Consider the rate below
r=k[a][b]^2
which step would quadruple the rate?
doubling the concentration of a
doubling the concentration of b
doubling the concentration of both a and b
doubling the concentration of a but halving the concentration of b

B.Doubling the concentration of B.

Explanation:

Consider the rate below

We have to find the rate of reaction is quadruple means the rate of reaction is 4 times the rate of initial rate of reaction.

Let [A}=a,[B]=b then

a. doubling the concentration of A

It means  [A]=2a

Therefore , substituting the value

Then we get the rate of reaction

Therefore , the rate of reaction is 2 times the initial rate of reaction.Hence, option A is false.

B.Doubling the concentration of B

It means [B]=2b

Therefore , substituting the value

Then we get the rate of reaction

Hence, the rate of reaction is 4 times the initial rate of reaction .Therefore, the rate of reaction is quadruple.Therefore, option B is true.

C.Doubling the concentration of both A and B

[A]=2a, [B]=2b

Substitute the values then the rate of reaction

Hence, the rate of reaction is 8 times the initial rate of reaction .Therefore, it is not quadruple.Therefore, option C is false.

D.Doubling the concentration of A but halving the concentration of B

[A]=2a, [B]=

Substitute the values then the rate of reaction

Hence, the rate of reaction  is times the rate of initial rate of reaction.Therefore, option D is false.