An ideal gas is a theoretical gas whose particles have no volume and no attraction to each other. No real gas meets these criteria perfectly, but the concept gives scientists and engineers a simple, powerful model for predicting how gases behave under most everyday conditions. Understanding what makes a gas “ideal” comes down to a handful of assumptions about how its particles move and interact.
The Five Core Assumptions
The ideal gas model is built on kinetic molecular theory, which describes gas behavior at the particle level. Five assumptions define what “ideal” means:
- Constant, random motion. Gas particles behave like tiny, hard spheres that move in straight lines until they hit something.
- Negligible particle size. The particles themselves are so small compared to the space between them that their individual volume is essentially zero.
- No attractive or repulsive forces. Particles don’t pull on each other or push each other away. They only interact during collisions.
- Perfectly elastic collisions. When particles slam into each other or into the walls of their container, no kinetic energy is lost. The total energy before and after the collision is exactly the same.
- Energy tied to temperature. The average kinetic energy of the particles depends only on the gas’s absolute temperature. Hotter gas means faster particles.
None of these assumptions are literally true for any real substance. Every real gas particle takes up some space, and every real molecule exerts at least a slight pull on its neighbors. But under the right conditions, these effects become so small that ignoring them introduces almost no error.
The Ideal Gas Law
These assumptions lead to a single, clean equation that ties together everything measurable about a gas: pressure (P), volume (V), temperature (T), and the amount of gas in moles (n). The relationship is PV = nRT, where R is the universal gas constant, the same value for every gas. This equation, developed by combining the earlier gas laws of Boyle, Charles, and Gay-Lussac, lets you predict any one of those four properties if you know the other three.
The equation works because of those simplifying assumptions. If particles had significant volume, you’d need to subtract that volume from V. If particles attracted each other, you’d need to adjust P downward because attractions pull particles away from the container walls, reducing the force they exert. The ideal gas law skips both corrections and still gives accurate results in a wide range of real situations.
Energy in an Ideal Gas
One useful consequence of the ideal gas model is that a gas’s internal energy depends only on its temperature. This means that if you hold temperature constant, the energy stays the same regardless of pressure or volume changes. The relationship is straightforward: a small change in temperature produces a proportional change in internal energy, scaled by the gas’s heat capacity. For real gases this relationship gets messier because intermolecular forces store and release energy as particles move closer together or farther apart. In an ideal gas, with no such forces, temperature tells you everything you need to know about energy.
When Real Gases Act Ideal
Real gases behave most like ideal gases under two conditions: low pressure and high temperature.
Low pressure means the particles are spread far apart. When there’s a lot of space between them, each particle’s tiny volume becomes truly negligible compared to the total volume of the container. The large distances also mean intermolecular attractive forces, which weaken rapidly with distance, have almost no effect.
High temperature means the particles are moving fast. Fast-moving particles spend less time near each other, giving attractive forces less opportunity to influence their paths. A particle zooming past a neighbor barely feels the tug compared to one drifting slowly by.
There’s a handy number for checking how “ideal” a gas is behaving: the compressibility factor, Z. For a perfect ideal gas, Z equals exactly 1. As pressure drops toward zero, Z for any real gas converges toward 1. Near a substance’s critical point (the temperature and pressure where liquid and gas phases become indistinguishable), Z can drop to around 0.78 or lower, meaning the ideal gas law would give you significantly wrong answers.
Which Gases Come Closest?
Some real gases are better approximations of ideal behavior than others, and the reason comes down to intermolecular forces. Helium is one of the most ideal gases in existence. Its atoms are tiny, with only two electrons, so the weak attractive forces between them (called dispersion forces) are about as small as they can get. Neon is also very ideal, though slightly less so than helium because it has more electrons and therefore slightly stronger dispersion forces.
Hydrogen gas behaves nearly ideally for similar reasons: its molecules are small and lightweight with minimal attraction between them. On the other end of the spectrum, water vapor is far less ideal because water molecules attract each other through hydrogen bonding, a much stronger type of intermolecular force. At the same temperature and pressure, water vapor deviates from ideal gas predictions far more than helium or neon would.
How Scientists Correct for Real Behavior
When the ideal gas law isn’t accurate enough, the most common fix is the van der Waals equation. It adds two correction constants to account for the assumptions that break down in real gases. The first constant, typically labeled “a,” corrects for the attractive forces between particles. Gases with strong intermolecular attractions have large “a” values. The second constant, “b,” accounts for the actual physical volume that gas particles occupy. Larger molecules have larger “b” values.
These corrections matter most when gases are at high pressures (particles squeezed close together), low temperatures (particles moving slowly enough to feel each other’s pull), or near the point where the gas could condense into a liquid. For routine calculations involving gases at or near room temperature and atmospheric pressure, the basic ideal gas law remains remarkably accurate and far simpler to work with.