Mistake Master
Deviation from the ideal gas law
The ideal gas law assumes gas particles are points that never attract each other. Real molecules have size and do attract — and under the right squeeze or chill, those two facts make a gas stop obeying PV = nRT.
§1
When the ideal picture breaks.
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The ideal gas law rests on two assumptions: gas particles have negligible volume and no attractions. Real gases obey it well at ordinary conditions but deviate when those assumptions fail.
At high pressure, the particles are crowded, so their own volume becomes a significant fraction of the container — the gas takes up more room than ideal predicts. At low temperature, the particles move slowly enough that intermolecular attractions pull them together, lowering the pressure below ideal.
So deviations grow at high pressure and low temperature — the conditions where real particle volume and real attractions can no longer be ignored. Gases with stronger IMFs deviate more.
§2
Diagnosing a deviation.
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Tie each deviation to the assumption that broke and the condition that broke it.
- Recall the two assumptions. No particle volume; no intermolecular attractions.
- High pressure → volume matters. Crowded particles occupy real space, so the gas resists compression more than ideal predicts.
- Low temperature → attractions matter. Slow particles feel their mutual attractions, pulling inward and lowering pressure.
- Stronger IMFs → bigger deviation. A gas with strong intermolecular forces (like water vapor) deviates more than a weakly attracting one (like helium).
§3
The pieces you'll meet.
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Two assumptions, two failure conditions.
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Worked example: which gas is more ideal, and when?
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Question. Compare helium and water vapor. Which behaves more ideally, and under what conditions do both deviate most?
Which is more ideal. Helium is tiny and has only weak dispersion forces, so it barely attracts and takes little space — it behaves nearly ideally. Water vapor hydrogen-bonds strongly, so it deviates more.
When deviation is worst. Both deviate most at high pressure (particle volume matters) and low temperature (attractions matter).
Reasoning. The deviation is not random: it appears exactly where the ideal assumptions of no-volume and no-attraction stop being good approximations.
§5
Mistakes that cost real points.
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"Real gases deviate most at low pressure and high temperature."
It is the reverse. At low pressure and high temperature the particles are far apart and fast, so their volume and attractions are negligible — the gas is nearly ideal. Deviations grow at high pressure and low temperature.
Fix. Remember the failure conditions: high pressure (volume matters) and low temperature (attractions matter). Low P and high T are the ideal-friendly conditions.
"Deviation happens because the gas particles get heavier."
Mass does not change; deviation comes from particle volume and intermolecular attractions becoming significant. Attributing it to changing mass misreads the cause. The molecules are the same — the conditions changed.
Fix. Attribute deviation to the correct cause: real particle volume (at high P) and real attractions (at low T), not a change in the particles.
"All gases deviate from ideal behavior by the same amount."
Gases with stronger intermolecular forces deviate more. Water vapor, which hydrogen-bonds, departs from ideal much more than helium, which has only weak dispersion. The particle model, including IMF strength, predicts how much.
Fix. Rank deviation by intermolecular-force strength and particle size. Small, weakly attracting gases stay closer to ideal.
§6
Skill Check.
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Ten scenarios. Pick the chips that match your answer, then check. A scenario marks complete the first time every part is right. Progress saves on this device.