one model of ideal gas is that 1 they are composed of particles so tiny compared to volume of the gas that they can be considered zero-volume point in space, and 2 they are no interactions,attractive or repulsive, between the individual gas particles. However,real gas ultimately have behaviors due to the facts that 1 gas atoms and molecules do have a size, and 2 there is some interaction between the gas particles, which can range from minimal to very large. In considering the state variables of a gas, the volume of the gas particles should have an effect on the volume V of the gas. the interaction between gas particles would have an effect on the pressure P of the gas. Perhaps a better equation of state for a gas should take these effect into account.
In 1873, suggested a somewhat corrected version of the ideal gas law. It is one of the simpler equations of state for real gas, and it referred to as the van der walls equation.
where n is the number of moles of gas, and a and b are the van der waals constants for a particular gas. the van der waals constants a represents the pressure