Topic 3.6 Notes – Deviation from Ideal Gas Law

1. Why the Ideal Gas Law Sometimes Fails

The Ideal Gas Law comes from the Kinetic Molecular Theory (KMT). Two assumptions matter most here:

• Gas particles have no attractive or repulsive forces between them.
• Gas particles have negligible volume compared to the container.

Those assumptions work pretty well at:

• High temperature (fast particles)
• Low pressure (particles far apart)

They fail at:

• Low temperature
• High pressure

When that happens, we say the gas shows non‑ideal behavior.

The key is always this question:
Which KMT assumption is breaking?

2. The Two Causes of Non‑Ideal Behavior

a. Interparticle Attractions (IMFs)

When particles attract each other, the “no forces” assumption is violated.

This matters most when:

• Temperature is low → particles move slower.
• Pressure is high → particles are closer together.
• Molecules are polar or large → stronger intermolecular forces.

What happens to pressure?

Attractive forces pull particles slightly inward. That means:

• Fewer strong collisions with the walls.
• Measured pressure is lower than predicted by $PV = nRT$.

So if you see:

$$P_{\text{real}} < P_{\text{ideal}}$$

The explanation is almost always attractive forces reducing wall collisions.

This comes up a lot in free-response questions. If they say “the measured pressure is lower than predicted,” they want you to mention:

• Intermolecular attractions
• Reduced frequency/force of collisions

That’s the scoring language.

b. Finite Particle Volume

Now the other assumption breaks: particles do have volume.

At very high pressure:

• The container volume shrinks.
• Particles take up a measurable fraction of that space.
• The “empty space” available for motion is smaller than assumed.

Because the ideal gas law treats particles as point masses, it overestimates how much free space exists.

At extremely high pressures:

• The gas resists compression more than expected.
• Measured pressure becomes higher than predicted.

So:

$$P_{\text{real}} > P_{\text{ideal}}$$

That’s the particle volume effect dominating.

A helpful way to think about it:

• Moderate pressure → attractions dominate.
• Extremely high pressure → particle size dominates.

3. Conditions That Increase Deviation

Three main factors control how ideal a gas behaves.

Temperature

Lower temperature:

• Lower kinetic energy
• Attractions matter more
• Gas may approach condensation
  → Greater deviation

Pressure

Higher pressure:

• Particles closer together
• IMFs increase
• Volume becomes significant
  → Greater deviation

Molecular Identity

Small, nonpolar gases at high temperature and low pressure behave most ideally.

4. Interpreting Graphs of Deviation

You’ll often see a graph of the compressibility factor, $Z = \frac{PV}{RT}$, versus pressure. Take a second to read it from left to right and notice how the real gas curve compares to the ideal line at $Z = 1$.

Compressibility factor (Z) vs. pressure for an ideal and real gas

For an ideal gas:

$$Z = 1$$

For real gases:

• Z < 1 → attractions dominate.
• Z > 1 → particle volume dominates.

Students often mix up which side is which. Just remember: attractions pull particles inward, which lowers the measured pressure and gives a lower Z.

5. Correcting the Ideal Gas Law Conceptually

The Van der Waals equation adjusts the ideal gas law to account for both problems.

Conceptually:

• Add a correction to pressure (because attractions lower measured pressure).
• Subtract a correction from volume (because particles take up space).

You do not need to memorize or calculate with this equation for AP. Just understand:

• “a” term corrects for attractions.
• “b” term corrects for particle volume.