The reaction A + 2 B → C has the rate law rate = k[A][B]. By what factor does the rate of reaction increase when both [A] and [B] are doubled?

Question

The reaction A + 2 B → C has the rate law rate = k[A][B]. By what factor does the rate of reaction increase when both [A] and [B] are doubled?

Answer 1

Rate = k[A][B]

This means the rate is directly proportional to the concentration of A and B, i.e. first order in both.

So, if [A] doubles, and [B] stays the same, the rate will double.

If [B] doubles, and [A] stays the same, the rate will double.

If both [A] and [B] double, the rate will increase by 4 times.

You can see this mathematically from the rate law as follows:

Rate = k[2][2] = 4k and since k is constant, the rate will be 4x what it was when the [A] and [B] were each 1.