Deviation from Ideal Gas Law — AP Chemistry
1. What Is Deviation from Ideal Gas Law? ★★☆☆☆ ⏱ 3 min
The ideal gas law $PV = nRT$ is derived from kinetic molecular theory (KMT) that makes two key simplifying assumptions: gas molecules have no volume of their own, and they experience no intermolecular attractive forces.
This topic contributes ~2-4% of your total AP Chemistry exam score, appearing in both multiple-choice and free-response sections. It tests both conceptual understanding of intermolecular forces and quantitative application of corrected gas laws.
2. Sources of Deviation from Ideal Behavior ★★☆☆☆ ⏱ 3 min
The two failed KMT assumptions lead to two distinct sources of deviation, which dominate under different conditions:
- **Molecular volume effect**: Real gas molecules have finite volume. As pressure increases, molecules are pushed closer together, so molecular volume becomes a large fraction of total container volume. Free volume available for movement is smaller than measured container volume $V$, so observed $PV$ is larger than the ideal value $nRT$.
- **Intermolecular attraction effect**: Real gas molecules experience intermolecular attractions. As a molecule moves toward the container wall, neighboring molecules pull it inward, reducing the force exerted on the wall. Observed pressure $P$ is lower than ideal pressure, so $PV$ is smaller than $nRT$. This effect dominates at low temperature, where kinetic energy is too low to overcome attractions.
3. Compressibility Factor Z ★★★☆☆ ⏱ 3 min
The compressibility factor $Z$ is a dimensionless quantity that directly quantifies the magnitude and direction of deviation from ideal gas behavior. It is defined as:
Z = \frac{PV}{nRT}
- Ideal gas: $Z = 1$ at all conditions
- Real gas $Z < 1$: Observed $PV$ < ideal $nRT$, so intermolecular attraction effect dominates
- Real gas $Z > 1$: Observed $PV$ > ideal $nRT$, so molecular volume effect dominates
For all real gases, $Z$ approaches 1 as pressure approaches 0 (low pressure brings behavior close to ideal). As pressure increases from 0, $Z$ typically dips below 1 then rises above 1 at high pressure. Higher temperatures shift the $Z$ curve closer to $Z=1$.
4. The van der Waals Equation for Real Gases ★★★★☆ ⏱ 5 min
The van der Waals equation modifies the ideal gas law to correct for both sources of deviation, adding two gas-specific empirical correction terms. The full form is:
\left(P + a\frac{n^2}{V^2}\right)(V - nb) = nRT
- $nb$: Volume correction. $b$ is proportional to molecular size, so we subtract $nb$ from measured container volume $V$ to get actual free volume. Larger molecules have larger $b$.
- $a\frac{n^2}{V^2}$: Pressure correction. $a$ is proportional to intermolecular force strength, so we add this term to measured pressure $P$ to get ideal pressure with no attractions. Stronger intermolecular forces have larger $a$.
Common Pitfalls
Why: Students mix up which effect causes which direction of $Z$ deviation, confusing corrected and measured values.
Why: Students misremember which correction applies to which variable.
Why: Students remember two sources of deviation but prioritize the wrong one for moderate pressure conditions.
Why: Students generalize from low-to-moderate pressure behavior where attraction often dominates.
Why: Students only see examples with strong attractive forces near room temperature and generalize incorrectly.