Liquid solutions fugacity

It is strictly for convenience that certain conventions have been adopted in the choice of a standard-state fugacity. These conventions, in turn, result from two important considerations (a) the necessity for an unambiguous thermodynamic treatment of noncondensable components in liquid solutions, and (b) the relation between activity coefficients given by the Gibbs-Duhem equation. The first of these considerations leads to a normalization for activity coefficients for nonoondensable components which is different from that used for condensable components, and the second leads to the definition and use of adjusted or pressure-independent activity coefficients. These considerations and their consequences are discussed in the following paragraphs. 

For such components, as the composition of the solution approaches that of the pure liquid, the fugacity becomes equal to the mole fraction multiplied by the standard-state fugacity. In this case,the standard-state fugacity for component i is the fugacity of pure liquid i at system temperature T. In many cases all the components in a liquid mixture are condensable and Equation (13) is therefore used for all components in this case, since all components are treated alike, the normalization of activity coefficients is said to follow the symmetric convention. ... 

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. 

The residual Gibbs energy and the fugacity coefficient are useful where experimental PVT data can be adequately correlated by equations of state. Indeed, if convenient treatment or all fluids by means of equations of state were possible, the thermodynamic-property relations already presented would suffice. However, liquid solutions are often more easily dealt with through properties that measure their deviations from ideal solution behavior, not from ideal gas behavior. Thus, the mathematical formahsm of excess properties is analogous to that of the residual properties. 

Activity coefficient models offer an alternative approach to equations of state for the calculation of fugacities in liquid solutions (Prausnitz ct al. 1986 Tas-sios, 1993). These models are also mechanistic and contain adjustable parameters to enhance their correlational ability. The parameters are estimated by matching the thermodynamic model to available equilibrium data. In this chapter, vve consider the estimation of parameters in activity coefficient models for electrolyte and non-electrolyte solutions. 

For concentrated solutions, the activity coefficient of an electrolyte is conveniently defined as though it were a nonelectrolyte. This is a practical definition for the description of phase equilibria involving electrolytes. This new activity coefficient f. can be related to the mean ionic activity coefficient by equating expressions for the liquid-phase fugacity written in terms of each of the activity coefficients. For any 1-1 electrolyte, the relation is ... 

Henry s law physchem The law that at sufficiently high dilution in a liquid solution, the fugacity of a nondissodating solute becomes proportional to Its concentration. hen-rez, 16 ... 

Using the concept of fugacity we can now, in analogy to the gaseous phase (Eq. 3-28), express the chemical potential of a compound i in a liquid solution by ... 

The aqueous solubility of a gaseous compound is commonly reported for 1 bar (or 1 atm = 1.013 bar) partial pressure of the pure compound. One of the few exceptions is the solubility of 02 which is generally given for equilibrium with the gas at 0.21 bar, since this value is appropriate for the earth s atmosphere at sea level. As discussed in Chapter 3, the partial pressure of a compound in the gas phase (ideal gas) at equilibrium above a liquid solution is identical to the fugacity of the compound in the solution (see Fig. 3.9d). Therefore equating fugacity expressions for a compound in both the gas phase and an equilibrated aqueous solution phase, we have ... 

Assuming ideal gas behavior, the equilibrium partial pressure, ph of a compound above a liquid solution or liquid mixture is a direct measure of the fugacity, fu, of that compound in the liquid phase (see Fig. 3.9 and Eq. 3-33). 

In Equation 3.14, the liquid concentration may be replaced by fugacity if three assumptions are made (a) constant temperature and pressure, (b) ideal liquid solutions, and (c) constant total molar concentration (ctot). With these assumptions the fugacity (ft) is related to the concentration (a) by the expression ... 

Figure 12.19 Composition dependence of the fugacity of acetone in two binary liquid solutions at...

In this definition, the activity coefficient takes account of nonideal liquid-phase behavior for an ideal liquid solution, the coefficient for each species equals 1. Similarly, the fugacity coefficient represents deviation of the vapor phase from ideal gas behavior and is equal to 1 for each species when the gas obeys the ideal gas law. Finally, the fugacity takes the place of vapor pressure when the pure vapor fails to show ideal gas behavior, either because of high pressure or as a result of vapor-phase association or dissociation. Methods for calculating all three of these follow. 

The ultimate leaching efficiency in the absence of mass-transfer limitations is governed by the solubility of the solute in the solvent the extent to which solid can dissolve in liquids vary enormously. The solubility can be either experimentally determined or, alternatively, it can be estimated based on thermodynamics principles. If the pure solute is a solid at the extraction temperature, the following relates the fugacity of this pure solid solute to its fugacity in the liquid solution ... 

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. 

The exponential term in Equation 7-13 is a correction factor for the effect of pressure on liquid-phase fugacity and is known as the Poynting factor. In Equation 7-13, V[ can be replaced by the partial molar volume of component i in the liquid solution for greater accuracy. Eor low to moderate pressure, V is assumed as the saturated liquid molar volume at the specified temperature. Equation 7-13 is simplified to give... 

This is based on the fact that the solid state fugacity of pure solute 3 at the triple-point pressure Ptp is related to the liquid state fugacity of the pure solute... 

The /<-values are calculated by Equation 1.25, with the vapor phase fugacity coefficients calculated from the equation of state and the liquid phase fugacity coefficients for an ideal solution calculated as... 

The fugacity of liquid solutions is basic to phase equilibrium and chemical equilibrium of liquids. Raoult observed that the equilibrium partial pressure of a component of a liquid solution with like substances is given by... 

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