Activity coefficient dilution data

In order to use solubility data for salts of moderate solubility in the calculation of thermodynamic values, one must also have the corresponding activity coefficients. Such data, particularly at the higher concentrations, are exceedingly scarce. Most activity coefficient data which now exist are primarily for dilute solutions and have been derived from electrochemical measurements. This subject is covered elsewhere in this chapter, and some of the activity coefficients derived from this source are listed in the appendices. Some interesting data obtained from other sources, particularly from freezing point measurements, are now beginning to appear. ... 

Activity-coefficient data at infinite dilution often provide an excellent method for obtaining binary parameters as shown, for example, by Eclcert and Schreiber (1971) and by Nicolaides and Eckert (1978). Unfortunately, such data are rare. 

Table 3 shows results obtained from a five-component, isothermal flash calculation. In this system there are two condensable components (acetone and benzene) and three noncondensable components (hydrogen, carbon monoxide, and methane). Henry s constants for each of the noncondensables were obtained from Equations (18-22) the simplifying assumption for dilute solutions [Equation (17)] was also used for each of the noncondensables. Activity coefficients for both condensable components were calculated with the UNIQUAC equation. For that calculation, all liquid-phase composition variables are on a solute-free basis the only required binary parameters are those for the acetone-benzene system. While no experimental data are available for comparison, the calculated results are probably reliable because all simplifying assumptions are reasonable the... 

If the mutual solubilities of the solvents A and B are small, and the systems are dilute in C, the ratio ni can be estimated from the activity coefficients at infinite dilution. The infinite dilution activity coefficients of many organic systems have been correlated in terms of stmctural contributions (24), a method recommended by others (5). In the more general case of nondilute systems where there is significant mutual solubiUty between the two solvents, regular solution theory must be appHed. Several methods of correlation and prediction have been reviewed (23). The universal quasichemical (UNIQUAC) equation has been recommended (25), which uses binary parameters to predict multicomponent equihbria (see Eengineering, chemical DATA correlation). 

A sampling of appHcations of Kamlet-Taft LSERs include the following. (/) The Solvatochromic Parameters for Activity Coefficient Estimation (SPACE) method for infinite dilution activity coefficients where improved predictions over UNIEAC for a database of 1879 critically evaluated experimental data points has been claimed (263). (2) Observation of inverse linear relationship between log 1-octanol—water partition coefficient and Hquid... 

Concentrated, Binary Mixtures of Nonelectrolytes Several correlations that predict the composition dependence of Dab. re summarized in Table 5-19. Most are based on known values of D°g and Dba- In fact, a rule of thumb states that, for many binary systems, D°g and Dba bound the Dab vs. Xa cuiwe. CuUinan s equation predicts dif-fusivities even in hen of values at infinite dilution, but requires accurate density, viscosity, and activity coefficient data. 

Gmehhng and Onken (op. cit.) give the activity coefficient of acetone in water at infinite dilution as 6.74 at 25 C, depending on which set of vapor-liquid equilibrium data is correlated. From Eqs. (15-1) and (15-7) the partition ratio at infinite dilution of solute can he calculated as follows ... 

Examples of this procedure for dilute solutions of copper, silicon and aluminium shows the widely different behaviour of these elements. The vapour pressures of the pure metals are 1.14 x 10, 8.63 x 10 and 1.51 x 10 amios at 1873 K, and the activity coefficients in solution in liquid iron are 8.0, 7 X 10 and 3 X 10 respectively. There are therefore two elements of relatively high and similar vapour pressures, Cu and Al, and two elements of approximately equal activity coefficients but widely differing vapour pressures. Si and Al. The right-hand side of the depletion equation has the values 1.89, 1.88 X 10- , and 1.44 X 10 respectively, and we may conclude that there will be depletion of copper only, widr insignificant evaporation of silicon and aluminium. The data for the boundaty layer were taken as 5 x lO cm s for the diffusion coefficient, and 10 cm for the boundary layer thickness in liquid iron. 

