₃H₈) = 22.3 kPa"
}

[
 {
  "value": 1.5,
  "misconception": "you left one known gas in the total — all three known shares come off",
  "feedback": null
 },
 {
  "value": 3.15,
  "misconception": "you found the sum of the known gases — now subtract it from the total to get the unknown",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP(total) = 4.00 atm\nP₁ = 1.35 atm\nP₂ = 1.15 atm\nP₃ = 0.65 atm\nWrite down the equation, one term per gas:\nP(total) = P₁ + P₂ + P₃ + P₄\nExpand it in this problem's own gases:\nP(total) = P₁ + P₂ + P₃ + P₄\nMake P₄ the subject:\nP₄ = P(total) − P₁ − P₂ − P₃\nSubstitute in the values, and calculate:\nP₄ = 4.00 − 1.35 − 1.15 − 0.65\nP₄ = 0.85 atm"
}

[
 {
  "value": 532.23,
  "misconception": "you added the raw numbers without converting — 532 mmHg is 0.70 atm",
  "feedback": null
 },
 {
  "value": 5.55,
  "misconception": "you shifted the decimal instead of dividing by 760 — converting mmHg to atm divides by 760, so 532 mmHg is 0.70 atm",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP(gas 1) = 0.23 atm\nP(gas 2) = 532 mmHg\nCheck the units — they differ, so convert first (1 atm = 760 mmHg):\nP(gas 2) = 532 ÷ 760 = 0.70 atm\nWrite down the equation, one term per gas:\nP(total) = P₁ + P₂\nSubstitute in the values, and calculate:\nP(total) = 0.23 + 0.70\nP(total) = 0.93 atm"
}

[
 {
  "value": 0.86,
  "misconception": "you left the smallest gas out of the sum — one term per gas, all of them",
  "feedback": null
 },
 {
  "value": 0.33,
  "misconception": "you averaged the partial pressures instead of adding them",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP(gas 1) = 0.45 atm\nP(gas 2) = 0.41 atm\nP(gas 3) = 0.13 atm\nCheck the units: every partial pressure is in atm.\nWrite down the equation, one term per gas:\nP(total) = P₁ + P₂ + P₃\nSubstitute in the values, and calculate:\nP(total) = 0.45 + 0.41 + 0.13\nP(total) = 0.99 atm"
}

[
 {
  "value": 78.3,
  "misconception": "you left the last gas out of the sum — one term per gas, all of them",
  "feedback": null
 },
 {
  "value": 31.4,
  "misconception": "you averaged the partial pressures instead of adding them",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP(gas 1) = 44.7 kPa\nP(gas 2) = 33.6 kPa\nP(gas 3) = 15.9 kPa\nCheck the units: every partial pressure is in kPa.\nWrite down the equation, one term per gas:\nP(total) = P₁ + P₂ + P₃\nSubstitute in the values, and calculate:\nP(total) = 44.7 + 33.6 + 15.9\nP(total) = 94.2 kPa"
}

[
 {
  "value": 2.1,
  "misconception": "you subtracted only the H₂ — the N₂'s share comes off too",
  "feedback": null
 },
 {
  "value": 8.75,
  "misconception": "you added everything together — the unknown share is the total MINUS the known shares",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP(total) = 4.65 atm\nP(H₂) = 2.55 atm\nP(N₂) = 1.55 atm\nWrite down the equation, one term per gas:\nP(total) = P₁ + P₂ + P₃\nExpand it in this problem's own gases:\nP(total) = P(H₂) + P(N₂) + P(NH₃)\nMake P(NH₃) the subject:\nP(NH₃) = P(total) − P(H₂) − P(N₂)\nSubstitute in the values, and calculate:\nP(NH₃) = 4.65 − 2.55 − 1.55\nP(NH₃) = 0.55 atm"
}

[
 {
  "value": 51.4,
  "misconception": "you subtracted only the CH₄ — the C₂H₆'s share comes off too",
  "feedback": null
 },
 {
  "value": 68.1,
  "misconception": "you found the sum of the known gases — now subtract it from the total to get the unknown",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP(total) = 87.6 kPa\nP(CH₄) = 36.2 kPa\nP(C₂H₆) = 31.9 kPa\nWrite down the equation, one term per gas:\nP(total) = P₁ + P₂ + P₃\nExpand it in this problem's own gases:\nP(total) = P(CH₄) + P(C₂H₆) + P(C₃H₈)\nMake P(C₃H₈) the subject:\nP(C₃H₈) = P(total) − P(CH₄) − P(C₂H₆)\nSubstitute in the values, and calculate:\nP(C₃H₈) = 87.6 − 36.2 − 31.9\nP(C₃H₈) = 19.5 kPa"
}

[
 {
  "value": 1.5,
  "misconception": "you left one known gas in the total — all three known shares come off",
  "feedback": null
 },
 {
  "value": 6.05,
  "misconception": "you found the sum of the known gases — now subtract it from the total to get the unknown",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP(total) = 7.00 atm\nP₁ = 3.05 atm\nP₂ = 2.45 atm\nP₃ = 0.55 atm\nWrite down the equation, one term per gas:\nP(total) = P₁ + P₂ + P₃ + P₄\nExpand it in this problem's own gases:\nP(total) = P₁ + P₂ + P₃ + P₄\nMake P₄ the subject:\nP₄ = P(total) − P₁ − P₂ − P₃\nSubstitute in the values, and calculate:\nP₄ = 7.00 − 3.05 − 2.45 − 0.55\nP₄ = 0.95 atm"
}

