Transfer functions, thermodynamic

This is a book on aqueous electrolytes, but it is imperative that something is said about the solvation of non-polar solutes. This is a topic of prime concern for biochemists and biologists, but it is also very important for chemists because many of the phenomena observed for nonpolar and apolar solutes bear a superficial simUarity to those for electrolytes. However, it is important to point out that, despite this similarity, the physical and molecular details are totally different for ions and apolar solutes. A study of the reasons for the difference in molecular behaviour involved in the solvation of ions and apolar molecules has resulted in an increased understanding of solvation phenomena in general. It has also led to an upsurge in the number of investigations, both experimental and theoretical. 

FIGURE 1.3 Vapor pressure over binary solutions. Dashed lines ideal (Raoult s Law). Solid curves positive deviations from Raoult s Law. Note that where x Kl, P, is close to ideal, and vice versa. 

For each participating substance I, the term S G can be obtained from vapor pressure, solubility, electrical potential, or other measurements that enable the calculation of activity coefficients and hence of standard Gibbs energies, using Equation 1.7. 

Since the Gibbs energy and the activity coefficient are related through Equation 1.8, this development could have been carried out iu terms of In a or In/ 

Because of the analogy between the transition states in kinetics and the products in equilibrium (see later. Section 1.6), similar considerations can be applied to the understanding of solvent effects on reaction rates. This will be illustrated in Chapter 6. 

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Figure 4. Thermodynamic transfer functions for n-Bu NBr from water to water-acetone mixtures at 298.15°K...

A more exact analysis of the effect of solvent variation and hence of solvent—solute interactions could be obtained through the thermodynamic transfer functions.21 The application of these to the equilibrium situation can be seen by referring to Figure 6. SAG, is defined as the difference in standard free energy of reaction between the two solvents A and B (equation 32), which by reference to Figure 6 leads to equation (33) ... 

In particularly thorough examples of the traditional physical organic approach, Parker (1969) and Abraham (1974) interpreted solvent effects on Walden inversion reactions by using thermodynamic transfer functions. However, in order to explain the reaction rate decrease upon solvation from a microscopic point of view, quantum mechanical electronic structure calculations must be carried out. Micro-solvated Sn-2 reactions were initially studied in this way, with the CNDO/2 semiempirical molecular orbital (MO) method, by using the supermolecule... 

The first section, under the heading solute-solvent interactions, considers the origin of the medium effect which is exhibited for reactions on changing from a hydroxylic solvent to a dipolar aprotic medium such as DMSO. This section is subdivided into two parts, the first concentrating on medium effects on rate processes, the second on equilibria of the acid-base variety. The section includes discussion of the methods used in obtaining and analysing kinetic and thermodynamic transfer functions. There follows a discussion of proton transfers. The methods and principles used in such studies have a rather unique character within the context of this work and have been deemed worthy of elaboration. The balance of the article is devoted to consideration of a variety of mechanistic studies featuring DMSO many of the principles developed in earlier sections will be utilized here. 

Additionally, examination of pKa values in DMSO and mixtures of DMSO with hydroxylic solvents, as obtained by different methods, has revealed considerable variation. This is illustrated in Table 6 for two compounds frequently used as anchors for acidity function scales. If one is to correlate pATa values with thermodynamic transfer functions [eqn (6)], rationalize varying orders of acidity in different solvents (Table 6), or use them inBr nsted relationships (Section 3),... 

It should be noted at this point that there is a consistency in the pKa values measured in pure DMSO by the various techniques. However, there is some uncertainty at present relating to pKa values obtained by acidity function procedures in alcoholic and aqueous DMSO media. Thus one has the unexpected situation that theoretical analysis of the medium effect on p/ a is hampered because the values for a number of weak acids referring to the standard state in water are in doubt. Under these circumstances less than critical application of (6) to many weak acids, including some carboxylic acids, phenols as well as carbon acids, is inadvisable. Of course, (6) is strictly applicable to those cases in which the p/sfa values can be measured in the pure hydroxylic solvents and also for those weak acids which obey the criteria outlined by Cox and Stewart (1976). Despite this difficulty there is now a large body of reliable pKa data in both DMSO and water. Thus in principle it should be possible to account for variations, or reversals, in acidity order in terms of the thermodynamic transfer functions in (6). 

DMSO has been used in a multitude of mechanistic investigations. In the present section we have chosen to highlight certain studies which illustrate the principles and methods discussed in earlier sections of this article. This will be done by reference to several contrasting situations. The systems chosen illustrate rate phenomena, both retardation and acceleration, resulting from use of DMSO. Various techniques for analysing these effects are presented, including the use of acidity functions and thermodynamic transfer functions, and their value as a guide to mechanisms demonstrated. 

Another area to which the thermodynamic transfer function approach has been applied is that of ionization of carbon acids. One such example is the racemization of D-a-methyl-a-phenylacetophenone (MPA) in hydroxide/water/DMSO mixtures, where heats of solution of reactant species have been combined with previously reported kinetic data(41). In Figure 7 are shown the enthalpy of transfer functions for the individual and combined reactants, and the enthalpies of activation for this system. The resulting calculated has a... 

Approaching solvent effects from the viewpoint of thermodynamic transfer functions allows one to examine in a systematic manner the outcome of medium change, from a protic to a dipolar aprotic reaction medium, in terms of structure and charge distribution in reactants, transition states, and products (Buncel and Wilson, 1979,1980). 

The effect of organic cosolvent on the rate of base hydrolysis of the [Co(NH3)5Br] ion has been studied in mixtures of water with MeOH, EtOH, Pr OH, Bu OH, and dioxane. The thermodynamic transfer functions, corresponding to the transfer of reactants and activated complex from water to the solvent mixtures, were evaluated from the kinetic studies and from solubilities of the complex salt. The results are in good agreement with a Dqb mechanism for the reaction. 

Perron, G., DeLisi, R., Davidson, L, Genereux, S., Desnoyers, J.E. On the use of thermodynamic transfer functions for the study of the effect of additives on micellization volumes and heat capacities of solutions of sodium octanoate systems. J. Colloid Interface Sci. 1981, 79(2), 432-442. 

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