A particular reactant decomposes with a half‑life of 137s when its initial concentration is 0.289 M. The same reactant decomposes with a half‑life of 233s when its initial concentration is 0.170 M.

Question

A particular reactant decomposes with a half‑life of 137s when its initial concentration is 0.289 M. The same reactant decomposes with a half‑life of 233s when its initial concentration is 0.170 M.

Determine the reaction order.

A). 0

B). 1

C). 2

What is the value and units of the rate constant for this reaction?

K=?

Answer 1

The relationship of half life to concentration for the different order reactions is as follows:

zero order: t_1/2 = [A]_o / 2k

1st order: t_1/2 = ln (2) / k

2nd order: t_1/2 = 1 / k[A]_o

Since the half life in the current example changes with the initial concentration [A]_o, we know it cannot be first order.

Also notice that the half life in this example is INVERSELY related to the initial concentration [A]_o. That is, when [A]_o = 0.289 M, t_1/2 = 137 s and when [A]_o = 0.170 M, t_1/2 = 233 s. Of zero and 2nd order, only 2nd order shows such a relationship. So, we can conclude the reaction is 2nd order.

To find k, simply solve the equation for k, and if this is the correct answer, k should be the same for both conditions.

t_1/2 = 1 / [A]_ok

For [A]_o = 0.289 M, t_1/2 = 137 s

137 s = 1 / 0.289 k

k = 0.0253 M^-1s^-1

For [A]_o = 0.170 M, t_1/2 = 233 s

233 = 1/ 0.170 k

k = 0.0252 M^-1s^-1