Review of Chemical Kinetics

Before beginning a quantitative treatment of enzyme kinetics, it will be fruitful to review briefly some basic principles of chemical kinetics. Chemical kinetics is the study of the rates of chemical reactions. Consider a reaction of overall stoichiometry

A ® P

Although we treat this reaction as a simple, one-step conversion of A to P, it more likely occurs through a sequence of elementary reactions, each of which is a simple molecular process, as in

A ® I ® J ® P

where I and J represent intermediates in the reaction. Precise description of all of the elementary reactions in a process is necessary to define the overall reaction mechanism for A ® P.

Let us assume that A ® P is an elementary reaction and that it is spontaneous and essentially irreversible. Irreversibility is easily assumed if the rate of P conversion to A is very slow or the concentration of P (expressed as [P]) is negligible under the conditions chosen. The velocity, v, or rate, of the reaction A ® P is the amount of P formed or the amount of A consumed per unit time, t. That is,

or (14.1)

The mathematical relationship between reaction rate and concentration of reactant(s) is the rate law. For this simple case, the rate law is

(14.2)

From this expression, it is obvious that the rate is proportional to the concentration of A, and k is the proportionality constant, or rate constant. k has the units of (time) ^-1, usually sec^-1. v is a function of [A] to the first power, or, in the terminology of kinetics, v is first-order with respect to A. For an elementary reaction, the order for any reactant is given by its exponent in the rate equation. The number of molecules that must simultaneously interact is defined as the molecularity of the reaction. Thus, the simple elementary reaction of A ® P is a first-order reaction. Figure 14.4 portrays the course of a first-order reaction as a function of time. The rate of decay of a radioactive isotope, like ¹⁴C or ³²P, is a first-order reaction, as is an intramolecular rearrangement, such as A ® P. Both are unimolecular reactions (the molecularity equals 1).

Figure 14.4 •Plot of the course of a first-order reaction. The half-time, t_1/2, is the time for one-half of the starting amount of A to disappear.

Date: 2016-01-03; view: 963