Activity coefficients in mixtures

To examine the validity of the ionic strength principle using measurements of solubility. 

Brfinsted and La Mer (J. Amer. Chem. Soc. 1924,46, 571) determined the solubility of the uni-bivalent salt rCo(NH3)4C20Jg [SjOg] in water and in solutions of several salts. The results obtained at 15 °C are given in table 1 below, where c denotes the concentration of added electroljde, and s the solubility. 

At 15 C the dielectric constant of water is 82.2, which gives A = 0.500 (l/mole)i (compare problem 78). 

The solubility s is related to the mean activity coefiSicient / (both on the volume concentration scale) by 

When we draw the best straight line through all the points on the graph of log (s 7 ole H) against I, the individual deviations from the line in no case exceed 0.003 or 0.7 % in/. Within this accuracy, therefore, the mean activity coefficient of the slightly soluble salt in the presence of any of the electrolytes added can be represented at least up to r = 0.011 mole H by the expression 

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Note that in all ion interaction approaches, the equation for mean activity coefficients can be split up to give equations for conventional single ion activity coefficients in mixtures, e.g., Eq. (6.1). The latter are strictly valid only when used in combinations that yield electroneutrality. Thus, while estimating medium effects on standard potentials, a combination of redox equilibria with H " + e 5112(g) is necessary (see Example 3). 

Consequently, by a regression analysis of very large quantities of activity coefficient (or, as we will see in Sec. 10.2, actually vapor-liquid equilibrium) data, the binary parameters Onm Omn for many group-group interactions can be determined. These parameters can then be used to predict the activity coefficients in mixtures (binary or multicomponent) for which no experimental data are available. 

Equation (B.l) will allow fairly aecurate estimates of the activity coefficients in mixtures of electrolytes if the ion interaction coefficients are known. Ion interaction coefficients for simple ions can be obtained from tabulated data of mean activity coefficients of strong electrolytes or from the corresponding osmotic coefficients. Ion interaction coefficients for complexes can either be estimated from the charge and size of the ion or determined experimentally from the variation of the equilibrium constant with the ionic strength. 

A.ctivity Coefficients. Activity coefficients in Hquid mixtures are directiy related to the molar excess Gibbs energy of mixing, AG, which is defined as the difference in the molar Gibbs energy of mixing between the real and ideal mixtures. It is typically an assumed function. Various functional forms of AG give rise to many of the different activity coefficient models found in the Hterature (1—3,18). Typically, the Hquid-phase activity coefficient is a function of temperature and composition expHcit pressure dependence is rarely included. 

Some organic compounds can be in solution with water and the mixture may still be a flammable mixture. The vapors above these mixtures such as ethanol, methanol, or acetone can form flammable mixtures with air. Bodurtha [39] and Albaugh and Pratt [47] discuss the use of Raoult s law (activity coefficients) in evaluating the effects. Figures 7-52A and B illustrate the vapor-liquid data for ethyl alcohol and the flash point of various concentrations, the shaded area of flammability limits, and the UEL. Note that some of the plots are calculated and bear experimental data verification. 

In Section HI, we discussed the relation between fugacities and activity coefficients in liquid mixtures, and we emphasized that we have a fundamental choice regarding the way we wish to relate the fugacity of a component to the pressure and composition. This choice follows from the freedom we have in choosing a convention for the normalization of activity coefficients. 

Methodically, there is no great difference between measuring the mean activity coefficient in a solution of one electrolyte and measuring this quantity in a mixture of electrolytes. Binary mixtures have been studied most extensively. If osmotic methods are used, then the coefficients ocx and... 

Fredenslund, A., Jones, R. L., Prausnitz, J. M. (1975) Group-contribution estimation of activity coefficients in nonideal liquid mixtures. AIChEJ. 21, 1086-1099. 

Group-Contribution Estimation of Activity Coefficients in Nonideal Liquid Mixtures", AIChE Journal, 21(6), 1975... 

By analogy with the treatment of mixed micelles, we now assume that the free energy of mixing of the surface phase can be calculated using the standard regular solution expression for the activity coefficients in a binary mixture ... 

Explain in words how organic cosolvents affect the activity coefficients in water-solvent mixtures Which organic solvents are most effective Is it true that the effect of an organic cosolvent is linearly related to its volume fraction in the solvent-water mixture Below which volume fraction can the effect of an organic cosolvent be neglected ... 

In order to calculate the aqueous concentration of compound / at equilibrium, one needs to know its mole fraction, jcimix, in the mixture (or its molar concentration, Cimix, and the molar volume, Vmix, of the mixture), as well as its activity coefficients in the organic (ymix) and the aqueous (yiw) phases. Very often, when dealing with complex mixtures, V is not known and has to be estimated. At a first approximation, this can be done from the density, pmix, of the liquid mixture, and by assuming an average molar mass, M, of the mixture components ... 

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