Final answer:
The rate of the reaction will increase by a factor of 4 when both concentrations of [A] and [B] are doubled.
Step-by-step explanation:
The rate of the reaction will increase by a factor of 4 when both concentrations of [A] and [B] are doubled.
The rate law for this reaction is rate = k[A][B]. Doubling the concentration of A will result in the rate becoming 2k[A][B] and doubling the concentration of B will result in the rate becoming k[2A][2B].
When both concentrations are doubled, the rate becomes 2k[2A][2B], which simplifies to 4k[A][B]. Therefore, the rate of the reaction increases by a factor of 4.