What is the van der Waals equation of state?

The van der Waals equation of state is a modified version of the ideal gas law that accounts for the finite size of particles and the interactions between them. It is represented as (p + a(n/v)²)(V - nb) = RT, where p is the pressure, V is the volume, n is the number of moles of the gas, R is the gas constant, T is the temperature, and a and b are van der Waals constants specific to each gas.

The term "a(n/v)²" corrects for the attractive forces between gas molecules, which become significant at high pressures and low volumes, while the term "nb" accounts for the volume occupied by the gas molecules themselves, recognizing that gas particles do not occupy zero space. This modified approach provides a more accurate description of real gases under non-ideal conditions compared to the ideal gas law, which assumes that gas particles do not interact and that they occupy no volume.

In summary, the van der Waals equation incorporates corrections for both molecular volume and intermolecular forces, making it essential for understanding the behavior of real gases as opposed to the ideal gas behavior described by other equations like the ideal gas law (pV = nRT).