For a certain reaction, rate = \(k[A]^2[B]\). When the initial concentration of A is tripled, keeping the concentration of B constant, the initial rate would
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → increase by a factor of nine.
In a rate law, each concentration is raised to its order. Here the reaction is second order in A and first order in B, so the rate changes as the square of [A].
Initial rate:
\( \displaystyle r_1=k[A]^2[B] \)
With [A] tripled and [B] unchanged:
\( \displaystyle r_2=k(3[A])^2[B]=9\,k[A]^2[B] \)
\( \displaystyle \frac{r_2}{r_1}=9 \)
The initial rate would increase by a factor of nine.