Activity coefficient complex ions

The solubility product principle can only be strictly applied to equilibrium conditions, although it has often been used to explain such precipitations as those encountered in qualitative analysis by the traditional wet-test methods. However, these sudden precipitations do not take place under anything like equilibrium conditions and the fact that reasonably successful predictions can usually be made is mainly due to the enormous excess ionic concentrations (supersaturations) generated compared with those required by the corresponding solubility products. Errors of magnitude of 10 —10 per cent have been estimated (Lewin, 1960) for such calculations and these clearly swamp other variations such as neglect of solute activity coefficients, complex ion formation, etc. 

In spite of uncertainties with respect to the assessment of ion activity coefficients in ion-exchanger phases, it has been experimentally demonstrated that use of distribution measurements in Eq. (20) promotes valid identification of the monomeric complex species absorbed by the anion... 

The formation of methoxide complexes was studied by measuring the pH in titrations, with methylate, of the chlorides and methylates of metals, in absolute methanol. The pH determinations were carried out with Pt/H or Pd/Hj electrodes, which were found to respond rapidly, reproducibly and strictly proportional to the logarithms of the concentrations of solvated protons. The problem of changing activity coefficients and ion-pair formation were... 

In Fig. 13, calculated activity coefficients for solute cations in Debye— Hfrekel solutions (lines a and b) for eation-surface site complexes at the primitive interface (lines c, d, e, g, h, and k) are plotted. One can see that activity coefficients for ions in solution and at interfaces are of a similar magnitude. For the activity coefficient of the surface site ions, mostly negative values for the mean surface site electrostatic... 

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 ... 

Note that a number of complicating factors have been left out for clarity For instance, in the EMF equation, activities instead of concentrations should be used. Activities are related to concentrations by a multiplicative activity coefficient that itself is sensitive to the concentrations of all ions in the solution. The reference electrode necessary to close the circuit also generates a (diffusion) potential that is a complex function of activities and ion mobilities. Furthermore, the slope S of the electrode function is an experimentally determined parameter subject to error. The essential point, though, is that the DVM-clipped voltages appear in the exponent and that cheap equipment extracts a heavy price in terms of accuracy and precision (viz. quantization noise such an instrument typically displays the result in a 1 mV, 0.1 mV, 0.01 mV, or 0.001 mV format a two-decimal instrument clips a 345.678. .. mV result to 345.67 mV, that is it does not round up ... 78 to ... 8 ). 

In the virial methods, therefore, the activity coefficients account implicitly for the reduction in the free ion s activity due to the formation of whatever ion pairs and complex species are not included in the formulation. As such, they describe not only the factors traditionally accounted for by activity coefficient models, such as the effects of electrostatic interaction and ion hydration, but also the distribution of species in solution. There is no provision in the method for separating the traditional part of the coefficients from the portion attributable to speciation. For this reason, the coefficients differ (even in the absence of error) in meaning and value from activity coefficients given by other methods. It might be more accurate and less confusing to refer to the virial methods as activity models rather than as activity coefficient models. 

The activities of the free ions remain roughly constant with NaCl concentration, and their concentrations increase only moderately, reflecting the decrease in the B-dot activity coefficients with increasing ionic strength (Fig. 8.3). Formation of the complex species CaCl+ and NaSOj drives the general increase in gypsum solubility with NaCl concentration predicted by the B-dot model. 

The triple layer model has been described in detail elsewhere (11, 16, 17) however, the model as reported here has been slightly modified from the original versions (11, 15) in two ways (i) metal ions are allowed to form surface complexes at either the o- or 8-plane insted of at the 8-plane only, and (ii) the thermodynamic basis of the TLM has been modified leading to a different relationship between activity coefficients and interfacial potentials. The implementation and basis for these modifications are described below. 

