Fugacity graphical

Generalized charts are appHcable to a wide range of industrially important chemicals. Properties for which charts are available include all thermodynamic properties, eg, enthalpy, entropy, Gibbs energy and PVT data, compressibiUty factors, Hquid densities, fugacity coefficients, surface tensions, diffusivities, transport properties, and rate constants for chemical reactions. Charts and tables of compressibiHty factors vs reduced pressure and reduced temperature have been produced. Data is available in both tabular and graphical form (61—72). 

The ratio of the fugacity/2 at the pressure P2 to the fugacity/i at the pressure Pj can be obtained by graphical or numerical integration, as indicated by the area between the two vertical lines under the isotherm for the real gas in Figure 10.6. However, as Pi approaches zero, the area becomes infinite. Hence, this direct method is not suitable for determining absolute values of the fugacity of a real gas. 

The value of the fugacity of a gas in a given state must be calculated by means of an equation of state, either algebraic or graphic it is not determined directly by experimental means. An expression for the fugacity of the fcth substance in a gas mixture can be obtained by comparison of Equations (7.67) and (7.77). These equations give two different ways of expressing the chemical potential, and consequently the two expressions must be equal. Thus,... 

The virial coefficients can be determined from studies of the pressure-volume-temperature relations of gases. A graphical method for determining the fugacity may be illustrated by the use of the equation of state... 

Pyrite-Pyrrhotite Stability Field. The first graphical representation (Figure l) is of a pyrite-pyrrhotite stability field, in the form log fugacity of sulfur (log fc ) vs. temperature, T. This diagram derives... 

The integrals in these equations may be evaluated numerically or graphically for various values of Tr and Pr from the data for and Z given in Tables E.l through E.4 (App. E). Another method, and the one adopted by Lee and Kesler to extend their correlation to fugacity coefficients, is based on an equation of state. 

As a first approximation, Cp may be treated as independent of the pressure, and if MJ.T. is expressed as a function of the pressure, it is posnble to carry out the integration in equation (29.24) alternatively, the integral may be evaluated graphically. It is thus posdble to determine the variation of the fugacity with temperature. 

If P-F data are available for the gas mixture, it is possible to determine the partial molar volume of any constituent (see Chapter XVIII), and hence at various total pressures may be calculated from equation (30.22). The integral in equation (30.24) can thus be evaluated graphically, and hence the fugacity / of the gas whose mole fraction is n - in the given mixture, at the total pressure P, can be determined. ... 

Determine by the graphical method the fugacity of nitrogen in the mixture at the various total pressures, and compare the results with those obtained for the pure gases hence, test the Lewis-Randall rule for the fugacity of a gas in a mixture [cf. Merz and Whittaker, J, Am. Chem, Soc., 50, 1522 (1928)]. 

The foregoing conclusions are depicted graphically in Fig. 24, which shows the partial vapor pressure (or fugacity) curves of three types. Curve I is for an ideal system obeying Raoult s law over the whole concentration range for such solutions k in equation (36.3) is equal to / , and Henry s law and Raoult s law are identical. For a system exhibiting positive deviations, curve II may be taken as typical in the dilute range,... 

Calculate the fugacity of COj at 37.7 °C and 13.8 bar with the following methods (a) from experimental pressure-volume data (Kyle, 1999), (b) from a graphical correlation, (c) with a cubic EOS, and (d) with Virial EOS. The experimental data are ... 

Thus we continued with numerical methods for the fugacity, entropy, and enthalpy functions (13), although we did present an empirical equation for the second virial coefficient (14). This work was done by Bob Curl he did an excellent job but found the almost interminable graphical work very tiresome. Thus I was pleased that the British Institution of Mechanical Engineers Included Curl in the award of their Clayton Prize for this work. A fifth paper with Hultgren (15) treated mixtures on a pseudocritical basis, and a sixth with Danon (16) related Kihara core sizes to the acentric factor. 

Partial pressures were replaced with fugacities calculated according to Lewis and Randall rules, and the data sets were recalculated. The rate constant k still showed considerable variations with operating conditions. Below 400 °C it decreased with space velocity and above 400 °C it increased. It decreased with both pressure and H2/N2 ratio. In view of this, Adam and Comings resorted to a graphical approach to reactor design. 

Equilibrium phenomena of liquid and vapour phases of binary and ternary mixtures, as well as the analytical and graphic representation of the equilibrium of the two phases have been discussed in the introduction written b) Hausen. The introduction also contains discussion of the thermodynamic basis of phase equilibria, definitions of the characteristic concepts of the activity coefficient and the fugacity as well as equations that represent phase equilibria. More references can be found in the papers quoted in the next section entitled "References on the Thcrmodjmamics of the Liquid-Vapour Equilibrium . 

Eq.9.11.4 can be used along with experimental PVT data for the evaluation of fugacity coefficients through graphical integration. As with the evaluation of enthalpy and entropy departures, however, the integration is carried out by first fitting the Fl tiata to an accurate equation of state. And since such EoS express P =f(V,T), rather than V = f P,T)y direct use of Eq.9.11.4 is not possible. 

As we saw in Chapter 4, there are charts available for the compressibility factor as a function of the reduced variables, Tr and Pr- It is straightforward, in principle, to graphically integrate the right-hand side of Equation (7.10) and come up with a chart for the fugacity coefficient in reduced coordinates. Alternatively, we can analytically integrate Equation (7.10) with the appropriate equation of state. Figures 7.1 and 7.2 show values... 

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