kinetics summary

Question

In reaction A + B ---> P the following results were obtained for the initial rates of reaction for different initial concentrations. Deduce the rate equation and calculate the rate constant.

Experiment [A] [B] Rate [M s^-1]

1 10 10 0.002

2 20 10 0.004

3 40 20 0.016

Answer 1

Rate equation is of the form rate = k[A]^a[B]^b

In order to find a and b, we use the data supplied and compare 2 experiments in which [A] varies and [B] is constant to find a, and then compare 2 others where [B] varies and [A] is constant.

To find a, compare experiments 1 and 2. [A] doubles and [B] is constant. The rate doubles. This tells us the reaction is first order in A, and a = 1.

To find b, compare experiments 1 and 3. [B] doubles, but unfortunately [A] also changes by 4 times. There are no experiments where [A] is constant. But since we already that the rate should increase by 4 x when [A] increases by 4x (from the first comparison above), we can use this anyway. The rate between experiments 1 and 3 increases by 8 times. Since it would have increased by 4x anyway even without a change in [B], we can conclude the extra increase is due to B and so doubling [B] from 10 to 20 increased the rate by 2x, so it is first order in B and b= 1. (note: we could have compared expts 2 and 3 and obtained the same result)

The rate equation thus becomes:

rate = k[A]¹[B]¹ = k[A][B]

To find the rate constant k, just choose any experiment and plug in the corresponding values into the rate equation. I'll choose experiment #1.

rate = k[A][B]

0.002 Ms^-1 = k[10 M][10 M] (assuming the concentrations are given in M)

k = 0.002 Ms^-1 / 100 M²

k = 2x10^-5 M^-1s^-1