# Summary

The ideal gas law is used to relate volume, pressure and temperature for gases. The ideal gas law is an approximation and is generally more accurate at mild temperatures and pressures. The properties of gases increasingly deviate from ideal as conditions become more extreme, i.e. low temperature or high pressure. In these cases a compressibility factor may be used to correct for non-ideal behaviour when using the ideal gas relationship.

# Definitions

 : Mass of the gas : Molecular weight of gas : Number of moles : Pressure : Ideal/universal gas constant : Temperature of the gas : Volume of the gas : Compressibilty factor : Density

# Introduction

For solids or liquids, where the molecular structure is compact, it is often reasonable to use a constant density over a range of temperatures and pressures. However, for gases the effect of temperature and pressure on the bulk properties is significant and therefore the density of the gas will change as temperature and pressure changes. This is where the ideal gas law, relating pressure, temperature and volume, may be used to estimate gas properties.

The ideal gas law relates the number of moles of a gas with its pressure, temperature and volume through the universal gas constant as follows.

For gases exhibiting ideal behaviour the compressibility factor, which is a ratio of the actual molar volume to the ideal gas molar volume is equal to 1. However as the pressure increases or temperature becomes extreme the gases behaviour will deviate from ideal and therefore the compressibility factor will deviate from 1. Compressibility factors are often tabulated from experimental data and may be found for various gases in textbooks such as Perry's Chemical Engineers handbook.

# Universal Gas Constant

The universal gas constant (R) is a constant of proportionality relating the energy and temperature scales. Its value is dependent on the set of unit being used with common values of the constant being displayed in the table below. It is important to ensure that you use the correct universal gas constant for the unit set you are working in.

Units Value

8.314462

82.05746

10.73159

1.985875

# Useful forms of the Ideal Gas Law

Using the relationships for density and moles below, the ideal gas law may be rearranged to obtain a number of gas properties.

Property Formulae
Pressure

Volume

Temperature

Mass

Density

Compressibility