Determination of Rate Laws

The simplest way to determine a rate law is the method of initial rates. If a reaction is slow enough, it can be allowed to proceed for a short time, Δt, and the change in a reactant or product concentration measured. Repeating the experiment for different concentrations, the concentration-dependence of the rate can be deduced.

Example 1

For the reaction, A + B → C, three rate experiments yielded the data shown in the first four columns of the table, where [A]₀ and[A]_f are [A] values at the beginning and end of the experiment, repectively:

Determine the orders of the reaction in A and B, the overall order, and the rate constant k.  Since we know Δ[A] for the three experiments, the initial rate is

and these values are given in the fifth column of the table. Compare the first and second experiments. [A] was held constant, [B] was doubled, and the rate increased by a factor of 4; we conclude that the reaction is second-order in B. Compare the first and third experiments where [B] was constant and [A] was halved; the rate decreased by a factor of 2, and we conclude that the reaction is first-order in A. Thus the reaction is third-order overall. The first experiment gives: