For a reaction : ` A to B to ` Products , the rate of the reaction at various concentrations are given below :

The rate law for the above reaction is

Options

A. A) `r = k [A]^(2) [B]`
B. B) `r = k [A] [B]^(2)`
C. C) `r = k [A]^(3) [B]`
D. D) `r = k [A]^(2) [B]^(2)`

Answer

A

Explanation

`A to B to ` Products
Rate = `k [A]^(alpha) [B]^(beta)`
From expt. No. 1
`2 = k[0.2]^(alpha) [0.2]^(beta) " " … (1)`
From expt. No. 2
`4 = k [0.2]^(alpha) [0.4]^(beta) " " …. (2)`
dividing eq. (1) and (2) we get `(2)/(4) = (k[0.2]^(alpha) [0.2]^(beta))/(k[0.2]^(alpha) [0.4]^(beta)) or (1)/(2) = [(1)/(2)]^(beta) implies beta = 1`
From expt. No. 3
`36 k = [0.6]^(alpha) [0.4]^(beta) " " ... (3)`
dividing eqn. (2) and (3) we get
`(4)/(36) = (k[0.2]^(alpha) [0.4]^(beta))/(k[0.6]^(alpha) [0.4]^(beta)) or (1)/(9) = [(1)/(3)]^(alpha) implies alpha = 2 `
`implies` Rate law for the given reaction is `r = k [A]^(2) [B]^(1)`