Aqueous solutions activity coefficients

Using the experimental solution compositions (Table IV) and the calculated aqueous solution activity coefficient ratio Ygr-/Y( - (Table VI), Figure 4 shows the slopes of log K... 

Many additional consistency tests can be derived from phase equiUbrium constraints. From thermodynamics, the activity coefficient is known to be the fundamental basis of many properties and parameters of engineering interest. Therefore, data for such quantities as Henry s constant, octanol—water partition coefficient, aqueous solubiUty, and solubiUty of water in chemicals are related to solution activity coefficients and other properties through fundamental equiUbrium relationships (10,23,24). Accurate, consistent data should be expected to satisfy these and other thermodynamic requirements. Furthermore, equiUbrium models may permit a missing property value to be calculated from those values that are known (2). 

The clay ion-exchange model assumes that the interactions of the various cations in any one clay type can be generalized and that the amount of exchange will be determined by the empirically determined cation-exchange capacity (CEC) of the clays in the injection zone. The aqueous-phase activity coefficients of the cations can be determined from a distribution-of-species code. The clay-phase activity coefficients are derived by assuming that the clay phase behaves as a regular solution and by applying conventional solution theory to the experimental equilibrium data in the literature.1 2 3... 

The most important factor in determining KQW is the aqueous-phase activity coefficient (aqueous solubility) of the organic solute. The observed partition coefficients are less than the ideal partition coefficients (K w) as result from 1) the incompatibility of the solute in water-saturated octanol and, to a lesser degree,... 

Although nearly identical solid-aqueous solution compositions are observed in recrystallization from two directions under conditions of total constant composition, this alone is insufficient proof of the establishment of equilibrium. In order to test for equilibrium, the solid solution activity coefficients must be determined and used to compare observed solid and aqueous solution compositions with the appropriate values expected at equilibrium. 

Table VI summarizes values of the activity coefficient ratio Ygr-/YC].- in the saturated solution for each average solid composition (as calculated from the model of Table II), the calculated provisional equilibrium distribution coefficient (Equation 12) and the provisional equilibrium aqueous solution activity ratio of Br to Cl- (Equation 13) based on the data of Table V.

For solutions of fixed ionic strength, or, for example, where major ions in solution, e.g. conservative cations and anions, are present at concentrations several orders of magnitude greater than the species involved in the chemical equilibrium, e.g. A, B, C, and D in Equation (3.13), it can be assumed that the solute activity coefficients are also constants and can be incorporated into the equilibrium constant. The equilibrium constant for a fixed ionic strength aqueous solution is termed a constant ionic strength equilibrium constant, K. 

Many nonionizable organic solutes in water are described thermodynamically on the mole fraction scale, although their solubilities may commonly be reported in practical units, for example, molality. [Refer to Schwarzenbach et al. (1993) and Klotz (1964) for detailed discussion of such aqueous solutions.] Here, the standard state is the pure liquid state of the organic solute, that is, Xj = 1. The reference state is Xi - 1, that is, a solution in which the organic solute molecules interact with one another entirely. Activity coefficients of solute molecules in dilute aqueous solutions are generally much greater than unity for this reference state choice, jc, 1. For example, with this reference state, aqueous benzene has an experimental infinitely dilute solution activity coefficient, T nzeno of 2400 for an infinite dilution reference state, jc, - 0, the activity coefficient would be approximately 1 (Tanford, 1991). 

As presented above, and in most of the published literature, the isotherm model equations are expressed in terms of total sorbate concentrations. In MINTEQA2, however, aqueous species activities are used rather than their concentrations. This is preferable in that reactions are written in terms of activities. Also, so that the concentrations of sorption sites, sorbed species, and dissolved species are computationally equivalent, the former are entered in MINTEQA2 as moles of sites per liter of solution. Activity coefficients of sorption sites and sorbed species are generally taken to be equal to unity by most authors and in MINTEQA2. 

In our discussion of aqueous species of iron, it is appropriate to first consider the Fe(II) and Fe(III) hydroxyl complexes (Table 12.1). To judge their importance, we will construct plots to show the fractional distribution of these complexes as a function of pH. The computational approach is as presented in Chap. 3. Solute activity coefficients are ignored. 

Variations of aqueous heat capacities with respect to temperature should also be taken into account, where possible, when estimating activity coefficients. However, errors arising from lack of knowledge of the temperature variation of solute activity coefficients may be less than the uncertainty in Kh or K h, which remains high for many gases. 

If the solid solution is ideal, yi = 1.0, and the solubility can be computed using the pure component solubility to approximate the aqueous phase activity coefficient yi via equation (16). 

Thermodynamic calculations for multicomponent atmospheric particulate matter involve either the minimization of the Gibbs free energy of the system (see Section 10.1.3) or solution of a system of nonlinear algebraic equations [see equation (10.30)] corresponding to the equilibrium reactions taking place in the system. However, there are two major complications (1) the composition of the system (e.g., existence of a given salt) is not known a priori and (2) if the particles are aqueous, the activity coefficient of each... 

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. 

O Connell, J. P., Y. Q. Hu, and K. A. Marshall. 1999. Aqueous strong electrolyte solution activity coefficients and densities from fluctuation solution theory. Fluid Phase Equilibria,... 

An extensive review of neutral solutes in aqueous salt solutions is given by Randell and Failey (1927a, b, c). See also Long and McDevit (1952) and Oelkers and Helgeson (1991). Note that we have only spoken of neutral species of the type that can be obtained as the dominant species in a solution activity coefficients for the neutral species of weak electrolytes and other neutral species in a matrix of charged particles constitute a more difficult problem. Their activity coefficients are usually assumed to be 1.0, or are taken as equal to those... 