For applications where the ionic strength is as high as 6 M, the ion activity coefficients can be calculated using expressions developed by Bromley (4 ). These expressions retain the first term of equation 9 and additional terms are added, to improve the fit. The expressions are much more complex than equation 9 and require the molalities of the dissolved species to calculate the ion activity coefficients. If all of the molalities of dissolved species are used to calculate the ion activity coefficients, then the expressions are quite unwieldy. However, for the applications discussed in this paper many of the dissolved species are of low concentration and only the major dissolved species need be considered in the calculation of ion activity coefficients. For lime or limestone applications with a high chloride coal and a tight water balance, calcium chloride is the dominant dissolved specie. For this situation Kerr (5) has presented these expressions for the calculation of ion activity coefficients. 

The statistical thermodynamic approach of Pitzer (14), involving specific interaction terms on the basis of the kinetic core effect, has provided coefficients which are a function of the ionic strength. The coefficients, as the stoichiometric association constants in our ion-pairing model, are obtained empirically in simple solutions and are then used to predict the activity coefficients in complex solutions. The Pitzer approach uses, however, a first term akin to the Debye-Huckel one to represent nonspecific effects at all concentrations. This weakens somewhat its theoretical foundation. 

It is to be expected that curves of this kind show irregularities when the complexity of the system and the drastic effect certain ions exert on activity coefficients are considered. 

Despite the additional complexity, all the equations in Table 5.3 are functionally equivalent. That is, the activity coefficients approach a value of 1 as the ionic strength of the solution is decreased to 0 m. Thus, in dilute solutions, w,. In other words, the effective concentration of an ion decreases with increasing ionic strength. In contrast, the activity coefficients of uncharged solutes can be greater than 1 in solutions of high ionic strength, such as seawater. 

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... 

Recall from transition state theory that the rate of a reaction depends on kg (the catalytic rate constant at infinite dilution in the given solvent), the activity of the reactants, and the activity of the activated complex. If one or more of the reactants is a charged species, then the activity coefficient of any ion can be expressed in terms of the Debye-Htickel theory. The latter treats the behavior of dilute solutions of ions in terms of electrical charge, the distance of closest approach of another ion, ionic strength, absolute temperature, as well as other constants that are characteristic of each solvent. If any other factor alters the effect of ionic strength on reaction rates, then one must look beyond Debye-Hiickel theory for an appropriate treatment. 

The level of impurity uptake can be considered to depend on the thermodynamics of the system as well as on the kinetics of crystal growth and incorporation of units in the growing crystal. The kinetics are mainly affected by the residence time which determines the supersaturation, by the stoichiometry (calcium over sulfate concentration ratio) and by growth retarding impurities. The thermodynamics are related to activity coefficients in the solution and the solid phase, complexation constants, solubility products and dimensions of the foreign ions compared to those of the ions of the host lattice [2,3,4]. 

The methods described above are appropriate for simple ions, but not for the calculation of the activity coefficients of more complex compounds such as zwitterions, i.e., those which bear more than one functional group, have a low molecular weight, which is arbitrarily put at less than 500, and are approximately spherical in shape so that both the quasi-spherical assumption used in the van der Waals integral and the present definition of cavity area are satisfied. Many substances of interest... 

The hydrogen ion in protophobic aprotic solvents is very reactive. For example, judging from the values of transfer activity coefficient, H+ in AN is 10s times more reactive than in water. Thus, if basic substances are added to the solution in AN, they easily combine with H+. Table 3.6 shows the complex formation con-... 

The circular dichroic spectrum of cobalt alkaline phosphatase (Fig. 16) shows more clearly the complexity of the visible absorption. Although it can not be ruled out that the spectrum of this Co (I I) enzyme represents two slightly different Co(II) sites, there are striking similarities with Co(II) carbonic anhydrase, which has only one metal-binding site. At high pH, cobalt carbonic anhydrase and cobalt alkaline phosphatase have several spectral features in common, and both may have a similar kind of irregular coordination. It should be noted, however, that the absorption coefficient for Co(II) alkaline phosphatase per equivalent of activity-linked metal ion is only half of the value for Co(II) carbonic anhydrase. 

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