II. Absolute and Relative Rate Constants

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Two types of rate constants commonly are associated with radical reactions. One of these is the actual (sometimes call absolute) rate constant for a reaction, and the other is a relative rate constant, that is, a value determined by comparing the rate of one reaction to that of another.

The absolute rate constant k_a for the reaction shown in eq 1 is defined mathematically in eq 2.¹ Although the value of k_a is expressed in terms of the rate of disappearance of AB or appearance of RAB· and the concentrations of R· and AB, rarely can k_a be determined directly from this information. Because most radicals are highly reactive species that are present in a reaction mixture in concentrations typically too low to be measured accurately, direct determination of rate constants such as k_a seldom is possible. When a direct determination cannot be made, sometimes an indirect one can.

(1), (2).png

On way for determining indirectly the rate constant for the reaction shown in eq 1 depends upon being able to measure the buildup of trace amounts of RAB· at different AB concentrations. Even though the actual concentration of RAB· is unknown, for some radicals it is possible to determine accurately their rate of appearance from the change in one of their properties (e.g., UV absorption). This information can provide a basis for indirectly determining the rate constant k_a.²

Relative rate constants are far easier to determine than actual rate constants because relative ones can be obtained without knowing radical concentrations or making any measurements on radicals. When CD and EF are present in the same reaction mixture, eq 5 describes a relation between the rate constants k₁ and k₂ for the competing reactions shown in equations 3 and 4. The ratio k₁/k₂ is determined by the concentrations of CD and EF and their rates of disappearance.¹ If, for example, the concentrations of CD and EF are equal and CD disappears ten times more rapidly than EF, the relative rate constants of 10 and 1 can be assigned to k₁ and k₂, respectively. Further, if the absolute rate constant is known for one of these two reactions, the relative rate constant for the other can be converted into an absolute one. More generally, if the absolute rate constant is known for one member of a group of reactions for which relative rate constants have been determined, the relative rate constants all can be converted into absolute ones.

(3)-(5).png

Although measuring product ratios provides relative rate constants for reactions of a radical with two or more compounds, determining the relative rate constants for reaction of two different radicals with a single compound is a much more difficult task. There is no reliable way to run a competition experiment. Comparing the reactivity of two (or more) radicals with a particular compound usually requires determining absolute rate constants.³