Van der Waals equation

In chemistry and thermodynamics, the Van der Waals equation (or Van der Waals equation of state) is an equation of state which 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. The ideal gas law treats gas molecules as point particles that interact with their containers but not each other, meaning they neither take up space nor change kinetic energy during collisions (i.e. all collisions are perfectly elastic). The ideal gas law states that the volume V occupied by n moles of any gas has a pressure P at temperature T given by the following relationship, where R is the gas constant: To account for the volume occupied by real gas molecules, the Van der Waals equation replaces in the ideal gas law with , where Vm is the molar volume of the gas and b is the volume occupied by the molecules of one mole, given by Avogadro constant times the volume of a single molecule: The second modification made to the ideal gas law accounts for interaction between molecules of the gas. The Van der Waals equation includes intermolecular interaction by adding to the observed pressure P in the equation of state a term of the form , where a is a constant whose value depends on the gas. The complete Van der Waals equation is therefore: For n moles of gas, it can also be written as: When the molar volume Vm is large, b becomes negligible in comparison with Vm, a/Vm2 becomes negligible with respect to P, and the Van der Waals equation reduces to the ideal gas law, PVm=RT. This equation approximates the behavior of real fluids above their critical temperatures and is qualitatively reasonable for their liquid and low-pressure gaseous states at low temperatures. However, near the phase transitions between gas and liquid, in the range of p, V, and T where the liquid phase and the gas phase are in equilibrium, the Van der Waals equation fails to accurately model observed experimental behavior. In particular, p is a constant function of V at given temperatures in these regions.