Fugacity gaseous mixtures

Fugacity of a Component in a Gaseous Mixture One could guess that the determination of fugacities, /, for the individual components in a gaseous mixture can become complicated as one takes into account the different types of interactions that are present. The mathematical relationship that applies is obtained by starting with the defining equations... 

To calculate the fugacity of each species in a gaseous mixture using the above equation at specified T, P, and mole fractions of all components yi. y2., the following procedure is used... 

Amagat s law of additive volumes holds for all pressures, which means that the ideal-solution law holds for the gaseous mixture, but not necessarily for the pure gases per se, and therefore the fugacity (/) is given by... 

The value of the parameter 2 13 in a gas mixture can he calculated from PVT data using any traditional EOS. Eor the mixtures that obey the Lewis-Randall rule [16] (the fugacity of a species in a gaseous mixture is the product of its mole fraction and the fugacity of the pure gaseous component at the same temperature and pressure), the fugacity coefficients of the components of the mixture are independent of composition. In such cases, the KB equation [13] for the binary mixtures 1-3 ... 

Expressions for the constants A(P,T) and B(P,T) can be obtained using the following limiting relationships for the fugacity coefficient of a solute at infinite dilution in the binary gaseous mixture 1—3 ... 

Expression for the Solubility of a SoUd in a Gaseous Mixture Formed of Two SC Fluids. Assuming that the solute solubilities are very small and that the fugacity coefficients have the same values as those at infinite dilution, eqs 1—3 can be recast as... 

Comparison of this with equation 7.9 shows that the final term merely allows for nonideality. It is no more than a correction term. (When gaseous mixtures are involved, it is the various partial pressures p or partial fugacities,, which become important. In such a case, f would represent the fugacity of the compound i in the particular environment in which it found itself.)... 

Several methods are commonly used for estimating the fugacity of a species in a gaseous mixture. The most approximate method is based on the observation that some gaseous mixtures follow Amagat s law, that is,... 

This result, which relates the fugacity of a species in a gaseous mixture only to its mole fraction and.the fugacity of the pure gaseous component at the same ternperature and pressure, is known as the Lewis-Randall rule. 

At higher pressures, Eq. 9.2-13 can still be used to compute the fugacity of a species in a gaseous mixture, but more accurate equations of state must be used. One can, for example, use the Peng-Robinson equation of state... 

To estimate the fugacity of a species in a gaseous mixture using the Lewis-Randall rule. 

For mixtures that display significant deviations from ideality, correcting factors from the ideal mixture assumption are used. For gaseous mixtures, one defines the fugacity coefficient, as follows... 

Activity derivative, concentration fluctuation term (Equation 1.73) Fugacity of a substance i in a gaseous mixture (Equation 1.21) Gibbs energy (function)... 

F fi- molar Helmholtz energy. fugacity of the component / in a gaseous mixture. 

Fugacity of Pure Gases. In order to utilize Eq. (3-12) it is necessary to have information on the actual molal volume as a function of the pressure at the temperature in question. The lack of these data limits the utility of this equation. However, it has been found possible to develop correction factors to the perfect-gas law that will apply to almost all gases and gaseous mixtures. One method of representing these deviation factors is to plot the compressibility factor p, which is equal to PV/RT, as a function of the reduced pressure at constant reduced temperature, where reduced pressure Pr is the pressure divided by the critical pressure, and reduced temperature Tr is the absolute temperature divided by the absolute critical temperature. Such a plot is given in Fig. 3-4 similar plots for higher temperatures and pressures are available. 

The heart of the question of non-ideality deals with the determination of the distribution of the respective system components between the liquid and gaseous phases. The concepts of fugacity and activity are fundamental to the interpretation of the non-ideal systems. For a pure ideal gas the fugacity is equal to the pressure, and for a component, i, in a mixture of ideal gases it is equal to its partial pressure yjP, where P is the system pressure. As the system pressure approaches zero, the fugacity approaches ideal. For many systems the deviations from unity are minor at system pressures less than 25 psig. 

Any cubic equation of state can give an expression for the fugacity of species i in a gaseous or in liquid mixture. For example, the expression for the... 

As the mixture approaches ideality as the total pressure approaches zero, Equation (10.81) should approach Equation (10.17). The second part of the definition of fugacity for a gaseous component, which is analogous to Equation (10.24), is... 

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