Ion pairing and activity coefficients

In high-salinity waters such as seawater, both ion-pairing and activity-coefficient effects (see Chap. 4) increase the concentrations of species limited by the solubility of minerals. For example, in pure water saturated with respect to calcite, the molal solubility product ZmCa x ZmCOf" = 10 whereas in seawater this product equals 10 If the concentration of carbonate is constant, this corresponds to a 250-fold increase in the concentration of dissolved calcium in seawater relative to that in pure water. 

Vadose water from Lower Carboniferous rocks in Kentucky, U.S.A., was analyzed monthly in Mammoth Cave and in the caves and overlying soil at two other caves. Calcite saturation and equilibrium CO2 pressures of water were calculated after correcting for ion pairing and activity coefficients. Soil gas CO2 concentrations were determined directly. 

Activity coefficients in most concentrated solutions reflect deviation from ideal behavior because of (1) the general electric field of the ions, (2) solute-water interactions, and (3) specific ionic interactions (association by ion pair and complex formation). None of the major cations of seawater appears to interact significantly with chloride to form ion pairs hence activity coefficients in these solutions appear to depend primarily on the ionic strength modified by the extensive hydration of ions. Thus synthetic solutions of these chlorides provide reference solutions in obtaining activity coefficients of the cations. The single activity coefficients for free ions in seawater can be obtained from mean activity coefficient data in chloride solutions at the corresponding ionic strength by various ways. 

The Pitzer-equation computations for Figures 3 and 4 are based upon experimentally derived 25°C ion-pair and interaction coefficients taken from the literature. From the extensive prior work validating the theory and parameters, these curves should deviate from experiment by less than 20%. However, as Figures 1-4 show, solubility calculations are very sensitive to variations in activity coefficients and the approximations made in eqs. (l)-(9) limit the accuracy of the solubility curves which can be calculated. When higher-order terms are included, Pitzer s equations accurately oredict solubility in the CaSO -MgSO system up to... 

Here, (A) is the concentration of a substance measured in moles/1 and is the activity coefficient calculated as a function of the overall ionic strength in the solution. For infinitesimal diluted solutions, the activity coefficients assume the value of 1 hence, activity equals concentration. In ocean water, the various monovalent ions, or ion pairs, display activity coefficients somewhere around 0.75 whereas the various divalent ions, or ion pairs, display values around 0.2 (cf. Table 15.2, last column). 

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. 

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... 

SH Considering just acid-base chemistry, not ion pairing and not activity coefficients, use the systematic treatment of equilibrium to find the pH and concentrations of species in 1.00 L of solution containing 0.100 mol ethylenediamine and 0.035 mol HBr. Compare the pH with that found by the methods of Chapter 11. 

Furthermore, in very dilute solutions (1) The ions rarely come close enough together (i.e., to within a distance q) to form ion pairs, and one can consider I or 1 - = 1 (2) activity coefficients tend to unity, i.e., / or / -> 1. 

Activity Coefficients, Bjerrum s Ion Pairs, and Debye s Free Ions... 

In these expressions, the square brackets represent the molar concentrations of the species indicated, and y is the activity coefficient of a Z valent species. In order to calculate the free ionic concentrations in these expressions, it is necessary to take into account ion-pair and complex formation. The equilibria in pure calcium phosphate solutions are -... 

Thirdly, another corollary of the first limitation, is the inconsistency and inadequacy of activity coefficient equations. Some models use the extended Delbye-Huckel equation (EDH), others the extended Debye-Huckel with an additional linear term (B-dot, 78, 79) and others the Davies equation (some with the constant 0.2 and some with 0.3, M). The activity coefficients given in Table VIII for seawater show fair agreement because seawater ionic strength is not far from the range of applicability of the equations. However, the accumulation of errors from the consideration of several ions and complexes could lead to serious discrepancies. Another related problem is the calculation of activity coefficients for neutral complexes. Very little reliable information is available on the activity of neutral ion pairs and since these often comprise the dominant species in aqueous systems their activity coefficients can be an important source of uncertainty. 

The bare proton has an exceedingly small diameter compared with other cations, and hence has a high polarising ability, and readily forms a bond with an atom possessing a lone pair of electrons. In aqueous solution the proton exists as the H30+ ion. The existence of the H30+ ion in the gas phase has been shown by mass spectrometry [4], and its existence in crystalline nitric acid has been shown by NMR [5], Its existence in aqueous acid solution may be inferred from a comparison of the thermodynamic properties of HC1 and LiCl [6]. The heat of hydration of HC1 is 136 kcal mole"1 greater than that of LiCl, showing that a strong chemical bond is formed between the proton and the solvent, whereas the molar heat capacity, molar volume and activity coefficients are similar,... 

On account of the low dielectric constants of aprotic solvents, considerable proportions of ion-pairs and triple ions are present, but spectro-metric methods are unable to distinguish between these and single ions the determinations of the amounts of free ionSy which are required by the calculations, will thus be in error. The activity coefficient factor, neglected in the above treatment, will also be of appreciable magnitude, but this can be diminished if the base is a negatively charged ion B ... 

For the specific case of a standard for fluoride ion activity KF rather than NaF has been suggested. KF is a better choice because ion pairing is much less. Further, the average hydration number of the fluoride ion is almost the same as that for potassium ion, so that activity coefficients of the two ions are similar. Suggested reference activity values (pM or pAJ for use in the operational definitions for ion-activity measurements [Equations (13-26) or (13-27)] are shown in Table 13-2. For the case of fluoride ion, measurements of its activity in NaF-NaCl mixtures up to 1 m and KF-KX mixtures up to 4 m yielded the same values as pure NaF or KF at the same ionic strength. 

Aqueous speciation. The distribution of dissolved components among free ions, ion pairs, and complexes. For example, dissolved iron in acid mine drainage (AMD) can be present as Fe( q) (free ferrous iron), FeS04(aq> (ion pair), Fef q) (free ferric iron), Fe(OH)(j q), and FeS04(aq) species. These species are present in a single phase, aqueous solution. Aqueous speciation is not uniquely defined but depends on the theoretical formulation of mass action equilibria and activity coefficients, i.e. it is model dependent. Some aqueous speciation can be determined analytically but operational definitions and assumptions are still unavoidable. 

One approach to determine the reliability of geochemical codes is to take well-defined input data and compare the output from several different codes. For comparison of speciation results, Nordstrom et al. (1979) compiled a seawater test case and a river-water test case, i.e., seawater and river-water analyses that were used as input to 14 different codes. TTie results were compared and contrasted, demonstrating that the thermodynamic databases, the number of ion pairs and complexes, the form of the activity coefficients, the assumptions made for redox species, and the assumptions made for equilibrium solubilities of mineral phases were prominent factors in the results. Additional arsenic, selenium, and uranium redox test cases were designed for testing of... 

The first step in the MSM is to measure the 7 M Xt of a KCl solution whose concentration is adjusted to he identical to the I of the electrolyte solution for which the activity coefficients are desired. For seawater a KCl solution of Ia 0.7 would he used. One begins with KCl because the K+ and Cl ions interact almost exclusively in an electrostatic manner, without formation of interfering ion pairs and other complexes. Next one assumes that 7 m X6 measured for any solution is the geometric mean of the individual activities of the component ions. The general formula for the geometric mean is... 

---