In this study for the first time a new description of compressibility factor is rendered based on the virial expansion. The compressibility factor as a function of M-factor is qualitatively and quantitatively expressed. At first, we present how may the third, fourth and higher order virial coefficients be logically ignored in order to simplify the virial equation. The results show, when the compressibility factor is presented as a function of M-factor instead of pressure, an improved regression operation on experimental data is possible. Moreover, the results show the compressibility factor will not depend on kind of substance, if it is considered as a function of M-factor. Also we found that the compressibility factor can easily be estimated by a second order polynomial in respect to M-factor or in more mature form at most by a third order polynomial. The simplifying effects of M-factor to present the compressibility factor of some binary mixtures are investigated. It was found that the classical mixing rules can never be applied for predicting the compressibility factor under special conditions. Also we affirm the distinct characteristics of M-factor compared to its composer parameters, qualitatively. A quantitative study on M-factor properties, which supplies a prolegomena to a new comprehensive equation of state, was accomplished as well. We find the favorable EOS is a multi-domain function estimating experimental data with high accuracy.

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