Fugacity of a pure liquid

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 use of the foregoing definition of an ideal solution implies certain properties of such a solution. The variation of the fugacity / of a pure liquid i with temperature, at constant pressure and composition, is given by equation (29.22), viz.. 

Calculate the fugacity of a pure liquid or solid when a volumetric equation of state is not available (Sec. 7.4)... 

The fugacity of a pure liquid species can be computed in a number of ways, depending on the data available. If the equation of state for the liquid is known, we can again start from Eq. 7.4-8, now written as... 

The fugacity of a pure liquid component is close, but not identical, to its vapour pressure. By assuming the liquid incompressible, by combining the equations (5.43) and (5.79), and by integrating at constant temperature between the saturation pressure and the system pressure P, gives the relation ... 

In a binary liquid solution containing one noncondensable and one condensable component, it is customary to refer to the first as the solute and to the second as the solvent. Equation (13) is used for the normalization of the solvent s activity coefficient but Equation (14) is used for the solute. Since the normalizations for the two components are not the same, they are said to follow the unsymmetric convention. The standard-state fugacity of the solvent is the fugacity of the pure liquid. The standard-state fugacity of the solute is Henry s constant. 

Solute/Solvent Systems The gamma/phi approach to X T.E calculations presumes knowledge of the vapor pressure of each species at the temperature of interest. For certain binary systems species I, designated the solute, is either unstable at the system temperature or is supercritical (T > L). Its vapor pressure cannot be measured, and its fugacity as a pure liquid at the system temperature/i cannot be calculated by Eq. (4-281). 

If we consider, for example, compound i in a liquid mixture, e.g., in organic or in aqueous solution (subscript t see Fig. 3.9pure liquid compound by [note that for convenience, we have chosen the pure liquid compound (superscript ) as our reference state] ... 

For the predominant component of a solution, i. e. the solvent, the 3tate of the pure liquid at the temperature of the systom and the pressure of 1 atm. is chosen as the standard state.. In so far as sufficiently diluted solutions are concerned (i. e. such solutions the composition of which differs but slightly from the pure solvent) the solvent can be considered to follow approximately Raoult s law valid for ideal solutions, according to which the fugacity / of the solvent in a solution can be expressed as the product of its molar fraction N-, ) and of the fugacity of the pure liquid substance f at the same temperature, thus ... 

The fugacity coefficient of a pure liquid or vapor is a function of its temperature and pressure. Fora saturated liquid or vapor, the equilibriumpressureis P.. Therefore Eq. (14.30) implicitly expresses the functional relation. 

If the solution were ideal over the whole range of composition, k in equation (37.2) would, of course, be equal to the fugacity of the pure liquid solute at 1 atm. pressure, and Henry s law and Raoult s law would be identical ( 36a). However, although the behavior of a soluie in solution may deviate considerably from Raoult s law, it almost invariably satisfies Henry s law at high dilutions. Consequently, for the study of not too concentrated solutions, the standard state under consideration has some advantages over that in III. A. 

CALCULATION OF THE LIQUID PHASE FUGACITY OF A PURE COMPONENT... 

Note that the fugacity of the pure liquid, P), in Eq. 9.3-11 can be found from the methods of Sec. 7.4b.] As will be seen in Chapters 10 to 12, the calculation of the activity coefficient for each species in a mixture is an important step in many phase equilibrium calculations. Therefore, much of this chapter deals with models (equations) for G and activity coefficients. 

To calculate the fugacity of a pure vapor from corresponding states that, at the conditions of the mixture, exists only as a liquid, we will use Eq. 7.8-1 with f- T, P) equal to the total pressure, if the pressure is low enough, or... 

Besides the standard fugacity. Route B needs a model for calculating the activity coefficient. The fugacity of the pure liquid at system pressure and system temperature is usually chosen as the standard fugacity. Therefore, standard fugacity is defined as... 

Figure 12.19 Effect of temperature on fugacity of a pure saturated liquid. Vapor-phase nonidealities (cpf) lower from the pure vapor-pressure curve, but the variation of /j-"with 1/T remains roughly linear. At supercritical temperatures, jnue vapor pressures do not exist nevertheless, for (0.9 < r /T < 1), we may choose the hypothetical pure liquid for the standard state and obtain a value of f° by extrapolation. These values were comjnited for pure water using data from steam tables [14].

In Approach A, the fugacity coefficients of the liquid (pf and vapor phase are needed. They describe the deviation from ideal gas behavior and can be calculated with the help of equations of state, for example, cubic equations of state and reliable mixing rules. In Approach B, besides the activity coefficients s value for the standard fugacity is required. In the case ofVLE usually the fugacity of the pure liquid at system temperature and system pressure is used as standard fugacity. For the calculation of the solubilities of supercritical compounds Henry constants are often applied as standard fugacity (see Section 5.7). 

Suppose we require the absolute fugacity of a pure subcooled liquid at some pressure P and that available data include the vapor-liquid saturation pressure PJ, an equation of state for the vapor i ase, and molar volumes vf for the liquid. Application of Eqs. (1.2-30) and (1.2-31), together with the criterion for pure-fluid vapor-liquid equilibrium. 

Equations (3-8) and (3-10) differ from Raoult s law by the exponential term, and fpi instead of Pi. These corrections are frequently small and can be neglected. However, in high-pressure equilibria the corrections become large, and even an ideal solution would not be expected to obey Raoult s law because (1) the. components in the liquid mixture at a given temperature are under a different total pressure than they would be as pure components and (2) the fugacity of the pure liquid is not equal to its vapor pressure. An equation similar to (3-8) applies to each of the components in an ideal mixture. 

From equilibrium consideration, the fugacity of the pure liquid under its own vapor pressure, /pi, is equal to the fugacity of the saturated vapor at the same temperature and pressure. Thus, Fig. 3-5 can be used to evaluate/p, but it should be emphasized that the reduced pressure is calculated at the vapor pressure of the pure component instead of at the total pressure. This application of the fugacity to the liquid phase corrects for the fact that the vapor is not a perfect gas, but it does not correct for the special phenomena associated with the liquid phase. 

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