Activation energy, apparent transition state theory

Relationships between reaction rate and temperature can thus be used to detect non-classical behaviour in enzymes. Non-classical values of the preexponential factor ratio (H D i 1) and difference in apparent activation energy (>5.4kJmoRi) have been the criteria used to demonstrate hydrogen tunnelling in the enzymes mentioned above. A major prediction from this static barrier (transition state theory-like) plot is that tunnelling becomes more prominent as the apparent activation energy decreases. This holds for the enzymes listed above, but the correlation breaks down for enzymes... 

Clyne and Stedman consider the discussion in terms of transition state theory to be more realistic since it predicts an increase with temperature of the apparent activation energy due to large increase with temperature of the vibrational partition function for the H-H-Cl bending mode. This increase occurs for a wide variety of models of the potential surface. 

However, there remains a serious problem in interpreting this work. Plots of both log and log 2 versus IjT show considerable curvature corresponding to an apparent increase in activation energy with temperature. Part of this increase, but by no means all of it, can be accounted for using transition state theory and allowing for excitation of vibrational modes. 

In this section we shall show that, if the apparent energy of activation is temperature-dependent, the same must be true for the pre-exponential factor. We shall then consider some results of the transition state theory, and describe two mathematical forms in which the temperature-dependence of In k and of Ea can conveniently be expressed. 

Krasnoperov LV, Peng J, Marshall P. (2006) Modified transition state theory and negative apparent activation energies of simple metathesis reactions Apphcation to the reaction CH3 + HBr —> CH4 + Br. J. Phys. Chem. A. 110 31KE3120. 

The application of Absolute Rate Theory to the interpretation of catalytic hydrogenation reactions has received relatively little attention and, even when applied, has only achieved moderate success. This is, in part, due to the necessity to formulate precise mechanisms in order to derive appropriate rate expressions [43] and, in part, due to the necessity to make various assumptions with regard to such factors as the number of surface sites per unit area of the catalyst, usually assumed to be 10 5 cm-2, the activity of the surface and the immobility or otherwise of the transition state. In spite of these difficulties, it has been shown that satisfactory agreement between observed and calculated rates can be obtained in the case of the nickel-catalysed hydrogenation of ethylene (Table 3), and between the observed and calculated apparent activation energies for the... 

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