Solute-activity coefficient

For gases, pure solids, pure liquids, and nonionic solutes, activity coefficients are approximately unity under most reasonable experimental conditions. For reactions involving only these species, differences between activity and concentration are negligible. Activity coefficients for ionic solutes, however, depend on the ionic composition of the solution. It is possible, using the extended Debye-Htickel theory, to calculate activity coefficients using equation 6.50... 

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). 

In an attempt to explain the nature of polar interactions, Martire et al. [15] developed a theory assuming that such interactions could be explained by the formation of a complex between the solute and the stationary phase with its own equilibrium constant. Martire and Riedl adopted a procedure used by Danger et al. [16], and divided the solute activity coefficient into two components. 

The net retention volume and the specific retention volume, defined in Table 1.1, are important parameters for determining physicochemical constants from gas chromatographic data [9,10,32]. The free energy, enthalpy, and. entropy of nixing or solution, and the infinite dilution solute activity coefficients can be determined from retention measurements. Measurements are usually made at infinite dilution (Henry s law region) in which the value of the activity coefficient (also the gas-liquid partition coefficient) can be assumed to have a constant value. At infinite dilution the solute molecules are not sufficiently close to exert any mutual attractions, and the environment of each may be considered to consist entirely of solvent molecules. The activity... 

Many reactions encountered in extractive metallurgy involve dilute solutions of one or a number of impurities in the metal, and sometimes the slag phase. Dilute solutions of less than a few atomic per cent content of the impurity usually conform to Henry s law, according to which the activity coefficient of the solute can be taken as constant. However in the complex solutions which usually occur in these reactions, the interactions of the solutes with one another and with the solvent metal change the values of the solute activity coefficients. There are some approximate procedures to make the interaction coefficients in multicomponent liquids calculable using data drawn from binary data. The simplest form of this procedure is the use of the equation deduced by Darken (1950), as a solution of the ternary Gibbs-Duhem equation for a regular ternary solution, A-B-S, where A-B is the binary solvent... 

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. 

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... 

Frequently it is necessary to convert solute activity coefficients based on mole fraction to a molality basis, or vice versa. The equation for making this conversion can be derived in the following way. 

Figure 17.11. Extrapolation of relative activity coefficients to obtain 1 /y2 for the calculation of solute activity coefficients. Data from Ref. 4. Dimethyl sulfoxide is the solvent, and water is the solute.

I. 46. The magnitude of the coefficient reflects the electric charge distribution of the ionic species. A 0.1 molal solution of Al2(S04)3 has an activity coefficient of only 0.035. It should also be noted that, in dilute solutions, activity coefficients of electrolytes decrease in magnitude with increasing concentration. A minimum is reached and the coefficient then increases with concentration. See Activity Debye-Huckel Law Biomineralization... 

We define the standard state of a liquid as ay = 1 and for gases as an ideal gas pressure of 1 bar, Pj = I- For ideal liquid solutions (activity coefficients of unity), we write ay = Cy so at chemical equilibrium... 

In many studies of the SLE of ILs, three methods have been used to derive the solute activity coefficients, pj, from the so-called correlation equations that describe the Gibbs free energy of mixing (GE), fhe Wilson [103], UNIQUAC ASM [104], and NRTLl [105] models. Historically, fhe UNIQUAC... 

For most of the systems with alcohols, the description of SLE was given by the average standard mean deviation (oj) < 2 K for UNIQUAC ASM and NRTL 1 equations. The procedure of correlation has been described in many articles [52-54,79,84-88,91-94]. Using GE models the solute activity coefficients in the saturated solution, y, were described. 

The solute activity coefficients, pj, of the saturated solutions were correlated for many mixtures by the NRTL model describing the excess Gibbs energy [140]... 

It has been suggested that such a sensor can be used for the accurate measurement of Ca2+ activity in dilute sample solutions because, in dilute solutions, activity coefficients tend to unity. Is that statement correct or not ... 

For infinitely dilute solutions activity coefficients approach unity so the activity and the concentration of an ion will be equal. For calculations involving more concentrated solutions corrections must be made using activity coefficients, especially when relating the calculated concentration of species to an imposed mass (mole) balance constraint. The activity coefficients can be calculated from a number of ion activity theories and the relevant equations for some of the commonly used ones are shown below. 

In addition to knowing the TP dependence of equilibrium constants (Eqs. 2.25 and 2.28), we must also know the T-P dependence of solute activity coefficients and the osmotic coefficient of the solution. A theoretical model, such as Pitzer s approach, is necessary for this purpose because activity coefficients and the osmotic coefficient must be defined at finite concentrations and not simply for the infinitely dilute state, which suffices for equilibrium constants (Eqs. 2.25 and 2.28). 

The chemical equilibrium model, FREZCHEM, requires calculation of solute activity coefficients (7) and the osmotic coefficient ((f)) in concentrated solutions (Chap. 3). In this work, the Pitzer approach is used to calculate these quantities. 

A fundamental concept in all theories for determining activity coefficients is that ionic interactions are involved. These interactions cause a deviation in the free energy associated with the ions from what it would be if they did not occur. Consequently, at the limit of an infinitely dilute solution, activity coefficients go to 1 because there are no ionic interactions. This basic consideration also leads to the idea that as the concentration of ions increases, their extent of interaction must also increase. Ionic strength is a measure of the overall concentration of ions in a solution and the fact that more highly charged ions exert a greater influence on ionic interactions. It is calculated as ... 

The standard state for solutes in the (HL) reference is therefore the hypothetical state of pure solute (x, = 1), but with solute molecules interacting only with solvent molecules (y, = 1). Practically, chemical potentials in the standard state are obtained by making measurements at very low concentrations and extrapolating them to X,- = 1, assuming that Henry s law continues to hold to this concentration. At nonzero concentration of solutes, activity coefficients in the (HL) reference measure deviations of the solution from ideally dilute behavior. 

The first term on the right side of this equation is the capacity factor, at zero ionic strength. The ratio of activity coefficients in the second term is the ratio of the solute activity coefficients at finite ionic strength over the solute activity coefficient at zero ionic strength. The activity coefficients of the mobile phase modifier are modeled by the Deye-Hiickel theory and can be approximated by... 

Concentration and activity of a solute are only the same for very dilute solutions, i.e. yi approaches unity as the concentration of all solutes approaches zero. For non-dilute solutions, activity coefficients must be used in chemical expressions involving solute concentrations. Although freshwaters are sufficiently dilute to be potable (containing less than about 1000 mg total dissolved solids (TDS)), it cannot be assumed that activity coefficients are close to unity. 

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. 

Empirically, the Setchenov equation [37,39] has been found to express the variation of the neutral solute activity coefficient (7 ) with the electrolyte concentration (Ce), at least for low electrolyte concentrations (a few tens molar) ... 

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