Activity coefficient of a solvent

When a condensable solute is present, the activity coefficient of a solvent is given by Equation (15) provided that all composition variables (x, 9, and ) are taicen on an (all) solute-free basis. Composition variables 9 and 4 are automatically on a solute-free basis by setting q = q = r = 0 for every solute. 

The activity coefficient of a solvent in a solution is given by the following equation ... 

Originally, it was assumed that the FH interaction parameter was a constant, characteristic for each polymer-solvent pair. In this case, it can be proved based on thermodynamics that the FH equation for the activity coefficient of a solvent in a binary solvent(l)-polymer(2) system is... 

In practice, determination of the activity coefficients of a solvent in a solution is easy, if the solute is nonvolatile. The vapor pressure of the solution and the pure solvent are measured and aA = PJP (Equation (166) applies). However, if the solute is volatile, then the partial pressure of both the solute and the solvent should be determined. 

Appendix A9.3 The Activity Coefficient of a Solvent in an Electrolyte Solution... 

Whereas the models given above can be used to correlate solvent activities in polymer solutions, attempts also have been made in the literature to develop concepts to predict solvent activities. Based on the success of the UNIFAC concept for low-molecular liquid mixtures,Oishi and Prausnitz developed an analogous concept by combining the UNIFAC-model with the free-volume model of Flory, Orwoll and Vrij. The mass fraction based activity coefficient of a solvent in a polymer solution is given by ... 

For example, even though the main objective of the isopiestic method is to determine the osmotic and activity coefficient of a solvent, the isopiestic technique is a precise measurement of the composition of liquid phase in liquid-gas equilibrium. Some details of isopiestic apparatus used for hydrothermal measurements will be discussed later in Methods of sampling . 

In a very similar manner to ebullioscopy, which we have just discussed, we can determine the activity, or the activity coefficient, of a solvent by cryoscopy, i.e. by looking at the depression of the fieezing point of the solvent T f) owing to the presence of the solutes. If the solvent is pure in... 

The activity coefficient of the solvent remains close to unity up to quite high electrolyte concentrations e.g. the activity coefficient for water in an aqueous solution of 2 m KC1 at 25°C equals y0x = 1.004, while the value for potassium chloride in this solution is y tX = 0.614, indicating a quite large deviation from the ideal behaviour. Thus, the activity coefficient of the solvent is not a suitable characteristic of the real behaviour of solutions of electrolytes. If the deviation from ideal behaviour is to be expressed in terms of quantities connected with the solvent, then the osmotic coefficient is employed. The osmotic pressure of the system is denoted as jz and the hypothetical osmotic pressure of a solution with the same composition that would behave ideally as jt. The equations for the osmotic pressures jt and jt are obtained from the equilibrium condition of the pure solvent and of the solution. Under equilibrium conditions the chemical potential of the pure solvent, which is equal to the standard chemical potential at the pressure p, is equal to the chemical potential of the solvent in the solution under the osmotic pressure jt,... 

Thermodynamic methods also measure the activity coefficient of the solvent (it should be recalled that the activity coefficient of the solvent is directly related to the osmotic coefficient—Eq. 1.1.19). As the activities of the components of a solution are related by the Gibbs-Duhem equation, the measured activity coefficient of the solvent can readily be used to calculate the activity coefficient of a dissolved electrolyte. 

Thus, the ideal solution is a reference for the solvent in a real solution, and the activity coefficient of the solvent measures the deviation from ideality. 

As we saw in Section 17.5, the activity coefficient of a nonelectrolyte solute can be calculated from the activity coefficient of the solvent, which, in turn, can be obtained from the measurement of colligative properties such as vapor pressure lowering, freezing point depression, or osmotic pressure. We used the Gibbs-Duhem equation in the form [Equation (17.33)]... 

The activity coefficients of solute and solvent are of comparable magnitudes in dilute solutions of nonelectrolytes, so that Equation (17.33) is a useful relationship. But the activity coefficients of an electrolyte solute differ substantially from unity even in very dilute solutions in which the activity coefficient of the solvent differs from unity by less than 1 x 10 . The data in the first three columns of Table 19.3 illustrate the situation. It can be observed that the calculation of the activity coefficient of solute from the activity coefficient of water would be imprecise at best. 

Activity Coefficient of a Dipolar Molecule. Our first application will be to the activity coefficients of a dipolar molecule as a function of the dielectric constant of the solvent. Harned and Ross (14) have determined the activity coefficient of methyl acetate in dioxane-water mixtures of various compositions at 25°C. Equation 32 can be applied to this data, and since the particles have no ionic charges, the first term can be omitted. For the difference between the activity coefficients of methyl acetate in dioxane-water mixtures and those in water we have from Equation 32... 

Furthermore, for most compounds of interest to us, the octanol molecules present as cosolutes in the aqueous phase will have only a minor effect on the other organic compounds activity coefficients. Also, the activity coefficients of a series of apolar, monopolar, and bipolar compounds in wet versus dry octanol shows that, in most cases, Yu values changes by less than a factor of 2 to 3 when water is present in wet octanol (Dallas and Carr, 1992 Sherman et al., 1996 Komp and McLachlan, 1997a). Hence, as a first approximation, for nonpolar solvents, for w-octanol, and possibly for other solvents exhibiting polar groups, we may use Eq. 6-11 as a first approximation to estimate air- dry organic solvent partition constants for organic compounds as illustrated in Fig. 6.2. Conversely, experimental KM data may be used to estimate K,aw or Kitvi, if one or the other of these two constants is known. 

We can now evaluate how a given organic cosolvent will affect the various parameters in Eq. 9-32. In Section 5.4 we discussed the dependence of the activity coefficient of a compound in a solvent-water mixture on the fraction of the cosolvent. We have seen that, depending on solute and cosolvent considered, this dependence may be quite complex (Figs. 5.6 and 5.7 Table 5.8). In the following discussion, we confine ourselves to rather small cosolvent concentrations (i.e.,/v < 0.2 to 0.3) for which we may assume a log-linear relationship (Eq. 5-32). We may then express the activity coefficient, Yu, of compound i in the solvent-water mixture as ... 

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