Ideal Gas vs Real Gas

Ideal gas versus real gas comes down to one question: when is $PV = nRT$ a good approximation? An ideal gas is a model whose particles have negligible volume and no intermolecular forces except during collisions; a real gas is an actual gas, so its molecules have finite size and can attract or repel one another. Gases behave most ideally at relatively low pressure and higher temperature, where molecules are far apart and unlikely to condense.

Ideal vs. real gas side by side

                  Ideal gas (the model)       Real gas (actual)
Particle volume   negligible                  finite
Forces            none except collisions      attractions and repulsions
Obeys PV = nRT?   exactly, by definition      approximately, condition-dependent
Compressibility Z  Z = 1 always               Z above or below 1
Behaves ideally   —                           low P, high T, far from condensation

The ideal model removes two real-world complications: it treats particles as taking up essentially no space and ignores intermolecular forces except for elastic collisions. Those assumptions make the math simple and are often close enough for introductory chemistry, even though they are not exactly true.

Why real gases deviate

Real gases deviate because molecules are not points and do interact. When attractive forces matter, molecules pull on one another and strike the walls a little less forcefully, so the measured pressure can fall below the ideal prediction for the same $n$, $V$, and $T$. When the gas is compressed strongly, the finite size of the molecules starts to matter and the gas resists compression more than the ideal model suggests. Which effect dominates depends on the gas and the conditions, so the direction of deviation is not fixed.

Worked example: the compressibility factor

A practical ideality check is the compressibility factor:

For an ideal gas $Z = 1$; for a real gas $Z$ can sit above or below $1$. Suppose $1.00\ \mathrm{mol}$ of a gas is held at $300\ \mathrm{K}$ in a $1.00\ \mathrm{L}$ container, with a measured pressure of $24.0\ \mathrm{atm}$. If it were ideal,

Comparing the measured state with ideal behavior,

Since $Z < 1$, this sample shows a small negative deviation, usually meaning attractive forces are lowering the pressure slightly relative to the ideal prediction.

Which model to reach for, and the traps

Use the ideal model when pressure is relatively low and the gas is far from condensation, since then molecular size and attractions matter less. Switch to thinking about real-gas behavior when pressure is high, temperature is low, or the gas is near a phase change, which is where the ideal assumptions break down most. The recurring traps:

• Thinking the ideal gas law is useless for real gases. Many real gases follow it closely enough for ordinary calculations.
• Assuming deviation happens only at high pressure. Low temperature matters too, as a gas approaches condensation.
• Assuming deviation always goes one direction. Attractions tend to give $Z < 1$; finite size and short-range repulsion tend to give $Z > 1$.
• Forgetting the condition. The same gas can be nearly ideal in one range and noticeably non-ideal in another, so pressure and temperature must be part of the label.

A second case to compare

Rework the worked example with the same $n$, $V$, and $T$ but a measured pressure of $26.0\ \mathrm{atm}$:

Now $Z > 1$, a positive deviation, suggesting finite molecular size and repulsion dominate here rather than attraction. Holding the $Z = 0.97$ and $Z = 1.06$ cases side by side shows both directions of deviation in one comparison. The natural follow-up is the ideal gas law itself, which shows how the simplified model is used in actual calculations.