Solvent activity coefficients

The competition model and solvent interaction model were at one time heatedly debated but current thinking maintains that under defined r iitions the two theories are equivalent, however, it is impossible to distinguish between then on the basis of experimental retention data alone [231,249]. Based on the measurement of solute and solvent activity coefficients it was concluded that both models operate alternately. At higher solvent B concentrations, the competition effect diminishes, since under these conditions the solute molecule can enter the Interfacial layer without displacing solvent molecules. The competition model, in its expanded form, is more general, and can be used to derive the principal results of the solvent interaction model as a special case. In essence, it seems that the end result is the same, only the tenet that surface adsorption or solvent association are the dominant retention interactions remain at variance. 

The above separation of charge and geometric progression of the transition state has at least one disturbing consequence. Reaction transition states are commonly characterized by various parameters. These include kinetic isotope effects, the Bransted parameter, and solvent activity coefficients. The question immediately arises do these measures of transition state structure measure charge or geometric progression On the basis of the previous discussion, they can, at best, measure one but not both of these parameters. Let us first consider the Bransted parameter a. 

Limited success has been achieved in predicting absolute rates of reaction between electrophiles and nucleophiles through the correlation of nucleophilic reactivity with the pKa (17) and the electrode potential of the nucleophile (18.19). or solvent activity coefficients (2Q). A summary and critical analysis of the correlation equations which have been devised for this purpose has been provided by Duboc (21). 

Note that if there is some mutual solubility of the two solvents, activity coefficients measured by this method are actually for solvents which are the dilute solutions of one of the solvents in the other. 

Introducing the area of surface layer per one micro- or nanoparticle A via the relation 0 = (o/A, and using, instead of Eq. (11) which expresses the enthalpy contribution to the solvent activity coefficient, the assumption that this contribution is independent of 0 (i.e., taking lnf0H to be constant, which corresponds better to the liquid-expanded monolayer33), with the condition n = (o/(0o 1 which is true for micro- and nanoparticles, one obtains from Eq. (13) the expression for the II-A isotherm valid for a monolayer of particles ... 

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

Data are available for equilibrium pressure-volume-temperature of pure polymer liquids, solvent activity coefficients at infinite dilution, solvent activity coefficients at finite concentrations, and liquid-liquid phase equilibria of binary and ternary polymer solutions. 

TEMP. WEIGHT FRACTION WEIGHT FRACTION (K) OF SOLVENT ACTIVITY COEFFICIENT... 

Also called the medium effect, solvent activity coefficient, or transfer activity coefficient, and also written as y (MX, O —> S). It is a constant characteristic of the solute MX (or the solute ions M and X ) and the two solvents O and S. 

Nonelectrolytes in nonaqueous solvents Activity coefficients of dilute solutions of solutes can be studied experimentally by liquid-liquid chromatography as well as techniques such as solvent extraction, light scattering, vapor pressure, and freezing point depression. 

Any consideration of sovent effects on rates or equilibria must start from solvent activity coefficients, VI for reactants, transition states and products (Wiberg, 1964 Laidler, 1950 Parker, 1966). Once solvent activity coefficients are available, or can be predicted, it is highly probable, as indicated at the end of this article, that an enormous amoimt of information on the kinetics of reactions in solution and on equilibrium properties such as solubility, acid-base strength, ion-association, complexing, redox potentials and kinetics of reactions in different solvents (Parker, 1962, 1965a, 1966) can be reduced to a relatively small number of constants which can then be used in appropriate linear free energy relationships. 

Solvent activity coefficients are defined (Parker, 1966) such that °y< reflects the change in the standard chemical potential fi of a solute, i (hypothetically ideal, in respect to Henry s Law, unimolar solution), on transfer from an arbitrarily chosen reference solvent (i.e. the standard... 

