Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation

Ideal gases follow the relation PV over nRT equals one. Recall Boyle’s law, which states that when the amount and temperature of a gas are held constant, increasing the pressure will invariably decrease the volume to maintain a constant ratio.

But when that ratio is plotted as a function of pressure for one mole of several real gases, it equals the ideal value “one” only at low pressures. As the pressure increases, the curves deviate significantly from ideality.

At low pressures, the combined volume of gas particles is negligible relative to the container volume — like a pea inside a basketball. Therefore, the volume available to ideal gas particles equals the total container volume.

At higher pressures, the gas density is much greater. Thus, the combined volume of the gas particles becomes significant — like a pea inside a ping-pong ball.

Therefore, the assumption of the kinetic molecular theory that gas particles occupy negligible volume is invalid at high pressures.

The volume occupied by a real gas is greater than the volume available to its particles, which is the volume it would occupy in an ideal case, by nb, where b is an experimentally determined constant that depends on t