Activity coefficient, variation with

Finally, the predicted activity coefficient behavior for nonionic—surface site complexes will be examined. In Fig. 15 the activity coefficient variation with the... 

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... 

Figure 5.13. Variation of the activity coefficient 7+ with Vmol/L (25 °C). The solid curves are experimental values of 7+. (From L. Pauling, General Chemistry, Dover, New York, 1970, with permission from Dover.)...

The activity coefficient varies with concentration. This variation is rather complex the activity coefficient of a particular ion being dependent upon the concentration of all ionic species present in the solution. As a measure of the latter, Lewis and Randall (1921) introduced the quantity called ionic strength, /, and defined it as the half sum of the products of the concentration of each ion multiplied by the square of its charge. With mathematical symbols this can be expressed as... 

Empirically, the Setchenov equation [37,39] has been found to express the variation of the neutral solute activity coefficient (7 ) with the electrolyte concentration (Ce), at least for low electrolyte concentrations (a few tens molar) ... 

We find that, as a result of changes in activity coefficients, the value of logic should decrease by 0.198, corresponding to a decrease in D by a factor of 1.58. The experimental decrease for the chloride system from Table 1 in [1975RAG/RAM] by a factor of 1.76 is in reasonable agreement with the changes due to activity coefficient variations. However, we cannot exclude the formation of chloride (and bromide) complexes, but they are certainly smaller than the values obtained without taking ionic medium variations into account. 

Figure A2.4.5. Theoretical variation of the activity coefficient with Tfroin equation (A2.4.61) and experimental results for 1-1 electrolytes at 25°C. From [7],...

Standard potentials Ee are evaluated with full regard to activity effects and with all ions present in simple form they are really limiting or ideal values and are rarely observed in a potentiometric measurement. In practice, the solutions may be quite concentrated and frequently contain other electrolytes under these conditions the activities of the pertinent species are much smaller than the concentrations, and consequently the use of the latter may lead to unreliable conclusions. Also, the actual active species present (see example below) may differ from those to which the ideal standard potentials apply. For these reasons formal potentials have been proposed to supplement standard potentials. The formal potential is the potential observed experimentally in a solution containing one mole each of the oxidised and reduced substances together with other specified substances at specified concentrations. It is found that formal potentials vary appreciably, for example, with the nature and concentration of the acid that is present. The formal potential incorporates in one value the effects resulting from variation of activity coefficients with ionic strength, acid-base dissociation, complexation, liquid-junction potentials, etc., and thus has a real practical value. Formal potentials do not have the theoretical significance of standard potentials, but they are observed values in actual potentiometric measurements. In dilute solutions they usually obey the Nernst equation fairly closely in the form ... 

In Section I, we indicated that significant progress in understanding high-pressure thermodynamics of mixtures requires a quantitative description of the variation of fugacity with pressure as given by Eq. (3). To obtain the effect of pressure on activity coefficient we substitute as follows ... 

For a dilute solution at high pressure, the variation of activity coefficient with pressure cannot be neglected. But when x2 is small, it is often a good approximation to assume, as above, that the activity coefficient is not significantly affected by composition. If we also assume that v2 the partial molar volume of the solute, is independent of both pressure and composition... 

In the HMW model, in contrast, Ca++ and SO4 are the only calcium or sulfate-bearing species considered. The species maintain equal concentration, as required by electroneutrality, and mirror the solubility curve in Figure 8.6. Unlike the B-dot model, the species activities follow trends dissimilar to their concentrations. The Ca++ activity rises sharply while that of SO4 decreases. In this case, variation in gypsum solubility arises not from the formation of ion pairs, but from changes in the activity coefficients for Ca++ and SO4 as well as in the water activity. The latter value, according to the model, decreases with NaCl concentration from one to about 0.7. 

If we are dealing with major elements, partition coefficients Dt may be expected to vary with many parameters, including temperature or liquid chemistry. For some elemental pairs and particularly for isotopes for which activity coefficients are correlated, there is a better chance, however, that the ratio of two partition coefficients Dn and Di2 shows lesser variations. We therefore subtract the distillation equation (1.5.3) for element or isotope il from that for i2 as... 

When the Krichevsky-Kasarnowsky equation fails it may be because of either changing activity coefficient of the solute gas with composition, changing partial molal volume of the gas with pressure, or both. The Krichevsky-Ilinskaya equation takes into account the variation in the activity coefficient of the solute gas with mole fraction by means of a two-suffix Margules equation. 

Figure 19.10. Variation of solubility of AgCl with ionic strength, from which activity coefficients can be calculated. Data from Ref. 3.

If the analyte cannot be pretreated in the way described above, methods must be found for the use of (3.1.5) or (3.1.7) even when activity coefficients and the liquid-junction potential vary with variations in the test solution composition. 

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