Fugacity from experimental data

Combining the last two results we obtain eg. fin.i V Example 10.4 Fugacity from Experimental Data... 

Vugacity Coefficients. An exact equation that is widely used for the calculation of fugacity coefficients and fugacities from experimental pressure—volume—temperature (PVT) data is... 

Equation 2-63 gives the fugacity at p and T in terms of an integral that is evaluated from experimental data. 

One possible discrepancy involves fugacity effects at high pressmes, bnt fii-gacity effects do not fully accoimt for the differences between permeability data and model predictions. The relative deviations of fugacity-based predictions from experimental data are somewhat smaller than those with pressure-based calculations for all three models (82). 

For synthesis processes it should be added that basic chemical equilibrium data such as the free energy and enthalpy of formations originally have been derived from experimental data using a specific method to correct for non-ideal gas fugacity coefficients. This must be taken into consideration when selecting an appropriate method. This is the case for methanol, where a generalised method only as a function of... 

The fugacity is dependent on temperature and pressure, and an equation for its calculation from experimental data may be derived as follows. For any single component fluid... 

This equation gives the fugacity at p and T in terms of an integral which can be computed from experimental data. The equation may be expressed in a more convenient form by defining the compreaai bility factor... 

The accuracy of the determined equilibrium composition is limited by the accuracy of the thermodynamic data. It is to be seen from the eq. (6.81), that there is no sense in demanding that the fugacity coefficient logarithm be determined to an accuracy better than that of the expression G jRT obtained from experimental data. Since values of (7°/KTare usually of the order of tens while In q>i values are usually of the order of tenths, excessive accuracy of determination of the fugacity coefficient is unnecessary. 

The first integral involves the vapor volume, V, and may be evaluated using an equation of state. The second integral, known as the Poynting correction factor, takes into account the effect of pressure on the fugacity in the liquid. The volume in this integral, is the liquid molar volume and may be obtained from experimental data or from hquid density estimation methods (API, 1978 Racket , 1970). 

Evaluation of fugacities from experimental PVT data can be thus accomplished with two approaches ... 

Enthalpies are referred to the ideal vapor. The enthalpy of the real vapor is found from zero-pressure heat capacities and from the virial equation of state for non-associated species or, for vapors containing highly dimerized vapors (e.g. organic acids), from the chemical theory of vapor imperfections, as discussed in Chapter 3. For pure components, liquid-phase enthalpies (relative to the ideal vapor) are found from differentiation of the zero-pressure standard-state fugacities these, in turn, are determined from vapor-pressure data, from vapor-phase corrections and liquid-phase densities. If good experimental data are used to determine the standard-state fugacity, the derivative gives enthalpies of liquids to nearly the same precision as that obtained with calorimetric data, and provides reliable heats of vaporization. 

NOTE - r NG GIl ES THE TENPERArURE RANGE tKl OF THE EXPERIMENTAL DATA USED TO FIT THE CONSTANTS CONSTANTS FOR NCNCONDENSABLES CCOMPONENTS 1-B) MERE DETERMINED FROM A GENERALIZED CORRELATION FOR THE HYPOTHETICAL REFERENCE FUGACITY. 

Thermodynamic consistency tests for binary vapor-liquid equilibria at low pressures have been described by many authors a good discussion is given in the monograph by Van Ness (VI). Extension of these methods to isothermal high-pressure equilibria presents two difficulties first, it is necessary to have experimental data for the density of the liquid mixture along the saturation line, and second, since the ideal gas law is not valid, it is necessary to calculate vapor-phase fugacity coefficients either from volumetric data for... 

Figure 10,12 Effects of oxygen fugacity on oxidation state of Ti and V in Na2Si205 melt at r = 1085 °C (experimental data from Johnston, 1964, 1965, and Johnston and Chelko, 1966).

Figure 10.13 Effect of oxygen fugacity on conventional partition coefficient of Cr. (A) Olivine/liquid partitioning experimental data of Bird (1971), Weill and McKay (1975), Huebner et al. (1976), Lindstrom (1976), and McKay and Weill (1976). (B) Subcalcic py-roxene/liquid partitioning experimental data of Schreiber (1976). Reprinted from A.J. Irving, Geochimica et Cosmochimica Acta, 42, 743-770, copyright 1978, with kind permission from Elsevier Science Ltd., The Boulevard, Langford Lane, Kidlington 0X5 1GB, UK.

Fig. 7. Mixed gas sorption isotherms for PMMA-C02> C2H4 in terms of fugacities f, at fC02 = 1.50 + 0.05 atm, T = 35 °C. Experimental data ( ) in comparison with lines calculated from pure...

These equations are restatements of Eqs. (6.37) and (6.38) wherein the restriction of the derivatives to constant composition is shown explicitly. They lead to Eqs. (6.40), (6.41), (6.42), and (11.20), which allow calculation of residual properties and fugacity coefficients from PVT data and equations of state. It is through the residual properties that this kind of experimental information enters into the practical application of thermodynamics. 

Numerical values for the fugacities of species in liquid mixtures are readily calculated from experimental VLE data. According to Eq. (11.30),... 

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