The Heat Capacity of Activation

An implicit assumption of the foregoing treatment is that A// remains independent of temperature over the range investigated. This is very nearly correct in general, and is particularly the case given that studies of reactions in solution are usually conducted over a temperature interval of only some 30-50°. In certain circumstances the temperature profiles show curvature outside the experimental error. Such cases have, or appear to have, temperature-dependent activation enthalpies. Here we explore one of the reasons for that another is given in Section 7.3. 

Extraordinarily precise kinetic data are required to detect the further temperature dependence of an activation parameter. If A// is temperature-dependent, then the temperature profile will be curved. By analogy with the equation relating AH and AC , we may define the heat capacity of activation by 

The interpretation of AC is that it is the difference in the standard molar heat capacities of the transition state and the reactants. Values of AC for the solvolysis of neutral molecules lie in the range 0 to -400 J mol-1 K l. The need for high-precision determinations of k (and 77) is emphasized by these values. 

Because dASt/dT = AC /T, from the thermodynamic definition, we have upon integration 

With these equations, the expression for the rate constant becomes 

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Thus curvature in an Arrhenius plot is sometimes ascribed to a nonzero value of ACp, the heat capacity of activation. As can be imagined, the experimental problem is very difficult, requiring rate constant measurements of high accuracy and precision. Figure 6-2 shows a curved Arrhenius plot for the neutral hydrolysis of methyl trifluoroacetate in aqueous dimethysulfoxide. The rate constants were measured by conductometry, their relative standard deviations being 0.014 to 0.076%. The value of ACp was estimated to be about — 200 J mol K, with an uncertainty of less than 10 J moE K. ... 

A similar relationship between AS and ACp, the heat capacity of activation (or reaction), follows also from eq. (79) ... 

If the heat capacity of activation is not zero, a knowledge of its value is also of importance when mechanistic conclusions are based on the kinetic parameters. For example, energies and entropies of activation will then vary as the temperature is altered and it is therefore essential that any comparison of the activation parameters of different reactions should refer to the same temperature (see Section IVC2). 

From Kirchhoff s equations and equations (2) and (9) we then obtain the relation between the heat capacity of activation and the other kinetic parameters as... 

The heat capacity of activation for proton transfer under conditions where the tunnel effect can be neglected (i.e. at the higher temperatures) is probably small (see Section IVCl) and the available results are un-fortimately not sufficiently accurate to allow the evaluation of this parameter. For similar reasons it cannot yet be shown that the temperature-dependent values of AC predicted by the differential form of equation (32) are observed in practice. 

This section describes the calculation of the activation parameters directly from the rate coefficients observed at various temperatures. It is assumed initially that the heat capacity of activation is linearly related to the temperature, i.e. 

The heat capacities of activation at constant pressure and constant volume are defined as... 

Tetrahedral Anions and Related Species. The hydrolysis of the [BHJ anion in moist acetonitrile is an acid-catalysed reaction, and when acetic add is used as a catalyst there appears to be complex formation. The observations are considered to be consistent with BHg as an intermediate, a species which molecular orbital calculations suggest could be metastable. The heat capacity of activation for the hydrolysis of [BHi] has been reported. The decomposition of [BHJ in alkaline solution is catalysed by platinum powder, and a PtH species is suggested as an unstable intermediate. There have been kinetic studies of the alkaline hydrolysis of [BF4]- and [Bp2(OH)2]. A F n.m.r. study of the alkaline hydrolysis of [BF OMe]" is considered to suggest an Nlcb mechanism for the hydrolysis of the first fluoride ion. The acid-catalysed hydrolysis of MeaNBHgNa has been studied in some detail. The kinetics are... 

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