## Key Concepts and Summary

Gas molecules possess a finite volume and experience forces of attraction for one another. Consequently, gas behavior is not necessarily described well by the ideal gas law. Under conditions of low pressure and high temperature, these factors are negligible, the ideal gas equation is an accurate description of gas behavior, and the gas is said to exhibit ideal behavior.

However, at lower temperatures and higher pressures, corrections for molecular volume and molecular attractions are required to account for finite molecular size and attractive forces. The van der Waals equation is a modified version of the ideal gas law that can be used to account for the non-ideal behavior of gases under these conditions.

## Key Equations

- \(\text{Z}=\phantom{\rule{0.2em}{0ex}}\frac{\text{molar}\phantom{\rule{0.2em}{0ex}}\text{volume of gas at same}\phantom{\rule{0.2em}{0ex}}T\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}P}{\text{molar volume of ideal gas at same}\phantom{\rule{0.2em}{0ex}}T\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}P}\phantom{\rule{0.2em}{0ex}}={\left(\frac{P\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{V}_{m}}{R\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}T}\right)}_{\text{measured}}\)
- \(\left(P+\frac{{n}^{2}a}{{V}^{2}}\right)\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}\left(V-nb\right)=nRT\)

## Glossary

### compressibility factor (Z)

ratio of the experimentally measured molar volume for a gas to its molar volume as computed from the ideal gas equation

### van der Waals equation

modified version of the ideal gas equation containing additional terms to account for non-ideal gas behavior