The Van der Waals equation is an equation of state that extends the ideal gas law to include the effects of interaction between molecules of a gas, as well as accounting for the finite size of the molecules. It was derived by Johannes Diderik van der Waals in 1873 and is a modified version of the Ideal Gas Law. The equation relates the relationship between the pressure, volume, temperature, and amount of real gases. For a real gas containing ‘n’ moles, the equation is written as:

$$\left(P+\frac{an^2}{V^2}\right)\left(V-nb\right)=nRT$$

where P, V, T, and n are the pressure, volume, temperature, and moles of the gas, respectively, and ‘a’ and ‘b’ are constants specific to each gas/02%3A_Gas_Laws/2.12%3A_Van_der_Waals_Equation).

The Van der Waals equation is based on the theory that fluids are composed of particles with non-zero volumes and subject to an inter-particle attractive force. It predicts the experimentally observed transition between vapor and liquid and adequately predicts and explains the Joule–Thomson effect (temperature change during adiabatic expansion), which is not possible in ideal gas. However, the equation has some shortcomings, and other models, such as those based on the principle of corresponding states, achieve a better fit with roughly the same work. Nonetheless, the Van der Waals equation is still important as a pedagogic tool to aid understanding fundamental physical chemistry ideas involved in developing theories of vapor–liquid behavior and equations of state.