For the reaction `A + B rarrC + D` , doubling the concentration of both the reactants increases the reaction rate by 8 times and doubling the concentration of only B simply doubles the reaction rate. Find the rate law for the above equation.

Options

A. `r=k[A]^(1//2)[B]^(1//2)`
B. `r=k[A][B]^(2)`
C. `r=k[A]^(2)[B]`
D. `r=k[A][B]`

Answer

C

Explanation

`(i) r = k a^(alpha) b^(beta)`
(ii) `8 r = k ( 2a)^(alpha) ( 2b)^(beta)`
`(iii) 2r = ka^(alpha)(2b)^(beta)`
Eqn. (ii) Eqn. (iii) gives `(8)/(2) = 2^(alpha)`
or `2^(alpha) = 4 = 2^(2) or alpha = 2.` ,
Eqn. (iii) Eqn. (i) gives `2 = 2^(beta) or beta = 1`, Hence rate ` = k[A]^(2) [B].`