Question

What is the order of a reaction if its rate increases by a factor of 13 when the reactant concentration increases by a factor of 3.6?

Answer 1

The reaction is second order.

Explanation:

For a reaction

`"A + … → products"`

the rate law is

`r = k"[A]"^m`

where

`rcolor(white)(l) =` the reaction rate
`k color(white)(l)=` the rate constant
`m =` an integer whose value we must determine

Consider two experiments.

We can divide one rate law by the other.

`r_2/r_1 = (color(red)(cancel(color(black)(k)))(["A"]_2) ^m)/(color(red)(cancel(color(2black)(k)))(["A"]_1)^m) = (["A"]_2/["A"]_1)^m`

If `(["A"]_2)/(["A"]_1) = 3.6` and `r_2/r_1 = 13`, we get

`3.6^m =13`

Take the logarithm of each side.

`color(blue)(mlog3.6 = log13)`

`color(blue)(m = log13/log3.6 = 2.0 ≈ 2)`

The reaction is second order in `"[A]"`.