3.6 Non-Ideal Gases

Deviation from the Ideal Gas Law

Two cylinders hold one mole each at one temperature: the left one obeys PV = nRT, the right one is a real gas. Compress them together and watch the pistons come apart, with the gap split into the two causes the exam names — the space the molecules occupy and the pull between them.

Measured vs PredictedAttractionsParticle Volume9 Gases
Topic 3.6

Deviation from Ideal Gas Law

Explain the relationship among non-ideal behaviors of gases, interparticle forces, and/or volumes.

The ideal gas law does not describe the actual behavior of real gases. The CED names exactly two causes, matching the two KMT assumptions that fail:

1. Interparticle attractions. Real molecules attract each other. As a molecule approaches the wall, its neighbors pull it back, so it strikes with less force than KMT predicts. The measured pressure is therefore lower than ideal. This matters most at conditions close to condensation: low temperature (particles move slowly enough for attractions to take hold) and moderately high pressure (particles are close together). Gases with strong IMFs — polar molecules, hydrogen bonders like H₂O and NH₃ — deviate most.

2. Particle volume. Real molecules occupy space. At extremely high pressures the particles themselves take up a significant fraction of the container, so the free volume available is less than the measured container volume, and the observed volume is larger than ideal prediction.

The two effects push in opposite directions, which is why a plot of PV/nRT versus pressure typically dips below 1 first (attractions winning) and then rises above 1 (volume winning) at very high pressure.

When do gases behave most ideally? High temperature and low pressure. High temperature means particles have enough kinetic energy that attractions are negligible; low pressure means they are far apart, so their own volume is negligible.

Key points

  • Ideal behavior requires high temperature and low pressure.
  • Attractions make measured pressure lower than ideal (PV/nRT < 1).
  • Particle volume makes measured volume larger than ideal (PV/nRT > 1) at extreme pressure.
  • The strongest deviations belong to gases with the strongest IMFs — H₂O and NH₃ deviate far more than He.

Common mistakes

  • Do not say gases deviate because "the molecules are too big". Specify which effect dominates under the stated conditions.
  • Low temperature, not high, causes attraction-driven deviation.
  • He and H₂ are the closest to ideal — tiny, nonpolar, with the weakest dispersion forces.
  • Deviation is not a failure of the gas. It is a failure of two idealizing assumptions.

Worked example

At 1.0 atm and 300 K, samples of He, CH₄, and NH₃ behave nearly ideally. As the temperature is lowered to 200 K at constant pressure, which shows the greatest negative deviation from ideal behavior? Explain.

NH₃ shows the greatest deviation.

Negative deviation (measured pressure lower than ideal, PV/nRT below 1) is caused by intermolecular attractions. As the temperature falls, particles have less kinetic energy and spend more time close enough to one another for those attractions to matter, so a particle heading for the wall is held back and strikes with less force.

The magnitude of the effect scales with IMF strength. NH₃ is polar and hydrogen bonds (N–H), giving it by far the strongest attractions of the three. CH₄ is nonpolar with only dispersion forces, and helium is a tiny monatomic species with the weakest dispersion forces of all — it stays nearly ideal even at low temperature.

Full notes for topic 3.6 →