Unit 3 Properties of Substances and Mixtures

AP Chemistry Real Gases

When and why a real gas stops obeying PV = nRT, and how to explain it in exam language.

The ideal gas law works remarkably well for most gases near room conditions, which is why you use it everywhere in Unit 3. Topic 3.6 asks the follow-up question: when does it fail, and why? The answer always comes down to the two simplifications built into the ideal model, and exam questions reward naming the right one for the conditions given.

The Two Ideal Gas Assumptions Real Gases Break

No attractions between particles. Real particles attract one another through intermolecular forces. This matters most near the conditions where the gas would condense: low temperature and high pressure.
Particles take up no volume. Real particles have size. This matters only when they are squeezed very close together, at extremely high pressure.

Both assumptions come from kinetic molecular theory, and both become good approximations when the particles are far apart and moving fast, at high temperature and low pressure.

Fig. 1 · How a real gas departs from ideal behavior as pressure rises (schematic)

For an ideal gas, PV/nRT is exactly 1 at every pressure. The real-gas curve is a schematic of the typical shape, not data for one gas: it falls below 1 where attractions dominate and rises above 1 where particle volume dominates. How deep the dip goes depends on the gas and the temperature.

How Attractions Lower a Real Gas’s Pressure

Pressure comes from particles striking the container walls. A particle about to hit a wall is tugged back by its neighbors behind it, so it strikes less often and less forcefully than an ideal particle would. The measured pressure is therefore lower than PV = nRT predicts, and PV/nRT drops below 1. The effect grows as the temperature falls (slower particles feel attractions longer) and as the gas approaches condensation, where attractions finally win and the gas becomes a liquid.

How Particle Volume Matters at Very High Pressure

The V in PV = nRT is the empty space the particles can move through. At ordinary pressures, the particles themselves fill a negligible fraction of the container. Squeeze the gas to hundreds of atmospheres and the particles’ own volume becomes significant: there is less free space than the container volume suggests, so the gas cannot be compressed as far as the ideal law predicts, and PV/nRT rises above 1.

Which Gases Deviate Most From Ideal Behavior

Compare gases at the same temperature and pressure by the strength of their intermolecular forces and the size of their particles. Strong forces and big particles mean large deviations.

Most ideal: He, Ne, H₂. Small, nonpolar, few electrons, so only weak London dispersion forces.
Least ideal: NH₃ and H₂O vapor (hydrogen bonding), polar molecules such as SO₂, and large, polarizable molecules such as CO₂.

Worked Example 1: Ranking Three Gases by Deviation

At the same temperature and pressure, rank He, N₂, and NH₃ from most to least ideal behavior.

He > N₂ > NH₃. Helium atoms are tiny with only two electrons, so dispersion forces are very weak. N₂ is nonpolar but has more electrons, so its dispersion forces are somewhat stronger. NH₃ molecules are polar and hydrogen bond to one another, so attractions are strongest and NH₃ deviates most.

Worked Example 2: Choosing the Most Ideal Conditions

Under which conditions does CO₂ behave most like an ideal gas: (a) 200 K and 50 atm, (b) 500 K and 1 atm, (c) 500 K and 50 atm, or (d) 200 K and 1 atm?

(b) 500 K and 1 atm. High temperature means fast particles that are barely affected by attractions, and low pressure means particles far apart, so their own volume is negligible. Choice (a) is the worst: cold and compressed, close to condensing.

Worked Example 3: Explaining a Measured Pressure Below PV = nRT

A student puts 1.00 mol of a gas in a rigid 1.00 L container at 300 K. PV = nRT predicts P = (1.00)(0.08206)(300) ÷ 1.00 = 24.6 atm. Real-gas models predict different values for different gases:

Gas	Predicted pressure (atm)	Compared with ideal	Main reason
Ideal gas	24.6	—	No attractions, no particle volume
He	25.2	Slightly higher	Attractions almost zero, so particle volume shows
CO₂	22.1	About 10% lower	Dispersion forces among large, polarizable molecules
NH₃	21.4	About 13% lower	Hydrogen bonding

The real-gas values come from the van der Waals equation, a model beyond the AP course; you would not calculate them on the exam. What the exam asks is the explanation: the measured pressure of CO₂ or NH₃ is lower than calculated because attractions between particles reduce the frequency and force of their collisions with the walls. Helium’s attractions are so weak that its particle volume wins, nudging its pressure slightly above ideal. You can check the ideal value with the gas law calculator.

Common Real Gas Mistakes

Saying attractions raise the pressure. Attractions make particles hit the walls less forcefully, so the pressure is lower than ideal.
Saying gases deviate most at high temperature. Heat makes a gas more ideal; deviations grow at low temperature and high pressure.
Ranking gases by molar mass alone. Rank by intermolecular forces and particle size; NH₃ (17 g/mol) deviates more than N₂ (28 g/mol).
Using particle volume to explain deviations at moderate pressure. Particle volume matters only at extremely high pressure; near condensation, attractions are the cause.

These explanations follow directly from the forces in Unit 3, and a one-sentence explanation like the one in Example 3 is a typical free-response point. To see how points like these add up to a 1–5 score, use the AP Chem Score Calculator.

Frequently Asked Questions

Why do real gases deviate from the ideal gas law?

The ideal gas law assumes gas particles have no attractions for each other and take up no volume. Real particles attract one another, which matters most near condensation (low temperature, high pressure), and they have their own volume, which matters at extremely high pressure.

Under what conditions does a gas behave most ideally?

At high temperature and low pressure. The particles are far apart, so their own volume is a tiny fraction of the container, and they move fast enough that attractions barely affect their collisions.

Is the pressure of a real gas higher or lower than the ideal gas law predicts?

Usually lower, at ordinary and moderately high pressures, because attractions pull particles back as they approach the walls, so they collide less forcefully. At extremely high pressure the particles' own volume takes over and the pressure can be higher than predicted.

Which gases deviate most from ideal behavior?

Gases with strong intermolecular forces and large particles, such as NH3 and H2O vapor (hydrogen bonding) or large, polarizable molecules like CO2. Small, nonpolar particles with few electrons, such as He and H2, behave most ideally.

Do I need the van der Waals equation for AP Chemistry?

No. It is not on the AP equation sheet. AP questions ask you to explain deviations from ideal behavior in terms of attractions and particle volume, not to calculate them with a real-gas equation.

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