Activity coefficient reference-solvent

AVhile we might use different labels for different activity coefficients (e.g., 7, 7/ ) we prefer to emphasize the matching of the scales with the activity coefficient reference states for different species (solvent, ionic solute, etc.). In Chapters 3 and 6, for example, we use the symbol /, or fi, to discuss activities on a molar scale. The usage will be clear in the context. 

In a binary liquid solution containing one noncondensable and one condensable component, it is customary to refer to the first as the solute and to the second as the solvent. Equation (13) is used for the normalization of the solvent s activity coefficient but Equation (14) is used for the solute. Since the normalizations for the two components are not the same, they are said to follow the unsymmetric convention. The standard-state fugacity of the solvent is the fugacity of the pure liquid. The standard-state fugacity of the solute is Henry s constant. 

For those dilute mixtures where the solute and the solvent are chemically very different, the activity coefficient of the solute soon becomes a function of solute mole fraction even when that mole fraction is small. That is, if solute and solvent are strongly dissimilar, the relations valid for an infinitely dilute solution rapidly become poor approximations as the concentration of solute rises. In such cases, it is necessary to relax the assumption (made by Krichevsky and Kasarnovsky) that at constant temperature the activity coefficient of the solute is a function of pressure but not of solute mole fraction. For those moderately dilute mixtures where the solute-solute interactions are very much different from the solute-solvent interactions, we can write the constant-pressure activity coefficients as Margules expansions in the mole fractions for the solvent (component 1), we write at constant temperature and at reference pressure Pr ... 

The reference pressure P for the activity coefficients is here taken as Pt3, the saturation pressure of pure solvent 1. 

In Eq. (128), the superscript V stands for the vapor phase v2 is the partial molar volume of component 2 in the liquid phase y is the (unsym-metric) activity coefficient and Hffl is Henry s constant for solute 2 in solvent 1 at the (arbitrary) reference pressure Pr, all at the system temperature T. Simultaneous solution of Eqs. (126) and (128) gives the solubility (x2) of the gaseous component as a function of pressure P and solvent composition... 

Other references in Table in discuss applications in precipitation of metal.compounds, gaseous reduction of metals from solution, equilibrium of copper in solvent extraction, electrolyte purification and solid-liquid equilibria in concentrated salt solutions. The papers by Cognet and Renon (25) and Vega and Funk (59) stand out as recent studies in which rational approaches have been used for estimating ionic activity coefficients. In general, however, few of the studies are based on the more recent developments in ionic activity coefficients. 

Thus, the ideal solution is a reference for the solvent in a real solution, and the activity coefficient of the solvent measures the deviation from ideality. 

Activity coefficients at infinite dilution, of organic solutes in ILs have been reported in the literature during the last years very often [1,2,12,45,64, 65,106,123,144,174-189]. In most cases, a special technique based on the gas chromatographic determination of the solute retention time in a packed column filled with the IL as a stationary phase has been used [45,123,174-176,179,181-187]. An alternative method is the "dilutor technique" [64,65,106, 178,180]. A lot of y 3 (where 1 refers to the solute, i.e., the organic solvent, and 3 to the solvent, i.e., the IL) provide a useful tool for solvent selection in extractive distillation or solvent extraction processes. It is sufficient to know the separation factor of the components to be separated at infinite dilution to determine the applicability of a compound (a new IL) as a selective solvent. 

This definition of x and y is more realistic at low and moderate salt concentrations and is in agreement with that of Sada and Morisue (17). Broul and Hala also assumed complete salt dissociation. The assumption of full dissociation of the salt may not be entirely valid at high salt concentrations, especially where the concentration of the nonaqueous solvent is also high. However, even in those instances where the assumption of full dissociation of the salt may be invalid, it appears to describe the system better than ignoring salt ionization completely. The terms x/ and y/ are referred to hereafter as ionic mole fraction and ionic activity coefficient, respectively. These should not be confused with the mean ionic terms used by Hala which are also based on complete salt dissociation, but are defined differently. No convergence problems were encountered when the ionic quantities were employed. 

An alternative approach is to estimate activity coefficients of the solvents from experimental data and correlate these coefficients using, for example, the Wilson equation. Rousseau et al. (3) and Jaques and Furter (4) have used the Wilson equation, as well as other integrated forms of the Gibbs-Duhem equation, to show the utility of this approach. These authors found it necessary, however, to modify the definitions of the solvent reference states so that the results could be normalized. 

Here 113 is completely defined by the variables Z and N3. For any given values of Z and N3, the reference of the activity coefficient will be chosen as the extremely dilute state (N3 = 0) of the given solute in a binary mixed solvent of the same composition Z. By the definition, the chemical potential of the reference state varies with Z. Hence, one obtains for the 1-1 salts... 

