Activity coefficients mean salt method

Figure 8JO Comparison between individual ionic activity coefficients obtained with Debye-Hiickel equation and with mean salt method for various ionic strength values. Reprinted from Garrels and Christ (1965), with kind permission from Jones and Bartlett Publishers Inc., copyright 1990.

Example 3.1 Determination of single-ion activity coefficients for Ca from mean values for CaCl2 using the mean-salt method. 

In the mean-salt method, the behavior of KCl in solution is the standard basis for obtaining individual ion activity coefficients. Various lines of evidence indicate that /k+ and fc - have similar values that is, as an approximation,... 

Single-ion activity coefficients at higher ionic strength are estimated by using an empirical approach in which complex ion and dipole interactions are accounted for by direct laboratory measurements. One such experimentally based approach that can be applied to seawater is the mean salt method (MSM). This procedure is based upon measurements... 

This assumption seemed reasonable in view of the similarity of the sizes and limiting conductances of the two ions. It gave rise to the Macinnes convention, which enables the activity coefficients of other ionic species to be evaluated from the known mean activity coefficients of selected electrolytes. This process, called the mean salt method", has been used extensively and with apparent success in studies of the seawater medium. Carrels and Thompson (40,41) used a glass electrode reversible to Na" to establish a reference point for the activity coefficient of that ion in seawater. The Macinnes convention was then applied to obtain data for the other ions present. The procedure proposed by Maronny and Valensi (42,43) for the determination of standard pH values utilizes Equation 6, where is... 

Similarly, the same method and the same mean salt furnish values of individual ionic activity coefficients for other ions—e.g., the sulfate group SO " ... 

Only mean activity coefficients can be experimentally determined for salts, not activity coefficients for single ions. The Maclnnes Convention is one method for obtaining single ion activity coefficients and states that because of the similar size and mobility of the potassium and chloride ions ... 

The method of calculation will be described with reference to thallous chloride, the solubility of which has been measured in the presence of various amounts of other electrolytes, with and without an ion in common with the saturating salt. By plotting the values of c for the thallium and chloride ions in solutions of different ionic strengths and extrapolating to zero, it is found that which in this case is equal to V, is 0.01428 at 25 (Fig. 58). It follows, therefore, from equation (122) that the mean activity coefficient of thallous chloride in any saturated solution is given by... 

Frequently, solubility measurements may be used in mixed electrolytes to obtain mean molar activity coefficients. This method hinges on the use of an electrolyte solution which is saturated with respect to any particular salt, so that the equilibrium My Ay (s) = v+M + -F v A prevails. This situation may be characterized by (among others) use of the equilibrium constant Kf specified by Eq. (3.7.8b). It is conventional either to ignore the product term [afJ"(T, P)Y as being equal to (at unit pressure) or close to unity, or to absorb this constant factor into the equilibrium constant as well. This then gives rise to the expression... 

Values of electrolyte activities, as measured by osmotic pressures, freezing point depression, and other experimental methods are in the literature (References 5 and 6, for example) or one can calculate activity coefficients based on models of molecular-level interactions between ions in electrolyte solutions. For illustrative purposes, mean molal activity coefficients for various salts at different aqueous molal (mj concentrations at 25°C are listed in Table 26.3 [7]. 

The individual-ion activity coefficients for the free ions were based on the Macinnis (18) convention, which defines the activity of Cl to be equal to the mean activity coefficient of KCl in a KCl solution of equivalent ionic strength. From this starting point, individual-ion activity coefficients for the free ions of other elements were derived from single-salt solutions. The method of Millero and Schreiber (14) was used to calculate the individual-ion, activity-coefficient parameters (Equation 5) from the parameters given by Pitzer (19). However, several different sets of salts could be used to derive the individual-ion activity coefficient for a free ion. For example, the individual-ion activity coefficient for OH could be calculated using mean activity-coefficient data for KOH and KCl, or from CsOH, CsCl, and KCl, and so forth. 

Frequently, solubility measurements may be used in mixed electrolytes to obtain mean molar activity coefficients. This method hinges on the use of an electrolyte solution that is saturated with respect to any particular salt, so that the equilibrium M,, (5) = prevails. This situation may... 

Mention should be made of polystyrenesulfcmic add and its salts. In the concentration rai in which the isopiestic method was used (17), the mean activity coefficient was found to increase with increasing concentration and the cube-root rule was not valid. This is due to strong solute-solvent interaction, specifically hydrophobic influences on water molecules. However, in a concentration range in vhich this interaction is not so intense, it is expected that the cube-root rule holds. As a matter of fact, the y values of polystyrenesulfonic add [reported by Dolar and Leskovsek (36)] fitted this rule at lowconcentrations, as is shown in Fig. 2. ... 

Jamison and Turner (52) have worked intensively on optical activation of various substituted i f-benzoyIdiphenylamines by means of alkaloids and have achieved particularly interesting results with the acid, iV-benzoyl-2,4,4 -tribromodiphenylamine-6-carboxylicacid (X). Conditions were here suitable for demonstrating the fairly marked temperature coefficient of the inversion process, for the acid in acetone solution is optically labile at room temperature, but stable at — 15°C. Crystallization of an equimolecular solution of the dl acid and cinchonidine from acetone at room temperature led to separation of pure cinchonidine (-I-) salt in almost 100% yield, a typical second-order asymmetric transformation. However, the same process at — 15°C. led to crystallization of cinchonidine (-I-) salt in only about 50% yield, and the residue on evaporation of the cold filtrate in vacuo was about two-thirds cinchonidine (—) salt—in other words, a typical resolution by the classical salt-formation method. 

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