Elucidation of Reaction Mechanisms - Kinetic Isotope Effects

Primary Kinetic Isotope Effects - PKI

The reaction rate of a chemical reaction is determined by the rate of the slowest individual step (elementary reaction), called the rate-determining step. The $Ea$ of the rate-determining step is the highest of all individual steps of the chemical reaction. The reaction rate, or rather the rate constant, is related to the activation energy $Ea$ by the Arrhenius equation. In the most fundamental case, which is a one-step reaction, the Arrhenius equation is:

ln k = - $Ea$ / RT + ln A

with k = rate constant of the reaction, R = general gas constant, T = temperature in Kelvin and A = constant.

The higher the activation energy $Ea$ is, the lower the reaction rate is, as well. Therefore, the overall reaction rate can be increased by lowering the activation energy $Ea$ of the rate-determining step. A decrease in the activation energy $Ea$ of one or more of the non-rate-determining steps virtually never influences the overall reaction rate, as all reactants still have to pass through the unaltered rate-determining step.

Fig.1
Examples of primary kinetic isotope effects.

Top) Lit. [1].   Middle) Lit. [2].   Below) Lit. [3].

When the overall reaction rate is decreased by the exchange of an H for a D from the X-H bond (X = C, O, N, S, etc.) that is cleaved during the rate-determining step, this effect is known as primary kinetic isotope effect. The cause of this effect is the elevation of the activation energy of the rate-determining step, arising from the H/D exchange. When a primary kinetic isotope effect appears as a result of an H/D exchange, the individual reaction step in which the corresponding X-H/X-D bond is cleaved proves to be the rate-determining step of the overall reaction. If, in spite of an H/D exchange, no primary isotope effect is obtained - that is, if the reaction rate has hardly been altered, if at all - the corresponding X-H/X-D bond is not cleaved during the rate-determining step.

The identification of the rate-determining step is often very significant to the chemist, as the overall reaction rate can be increased by stabilizing the of this reaction step (). The stabilization of the transition state is meant to lower its energy and, therefore, to also lower the activation energy $Ea$. In contrast, the overall reaction rate is not influenced by lowering the energy of the transition state of one of the non-rate-determining steps.

Literature

1. Wiberg, K.B., Slaugh, L.H., J. Am. Chem. Soc. 1958, 80, 3033.
2. Saunders, W.H., Ashe, Jr. and T.A., J. Am. Chem. Soc. 1969, 91, 4473.
3. Lynch, R.A., Vincenti, S.P., Lin, Y.T., Smucker, L.D., Subba Rao, S.C., J. Am. Chem. Soc. 1972, 94, 8351.
Page 2 of 5