Question

How do you determine the rate of a reaction that follows the rate law: rate = `k[A]^m[B]^n`, where k = `1 x 10^-2`, [A] = 2 M, [B] = 3 M, m = 2, and n = 1?

Answer 1

You insert the numbers into the rate law.

Explanation:

You must remember that the rate constant `k` has units.

Since `m + n = 2 + 1 = 3`, the overall order of the reaction is 3.

The units of the rate constant for a third order reaction are `"L"^2"mol"^"-2""s"^"-1".`

Then

`"rate" = k["A"]^m["B"]^n = 1 × 10^"-2" color(red)(cancel(color(black)("L"^2 "mol"^"-2")))"s"^"-1" × (2 color(red)(cancel(color(black)("mol·L"^"-1"))))^2 × (3 "mol·L"^"-1")^1`
`= 1 × 10^"-2" color(white)(l)"s"^"-1" × 4 × 3 color(white)(l)"mol·L"^"-1" = "0.1 mol·L"^"-1""s"^"-1"`