Fugacities in Gas Mixtures Fugacity Coefficients

The fugacity of a component i in a gas mixture is related to the total pressure P and to its mole fraction yt through the fugacity coefficient p, defined by 

The fugacity coefficient is a function of pressure, temperature, and gas composition. It has the useful property that for a mixture of ideal gases (Pi = 1 for all i. The fugacity coefficient is related to the volumetric properties of the gas mixture by either of the exact relations (B3, P5, R6)  

In order to simplify Eq. (5), it was suggested many years ago by Lewis (L3) that Amagat s law be used, viz., to assume that the partial molar volume of component i at any temperature and pressure is equal to the molar volume 

The limits of the Lewis fugacity rule are not determined by pressure but by composition the Lewis rule becomes exact at any pressure in the limit as y( - 1, and therefore it always provides a good approximation for any component i which is present in excess. However, for a component with small mole fraction in the vapor phase, the Lewis rule can sometimes lead to very large errors (P5, R3, RIO). 

The chemical literature is rich with empirical equations of state and every year new ones are added to the already large list. Every equation of state contains a certain number of constants which depend on the nature of the gas and which must be evaluated by reduction of experimental data. Since volumetric data for pure components are much more plentiful than for mixtures, it is necessary to estimate mixture properties by relating the constants of a mixture to those for the pure components in that mixture. In most cases, these relations, commonly known as mixing rules, are arbitrary because the empirical constants lack precise physical significance. Unfortunately, the fugacity coefficients are often very sensitive to the mixing rules used. 

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