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 præ-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 times^2–6. 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 theoretically^2,5: