AP® Chemistry review sheet from Aim for Five (aimforfive.com/chem/units/3/3-6)
Unit 3 · Topic 3.6
3.6 Deviation from Ideal Gas Law
Real gases follow PV = nRT only approximately. Attractions between particles make the measured pressure lower than predicted, especially near condensation, and the particles' own volume makes the real volume larger than predicted at very high pressure.
Key terms
- real gas
- ideal gas
- intermolecular attractions
- particle volume
- condensation
Where the ideal model breaks down
The ideal gas law comes from KMT, which assumes gas particles have no volume and don't attract each other. Real particles do have volume, and they do attract each other. Most of the time these effects are tiny, because gas particles are far apart. They become important under two kinds of conditions.
Attractions: low temperature
When a gas is cold and close to condensing, its particles move slowly. Attractions between them have time to act. A particle about to hit the wall is pulled back slightly by its neighbors, so it hits more gently. The result: the measured pressure is lower than PV = nRT predicts.
The stronger a gas's IMFs, the bigger this effect. Polar gases like NH₃ and H₂O, and large, polarizable gases, deviate more than small nonpolar gases like He and H₂.
Particle volume: very high pressure
At very high pressure, the particles are squeezed close together, and the space they take up is no longer negligible. The empty space they can move around in is smaller than the container's volume. The result: the real volume of the gas is larger than the ideal gas law predicts for that pressure, or, for a fixed volume, the measured pressure is higher than predicted.
Bigger particles make this effect larger.
Comparing real and ideal values
Some questions give the measured pressure or volume of a gas and ask you to compare it with the ideal value. Work out nRT/V (or nRT/P) for the sample, then compare.
If the measured pressure is lower than the ideal prediction, attractions between particles are the main effect. If the measured volume is larger than the ideal prediction, the particles' own volume is the main effect. Under ordinary lab conditions, most gases are within a few percent of ideal, which is why PV = nRT works well for everyday calculations.
If the attractions become strong enough, as when a gas is cooled enough or compressed enough, the gas condenses into a liquid. A real gas near that point is where the ideal gas law is least reliable.
Putting it together
The gas that behaves most ideally is small, light and nonpolar, like He, at high temperature and low pressure. The gas that deviates most is large or polar at low temperature or high pressure.
You won't need to calculate with real-gas equations such as the van der Waals equation; the particle-level explanations above are what the exam asks for.
| Condition | Main cause of deviation | Result compared with ideal |
|---|---|---|
| Low temperature, near condensation | attractions between particles | measured P lower than nRT/V |
| Very high pressure | particles' own volume | measured V larger than nRT/P |
| High temperature, low pressure | neither | close to ideal |
Worked examples
Try each one yourself first, then open the solution.
- Example 1
Which gas is most ideal?
Rank He, CH₄ and NH₃ from most ideal to least ideal behavior at the same temperature and pressure, and explain.
Show the solutionHide the solution
- Step 1: Deviations come from attractions and particle size.
- Step 2: He: tiny, with just 2 electrons, so very weak dispersion forces. Most ideal.
- Step 3: CH₄: nonpolar but larger, with 10 electrons, so stronger dispersion forces than He.
- Step 4: NH₃: polar and hydrogen bonds, so the strongest attractions. Least ideal.
Answer: He (most ideal) > CH₄ > NH₃ (least ideal)
- Example 2Calculator allowed
Predicting the direction of a deviation (classic trap)
1.00 mol of CO₂ is placed in a 1.00 L container at 300 K. The ideal gas law predicts a pressure of 24.6 atm. Will the measured pressure be higher or lower? Explain.
Show the solutionHide the solution
- Step 1: Ideal prediction: P = nRT/V = (1.00)(0.08206)(300) ÷ 1.00 = 24.6 atm.
- Step 2: At this pressure CO₂ molecules are fairly crowded and attract each other through dispersion forces (CO₂ has 22 electrons). At 300 K, CO₂ is not far from conditions where it liquefies under pressure.
- Step 3: Attractions pull molecules back from the walls, so collisions with the walls are softer.
- Step 4: So the measured pressure is lower than 24.6 atm. Many students guess higher because 'particles take up space', but under these conditions the attractions have the larger effect.
Answer: Lower than 24.6 atm, because attractions between CO₂ molecules reduce the force of their collisions with the walls.
Common mistakes
- Saying real gases deviate at high temperature. High temperature makes gases more ideal; low temperature makes attractions matter.
- Getting the direction wrong: attractions lower the measured pressure; particle volume raises the real volume.
- Explaining deviations without naming the type of IMF in the specific gas.
On the exam
- Expect a question asking whether a gas's measured pressure or volume is higher or lower than the ideal value, with a justification at the particle level.
- Questions often pair a real gas with a condition (low temperature, high pressure). Decide which factor, attractions or particle volume, dominates, and say so explicitly.
Connected topics
Videos
Check yourself
4 questions on 3.6 Deviation from Ideal Gas Law. Pick an answer to see if you got it, and why.
Under which of the following conditions would a gas behave most like an ideal gas?
A sample of CO₂ is cooled to a temperature just above the point where it condenses. The measured pressure is lower than the pressure calculated with PV = nRT. Which of the following best explains this result?
| Gas | PV ÷ nRT at 300 K and 50 atm |
|---|---|
| He | 1.02 |
| N₂ | 1.00 |
| CH₄ | 0.92 |
| CO₂ | 0.70 |
Approximate data. For an ideal gas, PV ÷ nRT equals exactly 1.
Based on the data, which gas has the strongest attractions between its particles?
Which of the following best explains why the value for helium is greater than 1?
0 of 4 answered