Deviation from the Ideal Gas Law

The ideal gas law assumes molecules are points with no volume and no attraction for each other. Real molecules fail both assumptions, and the failure shows up most when you squeeze a gas into a small space. At low pressure, molecules are far apart and spend most of their time acting ideal. Crank the pressure up and they get close enough for their size and their stickiness toward each other to matter.

Attractions pull molecules toward each other right as they are about to strike the container wall, softening each impact. That makes the measured pressure lower than an ideal gas would produce, so Z = PV/(nRT) dips below 1 at moderate pressure. Push the pressure even higher and the molecules themselves take up a real fraction of the container's volume, leaving less empty space than the ideal law assumes. Now the actual volume is bigger than ideal behavior predicts, and Z rises above 1 and keeps climbing. Plot Z against pressure for a real gas like CO₂ and you see exactly this: a dip below 1 at moderate pressure, a minimum, then a rise above 1 at high pressure, while an ideal gas would trace a flat line at Z = 1.

How far and how fast a gas deviates depends on what it is made of. Large, polar, or easily polarized molecules deviate hard, because they have more surface area and stronger attractions. Small nonpolar molecules like He or H₂ stay close to ideal almost up to very high pressures. This connects directly to intermolecular forces from earlier in the unit, and it sets up van der Waals' equation, which patches PV = nRT with correction terms for attraction and volume.