Solvent activity coefficients are applied to reaction rates in terms of the Absolute Rate Theory, which assumes an equilibrium between reactants and transition state, X. If the transmission coefficient is unity, the rate of a reaction is given by the product of a frequency factor kTjh and the concentration [X ] of the transition state,... 

In this article we are concerned with the differences between the rates of Sif2 reactions in protic and in dipolar aprotic solvents. For this reason, we choose a dipolar aprotic solvent, dimethylformamide, as the reference solvent and define a hypothetically ideal unimolar solution in DMF at 25°C as our standard state (Parker, 1966). All solvent activity coefficients, which are denoted by yf, are referred to this standard state, unless otherwise noted. 

Solvent Activity Coefficients, yf, for Polar Solutes in Water (W),... 

Solvent activity coefficients for a small number of polar solutes, referred to the standard state of unimolar solute in DMF, are given in Table 3. In the absence of more detailed observations, and applying many of my qualitative observations on the solubility of organic com-poimds, it is tentatively suggested that many polar organic compounds, which are not strong H-bond donors or acceptors, are from 2 to 60 times more solvated by DMF than by methanol or formamide. 

The solvent activity coefficient of a polar transition state can be measmred in the following way (Evans and Parker, 1966). Because in all saturated solutions of the salt AB, which would be in equilibrium with the same crystalline solid, AB has the same chemical potential, then the reactants in saturated solutions start at the same free energy level for reaction (10) in all solvents. 

The Menschutkin reaction (Menschutkin, 1890 Hinshelwood et al., 1936) between tertiary amines and alkyl halides, is a classical one in terms of solvent effects on rate. It is of the same charge type as the back reaction (14) and shows reasonable correlation with Kosower s Z values, for a series of protic solvents (Kosower, 1958). Many rate data are available, so that a meaningful discussion of solvent effects on bimolecular reactions between molecules might evolve, if the appropriate solvent activity coefficients for reactants and transition states of Menschutkin reactions were known. 

R—X, of reaction (15). It is then interesting to compare this solvent activity coefficient with those of species which may act as models for the transition state, such as ion pairs, dissociated ions, and polar 8 2 transition states (e.g. of Menschutkin reactions and of reaction (14)). In this way, some estimate of the nature of the 1 transition state can... 

There is an enormous amount of information on solvolyses in a variety of solvents, and linear free energy relationships, such as those of Grunwald and Winstein (1948), successfully correlate much of it. The Grunwald-Winstein Y relationship, in terms of solvent activity coefficients, becomes... 

Even for reactions in which the Sij2 contribution to ionization is negligible, one does not have a means of estimating from solvolysis rates, the solvent activity coefficients for the transition state corresponding to ionization of RX. Although Vrx easily found from Henry s Law constants, and equation (16) does produce an activity coefficient for some transition state, this may not be a simple transition state corresponding to ionization of RX. Solvolysis rates may be smaller than ionization rates of many compounds, in certain solvents, because of ion-pair return, a phenomenon which has been firmly established by the investigations of Winstein et al. (1965). No matter whether Ag is a titrimetric rate constant 7... 

The true 8 2 reaction, being a one-step process, shows less fiexibility in the nature of its transition state (Evans and Parker, 1966 Coniglio et al., 1966). It is better suited to free energy relationships between different reactions and to interpretation in terms of solvent activity coefficients. 

The change in the chemical potential of each anion, A, on transfer from DMF to methanol is given by the energy difference between the methanol and DMF curves in Fig. 1. The energy difference is related to the solvent activity coefficient, yA-, through (18). 

It may forever be impossible to estimate with complete confidence the individual solvent activity coefficients of anions and cations (Kolthoff and Bruckenstein, 1959). However, in an effort to attack this problem, a number of extrathermodynamic assumptions, which are not completely unreasonable, have been suggested. Three of these assumptions have... 

