Activity coefficient of solutions

Y- Mean ionic activity coefficient of solute Dimensionless Dimensionless... 

Y= activity coefficient of solute / = raffinate phase e = extract phase... 

Activity coefficients of solute species are calculated from... 

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. 

Assumption 2 may lead to substantial errors, because the salinity of the liquid normally increases during boiling. The consequent increase in ionic strength modifies the activity coefficients of solutes. In particular, if the gaseous species are polar and nonpolar, the activity coefficients of solutes diverge as the process advances (see section 8.7). 

Before concluding three items should be noted First, AHd values may be correlated with equilibrium constants and activity coefficients of solutions as shown later in Eq. (3.10.3), for example. Second, to convert AHd values from one temperature to another one uses the Kirchhoff relation, Eq. (1.18.30) (see also Exercise 3.8.3). Third, to convert AHd values from one pressure to another, the integrated form of Eq. (1.18.13b) may be used. 

As a concluding remark it is pertinent to observe that proving a theory requires several physical quantities that cannot unambiguously be determined simple and accurate prediction of salting coefficients should spur further theoretical development because their predictions are only fairly accurate. It is, however, clear that the logarithm of the activity coefficients of solutes in electrolyte solutions contains a term linear in the electrolyte concentration for a single electrolyte, a mixture of two electrolytes, and a non electrolyte. Equations 2.8,2.9, and 2.10, respectively, sanction the quantitative relationships. 

Many nonionizable organic solutes in water are described thermodynamically on the mole fraction scale, although their solubilities may commonly be reported in practical units, for example, molality. [Refer to Schwarzenbach et al. (1993) and Klotz (1964) for detailed discussion of such aqueous solutions.] Here, the standard state is the pure liquid state of the organic solute, that is, Xj = 1. The reference state is Xi - 1, that is, a solution in which the organic solute molecules interact with one another entirely. Activity coefficients of solute molecules in dilute aqueous solutions are generally much greater than unity for this reference state choice, jc, 1. For example, with this reference state, aqueous benzene has an experimental infinitely dilute solution activity coefficient, T nzeno of 2400 for an infinite dilution reference state, jc, - 0, the activity coefficient would be approximately 1 (Tanford, 1991). 

The prediction of the activity coefficients of solutes (such as gases and large molecules of biomedical and environmental significance) in saturated solutions of multicomponent mixtures constitutes the main difficulty in calculating the solute solubil-... 

Using a similar experimental set-up as for the determination of Abraham s solvation parameters, the activity coefficient of solutes at infinite dilution y" cm be determined from their retention times using gas-liquid chromatography [12, 67-72], Alternatively, the diluter technique is applied [67, 73] for which an inert gas transports the solute from the headspace (which is in equilibrium with the ionic liquid matrix) to a GC-column. The continuous decrease of the concentration in the headspace is measured as a function of time, generating an exponential function from which y°° is calculated. 

Unfortunately, the available experimental results suggest that the column saturation capacity is often not the same for the components of a binary mixture, so Eq. 4.5 does not account accurately for the competitive adsorption behavior of these components [48]. A simple approach was proposed to turn the difficulty (next subsection). Although it is applicable in some cases, more sophisticated models seem necessary. Numerous isotherm models have been suggested to solve this problem. Those resulting from the ideal adsorbed solution (IAS) theory developed by Myers and Prausnitz [49] are among the most accurate and versatile of them. Later, this theory was refined to accormt for the dependence of the activity coefficients of solutes in solution on their concentrations, leading to the real adsorption solution (RAS) theory. In most cases, however, the equations resulting from IAS and the RAS theories must be solved iteratively, which makes it inconvenient to incorporate those equations into the numerical calculations of column dynamics and in the prediction of elution band profiles. 

This chapter is concerned with the definition and determination of standard potentials. Such standard potentials are of use in obtaining Gibbs free energies of electrochemical reactions under definite standard conditions, and for obtaining activity coefficients of solutes, as will be discussed in detail below. However, in order to deal with such potentials it is first necessary to discuss the matter of standard states. 

Activity coefficients of solutes at infinite dilution, jT, are nearly constant (i.e., by Henry s law). By the Lewis and Randall rule, the activity coefficients of nearly pure solutes approach unity as xf 1.0. In this case. Equation (10.11) is approximately... 

In this equation, yx i he activity coefficient of solute X, and the bracketed term is the molar concentration of X. In some of the examples, however, for convenience we will assume that the activity coefficient is unity so that the molar concentration and the activity of a species are identical. 

It is possible to determine the activity coefficients of solute species in a given solvent by measuring their solubilities in that solvent. We consider a system in which pure solid component 2 is in equilibrium... 

Measurements of partition coefficients are frequently used to determine activity coefficients of solute species. We consider a system consisting of two immiscible solvents, phases 1 and 2 and a solute component 2. At equilibrium,... 

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