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A novel mathematical rigorous method to obtain the vapor-liquid equilibriumcurves near the critical point has been proposed covering the cases ofwell-known and commonly used equations of state for real gases - Van der Waalsand Dieterici, which are prototypes to determine the critical exponent value ofthe coexistence curves system. We explain that the critical exponent value ofthe vapor-liquid equilibrium curves can be regarded as the analogy to theresults based on classical assumptions - mean field theory. The novelty of ourmethod has been exposed in comparison to the standard thermodynamic limitdiscussed thoroughly and extensively in the literature.

Vapor-liquid equilibrium (VLE) properties versus critical exponent  theory - on new approximate mathematical approach to determine the critical  exponent value of the vapor-liquid coexistence curve