Activity Coefficient Corrections

The significant influence of the charge of an ion and of the ionic strength upon activity coefficient values is obvious from Equations 3-6 to 3-8. However, there are two other factors that affect the values of activity coefficients that also merit our interest, namely temperature and nature of solvent. In order to understand these effects, let us return to Equation 3-8 and observe that the parameter A is inversely proportional to the product of the dielectric constant, D, and the absolute temperature T raised to the 3/2 power. 

The parameter A is not too sensitive to temperature changes. A change in temperature of 5°C from 25 C will cause a change in A of less than 1%. 

Changing solvents would give rise to much more serious changes in activity coefficients since the resulting change in dielectric constant is relatively large. In a 50% v/v mixture of ethanol and water, the dielectric constant has a value of 49. Hence, the parameter A in this mixture is about twice its value in water. 

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Chidambarams, S., Narsimham, G. Generalized Chart Gives Activity Coefficient Correction Factors, Chemical Engineering, Nov. 23, 1964, p. 135. 

Very few generalized computer-based techniques for calculating chemical equilibria in electrolyte systems have been reported. Crerar (47) describes a method for calculating multicomponent equilibria based on equilibrium constants and activity coefficients estimated from the Debye Huckel equation. It is not clear, however, if this technique has beep applied in general to the solubility of minerals and solids. A second generalized approach has been developed by OIL Systems, Inc. (48). It also operates on specified equilibrium constants and incorporates activity coefficient corrections for ions, non-electrolytes and water. This technique has been applied to a variety of electrolyte equilibrium problems including vapor-liquid equilibria and solubility of solids. 

Bianchi and Longhi (53) Potential -pH diagram (25°C) for copper in sea water activity coefficient corrections included. 

K. A solution with an ionic strength of 0.10 M containing 0.010 0 M phenylhydrazine has a pH of 8.13. Using activity coefficients correctly, find pKa for the phenylhydrazinium ion found in phenylhydrazine hydrochloride. Assume that yBH< = 0.80. 

Experimental measurements show that molecules in highly compressed gases or highly concentrated solutions, especially if electrically charged, abnormally affect each other. In such cases the true activity or effective concentration may be greater or less than the measured concentration. Therefore, when the molecules involved in equilibrium are relatively close together, the concentration should be multiplied by an activity coefficient, which is determined experimentally. At moderate pressure and solutions, the activity coefficient for nonionic compounds is close to unity, indicating little in the way of molecular interactions. In any event, the activity coefficient correction will not be made in the problems in this book. 

The consensus of experts is that pH cannot be measured more accurately than 0.05 in natural waters. Two important limitations on accuracy arc activity coefficient corrections and liquid junction potentials. 

Calculate pH versus -log[H+]e at 298 K for 0 < Ief < 0.5 mol dm 3 with the two derived relationships and estimate the inaccuracy of pH that could result from activity coefficient corrections. ... 

If the activity coefficient correction is not considered, the pH of the solution is given by ... 

For example, in diffusion between solutions that have a large concentration difference, such as 0.1 to 0.01 mol dm"- , a rough calculation suggests that the activity-coefficient correction is on the order of a few... 

Electron and hole concentrations follow a Boltzmann distribution, i.e., activity coefficient corrections can be neglected. 

Liquid-liquid equilibria are treated essentially in the same way as nonideal vapor-liquid equilibria with activity-coefficient corrections in both phases. For liquid-solid equilibria, engineers rdy almost entirely on recorded experimental data, as prediction of the liquid-phase composition is quite difficult. Refer to Prausnitz et al, for more information. 

Table 19-1 shows that cell potentials calculated without activity coefficient corrections exhibit significant error. It is also clear from the data in the fifth column of the table that potentials computed with activities agree reasonably well with experiment. 

Ignoring activity-coefficient corrections (a very approximate approach for seawater), and assuming that the total concentrations of sulfate and chloride given above are so large relative to that of the lead that they can be assumed constant, derive an equation that describes the total molal concentration of lead in the seawater,... 

Ratio of one liquid phase to total liquid Relative volatility Activity coefficient Correction factor Eugacity coefficient... 

A major uncertainty in log, K° (V.24) arises from the activity coefficient correction. This correction has been applied under the initial assumption, but with more recent data from Harned and Robinson [41HAR/ROB]. An estimate of the activity coefficient was also made with the SIT approach using s(H, ClOj) = 0.12 kg-moP from [92GRE/FUG], and e(H, 1) = 0.18 and s(K, I ) = 0.014 kg-mol calculated from data in [59ROB/STO]. The results of the calculations were ... 

The formation of Hg(SeCN)4 is well established by the potentiometric work of Toropova [56TOR], while her experimental data pertaining to the formation and the formation constant of Hg(SeCN)3 only comprise a few points. In their polarographic work Murayama and Takayanagi [72MUR/TAK] studied the anodic mercury wave in the presence of 0.001 to 0.003 M SeCN . The electrode process was assumed to comprise the charge transfer Hg(l) Hg + 2e combined with the formation of Hg(SeCN)2(aq) and Hg(SeCN)3. No primary data are provided and the evaluation procedure is rather involved, which makes the assessment difficult. The results are mixed equilibrium constants, since an activity coefficient correction was applied to the Hg ion. The following complexes are thus proposed to prevail in the Hg -SeCN system ... 

