Real Gas equation of state

For any gas at moderate to high pressure, behaves differently from ideal gas due to significant attractive/ repulsive forces between the molecules and volume occupied by molecules. There are different equations which can be used for the calculation of properties of real gas. Some of these are described here:

1. Cubic equation of state:

vander Waal equation of state: 

The attraction forces are taken as a/V^2, therefore the real pressure will be less by the quantity a/V^2 and volume occupied per mole of particles is b; the free volume available is v-b the equation is:

(P+a/V^2)(V-b)=RT

here a and b are substance dependent and we have values of these in literature. vander Waal equation of state gives reasonable values for real gases, to get more accurate values other cubic equation of states are used like Redlich-Kwong equation of state, SRK equation of state; which are modified form of vander Waal equation of state.

2. Virial Equation of State:

These equation are based on the interaction between 2 particles, 3 particles, 4 particles and more; used to find compressibility factor (Z) as expansion in the series of 1/v

PV/RT = Z = 1+ B/V + C/V^2+........

where B, C, .... are second and third virial coefficients; which depend on temperature and substance. The values of these coefficients are available. If volume is unknown we can expand the series in P as:

PV/RT = Z = 1+ B'P + C'P^2+........

3. Law of corresponding state

a) 2 Parameter Law of corresponding states:

This law is based on assumption that all gases at same reduced temperature(Tr) and same reduced pressure (Pr) have same compressibility factor (Z); which is given as a function of Tr and Pr.

b)  3 Parameter Law of corresponding states:

 This law is based on assumption that all gases at same reduced temperature(Tr) and same reduced pressure (Pr) and which have same value of acentric factor (ω) have same compressibility factor (Z); here 

Z = Zo +ωZ1 where Zo and Z1 is given as a function of Tr and Pr.

acentric factor (ω) is defined as ω = log(Pr)sat(SF)_Tr=0.7 - log(Pr)sat_Tr=0.7

                                                    = -1-log(Pr)sat)_Tr=0.7