Electrolyte activity calculation

Once the composition of the aqueous solution phase has been determined, the activity of an electrolyte having the same chemical formula as the assumed precipitate can be calculated (11,12). This calculation may utilize either mean ionic activity coefficients and total concentrations of the ions in the electrolyte, or single-ion activity coefficients and free-species concentrations of the ions in the electrolyte (11). If the latter approach is used, the computed electrolyte activity is termed an ion-activity product (12). Regardless of which approach is adopted, the calculated electrolyte activity is compared to the solubility product constant of the assumed precipitate as a test for the existence of the solid phase. If the calculated ion-activity product is smaller than the candidate solubility product constant, the corresponding solid phase is concluded not to have formed in the time period of the solubility measurements. Ihis judgment must be tempered, of course, in light of the precision with which both electrolyte activities and solubility product constants can be determined (12). 

Edwards et al. (6) made the assumption that was equal to 4>pure a at the same pressure and temperature. Further theyused the virial equation, truncated after the second term to estimate pUre a These assumptions are satisfactory when the total pressure is low or when the mole fraction of the solute in the vapor phase is near unity. For the water, the assumption was made that <(>w, , aw and the exponential term were unity. These assumptions are valid when the solution consists mostly of water and the total pressure is low. The activity coefficient of the electrolyte was calculated using the extended Debye-Hiickel theory ... 

In applying this equation to multi-solute systems, the ionic concentrations are of sufficient magnitude that molecule-ion and ion-ion interactions must be considered. Edwards et al. (6) used a method proposed by Bromley (J7) for the estimation of the B parameters. The model was found to be useful for the calculation of multi-solute equilibria in the NH3+H5S+H2O and NH3+CO2+H2O systems. However, because of the assumptions regarding the activity of the water and the use of only two-body interaction parameters, the model is suitable only up to molecular concentrations of about 2 molal. As well the temperature was restricted to the range 0° to 100 oc because of the equations used for the Henry1s constants and the dissociation constants. In a later study, Edwards et al. (8) extended the correlation to higher concentrations (up to 10 - 20 molal) and higher temperatures (0° to 170 °C). In this work the activity coefficients of the electrolytes were calculated from an expression due to Pitzer (9) ... 

The standard state for the mean ionic activity coefficient is Henry s constant H., f is the standard-state fugacity for the activity coefficient f- and x. is the mole fraction of electrolyte i calculated as though thi electrolytes did not dissociate in solution. The activity coefficient f is normalized such that it becomes unity at some mole fraction xt. For NaCl, xi is conveniently taken as the saturation point. Thus r is unity at 25°C for the saturation molality of 6.05. The activity coefficient of HC1 is normalized to be unity at an HC1 molality of 10.0 for all temperatures. These standard states have been chosen to be close to conditions of interest in phase equilibria. 

A useful concept that is used when the activities of electrolytes are calculated is that of the ionic strength of the solution. This is defined (on the molar scale) as ... 

The parameters can be evaluated from data on mixtures of electrolytes by calculating the differences between the experimental value of and the value calculated with the appropriate values for all pure electrolyte terms and terms but zero values for and j/ terms. For the activity coefficient of MX in a MX-NX mixture one has Eq. (6.42) and equivalent expressions for other cases. 

Here t is the ionic transport number, a is the electrolyte activity, and the subscripts 1 and 2 refer to the left and right sides of the junction. For Omxi = mx2. Ej(i)=0. If the experimental (actual) variations in component (i), obtained by changing the ratio C /c2, are plotted against the values calculated by Eq. (6.16), lin-... 

The activity coefficients of the nonelectrolyte and electrolyte were calculated by means of Equations 14 and 15 for chosen concentrations, and are listed in Tables V-VIII. 

Figure 18.4 Comparison of activity coefficients at T = 298.15 K for three different electrolytes as calculated from Pitzer s equations (solid lines) with the experimental results (symbols).

Plot the values for the activity coefficient of the electrolyte as calculated in Problem 3 against the ionic strength. Then see what degree of match you can obtain from the Debye-Htickel law (one-parameter equation). Do a similar calculation with the equation in the text which brings in the distance of closest approach (a) and allows for the removal of water from the solution (two-parameter equation). Describe which values ofa,andn (the hydration number) fit best. Discuss the degree to which the values you had to use were physically sensible. 

Solute and Solvent Activity Calculations. For the purposes of this study, the derivations necessary to the calculation of the solute and solvent activities will begin with the equation for the prediction of the excess free energy of a single electrolyte solution based on the work of Friedman (9). 

A 0.1 m solution of MgCl2 in water has a density of 1.0047 gmL at 25°C. The mean ionic activity coefficient on the molal scale is 0.528. Calculate the mean activity and electrolyte activity on this scale. Repeat the calculations for the molarity scale. 

Use the extended Debye-Hiickel theory to estimate the mean ionic activity coefficient for Na2S04 at concentrations of 0.01 and 0.1 M and 25°C assuming an ion size parameter of 400 pm. Also calculate the mean electrolyte activity and the electrolyte activity. 

