Real gases behave like ideal gases in the limits of low pressures and high temperatures, but they deviate significantly at high pressures and low temperatures. The compressibility factor Z = PV/nRT is a convenient measure of the deviation from ideal gas behavior. If the ratio (Z = PV/nRT) is plotted against P at constant temperature, then the values of Z deviate from ideal behavior, which is unity for an ideal gas.
This is attributed to the pressure build-up as gas molecules collide on the walls of a container. If the gas molecules adjacent to the walls exert intermolecularly attractive forces, the momentum of the gas molecules toward the wall will be decreased. Thus, the collisions of the gas molecules will be reduced, resulting in the pressure of the gas being less than that of an ideal gas. At high pressure, the gas molecules pack the container very closely together, causing the volume of the gas molecules to be a significant part of the total volume.
Van der Waals Equation for Real Gases
Van der Waals proposed the incorporation of two additional terms into the ideal gas law to account for the deviations from ideal behavior. The ideal gas law equation then becomes:
$$ (P+\frac{a}{V^2})(V-b)=RT $$
where a and b are constants and are determined experimentally. The constant a accounts for the cohesive forces between the gas molecules, which drag other gas molecules around a single molecule, causing the pressure of the gas to be less than that of an ideal gas. The cohesive forces are dependent on the intermolecular distances and related to the density of the gas. The term a/V2 is called the internal pressure per mole.
The constant b in accounts for the incompressibility of the gas molecules, known as the excluded volume occupied by the gas molecules. The excluded volume is approximately four times the volume of the gas molecules. The term (V – b) represents the effective volume of the gas molecules that expand freely.
At low pressure, the volume of the gas molecules is so large that the contribution of the excluded volume toward the total volume is very small and the term a/V2 becomes negligible. Thus, under these conditions,Van der Waals equation is reduced to the ideal gas law.
Reference:
- Kim, C. (2004). Advanced pharmaceutics : physicochemical principles. London: CRC Press LLC.