Solvation Effects. Many previous accounts of the activity coefficients have considered the connections between the solvation of ions and deviations from the DH limiting-laws in a semi-empirical manner, e.g., the Robinson and Stokes equation (3). In the interpretation of results according to our model, the parameter a also relates to the physical reality of a solvated ion, and the effects of polarization on the interionic forces are closely related to the nature of this entity from an electrostatic viewpoint. Without recourse to specific numerical results, we briefly illustrate the usefulness of the model by defining a polarizable cosphere (or primary solvation shell) as that small region within which the solvent responds to the ionic field in nonlinear manner the solvent outside responds linearly through mild Born-type interactions, described adequately with the use of the dielectric constant of the pure solvent. (Our comments here refer largely to activity coefficients in aqueous solution, and we assume complete dissociation of the solute. The polarizability of cations in some solvents, e.g., DMF and acetonitrile, follows a different sequence, and there is probably some ion-association.)... 

Table 32 Activity Coefficients °, yu > of Hexane (apolar), Benzene (monopolar), Diethylether (monopolar), and Ethanol (bipolar) in Different Solvents at Infinite Dilution at 25°C. Reference Pure Liquid Organic Compound.

Thus, firstly, the choice of the pure solvent as the reference state for the definition of activities of solutes in fact impairs a fair comparison of the activity of dilute solutes such as general adds to the activity of the solvent itself. Secondly, the observed first-order rate constants k or k0 for the reaction of a solute with the solvent water are usually converted to second-order rate constants by division through the concentration of water, h2o = oA iho, for a comparison with the second-order rate coefficients HA. Again, it is questionable whether the formal h2o coefficients so calculated may be compared with truly bimolecular rate constants kUA for the reactions with dilute general acids HA. It is then no surprise that the values for the rate coefficients determined for the catalytic activity of solvent-derived acids scatter rather widely, often by one or two orders of magnitude, from the regression lines of general adds.74... 

By far the biggest problems with the stability and the magnitude of the liquid junction potentials arise in applications where the osmotic or hydrostatic pressure, temperature, and/or solvents are different on either side of the junction. For this reason, the use of an aqueous reference electrode in nonaqueous samples should be avoided at all cost because the gradient of the chemical potential of the solvent has a very strong effect on the activity coefficient gradients of the ions. In order to circumvent these problems one should always use a junction containing the same solvent as the sample and the reference electrode compartment. 

The reference state of the electrolyte can now be defined in terms of thii equation. We use the infinitely dilute solution of the component in the solvent and let the mean activity coefficient go to unity as the molality or mean molality goes to zero. This definition fixes the standard state of the solute on the basis of Equation (8.184). We find later in this section that it is neither profitable nor convenient to express the chemical potential of the component in terms of its molality and activity. Moreover, we are not able to separate the individual quantities, and /i . Consequently, we arbitrarily define the standard chemical potential of the component by... 

These equations are used whenever we need an expression for the chemical potential of a strong electrolyte in solution. We have based the development only on a binary system. The equations are exactly the same when several strong electrolytes are present as solutes. In such cases the chemical potential of a given solute is a function of the molalities of all solutes through the mean activity coefficients. In general the reference state is defined as the solution in which the molality of all solutes is infinitesimally small. In special cases a mixed solvent consisting of the pure solvent and one or more solutes at a fixed molality may be used. The reference state in such cases is the infinitely dilute solution of all solutes except those whose concentrations are kept constant. Again, when two or more substances, pure or mixed, may be considered as solvents, a choice of solvent must be made and clearly stated. 

Equation (12.134) gives the required relation between the equilibrium molalities, the activity coefficients, and the two pressures for osmotic equilibrium. It is evident that the two pressures are not independent. We could write P" as F + II, where II is the difference of the osmotic pressures of the two solutions referred to the pure solvent. The solution of the two equations would then give a value of II. 

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. 

Sketch the partial pressures above a solution in which both solute and solvent show positive deviation from ideal solution behavior. Using Raoult s law reference for both solute and solvent, sketch the activity coefficients for this solution. 

The expressions for single-species activity coefficients in Eqs. 1.21-1.24 suffice to calculate activities of dissolved solutes like H+ or C02 in Eq. 1.11. For the solvent, H20, it is still necessary to define a Reference State, which is that of the pure liquid at 298.15 K under 1 atm pressure.12 The activity of the solvent is conventionally set equal to the product of a rational activity coefficient f and the mole fraction of the solvent x 12... 

Solvent activity coefficients of some cations and anions at 25°C [Reference solvent methanol (M)]6... 

Equation 7 describes the relationship between the solvent lattice and dissociation products, assuming constant species activity coefficients CdA designates cadmium atoms in less tightly bound sites—e.g., interstitials Cdn refers to solvent units lacking a cadmium atom (cadmium vacancies). The cadmium activity,... 

Assume the vapor phase to be characterized as an ideal gas. Determine the activity coefficients for components A and B at xA - 1/4, 1/2, 3/4 at 500°C relative to the solvent and the solute reference states involving mole fractions. 

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