The ideal gas law holds good sufficiently at high temperatures and low pressures but as the pressure increases and the temperature decreases, real gases deviates from the ideal gas law. This is because molecules of real gases interact with one another wherein repulsive forces between molecules aid expansion while attractive forces aid compression (Atkins 2006). Several equations of state such as Redlich-Kwong, Benedict-Webb-Rubin, and Beattie Bridgeman equations have been proposed to represent the data of real gases more accurately (Rao 2004). To quantify the deviation of real gases from the ideal gas behavior, compressibility factor or compression factor, Z, has been introduced (Rao 2004). It is defined to be the ratio of the measured molar volume of a real gas to the molar volume of an ideal gas at a given pressure and temperature (Atkins 2006).  The compressibility factor, Z, is given by equation 3.1. 

                                                        [Eq’n 3.1]

For real gases, Z is always equal to 1 while for real gases, Z>1 at high pressures and Z<1 at intermediate pressures (Atkins 2006). The compressibility factor of a gas can also be expressed by using an infinite power expansion series of a virial equation (Bello 2017).

Another parameter that quantifies deviation of real gases from the ideal gas behavior is the fugacity coefficient, Φ, which depends on the temperature, pressure, and identity of the gas (Atkins 2006). It is simply the ratio of fugacity to pressure (see equation 3.2).