During the kinetic study of the reaction, 2A + B `rarr` C + D, following results were obtained :

Based on the above data which one of the following is correct?

Options

A. Rate = `k[A]^(2)`[B]
B. Rate = k[A][B]
C. Rate = `k[A]^(2) [B]^(2)`
D. Rate = `k[A][B]^(2)`

Answer

D

Explanation

Let the rate of reaction be given by : rate = `k[A]^a[B]^b`.
Now consider II and III run, where [A] is constant.
`(7.2xx10^(-2))/(2.88xx10^(-1))=([0.3]^a[0.2]^b)/([0.3]^a[0.4]^b)1/4=(1/2)^bimplies b=2`
Now consider I and IV run,
`(6.0xx10^(-3))/(2.4xx10^(-2))=([0.1]^a[0.1]^b)/([0.4]^a[0.1]^b)1/4=(1/4)^b` a=1
`therefore` Rate =k[A]`[B]^2`