Real gases deviate from ideal behavior because their molecules take up physical space and attract (or repel) each other. The ideal gas law assumes neither of these things is true, which works well enough under everyday conditions but breaks down at high pressures and low temperatures, where molecules are squeezed close together and those ignored factors start to matter.
The Two Assumptions That Break Down
The ideal gas model rests on the kinetic molecular theory, which makes two simplifying assumptions: gas molecules have zero volume, and they exert no forces on each other. In reality, every molecule occupies a small but real amount of space, and every molecule interacts with its neighbors through attractive and repulsive forces. At low pressures and high temperatures, molecules are far apart and moving fast, so these simplifications barely matter. But change the conditions, and the simplifications stop working.
Think of it this way. If you have a handful of marbles in a large room, you can treat them as tiny points that never interact. Shrink the room (raise the pressure) or slow the marbles down (lower the temperature), and suddenly their size and their tendency to stick together become impossible to ignore.
How Intermolecular Attractions Lower Pressure
When gas molecules approach each other, they experience a small cohesive pull. This attraction helps hold the gas together slightly, which means molecules heading toward the container wall get tugged back by their neighbors. The result: they hit the wall with less force, and the measured pressure drops below what the ideal gas law predicts.
This effect depends on how tightly packed the molecules are. The pressure reduction is proportional to the square of the number of molecules per unit volume. So for a fixed amount of gas, shrinking the volume brings molecules closer together, amplifies the attraction, and makes the deviation worse. Heavier molecules generally have stronger intermolecular attractions, which is why gases like carbon dioxide or ammonia deviate more than helium or hydrogen under the same conditions.
How Molecular Volume Raises Pressure
The ideal gas law assumes molecules are infinitely small points. Real molecules have finite size, and at high enough pressures, that size matters. Each molecule’s physical bulk reduces the free space available for other molecules to move in. The gas effectively has less room than the container’s total volume suggests, so the molecules collide with the walls more often than the ideal model predicts. This pushes the measured pressure above the ideal value.
At moderate pressures, the attractive force effect (lowering pressure) tends to dominate. At very high pressures, though, molecules are packed so tightly that repulsive forces and finite molecular size take over, and the gas exerts more pressure than expected. This tug-of-war between attraction and repulsion is the core reason real gas behavior can swing in both directions relative to the ideal prediction.
When Deviations Are Largest
Two conditions push real gases furthest from ideal behavior: high pressure and low temperature.
- High pressure forces molecules close together, magnifying both the effect of intermolecular forces and the impact of molecular volume. The closer the molecules, the more strongly they interact.
- Low temperature slows molecules down. Slower molecules spend more time near each other, giving attractive forces more opportunity to influence their motion. At low enough temperatures, attractions can even cause the gas to condense into a liquid, something no ideal gas would ever do.
The worst-case scenario is near a gas’s critical point, the specific temperature and pressure where the distinction between liquid and gas phases starts to blur. At the critical point, real gas behavior departs most dramatically from the ideal model.
Conversely, at low pressures and high temperatures, molecules are far apart and moving fast. Under those conditions, intermolecular forces are negligible and molecular volume is tiny compared to the container, so the ideal gas law works well.
The Compressibility Factor
Scientists quantify how far a gas strays from ideal behavior using a number called the compressibility factor, Z. It’s defined as the ratio of the gas’s actual pressure-volume product to the value predicted by the ideal gas law. For a perfect ideal gas, Z equals exactly 1.
When Z drops below 1, attractive forces are winning: the gas is being pulled inward, occupying less volume than predicted. When Z rises above 1, molecular size and repulsive forces dominate, and the gas takes up more space than the ideal model expects. At very low pressures, Z approaches 1 for all gases regardless of temperature, confirming that every real gas behaves ideally when its molecules are spread far enough apart.
There is also a specific temperature for each gas, called the Boyle temperature, where attractive and repulsive intermolecular effects roughly cancel each other out. At this temperature, the gas mimics ideal behavior over a wider range of pressures than it otherwise would. The Boyle temperature is different for every gas because it depends on the strength of that gas’s intermolecular forces.
The Van der Waals Correction
In 1873, Johannes van der Waals proposed a modified version of the ideal gas law that accounts for both problems. His equation introduces two constants, typically labeled “a” and “b,” that are unique to each gas.
- Constant a corrects for intermolecular attractions. A larger “a” value means stronger attractive forces between molecules.
- Constant b corrects for the actual volume occupied by the molecules themselves. It represents the volume of one mole of atoms or molecules.
The van der Waals equation isn’t perfect, but it captures the essential physics that the ideal gas law ignores. For gases with very weak intermolecular forces (like helium), “a” is tiny and the correction barely changes the result. For gases with strong attractions (like water vapor), “a” is much larger and the correction is significant.
Why This Matters: Gas Liquefaction
The deviations from ideal behavior aren’t just a textbook curiosity. They’re the reason gases can be cooled and turned into liquids, a process that makes everything from industrial refrigeration to medical oxygen possible.
When a real gas expands, its molecules move farther apart and must work against their mutual attractions. That work costs energy, which comes from the gas’s own thermal energy, so the gas cools down. This is the Joule-Thomson effect. If the cooling is large enough, the gas condenses into a liquid. An ideal gas, by definition having no intermolecular forces, would never cool on expansion and could never be liquefied this way. The very “imperfections” of real gases are what make liquefaction physically possible.