Equations (76) and (77) contain two constants, A and B, which, for any binary pair, are functions of temperature only. These equations appear to be satisfactory for accurately representing activity coefficients of nonpolar binary mixtures from the dilute region up to the critical composition. As examples, Figs. 12 and 13 present typical results of data reduction for two systems in these calculations, the reference pressure Pr was set equal to zero. 

Diedenhofen, M., Eckert, F., Mamt, A. Prediction of infinite dilution activity coefficients of organic compounds in ionic liquids using COSMO-RS. J. Chem. Eng. Data 2003, 48, 475 79. 

The net retention volume and the specific retention volume, defined in Table 1.1, are important parameters for determining physicochemical constants from gas chromatographic data [9,10,32]. The free energy, enthalpy, and. entropy of nixing or solution, and the infinite dilution solute activity coefficients can be determined from retention measurements. Measurements are usually made at infinite dilution (Henry s law region) in which the value of the activity coefficient (also the gas-liquid partition coefficient) can be assumed to have a constant value. At infinite dilution the solute molecules are not sufficiently close to exert any mutual attractions, and the environment of each may be considered to consist entirely of solvent molecules. The activity... 

Pieratti et ol. (1955) have developed correlations for the prediction of the activity coefficients at infinite dilution for systems containing water, hydrocarbons and some other organic compounds. Their method, and the data needed for predictions, is described by Treybal (1963) and Reid et al. (1987). 

Gruber, D., Langenheim, D., Gmehling, J. (1997) Measurement of activity coefficients at infinite dilution using gas-liquid chromatography. 6. Results for systems exhibiting gas-liquid interface adsorption with 1-octanol. J. Chem. Eng. Data 42, 882-885. 

Tse, G., Sandler, S.I. (1994) Determination of infinite dilution activity coefficients and 1-octanol/water partition coefficients of volatile organic pollutants. J. Chem. Eng. Data 39, 354-357. 

In fitting these data, we note that at pH 7.5 selenate is present almost exclusively as the SeO " oxyanion, and the species activity coefficient in the dilute fluid is nearly one. We can, therefore, take the species activity as equal to its dissolved concentration, in mol kg-1. If this had not been the case, we would need to account for the speciation and activity coefficient in determining the value of se04 for each experiment. 

Many reactions encountered in extractive metallurgy involve dilute solutions of one or a number of impurities in the metal, and sometimes the slag phase. Dilute solutions of less than a few atomic per cent content of the impurity usually conform to Henry s law, according to which the activity coefficient of the solute can be taken as constant. However in the complex solutions which usually occur in these reactions, the interactions of the solutes with one another and with the solvent metal change the values of the solute activity coefficients. There are some approximate procedures to make the interaction coefficients in multicomponent liquids calculable using data drawn from binary data. The simplest form of this procedure is the use of the equation deduced by Darken (1950), as a solution of the ternary Gibbs-Duhem equation for a regular ternary solution, A-B-S, where A-B is the binary solvent... 

About the same time Beutier and Renon (11) also proposed a similar model for the representation of the equilibria in aqueous solutions of weak electrolytes. The vapor was assumed to be an ideal gas and < >a was set equal to unity. Pitzer s method was used for the estimation of the activity coefficients, but, in contrast to Edwards et al. (j)), two ternary parameters in the activity coefficient expression were employed. These were obtained from data on the two-solute systems It was found that the equilibria in the systems NH3+ H2S+H20, NH3+C02+H20 and NH3+S02+H20 could be represented very well up to high concentrations of the ionic species. However, the model was unreliable at high concentrations of undissociated ammonia. Edwards et al. (1 2) have recently proposed a new expression for the representation of the activity coefficients in the NH3+H20 system, over the complete concentration range from pure water to pure NH3. it appears that this area will assume increasing importance and that one must be able to represent activity coefficients in the region of high concentrations of molecular species as well as in dilute solutions. Cruz and Renon (13) have proposed an expression which combines the equations for electrolytes with the non-random two-liquid (NRTL) model for non-electrolytes in order to represent the complete composition range. In a later publication, Cruz and Renon (J4J, this model was applied to the acetic acid-water system. 

