Mean activity coefficient evaluating

The mean activity coefficient is the standard form of expressing electrolyte data either in compilations of evaluated experimental data such as Hamer and Wu (2) or in predictions based on extensions to the Debye-Huckel model of electrolyte behavior. Recently several advances in the prediction and correlation of mean activity coefficients have been presented in a series of papers starting in 1972 by Pitzer (3, Meissner 04), and Bromley (5) among others. 

It can be shown that the virial type of activity coefficient equations and the ionic pairing model are equivalent, provided that the ionic pairing is weak. In these cases, it is in general difficult to distinguish between complex formation and activity coefficient variations unless independent experimental evidence for complex formation is available, e.g., from spectroscopic data, as is the case for the weak uranium(VI) chloride complexes. It should be noted that the ion interaction coefficients evaluated and tabulated by Cia-vatta [10] were obtained from experimental mean activity coefficient data without taking into account complex formation. However, it is known that many of the metal ions listed by Ciavatta form weak complexes with chloride and nitrate ions. This fact is reflected by ion interaction coefficients that are smaller than those for the noncomplexing perchlorate ion (see Table 6.3). This review takes chloride and nitrate complex formation into account when these ions are part of the ionic medium and uses the value of the ion interaction coefficient (m +,cio4) for (M +,ci ) (m +,noj)- Io... 

Although there is no straightforward and convenient method for evaluating activity coefficients for individual ions, the Debye-Hiickel relationship permits an evaluation of the mean activity coefficient (y+), for ions at low concentrations (usually <0.01 moll-1) ... 

Earlier, when discussing historical development, we mentioned that different workers have used different equations to describe the Debye-Hiickel constant (A, Eq. 2.35) as a function of temperature. For example, at 0°C, the value of this constant is 0.3781, 0.3764, and 0.3767 kg1/2 mol-1/2 for the FREZCHEM, Archer and Wang (1990), and Pitzer (1991) models, respectively. At NaCl = 5 m and 0 °C, the calculated mean activity coefficients using these three parameters evaluated with the FREZCHEM model are 0.7957, 0.7995, and 0.7988, respectively. The largest discrepancy is 0.48%, which is within the range of model errors for activity coefficients (Table 3.5). 

Rl/+X from w to o, a s are the mean activities, y s are the mean activity coefficients, and cRX s are the equilibrium electrolyte concentrations. A non-thermodynamic assumption has to be introduced to construct the scale of the inner (Galvani) potential differences from the partition measurements. The most commonly used hypothesis is that the tetraphenylarsonium cation (Ph4As+) and the tetraphenylborate anion (PI14 B ) have equal standard Gibbs energies of transfer for any combination of two solvents [iv]. This assumption enables the evaluation of AG 1 and AG j from the partition mea-... 

Evaluate the Debye-Hlickel constants A and B for ethyl alcohol and use the values to calculate the mean activity coefficients for 1 1, 1 2, and 2 2-valent electrolytes in ethyl alcohol at ionic strengths 0.1 and 0.01 at 25 °C. The mean distance of closest approach of the ions a may be taken as 300 pm in each case. Dielectric constant e = 24.3. (Constantinescu)... 

It will be seen later (p. 230) that there does not appear to be any experimental method of evaluating the activity coefficient of a single ionic species, so that the Debye-Hiickel equations cannot be tested in the forms given above. It is possible, however, to derive very readily an expression for the mean activity coefficient, this being the quantity that is obtained experimentally. The mean activity coefficient f of an electrolyte is defined by an equation analogous to (30), and... 

The mean activity coefficient of a sparingly soluble salt in any solution could thus be evaluated provided the solubility product (K ) and the mean concentration of the... 

Mean activity coefficients have been evaluated for hydrochloric acid by potential measurements in alcohols. The salt-effect activity coefficient (left) and its product with the transfer activity coefficient (right) are shown in Figure 4-1. The values of are lower than would be calculated from the appropriate modification of the Debye-Hiickel equation (2-21) applied in the usual way to account for interionic interactions. The low values result from significant ion pairing due to the low dielectric constant. Thus, 0.1 M hydrochloric acid in 95% ethanol is about half in the form of ion pairs rather than being completely dissociated. As shown in Figure (4-1), at low concentrations the salt-effect activity coefficients approach unity, as they must by definition, whereas at moderate concentrations they are somewhat less than unity. On... 

The mean activity coefficient of a sparingly soluble salt in any solution, containing other electrolytes, can thus be evaluated provided the solubility product and the mean molality of the ions of the salt in the given solution are known. In order to obtain X, the values of are determined from the experimentally observed solubilities of the sparingly soluble salt in the presence of various amounts of other electrolytes, and the results are extrapolated to infinite dilution (Fig. 27). In the latter case the activity coefficient is unity, in accordance with the chosen standard state, and hence, by equation (39.71), KV"" is equal to the extrapolated value of... 