Values of electrolyte activities, as measured by osmotic pressures, freezing point depression, and other experimental methods are in the literature (References 5 and 6, for example) or one can calculate activity coefficients based on models of molecular-level interactions between ions in electrolyte solutions. For illustrative purposes, mean molal activity coefficients for various salts at different aqueous molal (mj concentrations at 25°C are listed in Table 26.3 [7]. 

Pitzer s formulation offers a satisfactory and desirable way to model strong electrolyte activity coefficients in concentrated and complex mixtures. When sufficient experimental data are available, one can make calculations which are considerably more accurate than those presented in this paper. Attaining high accuracy requires not only experimentally-based parameters but also that one employ third virial coefficients and additional mixing terms and include explicit temperature dependencies for the various parameters. 

Solubility of a Pure Component Strong Electrolyte. The calculation of the solubility of a pure component solid in solution requires that the mean ionic activity coefficient be known along with a thermodynamic solubility product (a solubility product based on activity). Thermodynamic solubility products can be calculated from standard state Gibbs free energy of formation data. If, for example, we wished to calculate the solubility of KCI in water at 25 °C,... 

Some of the electrolytes to be tested precipitate in hydrated forms at 25 C. It is therefore necessary to calculate the water activities in addition to the electrolyte activity coefficients in order to model the solutions. The water activity may be calculated using an equation presented specifically for it s calculation, or from the results of an osmotic coefficient equation. 

Water activity in foods is usually determined from knowledge of the equUib rium relative humidity or can be measured using various hygrometers. In some foods it can be calculated from various theoretical and empirical models that take into account the food chemical composition, the content of electrolytes such as sodium chloride and non-electrolytes such as saccharose, respectively. Equations, varying in their levels of compUcation, are numerous, but their use is limited to certain commodities. One of the simple empirical equations for water activity calculation in jams has the form = 1/(1 + 0.21n), where... 

The above result states that at high concentrations the rational activity coefficient exhibits quadratic concentration dependence rather than the linear one predicted by Bahe s purely electrostatic pseudolattice treatment. As can be seen in Table I, this dependence can be proved to be valid for several electrolytes (Varela et al., 1997), where fn/+ + Ac — Be is fitted to Dc. As can be seen in the table, Varela et al. obtained that, for several 1 1 and 1 2 electrolytes, the calculated exponent is x=2, within the limits of experimental uncertainty for all the analyzed data. 

The holistic thermodynamic approach based on material (charge, concentration and electron) balances is a firm and valuable tool for a choice of the best a priori conditions of chemical analyses performed in electrolytic systems. Such an approach has been already presented in a series of papers issued in recent years, see [1-4] and references cited therein. In this communication, the approach will be exemplified with electrolytic systems, with special emphasis put on the complex systems where all particular types (acid-base, redox, complexation and precipitation) of chemical equilibria occur in parallel and/or sequentially. All attainable physicochemical knowledge can be involved in calculations and none simplifying assumptions are needed. All analytical prescriptions can be followed. The approach enables all possible (from thermodynamic viewpoint) reactions to be included and all effects resulting from activation barrier(s) and incomplete set of equilibrium data presumed can be tested. The problems involved are presented on some examples of analytical systems considered lately, concerning potentiometric titrations in complex titrand + titrant systems. All calculations were done with use of iterative computer programs MATLAB and DELPHI. 

Reliable pH data and activities of ions in strong electrolytes are not readily available. For this reason calculation of corrosion rate has been made using weight-loss data (of which a great deal is available in the literature) and concentration of the chemical in solution, expressed as a percentage on a weight of chemical/volume of solution basis. Because the concentration instead of the activity has been used, the equations are empirical nevertheless useful predictions of corrosion rate may be made using the equations. 

Most of the methods we have described so far give the activity of the solvent. Often the activity of the solute is of equal or greater importance. This is especially true of electrolyte solutions where the activity of the ionic solute is of primary interest, and in Chapter 9, we will describe methods that employ electrochemical cells to obtain ionic activities directly. We will conclude this chapter with a discussion of methods based on the Gibbs-Duhem equation that allow one to calculate activities of one component if the activities of the other are known as a function of composition. 

Equations (7.35) and (7.36) can be used to calculate the activity coefficients of individual ions. However, as we discussed in Chapter 6, 7+ and 7- cannot be measured individually. Instead, 7 , the mean ionic activity coefficient for the electrolyte, M +AV-, given by... 

According to Vitanov et a/.,61,151 C,- varies in the order Ag(100) < Ag(lll), i.e., in the reverse order with respect to that of Valette and Hamelin.24 63 67 150 383-390 The order of electrolytically grown planes clashes with the results of quantum-chemical calculations,436 439 as well as with the results of the jellium/hard sphere model for the metal/electro-lyte interface.428 429 435 A comparison of C, values for quasi-perfect Ag planes with the data of real Ag planes shows that for quasi-perfect Ag planes, the values of Cf 0 are remarkably higher than those for real Ag planes. A definite difference between real and quasi-perfect Ag electrodes may be the higher number of defects expected for a real Ag crystal. 15 32 i25 401407 10-416-422 since the defects seem to be the sites of stronger adsorption, one would expect that quasi-perfect surfaces would have a smaller surface activity toward H20 molecules and so lower Cf"0 values. The influence of the surface defects on H20 adsorption at Ag from a gas phase has been demonstrated by Klaua and Madey.445... 

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