Several techniques have been developed to determine the order of a reaction. The rate of a reaction cannot be predicted on the basis of the overall equation, but can be predicted on the basis of the rate-determining step. For instance, the following reaction can be broken down into three steps.
Step 1
(Slow)
Step 2
(fast)
Step 3
(fast)
Reaction 1
In this case, the first step in the reaction pathway is the rate-determining step. Therefore, the overall rate of the reaction must equal the rate of the first step, k1 [A] where k1 is the rate constant for the first step. (Rate constants of the different steps are denoted by kx , where x is the step number.)
In some cases, it is desirable to measure the rate of a reaction in relation to only one species. In a second-order reaction, for instance, a large excess of one species is included in the reaction vessel. Since a relatively small amount of this large concentration is reacted, we assume that the concentration essentially remains unchanged. Such a reaction is called a pseudo first-order reaction. A new rate constant, k', is established, equal to the product of the rate constant of the original reaction, k, and the concentration of the species in excess. This approach is often used to analyze enzyme activity.
In some cases, the reaction rate may be dependent on the concentration of a short-lived intermediate. This can happen if the rate-determining step is not the first step. In this case, the concentration of the intermediate must be derived from the equilibrium constant of the preceding step. For redox reactions, the
equilibrium can be correlated with the voltage produced by two half-cells by means of the Nernst equation.
This equation states that at any given moment:
Equation 1
When
Reaction 2
Note: R = 8.314 J/K-mol; F = 9.6485 x 104 C/mol.) In a test of the rate of Step 3 of Reaction 1, a solution is prepared containing a 0.1 M concentration of E and a 50 M concentration of C. The rate is calculated after the reaction has gone 50% to completion.
By what percent will the calculated rate differ from the true rate if we treat the reaction as pseudo first-order?