Fugacity of a pure gas

Just as the fugacity of a pure gas is a kind of effective pressure, the fugaeity of a constituent of a gas mixture is a kind of effective partial pressure. That is, f is the partial pressure substance i would have in an ideal gas mixture that is at the same temperature as the real gas mixture and in which the chemical potential of i is the same as in the real gas mixture. 

This relation includes what we call the Lewis equation. This relation is often a very good approximation, especially beyond critical conditions, to calculate the fugacity of a gas mixture from only the fugacity of a pure gas under the same pressure as the total pressure of the mixture. 

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 real gases should replace pressure in the application of laws or theoretical formulations that are defined for the ideal gas. For example, fugacity has to be used in evaluating adsorption potential at high pressures and/or low temperatures. The fugacity of a pure gas is a physical quantity that complies with the following relation ... 

Determine an expression for the fugacity of a pure gas from the van der Waals equation of state. 

Experimental data taken from 0 to 50 bar give the fugacity of a pure gas to be ... 

The fugacity of a pure liquid or solid can be defined by applying Eq. si.4 to the vapor in equilibrium with the substance in either condensed phase. Usually, the volume of the vapor will follow the ideal gas equation of state very closely, and the fugacity of the vapor may be set equal to the equilibrium vapor pressure. The thermodynamic basis of associating the fugacity of a condensed... 

The Lewis—Randall rule for the fugacity of a species in a gas mixture will be adopted hence, the fugacity of a component in a mixture is obtained by multipl5dng its fugacity as a pure gas with its mole fraction. In addition, for the sake of simplicity, the solubilities of both gases will be assumed small, and the concentration of the solvent in the gas phase will be neglected. Therefore, for the fugacities of the two species of the gas mixture, one can write... 

The fugacity of a pure component is calculated by integrating this equation between zero pressure and system pressure. At P = 0, /= P and (j) = 1. Also, as the pressure approaches zero, the ideal gas law applies. The integration may be carried out by first subtracting the equation... 

Calculate the fugacity of a pure substance that is a gas or a liquid when a volumetric equation of state is available (Sec. 7.4)... 

For an ideal gas Z = 1 and f (T,P) = P. Hence, we find again that at low pressure the fugacity of a pure species is just the total pressure. 

Equation (7-106) is the Lewis and Randall rule for computing the fugacity of a pure real gas. (Further methods of calculation are discussed in Gilbert Newton Lewis and Merle Randall, Thermodynamics and the Free Energy of Chemical Substances, chap. 17, McGraw-Hill Book Company, Inc., New York, 1923.)... 

In Eq. (77) p° is the standard pressure, p° = l atm quantity p

[Pg.28]

This expression gives the fugacity of the pure gas as a function of the second coefficient of the virial. 

Note that fugacity of a pure substance can be calculated using the corresponding equation of state [4] and a gas component fugacity can be calculated similarly to activity, that is, as a product of the component partial pressure and the fugacity coefficient. Details of such calculations can be found in any chemical thermodynamics and some physical chemistry books [4]. 

In Figure 7.1 we showed and in example 7.1 we estimated the fugacity coefficient//P = < for pure species. Equation 7.10 shows that this quantity could logically be used for both liquids and gases, but normally is only used for gases, where cf) represents the ratio of the pure gas fugacity to the fugacity of a pure ideal gas at the same T and P, computed by Eq. 7.10 or its equivalent. 

In order to obtain the fugacity of a real gas, we must have appropriate thermodynamic property data available. We will explore three possible sources of data for pure gases ... 

Expression for the Fugacity Coefficient of a Pure Gas Using Tables... 

Using the ideal gas reference state, the definition for fugacity of a pure species is ... 

Unfortunately, the ideal-gas assumption can sometimes lead to serious error. While errors in the Lewis rule are often less, that rule has inherent in it the problem of evaluating the fugacity of a fictitious substance since at least one of the condensable components cannot, in general, exist as pure vapor at the temperature and pressure of the mixture. 

The definition of fugacity of a species in solution is parallel to the definition of pure species fugacity. Equation 154 is analogous to the ideal gas expression ... 

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