For the reaction `A + B rarr C + D`, doubling the concentration of both the reactants increases the reaction rate by `8` times and doubling the initial concentration of only `B` ismply doubles the reaction rate. What is the rate law for the reaction ?

Explanation

For the reaction `A + B rarr C + D`
Rate of reaction:
`r_(1) = k[A]^(x)[B]^(y)` …(i)
`r_(2) = 8r_(1) = k[2A]^(x)[2B]^(y)` …(ii)
`r_(3) = 2r_(1) = k[A]^(x)[2B]^(y)` …(iii)
Dividing Eq. (iii) by Eq. (i).
`(2r_(1))/(r_(1)) = (k[A]^(x)[2B]^(y))/(k[A]^(x)[B]^(y))`
`(2)^(1) = (2)^(y)`
`y = 1`
Dividing Eq. (ii) by Eq. (i),
`(8r_(1))/(r_(2)) = (k[2A]^(x)[2B]^(y))/(k[A]^(x)[B]^(y))`
`8 = (2)^(x)(2)^(y)`
`8 = (2)^(x)(2)^(1)`
`4 = (2)^(x)`
`(2)^(2) = (2)^(x)`
`x = 2`
`:. r = k[A]^(2)[B]`