Vapor pressure to Boltzmann distribution law connection and its empirical corrections

Vapor pressure (P) data of pure substances in gas/solid-liquid equilibrium is important for scientific research and practical applications. Due to the large temperature range going from melting point to critical point, it is an impossible task to determine the P of a pure substance at each temperature point. Up to now, there is no general equation that can accurately describe the relation between temperature (T) and P for all pure substances. Utilizing Boltzmann distribution, we presented a general expression, ln P = a + bT + cln(T) + d(1/T), for the P of pure substances, that is, the P-T dependence is nearly exponential over the entire range of liquid and solid existence. Furthermore, on the base of above equation, we established a corrected general equation to express the liquid vapor pressure within temperature in going from melting point to critical point.

$\ln P=a+bT+c{T}^{T/T_b}+d\left(\ln \left(T\right)\right)+f{\left(\ln \left(T\right)\right)}^{T/T_b}+g\left(1/T\right)$

The results show that the corrected equation has the advantages of universality, simplicity, and high calculation accuracy for the vapor pressure involving liquid simple substances, liquid inorganic and liquid organic compounds.