Concerning the Isokinetic Relationship

Abstract

IN contemporary kinetic studies, the values of rate constants are often expressed by means of activation parameters, either by the activation energy E* and the prae-exponential factor A, or by the activation enthalpy ΔH≠ and entropy ΔS≠. For further discussions in terms of substituent or solvent effects and similar theories of organic chemistry, many authors1 prefer the free activation energy ΔG≠ (that is, the logarithm of the rate constant) at an arbitrary temperature before the activation energy E* or enthalpy ΔH≠. If the results of such discussions have to be independent of the arbitrary temperature, a functional dependence must exist between the activation parameters in a series of related reactions. This dependence is also the necessary condition2 for the validity of various linear free-energy relationships (for example, Hammett equation) at different temperatures. In fact, linear relationships obtained by plotting E* versus log A or ΔH≠ versus ΔH≠ have been described many times2–6. They are referred to as the isokinetic relationship2 or the compensation law4 (equations 1a and b). The proportionality factor β, called the isokinetic temperature, has been also discussed theoretically2,5: