The Three-Parameter Version

Furthermore, the expression depicted by Eq.8.7.1 indicates that all compounds should have the same value of the compressibility factor at the critical point, z. Indeed Zj.(Ar) = 0.291 and z (CH4) = 0.288, but z (nCjo) = 0.230. Actually, z values cover the range of about 0.23 to 0.30, as Table 8.1 demonstrates. 

Three such parameters have been proposed through the years the critical compressibility factor the Riedel factor and the acentric factor omega ( ). The last one, proposed by Pitzer in 1955, has found the widest application and is defined as follows  

only the vapor pressure at the reduced temperature of 0.7 is needed to establish the value of y. 

It should be noticed that accurate vapor pressure data in this temperature range are more readily available than values, which are difficult to establish experimentally. This is the main advantage of using as a third parameter. Values of a for a variety of compounds are given by Reid et al and by Daubert and Danner and for some selected ones, in Appendix C. 

For the functional dependency of zonT, P and a, Pitzer suggested the following power series in the acentric factor  

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The a, b and c parameters are determined by fitting to experimental data and depend on the chosen forms for and E°°, with typical values being a 0.2, b 0.7 and c 0.8. Subsequent versions denoted B97 and B98 employed ten fitting parameters, but the improvements were rather marginal relative to the three parameters version. 

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