The Van der Waals Equation

The ideal gas law is based on two simplifying assumptions: first, that there are no intermolecular attractions between gas molecules, and second, that the volume occupied by the molecules themselves is negligible compared with the volume of the container. However, these assumptions don't hold up under all conditions - specifically, at high pressures and low temperatures, as gas tends to deviate from ideal gas behavior.

The van der Waals equation is an enhanced version of the ideal gas law, incorporating corrections to account for the volume of gas molecules and the intermolecular forces acting between them. The first correction relates to the pressure term in the equation, acknowledging that the measured pressure is lower due to the attractive forces between gas particles. These intermolecular attractions reduce both the frequency and intensity of collisions with container walls, leading to a decrease in pressure. This pressure reduction is directly proportional to the square of the molar concentration of the molecules present in the sample.

The second correction is incorporated into the volume term of the equation. Assuming a gas contains 'n' moles, each occupying volume 'b', the total volume occupied by the gas molecules will be 'nb'. As a result, the actual volume available for the motion of gas molecules will be the total volume minus 'nb'.

In the van der Waals equation, the constants 'a' and 'b' are known as the Van der Waals coefficients. 'a' is the intermolecular attraction parameter, representing the strength of attraction between gas particles, where a larger ‘a’ means stronger cohesion and thus a larger pressure correction; The 'b' is the excluded-volume (molecular size) parameter, corresponding to the repulsive interactions between molecules, where a larger ‘b’ means less free volume. Each gas has its own unique set of 'a' and 'b' values, which are treated as temperature-independent parameters within the model, although real substances may show some temperature dependence. While the van der Waals equation offers valuable insights into the behavior of real gases, it is not a universal equation of state for all substances. For higher precision, particularly over a wide range of temperatures and pressures, the virial equation of state is often used. Virial coefficients, which capture deviations from ideal behavior more accurately, are commonly tabulated at various temperatures for numerical analysis.