Look up the gas's critical temperature, critical pressure and Pitzer's acentric factor in a chemical reference manual or database (see Resources). Interpret the acentric factor as the amount that a molecule lacks symmetry. For example, for methane, Tc = 190.6 Kelvin, Pc = 45.39 atmospheres and w = 0.011, where Tc is the critical temperature, Pc is the critical pressure and w is the acentric factor.
Calculate the molecular interaction constant "a" with the formula a = 0.42747*R²Tc²/Pc where R is the gas constant, which equals 0.08206 liters*atmospheres/moles*Kelvin. The molecular interaction constant approximates all the attractive and repulsive forces that are not due to chemical bonds or electrostatic forces. These forces are collectively called Van der Waal's forces. For example, a = 0.42747*0.08206²*190.6²/45.39 = 2.304 liters²*atmospheres/moles².
Calculate the volume correction constant "b" with the formula b = 0.08664*RTc/Pc. Think of b as the volume of the molecules if they were packed together as tightly as possible. For example, b = 0.08664*0.08206*190.6/45.39 = 0.02985 liters/mol.
Calculate the constant "m" with the formula m = 0.048508 + 1.55171w - 0.15613w². For example, m = 0.048508 + 1.55171*0.011 - 0.15613*0.011² = 0.06556.
Calculate "f," which is usually called alpha, with the formula f = (1 + m(1 - sqrt(T/Tc)))², where T is the temperature of the gas. For example, if the temperature is 350 Kelvin, f = (1 + 0.06556*(1 - sqrt(350/190.6)))² = 0.9540.
Calculate compressibility "Z" with the formula Z = Vm/(Vm - b) - fa/(RT(Vm + b)), where Vm is the molar volume, which is volume divided by the number of moles. When compressibility is equal to one, the gas is behaving like an ideal gas. Compressibility values less than one indicate that the gas occupies a smaller volume for a given pressure and temperature than an ideal gas would. For example, if the molar volume is 2.8 liters/mole, Z = 2.8/(2.8 - 0.0985) - 0.940*2.304/(0.08206*350(2.8 + 0.02985)) = 1.01. The value is close to 1, which indicates that methane behaves much like an ideal gas at the given temperature and molar volume.