An ideal gas is a theoretical model where gas particles take up no space and never attract or repel each other. A real gas is every gas that actually exists. The difference matters because the ideal gas model works beautifully under certain conditions but breaks down badly under others, and understanding why helps you predict how gases actually behave in the physical world.
The Two Key Assumptions That Define an Ideal Gas
The ideal gas concept rests on two simplifying assumptions. First, gas particles are so tiny compared to the distance between them that their own volume is essentially zero. Second, gas particles have no attractive or repulsive forces between them whatsoever. They bounce off each other and off container walls like perfectly elastic billiard balls, and nothing else happens between collisions.
These assumptions give us the ideal gas law: PV = nRT, where pressure times volume equals the amount of gas times the gas constant (8.314 joules per kelvin per mole) times temperature. It’s elegant, simple, and surprisingly useful. But no real molecule has zero volume, and no real molecule is completely indifferent to its neighbors.
Why Real Gases Deviate From the Model
Real gases deviate from ideal behavior for exactly the two reasons the model ignores: molecules do take up space, and molecules do attract each other. These effects are negligible under everyday conditions but become significant at high pressures and low temperatures.
At high pressures, gas molecules get squeezed closer together. The space the molecules themselves occupy starts to matter relative to the total volume of the container. This makes the actual volume of the gas larger than the ideal gas law predicts, because the equation assumes molecules are dimensionless points that don’t take up room.
At low temperatures, gas molecules move more slowly. When they pass near each other at lower speeds, the attractive forces between them have more time to act. These attractions pull molecules slightly toward each other and away from the container walls, reducing the number and force of collisions with the walls. The result is that the measured pressure drops below what the ideal gas law would predict. This is also why cooling a real gas enough will eventually turn it into a liquid. An ideal gas, by definition, could never liquefy because it has no intermolecular attractions to hold molecules together in a liquid state.
These two effects actually compete with each other. At moderately high pressures, attractions dominate and pressure dips below ideal predictions. At very high pressures, molecular volume dominates and the gas takes up more space than expected. This tug-of-war produces a characteristic dip-then-rise pattern when you plot how far a real gas strays from ideal behavior across a range of pressures.
The Compressibility Factor: Measuring the Gap
Scientists quantify how much a real gas deviates from ideal behavior using a value called the compressibility factor, Z. It’s calculated as PV/nRT. For a perfectly ideal gas, Z equals exactly 1 at all conditions. For a real gas, Z shifts above or below 1 depending on which effect is winning.
When Z is less than 1, intermolecular attractions are pulling molecules inward, making the gas more compressible than the ideal model predicts. When Z is greater than 1, the physical size of the molecules is forcing the gas to occupy more volume than expected. Plotting Z against pressure for different gases gives you a visual map of exactly where and how much each gas departs from ideal behavior.
When Real Gases Act Like Ideal Gases
Real gases approximate ideal behavior at high temperatures and low pressures, specifically below about 1 atmosphere. Under these conditions, molecules are far apart and moving fast, so their volume is negligible relative to the container and they zip past each other too quickly for attractions to matter much. This is why the ideal gas law works well for most calculations involving gases at room temperature and normal atmospheric pressure.
Every real gas also has a specific temperature, called its Boyle temperature, at which it behaves almost perfectly ideally across a broad range of lower pressures. At the Boyle temperature, the effects of molecular volume and intermolecular attraction essentially cancel each other out.
Not All Real Gases Deviate Equally
Some gases stay closer to ideal behavior than others, and the difference comes down to molecular size and how strongly molecules attract each other. Small, non-polar molecules like helium and hydrogen have very weak intermolecular forces and tiny volumes, so they behave nearly ideally under a wide range of conditions. Larger, more polar molecules deviate more dramatically.
You can see this in the correction constants scientists use. Helium’s intermolecular attraction constant is about 0.003 in standard units, while nitrogen’s is roughly 0.14, about 40 times larger. That means nitrogen molecules pull on each other far more strongly than helium atoms do, so nitrogen’s pressure drops further below ideal predictions under the same conditions. The molecular size corrections, by contrast, are much more similar across these gases, because even larger molecules are still extremely small in absolute terms.
How Scientists Correct the Ideal Gas Law
The most common correction is the van der Waals equation, which modifies the ideal gas law with two adjustments. One correction adds a term that accounts for intermolecular attractions, effectively bumping the pressure back up to what it would be without those attractions pulling molecules away from the walls. The other correction subtracts the actual volume of the molecules themselves from the total container volume, giving a more accurate picture of the free space available for molecular motion.
These corrections use two gas-specific constants. The attraction constant varies widely between gases (reflecting differences in intermolecular forces), while the volume constant stays relatively small for all gases. Together, they bring predictions much closer to experimentally measured behavior, especially in the moderate-pressure range where the simple ideal gas law starts to fail.
A Real-World Consequence: Gas Cooling During Expansion
One practical difference between ideal and real gases shows up when a gas expands rapidly from high pressure to low pressure without exchanging heat with its surroundings. A real gas typically cools down during this process, because the molecules must use some of their kinetic energy to overcome the attractive forces between them as they spread apart. This is the Joule-Thomson effect, and it’s the principle behind most refrigeration and air conditioning systems.
An ideal gas would experience no temperature change at all during the same expansion, because it has no intermolecular forces to overcome. The Joule-Thomson coefficient for an ideal gas is exactly zero. This is one of the clearest demonstrations that intermolecular attractions, the very thing the ideal model ignores, have tangible, engineerable consequences in the real world.