In order to obtain these numerical results the values of the constants of the individual component fluids a 11 , a 22 , b 11 , b 22 must be known. In addition, the effect of collisions between molecules of the different components, given by a 12 and b 12 , must also be specified. In he absence of experimental data, or computer modelling results to estimate their value, the empirical combining laws, a 12 = ( a 11 a 22 ) 1 / 2 and b 12 1 / 3 = ( b 11 1 / 3 + b 22 1 / 3 ) / 2 , the geometric and algebraic means respectively can be used. These relations correspond to the empirical combining laws for the intermolecular force constants, ϵ ϵ 12 = ( ϵ ϵ 11 ϵ ϵ 22 ) 1 / 2 and σ σ 12 = ( σ σ 11 + σ σ 22 ) / 2 , the first of which follows from a simple interpretation of the dispersion forces in terms of polarizabilities of the individual molecules while the second is exact for rigid molecules. Then, generalizing for n fluid components, and using these empirical combinig laws, the expressions for the material constants are: a x = ∑ ∑ i = 1 n ∑ ∑ j = 1 n ( a i i a j j ) 1 / 2 x i x j which can be written as a x = ( ∑ ∑ i = 1 n a i i 1 / 2 x i ) 2 b x = ( 1 / 8 ) ∑ ∑ i = 1 n ∑ ∑ j = 1 n ( b i i 1 / 3 + b j j 1 / 3 ) 3 x i x j Using these expressions in the vdW equation is apparently helpful for divers, as well as being important for physicists, physical chemists, and chemical engineers in their study and management of the various phase equilibria and critical behavior observed in fluid mixtures.