# For real gases, how does a change in pressure affect the ratio of PV to nRT?

Sep 9, 2016

DISCLAIMER: A real gas doesn't follow the ideal gas law.

For a real gas, if you wanted to consider the ratio of $P V$ to $n R T$, you may be talking about the compressibility factor $Z = \frac{P V}{n R T}$ for ideal gases, where $\overline{V} = \frac{V}{n}$ is what varies, based on the attractive forces in the real gas.

Real gases respond by being compressed either easily or not easily at higher pressures.

Thus, the idea is that at low pressures, $Z$ is close to $1$, i.e. real gases are more ideal than not, because little pressure is applied to compress the gas.

At high pressures, the gas deviates from ideal behavior because we start to try compressing it via adding pressure:

• If the gas is harder to compress, i.e. its attractive forces are weaker than its repulsive forces, its real molar volume gets larger and larger than its ideal molar volume. This means $Z > 1$.

• If the gas is easier to compress, i.e. its attractive forces are stronger than its repulsive forces, its real molar volume gets smaller and smaller than its ideal molar volume. This means $Z < 1$.