In addition to the activity and osmotic coefficients at room temperature, the first temperature derivatives and the related enthalpy of dilution data were considered for over 100 electrolytes (26, 29). The data for electrolytes at higher temperatures become progressively more sparse. Quite a few solutes have been measured up to about 50°C (and down to 0°C). Also, over this range, the equations using just first temperature derivatives have some validity for rough estimates in other cases. But the effects of the second derivative (or the heat capacity) on activity coefficients at higher temperatures is very substantial. 

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. 

Extension of Activity Coefficient Data to Additionai Temperatures with Enthalpy of Dilution Data... 

Raji Heyrovska [18] has developed a model based on incomplete dissociation, Bjermm s theory of ion-pair formation, and hydration numbers that she has found fits the data for NaCl solutions from infinite dilution to saturation, as well as several other strong electrolytes. She describes the use of activity coefficients and extensions of the Debye-Hiickel theory as best-fitting parameters rather than as explaining the significance of the observed results. ... 

Straver, E.J.M. and de Loos, T. Determination of Henry s law constants and activity coefficients at infinite dilution of flavor compounds in water at 298 K with a gas-chromatographic method, / Chem. Eng. Data, 50(4) 1171-1176, 2005. 

Tse, G., Orbey, H., and Sandler, S.I. Infinite dilution activity coefficients and Henry s law coefficients of some priority water pollutants determined by a relative gas chromatographic method, Environ. Sci Tecbnol, 25(10) 2017-2022, 1992. Tsierkezos, N.G., Kelarakis, A.E., and Palaiologou, M.M. Densities, viscosities, refractive indices, and surface tensions of dimethyl sulfoxide + butyl acetate mixtures at (293.15, 303.15, and 313.15) K, /. Chem. Eng. Data, 45(2) 395-398, 2000. Tsierkezos, N.G. and Molinou, I.E. Densities and viscosities of ethylene glycol mixtures at 293.15 K, /. Chem. Eng. Data, 44(5) 955-958, 1999. 

The specific ion interaction approach is simple to use and gives a fairly good estimate of activity factors. By using size/charge correlations, it seems possible to estimate unknown ion interaction coefficients. The specific ion interaction model has therefore been adopted as a standard procedure in the NEA Thermochemical Data Base review for the extrapolation and correction of equilibrium data to the infinite dilution standard state. For more details on methods for calculating activity coefficients and the ionic medium/ ionic strength dependence of equilibrium constants, the reader is referred to Ref. 40, Chapter IX. 

Stokes-Robinson Modification of Debye-Hiickel Theory Effect of Ion-Solvent Interaction. Debye-Hiickel theory explains the activity and activity coefficient data on the basis of ion-ion interaction for dilute solution. According to Eqs. (5.29) and... 

Experimenters would do well to avoid any unnecessary changes in the ionic composition of reaction samples within a series of experiments. If possible, chose a standard set of reaction conditions, because one cannot readily correct data from one set of experimental conditions in any reliable manner that reveals the reactivity under a different set of conditions. Maintenance of ionic strength and solvent composition is desirable, and correction to constant ionic strength often effectively minimizes or ehminates electrostatic effects. Even so, remember that Debye-Hiickel theory only applies to reasonably dilute electrolyte solutions. Another important fact is that ion effects and solvent effects on the activity coefficients of polar transition states may be more significant than more modest effects on reactants. 

Heintz, A., Kulikov, D.V., and Verevkin, S.R, Thermodynamic properties of mixtures containing ionic liquids. 1. Activity coefficients at infinite dilution of alkanes, alkenes, and alkylbenzenes in 4-methyl-M-butylpyridinium tetrafluo-roborate using gas-liquid chromatography, /. Chem. Eng. Data, 46,1526,2001. 

Krummen, M., Wasserscheid, R, and Gmehling, J., Measurements of activity coefficients at infinite dilution in ionic liquids using the dilutor technique, /. Chem. Eng. Data, 47, 1411, 2002. 

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