The Van der Waals Equation

The ideal gas law, based on the assumptions of negligible intermolecular attractions and negligible volume of gas molecules, fails at high pressures and low temperatures.

Here, the van der Waals equation, a modified version of the ideal gas law, compensates for these deviations by introducing corrections.

The first correction in the pressure term adjusts for the difference between real gas pressure and ideal gas pressure. As the gas molecules attract one another, the real gas pressure is lower than the ideal value.

These attractive forces reduce both the frequency and force of collisions with container walls. As a result, reducing pressure is directly proportional to the square of the molar concentration of molecules.

The second correction is in the volume term, calculating the actual volume available for gas molecules as total volume minus the volume excluded by intermolecular repulsive interactions.

The constants 'a' and 'b', known as the van der Waals coefficients, represent the strength of attractive and repulsive interactions between gas molecules, respectively. Note that both coefficients are empirical constants characteristic of each gas and remain unaffected by temperature.