3.6 Deviation from Ideal Gas Law

Real gases stop following the ideal gas law when their particles get close enough to attract each other or when the particles themselves take up a meaningful share of the container's volume. This happens most at low temperatures and high pressures. For AP Chemistry, explain deviations with interparticle attractions and particle volume, not just the ideal gas equation.

Why This Matters for the AP Chemistry Exam

This topic is where you connect particle-level behavior to what actually happens in a gas sample. On the AP Chemistry exam, you may be asked to explain why a real gas does not match the value the ideal gas law predicts, and you need to justify that claim using interparticle forces and particle volume. That kind of reasoning, linking what particles are doing to a measurable property, shows up in both multiple-choice and free-response questions. The ideal gas law (PV = nRT) and kinetic molecular theory set up the assumptions, and this topic explains where those assumptions break down.

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Key Takeaways

• The ideal gas law assumes no attractive forces between particles and that particles have negligible volume. Real gases violate both assumptions under certain conditions.
• Gases deviate most at low temperatures (slower particles spend more time near each other) and high pressures (particles are forced close together).
• Attractive forces cause the measured pressure to be lower than the ideal gas law predicts, because particles hit the walls less often.
• At high pressure, the actual volume taken up by particles becomes significant compared to the container volume, so real volume is larger than the ideal model assumes.
• Polar and larger molecules behave less ideally than small nonpolar molecules because their intermolecular forces are stronger.
• You only need to understand these ideas conceptually and connect them to particle behavior, not run advanced gas calculations for this objective.

Quick Review: The KMT Assumptions

Real gases do not always behave the way kinetic molecular theory predicts. The five assumptions of KMT are a useful starting point because deviations are basically the places where these assumptions fail:

1. There are no attractive or repulsive forces between gas particles.
2. The particles of an ideal gas are separated by great distances compared to their size, so gas particles are treated as having negligible volume.
3. Gas particles move in random, constant, straight-line motion.
4. Collisions are elastic: when gas particles collide, they transfer energy with no net loss.
5. A particle's kinetic energy is related to its velocity (KE = 1/2 mv^2), and all gases have the same average kinetic energy at a given temperature.

The two assumptions that break down for real gases are the first (no forces) and the second (negligible volume).

When Do Gases Deviate from the Ideal Gas Law?

Conditions of low temperature and high pressure cause gases to deviate from ideal behavior, for two main reasons.

Gas particles attract each other

When particles are close together or moving slowly, intermolecular forces become significant. At low temperatures, particles move slower and spend more time near each other, so attractions matter more. This violates the first KMT assumption that there are no forces between particles.

Polar molecules and larger molecules behave less ideally than small nonpolar molecules. Stronger intermolecular forces (such as dipole-dipole interactions or hydrogen bonding) pull these particles toward each other.

The result: the measured pressure of a real gas is usually lower than the ideal gas law predicts. When particles are attracted to one another, they collide with the container walls less often and with less force, so the pressure reads lower.

Particle volume becomes significant

At high pressure, the volume of the container decreases (Boyle's Law). When the container shrinks, the space taken up by the particles themselves is no longer negligible compared to the total volume. This violates the second KMT assumption that particle volume can be ignored.

Because the particles occupy real space, the actual volume available is larger than the ideal model would suggest for the same number of particles.

Reading the graphs

A common way to show deviation is to plot PV/RT (called the compressibility factor) against pressure. For one mole of an ideal gas, PV = RT, so PV/RT should equal 1 at all pressures. Real gases stray from 1:

• When attractive forces control behavior, PV/RT drops below 1.
• When particle volume controls behavior at very high pressure, PV/RT rises above 1.

Correcting the Ideal Gas Law: The van der Waals Equation

Because the ideal gas law has these exceptions, chemists adjusted it to account for attractive forces and particle volume. The result is the van der Waals equation. A few things to keep in mind:

1. You will not need to plug numbers into this equation on the AP Chemistry exam. You only need it conceptually, so do not stress about memorizing it.
2. It corrects the pressure and volume terms so that PV = nRT still works at high pressures and small volumes.
3. The correction adds to the pressure term (because real pressure is lowered by attractions) and subtracts from the volume term (because particles take up real space).

How to Use This on the AP Chemistry Exam

Free Response

A frequent prompt gives you a measured gas property and asks you to explain why it differs from the ideal gas law prediction. Connect the macroscopic observation to particle behavior.

Example prompt: a student measures the actual pressure of CO2(g) and finds it is lower than the pressure predicted by the ideal gas law. Explain this observation.

Strong response: The attractive forces between CO2 molecules result in a pressure lower than the ideal gas law predicts. Because the molecules are attracted to one another, they collide with the container walls less often than ideal particles (which have no attractive forces) would.

Common Trap

If a question describes conditions, identify which assumption fails:

• Low temperature or near-condensation conditions point to attractive forces and a lower-than-ideal pressure.
• Extremely high pressure points to particle volume becoming significant.

State the specific force or the specific assumption, not just "the gas is not ideal."

Diffusion and Effusion

Diffusion

Diffusion describes the mixing of gases. Two patterns to remember:

• As temperature increases, the rate of diffusion increases because particles move faster.
• Larger (heavier) molecules diffuse more slowly because they have more mass and move slower at the same temperature.

Effusion

Effusion is similar to diffusion, but it describes gas passing through a tiny opening into a vacuum, flowing from higher pressure to lower pressure through a pinhole.

The same patterns apply: higher temperature increases the rate of effusion, and higher molar mass decreases it. The difference is that effusion measures how fast particles move through the opening.

Graham's Law of Effusion

Graham's law states that the rate at which a gas effuses through a small opening is inversely proportional to the square root of its molar mass:

$\frac{\text{Rate}_1}{\text{Rate}_2} = \sqrt{\frac{M_2}{M_1}}$

where

• Rate_1 is the rate of effusion of the first gas
• Rate_2 is the rate of effusion of the second gas
• M_1 is the molar mass of the first gas
• M_2 is the molar mass of the second gas

This connects to kinetic molecular theory: at a given temperature, all gases have the same average kinetic energy, so lighter molecules must move faster. The lighter the gas, the faster it effuses. A useful habit is to put the lighter gas as gas 1, then state how many times faster gas 1 effuses compared to gas 2.

Common Misconceptions

• "Real gases always deviate from ideal behavior." Gases behave very close to ideal at high temperature and low pressure. Deviation becomes noticeable mainly at low temperature and high pressure.
• "Attractions make the pressure higher." Attractions pull particles inward, so they hit the walls less and the measured pressure is lower than ideal predictions.
• "Particle volume is always significant." Particle volume only matters at very high pressure, when the container is so small that the particles take up a real fraction of the space.
• "All gases deviate the same amount." Polar and larger molecules deviate more because their intermolecular forces are stronger than those of small nonpolar molecules.
• "You have to calculate with the van der Waals equation." You only need to explain it conceptually; the exam will not require you to run those calculations for this objective.
• "Intramolecular and intermolecular forces are the same thing." Deviation from ideal behavior is driven by intermolecular forces (attractions between separate particles), not the bonds within a molecule.

Related AP Chemistry Guides

• 3.1 Intermolecular and Interparticle Forces
• Unit 3 Overview: Properties of Substances and Mixtures
• 3.2 Properties of Solids
• 3.4 Ideal Gas Law
• 3.5 Kinetic Molecular Theory
• 3.3 Solids, Liquids, and Gases