The most satisfactory way of estimating solvent activity coefficients is by electrochemical measurements of the EMF of appropriate cells, or by polarographic methods (Kolthoff, 1964). Some measurements have been made (Kolthoff and Thomas, 1965 Nelson and Iwamoto, 1961 Koepp, Wendt and Strehlow, 1960 Coetzee et al., 1963 Alexander and Parker, 1966). The electrochemical methods are aimed at measuring liquid junction potentials between two half-cells in different solvents (Kolthoff and Thomas, 1965) and rely heavily on assumptions such as (i) and (ii). 

Solvent activity coefficients at 25°C in Solvents, S, Relative to a Standard State of 1 m Solute in Dimethylformamide (D). Calculation from Solubilities... 

A simple, but rough, way of applying assumptions (i), (ii) and (iii) is to measure the solubilities of the appropriate salts in the reference solvent and in other solvents of comparable dielectric constant. Provided that saturated solutions are not too concentrated, that there is no ion association, that the solutes do not react with the solvent and that the solid phase, which is in equilibrium with the saturated solution, is the same in each solvent, then solubilities lead directly to solvent activity coefficients. Since all saturated solutions of a salt, AB, have the same activity, we can write (19), in which is the concentration in saturated reference solvent and c is the concentration in the saturated solvent, S. 

This question is not easy to answer. One approach is to utilize individual solvent activity coefficients for anions, e.g. y - (cf. Table 5), which have been calculated by making certain assumptions, as already outlined. These can be combined with rates and measured values of °ycHsi equation (9) to give solvent activity coefficients for transition states. The results of such assumptions and calculations are shown in Table 9. Positive values of log yf mean that the solute i is more solvated by DMF than by the solvent S. 

The two extrathermodynamic assumptions used in Table 9 to derive solvent activity coefficients of anions, lead to different values of y cicHsi-)+ The assumption (i) that caesium cation is similarly solvated in methanol and in DMF, suggests that the large rate difference between reaction (27) in methanol and in DMF is as much due to differences in transition state solvation as to differences in solvation of chloride ion. This is the situation shown qualitatively in Fig. 1. On the other hand, the somewhat smaller rate difference between reaction (27) in formamide and in DMF is due entirely to differences in solvation of chloride ion, if the caesium assumption is applied to formamide and to DMF. 

Calculation of Solvent Activity Coefficients for the Transition State of Reaction (27)... 

The effect of transfer, from dimethylacetamide or dimethylformamide to 88 % MeOH-HgO or methanol, on a number of chemical processes involving bromide ion, such as the equilibrium constant for (31), the forward rate constant for (31) (Mac et al., 1967), the rate constant for reaction of bromide ion with methyl iodide (Parker, 1966), or with 2,4-dinitroiodobenzene (Parker, 1966), the redox potential of the Br /Brj couple (Parker, 1966), and the association constant for Br formation (Parker, 1966), can all be accounted for on the assumption that o/Br- is ca. 10 and that solvent activity coefficients of other species which are involved in the processes are unity or cancel each other. 

Application, through equation (9), of the solvent activity coefficient concept to the rate data in Table 17 for 8 2 reactions of Nj and SCN in methanol and in DMF, illustrates some interesting features of solvation of transition states (Coniglio et al., 1966). In equations (37) and (38) fc(Cl) and A (I) are rate constants and (Cl) and (I) are transition statesfor... 

The effect of solvent on nucleophilic tendencies relative to SCN is shown by solvent activity coefficients. Equation (40) is derived from equation (9) and applies to reactions of methyl iodide with a series of... 

For reasons already outlined, it is not possible to evaluate single-ion solvent activity coefficients, Vy-, with any degree of certainty. It is more satisfactory to choose one anion as a standard. We have chosen thiocyanate ion as a standard, and this leads to the linear free energy expressions (49) for solubilities of silver salts to (50) (cf. 29) for rates of reaction with methyl iodide and to (51) for acid strengths. In these equations, the value for an anion Y on transfer from DMF to... 

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