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Performing random number simulations, we obtained an approximate distribution of the number of ways arranging molecules in a binary lattice solution of nonrandom mixing with a specific interaction. From the distribution an approximate equation of excess Gibbs energy for a binary lattice solution was derived. Using the equation, liquid-vapor equilibrium at constant pressure for 15 binary solutions were calculated and compared with the result from Wilson equation, Van Laar equation and Redlich-Kister equation.

Using Carnahan-Starling equation for hard spheres and a lattice model with an attractive potential, a new twoparameter equation of state for pure gases is derived. Using this equation, compressibility factors are calculated and compared with Nelson-Obert generalized compressibility factor charts. The results show that the agreement of this equation with the experimental Nelson-Obert charts is similar to that of Redlich-Kwong equation in the average. But parameters and terms of the new equation have physical meanings which are more definite than those of Redlich-Kwong equation.

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