The paper features the mathematical model of computing phase diagrams and t
hermodynamic functions of the state in the liquid, gas and two-phase domain
with the help of statistical thermodynamics. The paper features all import
ant contributions (translation, rotation, internal rotation, vibration, int
ermolecular potential energy and influence of electron and nuclei excitatio
n). To calculate the thermodynamic properties of real gases we developed th
e cluster theory, which yields better results than the classical virial equ
ation. For the realm of real liquids the Johnson-Zollweg-Gubbins model base
d on the modified Benedict-Webb-Rubin equation was applied. The Lennard-Jon
es intermolecular potential was used. The analytical results are compared w
ith the thermodynamical data and models obtained by classical thermodynamic
s and show relatively good agreement.