Values of/x = Ac/A may be calculated from Kohlrausch s measurements of electrical conductivity of hydrochloric acid solutions. /h and fci can be evaluated from the potentiometric measurements on hydrochloric acid solutions performed by Scatchaed. These data are very reliable since the concentration chain was so arranged as to eliminate diffusion potentials. In this way, ScATCHARD determined the mean activity coefficient V/h/ci instead of the individual ion activities. If we assume that in a potassium chloride solution/ = /ci— which is plausible when we recall that both ions have the same structure—and that fci is the same in hydrochloric acid solutions and potassium chloride solutions of the same concentration, then we can calculate/h and fci in hydrochloric acid solutions. Naturally these values are not strictly correct since the effect of the potassium ions on the activity of the chloride ions probably is different from that of the hydrogen ions at the same ionic strength. In the succeeding table are given values of /x, /h, and fci calculated by the above method. 

The activity coefficients of uncharged species were assumed to be unity in the evaluation of the equilibrium constants. The activity coefficients of all monovalent ions were set equal and taken as the mean activity coefficient of hydrochloric or hydrobromic acid, respectively, at the concentration of the hydrogen ions in the equilibrium... 

The treatment of the solubility data in the paper for the determination of the standard enthalpy of dissolution could not be fully understood and the following treatment was resorted to by the evaluator. The data in the temperature interval 283 to 313 K were selected. Approximate activity coefficients were taken from the data for MgS04 in [50HAR/OWE]. A second order polynomial was fitted to these data and mean activity coefficients for CaSe04 in the saturated solutions obtained by interpolation. No attempt was made to correct for the temperature variation of the activity coefficient. 

P. C. Meier, Two-Parameter Debye-Huckel Approximation for the Evaluation of Mean Activity Coefficients of 109 Electrolytes, Anal. Chim. Acta, 136... 

By using Eqs (42)-(47), the values of Eq+, Eqx, E qjXjj the distribution constant m are evaluated. Corrections for the mean activity coefficient in the organic phase were made using the Marshall and Grunwald expression, and the values of m, and y ... 

This is the case with the evaluated mean activity coefficients tabulated by Goldberg (Z5). The activity coefficients were listed to 23.193 roolal and values were given for the parameters of the equation to which the activity coefficients were fit ... 

This evaluation gives values for the osmotic coefficients and mean activity coefficients of seventy-nine uni-univalent electrolytes in aqueous solution at 25 C, with values expressed on the molality scale. The data from the literature were fitted, by statistical procedures, to equations which express the quantities as functions of electrolyte concentration. Literature references are given to fifty-one additional uni-univalent electrolytes. Also see item [159]. 

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... 

The sulfate ion, SO, is an important source of sulfur used in the synthesis of the amino acids cysteine and methionine in plants and bacteria. To estimate the mean activity coefficient for the ions in 0.0010 m Na2S04(aq) at 25 C, we begin by evaluating the ionic strength of the solution from eqn 5.5 ... 

Strong and long-range Coulombic forces acting between ions are primarily responsible for the departures from ideality (the activity coefficients are lowered) and dominate all other contributions. The effect has been evaluated in the Debye-Htickel theory and there exist several equations, which are useful in estimating the mean activity coefficient [68, 69]. The latter is related to the ionic strength of the solution ... 

Meier PC (1982) 2-Parameter Debye-Huckel approximation for the evaluation of mean activity-coefficients of 109 electrolytes. Anal Chim Acta 136 363-368... 

Comparison of the concentrations of either the cation or the anion in the two phases thus has potential for evaluating the polyanion valence provided that estimates of the mean ion activity coefficient (y ) are available. Furthermore, as realized by Svensson [165], expression of the Donnan distribution of small ions in this manner has two advantages in that (i) Eq. 31 applies to each type of small ion in situations where the supporting electrolyte is not restricted to single cationic and anionic species and (ii) multivalence of a small ion is also accommodated. 

Activity coefficients on the molal scale were calculated from Equation 39 by means of a straightforward program containing library sub-routines for evaluation of integrals and modified Bessel functions. 

Potentiometry has found extensive application over the past half-century as a means to evaluate various thermodynamic parameters. Although this is not the major application of the technique today, it still provides one of the most convenient and reliable approaches to the evaluation of thermodynamic quantities. In particular, the activity coefficients of electroactive species can be evaluated directly through the use of the Nemst equation (for species that give a reversible electrochemical response). Thus, if an electrochemical system is used without a junction potential and with a reference electrode that has a well-established potential, then potentiometric measurement of the constituent species at a known concentration provides a direct measure of its activity. This provides a direct means for evaluation of the activity coefficient (assuming that the standard potential is known accurately for the constituent half-reaction). If the standard half-reaction potential is not available, it must be evaluated under conditions where the activity coefficient can be determined by the Debye-Hiickel equation. 

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