Generalized correlations second virial coefficient

The primary virtue of tlie generalized correlationfor second virial coefficients presented here is simplicity more accurate, but more complex, correlations appear in tlie literature."... 

Miscellaneous Generalized Correlations. Generalized charts and corresponding states equations have been pubhshed for many other properties in addition to those presented. Most produce accurate results over a wide range of conditions. Some of these properties include (/) transport properties (64,91) (2) second virial coefficients (80,92) (J) third virial coefficients (72) (4) Hquid mixture activity coefficients (93) (5) Henry s constant (94) and 6) diffusivity (95). 

Figure 3.16, drawn specifically for the compressibility-factor correlation, is also used as a guide to the reliability of the correlations of residual properties based on generalized second virial coefficients. However, all residual-property correlations are less precise than the compressibility-factor correlations on which they are based and are, of course, least reliable for strongly polar and associating ... 

The required values of By in Eq. (11.44) can be determined from the generalized correlation for second virial coefficients according to the equation,... 

Generalized correlations find widespread use. Most popular are correlations of die kind developed by Pitzer and cowoikers for the compressibility factor Z and for the second virial coefficient B. ... 

Generalized correlations for the compressibility factor, Z, as well as analytical expressions, based on the second virial coefficients, have been developed by Pitzer et a/. The correlation for Z takes the form ... 

Pitzer s Generalized Correlations In addition to the corresponding-states coorelation for the second virial coefficient, Pitzer and coworkers [Thermodynamics, 3d ed., App. 3, McGraw-Hill, New York (1995)] developed a full set of generalized correlations. They have as their basis an equation for the compressibility factor, as given by Eq. (2-63) ... 

The virial equation of state in Table 4.2 provides a sound theoretical basis for computing P-v-T relationships of polar as well as nonpolar pure species and mixtures in the vapor phase. Virial coefficients B, C, and higher can, in principle, be determined from statistical mechanics. However, the present state of development is such that most often (4-34) is truncated at B, the second virial coefficient, which is estimated from a generalized correlation. - In this form, the virial equation is accurate to densities as high as approximately one half of the critical. Application of the virial equation of state to phase equilibria is discussed and developed in detail by Prausnitz et al. and is not considered further here. 

The most satisfactory methods of data correlation are based on sound theory. In the case of the second virial coefficient, this depends on accurate knowledge of the intermolecular pair potential energy function, U(R, coi, oi) which, in general, depends on the orientations, Oh and ofe, as well as the separation, R, of the molecules ... 

Other, more complex forms of U(R) have been proposed [81-mai/rig] which have proved very satisfactory for the representation of specific rare gas interactions, for example. However, for the correlation and prediction of second virial coefficient data, empirical methods are generally used. Those methods which are based on the corresponding states principle usually represent the second virial coefficient by a series of terms in inverse powers of temperature, as suggested by results for the (n-6) potentials, but usually with integer powers. 

In the same period . Prausnitz (1969) C. Tsonopoulos(1974, 1975) and J. O Connell (1975), following the pioneering work of K. Pitzer in the middle 50 s, presented generalized correlations for the second virial coefficient. The theoretically based virial equation introduced by K. Onnes in 1901, could be now used in the prediction of the volumetric behavior of nonpolar and often polar gases and vapors, but only at low pres-... 

Develop an expression for the Joule-Thomson coefficient using the pressure-based expansion of the virial equation truncated at the second virial coefficient. Use the corresponding state relationships presented in Chapter 4 for the temperature dependence of B to develop a generalized correlation for fiyr... 

The generalexpressionforcalculationof In from second-virial-coefficientdata is given by Eq. (11.61). Values of tire pure-speciesvirial coefficients Bkk, Bu, etc., are foimd from die generalized correlation represented by Eqs. (3.59), (3.61), and (3.62). The cross coefficients Bik, Bij, etc., are found from an extension of the same correlation. For this purpose, Eq. (3.59) is rewrittenin the more general form ... 

---