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If this equation is integrated from zero pressure up to the pressure in question, the limits on the left-hand side are from 1.0 to the ratio of fugacity to pressure at the pressure in question. Thus In (f/p) equals the integral from zero to p of — 1) dp/p.

Equation (3-14) can be modified and dPR/PR used instead of dp/p. The limits of integration then become from zero to PR. At constant temperature, it is therefore obvious that the integral is a function only of Pr, Tr, and the variables determining If the m values are a func- Fig. 3-4.

tion of PR and Tr only, the ratio of fugacity to the pressure is also a unique function of the reduced pressure and the reduced temperature. Integration using the ¡x plots have been made, and one method of presentation is given in Fig. (3-5).

With an accuracy suitable for engineering purposes these plots make it possible to calculate the fugacity of a pure gas at any temperature and pressure, assuming that the critical constants of the gas are known. Even in cases where the critical constants are not known, highly satisfactory methods have been developed for estimating these constants.

Fugacity of Mixtures. When applying the n plot and the fugacity plot to mixtures, the question arises as to the proper values to be employed for the critical temperature and the critical pressure. Mixtures have critical temperatures and critical pressures, but it has been found that these values do not give satisfactory results when used for calculating reduced temperatures and pressures to be used with the charts, but pseudocritical constants can be calculated which give better agreement. For these pseudo constants one of the best methods of calculation is the mol fraction average; i.e., the calculated pseudo-critical temperature is equal to the sum of the products of the mol fraction times the critical temperature for each of the pure components. The pseudocritical pressure is calculated in an analogous manner. When these values are employed for calculating the reduced tempera- Fig. 3-5 Fugacities of hydrocarbon vapors.

ture and pressure, satisfactory agreement is attained with jlc charts. It should be emphasized that these calculated values are not true critical constants for the mixture.

Fugacity of a Component in a Mixture. In vapor-liquid equilibria, vapor mixtures are generally involved, and Eq. (3-6) requires, not the fugacity of the mixture, but the fugacity of the components in the mixture. In order to estimate the fugacity of the components in the mixture, Lewis and Randall (Ref. 16) suggested that this fugacity was equal to the mol fraction of the component in the mixture times the fugacity of the pure component at the same temperature and total pressure as the mixture. Thus,

### Fig. 3-5 Fugacities of hydrocarbon vapors.

ture and pressure, satisfactory agreement is attained with jlc charts. It should be emphasized that these calculated values are not true critical constants for the mixture.

Fugacity of a Component in a Mixture. In vapor-liquid equilibria, vapor mixtures are generally involved, and Eq. (3-6) requires, not the fugacity of the mixture, but the fugacity of the components in the mixture. In order to estimate the fugacity of the components in the mixture, Lewis and Randall (Ref. 16) suggested that this fugacity was equal to the mol fraction of the component in the mixture times the fugacity of the pure component at the same temperature and total pressure as the mixture. Thus,