The "kinetic compensation effect" arises from deficiencies in the Arrhenius equation. Determination of the pre-exponential factor generally comprises only the reconciliation of the expression of the temperature dependence of the rate (the exponential term) with the observed rate. The applicability of the Arrhenius equation to a particular reaction could be tested by finding constancy or a predictable variation in the "frequency factor" with changes in experimental conditions or sample treatment or history.The Arrhenius equation is widely used in heterogeneous kinetics for two reasons. First, the relationship is well established in homogeneous kinetics; second, the form of the equation assures the user that numbers for the constants in the equation can be calculated. It is only necessary to adjust the form of f(&~/dt) or, for non-isothermal reactions, f(&~/dt) until, subjectively, a straight-line relationship is found when the logarithm of that function is plotted against 1/T.When this plot has been prepared and the "best straight line" drawn, the slope is ascribed to an activation energy, divided, of course, by R In 10. The difference is ascribed to a frequency factor according to the equationThe value of this "frequency factor" can vary by several orders of magnitude for a given reaction by different observers and sometimes by the same observer with small changes in conditions. The variation suggests immediately that the equation k r = Ae -etRr
The wide variations of calculated activation energies for solid decomposition suggests that there is no discrete activated state. Further, the statistical distribution on which the calculations are based is not a realistic concept. The lowest energy possible --and most frequently occurring --is the energy of the bulk crystal. Within the crystalline solid, vibrational interactions transfer energy so rapidly that a substantial difference from the average energy is not achievable within the crystal. The lack of a statistical distribution rules out the use of the Arrhenius equation unless it is independently verified for the particular system. * Du-Pont-ICTA Award address presented at the Fifth International Conference on Thermal Analysis Kyoto, Japan, 1 August 1977. J. Thermal Anal. 13, 1978 GARN:KINETIC PARAMETEKS either process happening so rapidly that it is not a rate limiting step. If the relative probability of forming product remains unchanged, the rate is determined by the fraction of reactant reaching the activated state. In homogeneous systems, the distribution of energy states can be defined with reasonable certainty by statistics, and plotted as in Fig. 2a. As the average energy increases, the fraction having some particular extra energy increases. Under both these influences, the fraction having total energy enough to reach the activated state (E* or TR) increases with temperature. In effect, we are measuring the temperature dependence of this rate.
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