A rigorous test of multicomponent solution activity coefficient prediction methods is the calculation of the mutual solubilities of salts and the calculation of salt solubilities in aqueous electrolyte solutions. The salt solubilities are affected by the solution composition. In order to calculate the saturation molalities, the activity coefficients must be adequately predicted. 

Rosene and Manes studied the effect of pH on the total adsorption from aqueous solutions of sodium benzoate + benzoic acid by activated charcoal. They interpreted their data in terms of the Polanyi potential theory applied to bisolute adsorption (see later p. 117), in which the concentrations of neutral benzoic acid and benzoate anions depend on the pH of the solution (activity coefficient corrections were ignored). They confirmed that, at constant total equilibrium concentration, the adsorption dropped from a relatively high plateau for pH <2 down to a small adsorption at pH >10. The analysis of results is somewhat more complex than with essentially non-electrolyte adsorption, and in this case there were additional effects involving chemisorption of benzoate ion by residual ash in the carbon which had, therefore, to be eliminated. Even with ash-extracted carbon there was evidence of some residual chemisorption. The theoretical analysis correlated satisfactorily with the experimental data on the basis that at pH >10 sodium benzoate is not physically adsorbed and that the effect of pH is completely accounted for by its effect on the concentration of free acid. In addition the theory explains successfully the increase in pH (called by the authors hydrolytic adsorption ) when solutions of sodium benzoate are treated with neutral carbon. However, no account is taken in this paper of the effect of pH on the surface charge of the carbon. 

Assume that an aqueous solute adsorbs at the mercury-water interface according to the Langmuir equation x/xm = bc/( + be), where Xm is the maximum possible amount and x/x = 0.5 at C = 0.3Af. Neglecting activity coefficient effects, estimate the value of the mercury-solution interfacial tension when C is Q.IM. The limiting molecular area of the solute is 20 A per molecule. The temperature is 25°C. 

The following data (for 25°C) were obtained at the pzc for the Hg-aqueous NaF interface. Estimate and plot it as a function of the mole fraction of salt in solution. In the table,/ is mean activity coefficient such that a = f m , where m is mean molality. 

The Debye-Htickel limiting law predicts a square-root dependence on the ionic strength/= MTLcz of the logarithm of the mean activity coefficient (log y ), tire heat of dilution (E /VI) and the excess volume it is considered to be an exact expression for the behaviour of an electrolyte at infinite dilution. Some experimental results for the activity coefficients and heats of dilution are shown in figure A2.3.11 for aqueous solutions of NaCl and ZnSO at 25°C the results are typical of the observations for 1-1 (e.g.NaCl) and 2-2 (e.g. ZnSO ) aqueous electrolyte solutions at this temperature. 

Henry s law is useful for handling equiUbria associated with gas absorption (qv) and stripping problems. Henry s law coefficients are useful for estimating terminal activity coefficients and have been tabulated for many compounds in dilute aqueous solutions (27). 

There is a third experimental design often used for studies in electrolyte solutions, particularly aqueous solutions. In this design the reaction rate is studied as a function of ionic strength, and a rate variation is called a salt effect. In Chapter 5 we derived this relationship between the observed rate constant k and the activity coefficients of reactants l YA, yB) and transition state (y ) ... 

Select now a second neutral indicator base C that is weaker than B by roughly an order of magnitude thus, a solvent can be found of such acidity that a significant fraction of both B and C will be protonated, but this will no longer be a dilute aqueous solution, so the individual activity coefficients will in general deviate from unity. For this solution containing low concentrations of both B and C,... 

Examples of Values of L and AF°. As a first example we may evaluate both L and AF° for a moderately soluble salt in aqueous solution. At 25° a saturated solution of potassium perchlorate has a concentration of 0.148 mole of KCIO4 in a 1000 grams of water that is to say, y+ = y = 0.148/55.5. The activity coefficient in the saturated solution has been taken1 to be 0.70 + 0.05. Using this value, we can estimate the work required to take a pair of ions from the crystal surface to mutually distant points, when the crystal is in contact with pure solvent at 25°C ... 

As another example we may discuss silver iodide. As mentioned in Sec. 49 a saturated aqueous solution of this salt at 25°C contains only 9.08 X 10-9 mole in 1000 grams of water. At this low concentration the activity coefficient does not differ appreciably from unity we have then... 

The Change of Solubility with Temperature. The solubilities of various salts have been measured in aqueous solution at various temperatures. But from these measurements we cannot derive values of L as a function of temperature, until the activity coefficients in the various saturated solutions have been accurately measured. In dilute solutions... 

Lithium Carbonate in Aqueous Solution. As an illustration, we shall evaluate the conventional AF° and AS0 for lithium carbonate in aqueous solution. At 25°C the concentration of the saturated solution is 0.169 molal.1 In this solution the molality of the Li+ ion is of course 0.338. The activity coefficient of the Li2CO.t in the saturated solution is not accurately known, but its value is not far from y,at = 0.59. Substituting in (186) we have then... 

As an example, take the molecule aminoazobenzene, one of the solutes listed in Table 39. When colorimetric measurements were made at room temperature on very dilute aqueous solutions of HC1, containing a trace of this substance, it was found that neutral molecules and (BH)+ ions were present in equal numbers when the concentration of the HCl was 0.0016 molal.1 At this low concentration the activity coefficient of the HCl is very near unity, and we may use (216) to find how far the vacant proton level provided by the aminoazobenzene molecule in aque-... 

Fui. 70. Activity coefficient of lithium bromide in aqueous solution at 25°C. 

Activity Coefficients. Turning now to the experimental data on activity coefficients, Fig. 70 shows the results for lithium bromide in aqueous solution at 25°C, plotted against the square root of the concentration. 

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