Question

Van der Waals Gases

Under what conditions of volume does a van der Waals gas behave like an ideal gas? Use the van der Waals equation of state to justify your answer.

Answer 1

conditions under which van der waaal gases behave like an ideal gas are low pressure and high temperature.

reason:

the vander waal equation of state is: [P+an²/V²][V−nb]=nRT

an²/V² is added to the pressure in order to account for the intermolecular forces of attraction. The a is a value that accounts for the amount of attraction between each particle. This is multiplied by the amount of moles squared, n2, as the overall amount of attractive forces is dependent on how much of the gas is there. This is then divided by V2 and added to pressure because the measured pressure is lower than expected.

The value b is the omitted volume per mole, and is related to the volume of the gas moles. This value must be included because real gases have volume. Therefore, the measured volume includes the volume of the molecules as well. In order for the equation to be accurate, the volume per mole, nb, must be subtracted from the measured volume to represent the available volume within the gas.

when presure is low and temperature is high, molecules of gas are far enough to ignore any molecular interactions taking place between them. Also the volume of the gas is very large compared to the volume of particles.

So the equation reduces to ideal gas law.