[
 {
  "value": 608.31,
  "misconception": "you added the raw numbers without converting — 608 mmHg is 0.80 atm",
  "feedback": null
 },
 {
  "value": 6.39,
  "misconception": "you shifted the decimal instead of dividing by 760 — converting mmHg to atm divides by 760, so 608 mmHg is 0.80 atm",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP(gas 1) = 0.31 atm\nP(gas 2) = 608 mmHg\nCheck the units — they differ, so convert first (1 atm = 760 mmHg):\nP(gas 2) = 608 ÷ 760 = 0.80 atm\nWrite down the equation, one term per gas:\nP(total) = P₁ + P₂\nSubstitute in the values, and calculate:\nP(total) = 0.31 + 0.80\nP(total) = 1.11 atm"
}

[
 {
  "value": 1.12,
  "misconception": "you left the smallest gas out of the sum — one term per gas, all of them",
  "feedback": null
 },
 {
  "value": 0.32,
  "misconception": "you averaged the partial pressures instead of adding them",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP(gas 1) = 0.49 atm\nP(gas 2) = 0.34 atm\nP(gas 3) = 0.29 atm\nP(gas 4) = 0.16 atm\nCheck the units: every partial pressure is in atm.\nWrite down the equation, one term per gas:\nP(total) = P₁ + P₂ + P₃ + P₄\nSubstitute in the values, and calculate:\nP(total) = 0.49 + 0.34 + 0.29 + 0.16\nP(total) = 1.28 atm"
}

[
 {
  "value": 30.9,
  "misconception": "you subtracted the partial pressures — every gas adds its share to the total",
  "feedback": null
 },
 {
  "value": 42.85,
  "misconception": "you averaged the partial pressures instead of adding them",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP(gas 1) = 58.3 kPa\nP(gas 2) = 27.4 kPa\nCheck the units: every partial pressure is in kPa.\nWrite down the equation, one term per gas:\nP(total) = P₁ + P₂\nSubstitute in the values, and calculate:\nP(total) = 58.3 + 27.4\nP(total) = 85.7 kPa"
}

[
 {
  "value": 2.2,
  "misconception": "you subtracted only the H₂ — the N₂'s share comes off too",
  "feedback": null
 },
 {
  "value": 9.85,
  "misconception": "you added everything together — the unknown share is the total MINUS the known shares",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP(total) = 5.15 atm\nP(H₂) = 2.95 atm\nP(N₂) = 1.75 atm\nWrite down the equation, one term per gas:\nP(total) = P₁ + P₂ + P₃\nExpand it in this problem's own gases:\nP(total) = P(H₂) + P(N₂) + P(NH₃)\nMake P(NH₃) the subject:\nP(NH₃) = P(total) − P(H₂) − P(N₂)\nSubstitute in the values, and calculate:\nP(NH₃) = 5.15 − 2.95 − 1.75\nP(NH₃) = 0.45 atm"
}

[
 {
  "value": 64.6,
  "misconception": "you subtracted only the CH₄ — the C₂H₆'s share comes off too",
  "feedback": null
 },
 {
  "value": 125.5,
  "misconception": "you found the sum of the known gases — now subtract it from the total to get the unknown",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP(total) = 143.2 kPa\nP(CH₄) = 78.6 kPa\nP(C₂H₆) = 46.9 kPa\nWrite down the equation, one term per gas:\nP(total) = P₁ + P₂ + P₃\nExpand it in this problem's own gases:\nP(total) = P(CH₄) + P(C₂H₆) + P(C₃H₈)\nMake P(C₃H₈) the subject:\nP(C₃H₈) = P(total) − P(CH₄) − P(C₂H₆)\nSubstitute in the values, and calculate:\nP(C₃H₈) = 143.2 − 78.6 − 46.9\nP(C₃H₈) = 17.7 kPa"
}

[
 {
  "value": 3.1,
  "misconception": "you left one known gas in the total — all three known shares come off",
  "feedback": null
 },
 {
  "value": 7.85,
  "misconception": "you found the sum of the known gases — now subtract it from the total to get the unknown",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP(total) = 9.00 atm\nP₁ = 3.65 atm\nP₂ = 2.25 atm\nP₃ = 1.95 atm\nWrite down the equation, one term per gas:\nP(total) = P₁ + P₂ + P₃ + P₄\nExpand it in this problem's own gases:\nP(total) = P₁ + P₂ + P₃ + P₄\nMake P₄ the subject:\nP₄ = P(total) − P₁ − P₂ − P₃\nSubstitute in the values, and calculate:\nP₄ = 9.00 − 3.65 − 2.25 − 1.95\nP₄ = 1.15 atm"
}

[
 {
  "value": 646.22,
  "misconception": "you added the raw numbers without converting — 646 mmHg is 0.85 atm",
  "feedback": null
 },
 {
  "value": 6.68,
  "misconception": "you shifted the decimal instead of dividing by 760 — converting mmHg to atm divides by 760, so 646 mmHg is 0.85 atm",
  "feedback": null
 }
]

{
 "keyExplanation": "Write down the values in the question:\nP(gas 1) = 0.22 atm\nP(gas 2) = 646 mmHg\nCheck the units — they differ, so convert first (1 atm = 760 mmHg):\nP(gas 2) = 646 ÷ 760 = 0.85 atm\nWrite down the equation, one term per gas:\nP(total) = P₁ + P₂\nSubstitute in the values, and calculate:\nP(total) = 0.22 + 0.85\nP(total) = 1.07 atm"
}