Free energy change, mechanism

Another simple approach assumes temperature-dependent AH and AS and a nonlinear dependence of log k on T (123, 124, 130). When this dependence is assumed in a particular form, a linear relation between AH and AS can arise for a given temperature interval. This condition is met, for example, when ACp = aT" (124, 213). Further theoretical derivatives of general validity have also been attempted besides the early work (20, 29-32), particularly the treatment of Riietschi (96) in the framework of statistical mechanics and of Thorn (125) in thermodynamics are to be mentioned. All of the too general derivations in their utmost consequences predict isokinetic behavior for any reaction series, and this prediction is clearly at variance with the facts. Only Riietschi s theory makes allowance for nonisokinetic behavior (96), and Thorn first attempted to define the reaction series in terms of monotonicity of AS and AH (125, 209). It follows further from pure thermodynamics that a qualitative compensation effect (not exactly a linear dependence) is to be expected either for constant volume or for constant pressure parameters in all cases, when the free energy changes only slightly (214). The reaction series would thus be defined by small differences in reactivity. However, any more definite prediction, whether the isokinetic relationship will hold or not, seems not to be feasible at present. 

Pandey et al. have used ultrasonic velocity measurement to study compatibility of EPDM and acrylonitrile-butadiene rubber (NBR) blends at various blend ratios and in the presence of compa-tibilizers, namely chloro-sulfonated polyethylene (CSM) and chlorinated polyethylene (CM) [22]. They used an ultrasonic interferometer to measure sound velocity in solutions of the mbbers and then-blends. A plot of ultrasonic velocity versus composition of the blends is given in Eigure 11.1. Whereas the solution of the neat blends exhibits a wavy curve (with rise and fall), the curves for blends with compatibihzers (CSM and CM) are hnear. They resemble the curves for free energy change versus composition, where sinusoidal curves in the middle represent immiscibility and upper and lower curves stand for miscibihty. Similar curves are obtained for solutions containing 2 and 5 wt% of the blends. These results were confirmed by measurements with atomic force microscopy (AEM) and dynamic mechanical analysis as shown in Eigures 11.2 and 11.3. Substantial earher work on binary and ternary blends, particularly using EPDM and nitrile mbber, has been reported. 

Since work with the radical clock substrate probes indicated important differences in the hydroxylation mechanisms for M. capsulatus (Bath) and M. trickosporium OB3b, work with (R) and (S)-[1-2H,1-3H]ethane with both enzymes was carried out (93, 94). With M. tri-chosporium OB3b, approximately 65% of the product displays retention of stereochemistry (93). A rebound rate constant of 2 - 6 x 1012 s-1 was calculated, assuming a free energy change of 0.5 kcal mole-1 for rotation about the C-C bond (94). This estimate approaches the value obtained from the radical clock substrate probe analysis (59). 

A successful correlation of catalytic data for a series of related compounds is of little value for obtaining insight into the mechanism if its slope is not interpreted with respect to the sign and value. The slope a of Eq. (3) is proportional to the free energy change caused by the difference in mechanisms of the two processes being compared, the one under study and the reference one ... 

The reaction between OH and phenol lends itself to an analysis of its thermochemistry. On the basis of E7( OH) = 2.3V/NHE and E7(PhO ) = 0.97 V/NHE [42], the formation of PhO and H2O via an electron-transfer mechanism is exothermic byl.33V = 31 kcal mor In spite of this, the reaction proceeds by addition, as outlined in Eq. 24. Again, the propensity of OH to add rather than to oxidize can be understood in terms of the transition state for addition being stabilized by contributions from bond making, in contrast to electron transfer which requires pronounced bond and solvent reorganization which results in a large (entropy-caused) free energy change. 

In many physicochemical interactions which are subject to the same intrinsic mechanism, the free energy change is proportional to the enthalpy. 

---