Solute reference state

Assume the vapor phase to be characterized as an ideal gas. Determine the activity coefficients for components A and B at xA - 1/4, 1/2, 3/4 at 500°C relative to the solvent and the solute reference states involving mole fractions. 

Table 2.3 summarizes the essential relationships for pressure effects on chemical equilibrium for the variable-pressure standard-state convention. Note, that these relationships can apply to any consistent choice of standard part ial molar volumes, for example, one for which an ionic medium such as seawater is adopted as the solute reference state. For detailed discussion of applications to seawater see, for example, Millero (1969) and Whitfield (1975). A compie-... 

Prausnitz (1,2) has discussed this problem extensively, but the most successful techniques, which are based on either closed equations of state, such as discussed in this symposium, or on dilute liquid solution reference states such as in Prausnitz and Chueh (3), are limited to systems containing nonpolar species or dilute quantities of weakly polar substances. The purpose of this chapter is to describe a novel method for calculating the properties of liquids containing supercritical components which requires relatively few data and is of general applicability. Used with a vapor equation of state, the vapor-liquid equilibrium for these systems can be predicted to a high degree of accuracy even though the liquid may be 30 mol % or more of the supercritical species and the pressure more than 1000 bar. 

The expression in brackets in Eq. 9.4.23 is a function of T and p, but not of xb, and represents the chemical potential of B in a hypothetical solute reference state. This chemical potential will be denoted by B where the x in the subscript reminds us that the reference state is based on mole fraction. The equation then becomes... 

It is worthwhile to describe in detail the reference state to which refers. The general concept is also applicable to other solute reference states and solute standard states to be encountered presently. Imagine a hypothetical solution with the same constituents as the real solution. This hypothetic solution has the magical property... 

Again in each of these equations, we replace the expression in brackets, which depends on T and p but not on composition, with the chemical potential of a solute reference state ... 

This equation shows that the partial molar entropy varies with composition and goes to -1-00 in the limit of infinite dilution. From the expressions of Eqs. 9.4.27 and 9.4.28, we can derive similar expressions for 5b in terms of the solute reference states on a concentration or molality basis. 

Water and 1-butanol are two liquids that do not mix in all proportions that is, 1-butanol has Umited solubiUty in water. Figures 9.10(a) and 9.10(b) on the next page show the fugacity of 1-butanol plotted as functions of both mole fraction and molality. The figures demonstrate how, treating 1-butanol as a solute, we locate the solute reference state by a... 

Next consider a binary liquid mixture in which component B is neither volatile nor able to mix in all proportions with A. In this case, it is appropriate to treat B as a solute and to base its activity coefficient on a solute reference state. We could obtain an expression for In Yx,B similar to Eq. 9.6.10, but the integration would have to start at Xb=0 where the integrand Xa/xb would be infinite. Instead, it is convenient in this case to use the method described in the next section. 

Here ft and ifl are the chemical potentials of the cation and anion in solute reference states. Each reference state is defined as a hypothetical solution with the same temperature, pressure, and electric potential as the solution under consideration in this solution, the molality of the ion has the standard value m°, and the ion behaves according to Henry s law based on molality. y+ and y are single-ion activity coefficients on a molality basis. 

Equation 10.2.10 predicts that the activity of HCl in aqueous solutions is proportional, in the limit of infinite dilution, to the square of the HCl molality. In contrast, the activity of a nonelectrolyte solute is proportional to the first power of the molality in this limit. This predicted behavior of aqueous HCl is consistent with the data plotted in Fig. 10.1 on page 285, and is confirmed by the data for dilute HCl solurions shown in Fig. 10.2(a). The dashed line in Fig. 10.2(a) is the extrapolation of the ideal-dilute behavior given by o-m,B = (mB/m°). The extension of this line to niB = m° establishes the hypothetical solute reference state based on molality, indicated by a filled circle in Fig. 10.2(b). (Since the data are for solutions at the standard pressure of 1 bar, the solute reference state shown in the figure is also the solute standard state.)... 

Although it is not possible to determine absolute values of partial molar enthalpies, we can evaluate Ha and relative to appropriate solvent and solute reference states. 

Most aspects have not been worked out for the thermodynamic properties and equilibria of systems of macromolecules in the crystalline, glassy, or solution form. There is much uncertainty about the use of dilute solution reference states for supercritical components, particularly in multisolute, multisolvent solutions. 

Figure 7.5 Fugacity of a binary liquid mixture. Also shown are ideal solution reference states based on a-a interactions (Lewis/Randall rule) and a-b interactions (Henry s law).

In analogy to the gas, the reference state is for the ideally dilute solution at c, although at the real solution may be far from ideal. (Teclmically, since this has now been extended to non-volatile solutes, it is defined at... 

If appropriate enthalpy data are unavailable, estimates can be obtained by first defining reference states for both solute and solvent. Often the most convenient reference states are crystalline solute and pure solvent at an arbitrarily chosen reference temperature. The reference temperature selected usually corresponds to that at which the heat of crystallization A/ of the solute is known. The heat of crystallization is approximately equal to the negative of the heat of solution. For example, if the heat of crystallization is known at then reasonable reference conditions would be the solute as a soUd and the solvent as a Uquid, both at The specific enthalpies then could be evaluated as... 

FIG. 2-29 Enthalpy-concentration diagram for aqueous sodium hydroxide at 1 atm. Reference states enthalpy of liquid water at 32 F and vapor pressure is zero partial molal enthalpy of infinitely dilute NaOH solution at 64 F and 1 atm is zero. [McCahe, Trans. Am. Inst. Chem. Eng., 31, 129(1935).]... 

For ions in solution the standard reference state is the hydrogen ion whose standard chemical potential at = 1 is given an arbitrary value of zero. Similarly for pure hydrogen at Phj = = 0- Thus for the... 

We repeat that ideal solutions, like ideal gases, do not exist. But like the ideal gas, the ideal solution has an application as a reference state, and it is important to know the conditions under which Raoult s law is a good... 

From this expression it follows that the rate constant for any other solution is related to that in the reference state by... 

The value obtained by Hamm et alm directly by the immersion method is strikingly different and much more positive than others reported. It is in the right direction with respect to a polycrystalline surface, even though it is an extrapolated value that does not correspond to an existing surface state. In other words, the pzc corresponds to the state of a bare surface in the double-layer region, whereas in reality at that potential the actual surface is oxidized. Thus, such a pzc realizes to some extent the concept of ideal reference state, as in the case of ions in infinitely dilute solution. 

Thus when using the she scale one chooses as the reference state of electrons (and assigns the zero value to it) the state of an electron at the Fermi level of a metal electrode in equilibrium with an aqueous solution of pH=0 and Ph2=1 atm at 25°C. 

In equation (3), the term y is the reference chemical potential. We take the reference state for which the reference chemical potential is computed to be pure, saturated solvent at the temperature of the solution. 

---