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** Virial coefficient equations for **

Table 2 Parameters for the virial coefficient equat ions at 25 C |

Parameters for mixed electrolytes with the virial coefficient equations (at 25°C) [Pg.463]

Since the virial coefficients depend on T and composition only, the equa-tion-of-state parameters can depend at most on T and composition, as already noted. The second virial coefficient B is the only one for which a decent data base and reliable estimation procedures are available according to Equation 3a, values for B (as implied by our equation of state) are determined completely by specification of parameters b and . [Pg.57]

Equation 25 was developed from an empirical representation of thg second virial coefficient correlation of Pitzer and Curl (I) parameter b was left unchanged at its classical value of 0.0866. Because of the substantial improvement in the prediction of and its temperature derivatives for nonsimple fluids, the Barner modification of the RK equation gave improved estimates of enthalpy deviations for nonpolar vapors and for vapor-phase mixtures of hydrocarbons. However, the new equation was unsuitable for fugacity calculations. [Pg.70]

This fact can be demonstrated as follows. Let us determine the value of the well-known Flory parameter x, which corresponds to the 6 point (i.e. to the point of inversion of the second virial coefficient of the solution of rods) in the Flory theory of Ref. . This can be done by expanding the chemical potential of the solvent in the isotropic phase (Eq. (16) of Ref. ) into powers of the polymer volume fraction in the solution, and by equating the coefficient at the quadratic term of this expansion to zero this procedure gives x = 1/2 independently of p. On the other hand, it is well known that the value of xs decreases with increasing p and that X 1 at p S> 1. The contradiction obtained shows that the expressioas for the thermodynamic functions used in Ref. are not always correct [Pg.60]

We adopt the critical derivative constraints given by Equations 10 and 11 thus, the values of the equation-of-state parameters are not all independent, but are related by Equations 13, 14, and 15. Further, to ensure good behavior of the equation at low densities, we require that the equation generate an acceptable value for the second virial coefficient Bc. Since by Equation 9a [Pg.61]

Flgare 1.5-2 shows exparimental and correlated binary VLE data for three dioxane-n-alkane systems at 80°C.m The pressure levels are modest (0.2-1.4 amt) liquid-phase nonidealities are sufficiently large to promote a2eotropy in all threa cases. Equations (1.5-12)—(1.5-15) were used for the data reduction, with experimental values for the Pf1 and virial coefficients were estimated from the correlation of Tsono-poulos.7 Activity coefficients were assumed to be represented by the three-parameter Margules equation, aed (he products of the data rednction were seis of valnes for parameters Al2, Ait. and D in Eqs. (1.4-10) and (1.4-11). The parameters so determined produce the correlations of the data shown by the solid curves in Fig. 1.5-2. For all threa systems, the data are represented to within their exparimental uncertainty. [Pg.37]

It follows that atoms or molecules interacting with the same pair potential s( )(rya), but with different s and cj, have the same thermodynamic properties, derived from A INkT, at the same scaled temperature T and scaled density p. They obey the same scaled equation of state, with identical coexistence curves in scaled variables below the critical point, and have the same scaled vapour pressures and second virial coefficients as a function of the scaled temperature. The critical compressibility factor P JRT is the same for all substances obeying this law and provides a test of the hypothesis. Table A2.3.3 lists the critical parameters and the compressibility factors of rare gases and other simple substances. [Pg.462]

** Virial coefficient equations for **

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