Parker, Tice, and Thomason [97PAR/T1C] measured the Ca activity in solutions containing total Ca concentrations in the range 20 x 10 to 200 x 10 M and the selenate concentration 0.004, 0.01, or 0.03 M with a carefully calibrated ion-selective Ca electrode. Activity coefficient corrections were made by Davies equation. The equilibrium constant of the reaction ... 

The activity product was calculated with the accepted protonation constants of the selenite ion using the SIT approach for the activity coefficient correction. The value of Ag/AgjSeOj obtained from m was (309.5 18.9) mV with a systematic trend in the value with m. The value from iv was -(137.4 + 3.5) mV with no significant trend. Hence a reversal of the sign of the potentials from cell (I) is indicated. The values were calculated with qqh = 699.4 mV. With ° = 799.1 mV the corresponding solu-... 

The primary solubility data and the calculation of the solubility products, defined in the usual way, are presented. This presentation contains some unexpected results. The total solubility of the metal ion and selenite are approximately equal in water and in the inert salt solutions for the magnesium and manganese selenites. This is the expected result for a simple dissolution reaction. For calcium selenite, the metal ion concentration was about 100 times greater than the total selenite concentration whereas for zinc selenite the opposite was found. There is no comment in the paper on these results, which contradict the equilibrium reactions used in the paper to define the reported solubility products for calcium and zinc selenite. The review also noted that the calculation of the magnesium and selenite activities from the total concentrations introduces activity coefficients between 0.1 to 0.01 at moderate ionic strengths. Thus the values of these coefficients appear unreasonably small. On the whole, the activity coefficient corrections introduced appear to vary in an erratic way between the various systems studied. 

The way in which the activity coefficient corrections are performed in this review according to the specific ion interaction theory is illustrated below for a general case of a complex formation reaction. Charges are omitted for brevity. 

ACTIVITY COEFFICIENT CORRECTIONS. To eliminate uncertainties arising from activity constant variations, it is common practice to keep activity coefficients constant by use of a "background electrolyte or "constant ionic atmosphere" (e.g., 0.10 M NaC104). Since the glass electrode measu es (for practical purposes) hydrogen ion activity, i.e., pHmeas - -log H+] = -log[H+]y+, it is necessary to convert activity to concentration in the calculations that follow. The relationship of equation 22-4 may be used, where the activity correction C = log Y+-... 

The pH of a solution in equilibrium with CaC03 and atmospheric CO2 is 8.3. Equation 7.18 yields a value of pH 8.5 because activity coefficient corrections are ignored and because of rounding-off errors in the exponents of the equilibrium constants. 

Unfortunately, few of the published studies of extraction equilibria heve provided complete quantitative models that are useful for extrapolation of data or for predicting multiple metal distribution equilibria from single metal data. The chemical-reaction equilibrium formulation provides a framework for constructing such models. One of the drawbacks of purely empirical correlations of distribution coefficients is that pH has often been chosen as an independent variable. Such a choice is suggested by the form of Pigs. 8-3-5 and 8.3-8. Although pH is readily measured and contmlled on a laboratory scale, it is really a dependent variable, which is detenmined by mass belances and simultaneous reaction equilibria. An appropriate phare-equilibrium model should be able to predict equilibrium pH, at least within a moderate activity coefficient correction, concurrently with other species concemrations. 

We see from this illustration that the osmotic pressure of this sodium chloride solution, and therefore blood, is surprising high, above 7 bar, even though the solution is more than 99 percent water. Also, the activity coefficient of water is almost 1 however, in the case of the osmotic pressure, the activity coefficient correction should not be neglected. ... 

The data were included in the overall fit of hydrolysis relevant data (see Appendix D). SIT-based activity coefficient correction were applied to each data point. In this context, it turns out that solution concentrations are not at all controlled by monomeric species, but by the trimeric species Zrj(011)9. The fit results in a solubility constant logiQ K°q = - (4.23 + 0.06) (2ct). The overall fit also showed that nitrate complexes were negligible in the entire range of the experimental data. 

The work of the authors is a review of hydrolysis data and includes activity coefficient corrections, which are not directly compatible with the NBA standard. The dependency of stability constants of aqueous species and solid phases P replaced by K) on ionic strength is given by [76BAE/MES] as ... 

The importance of activity coefficients is evident in Figure 17.6, which shows measured y versus molal concentration for selected salts in 350°C hydrothermal solutions. Activity coefficient corrections (that is, correction to the concentration to get the activity) of one to two orders of magnitude such as these are not at all uncommon in aqueous systems. 

If activity coefficient corrections are required, use the concentrations calculated in step 5 to estimate activity coefficients. Repeat step 5 using these new activity coefficients. Iterate on steps 5 and 6 until successive concentrations and activities stop changing within some acceptable limit. 

Activity coefficient corrections are treated just as with the rote manual method already discussed. The first time through, all activity coefficients could be set to 1.0 (or some reasonable estimate). Concentrations of species calculated this way are then used to estimate a better set of activity coefficients in each successive iteration. 

Here we have represented concentration by molality, m, (instead of number of moles, rii) and include an activity coefficient correction, 7. As with equilibrium constant-based equilibrium calculations, the activity coefficients can be computed from successive estimates of the concentrations. 

As input, this model requires the standard state chemical potentials (or free energies) AfG° of all species and phases, and the bulk composition or total number of moles of each component, Bg. A specific method must always be selected to calculate activity coefficient corrections. 

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