For the reaction `A+BrarrC+D` , it is found that rate of reaction doubles when the concentration of B is doubled and increases by 8 times on doubling the concentration of both A and B . Write the rate equation of the reaction.

Explanation

`r=k[A]^(x)[B]^(y)" " ...[1]`
`8r=k[2A]^(x)[2B]^(y)=2^(x+y)k[A]^(x)[B]^(y)" " ..[2]`
`2r=k[A]^(x)[2B]^(y)=2^(y)k[A]^(x)[B]^(y)" " ..[3]`
By `(2)div(1) " we get " 8 = 2^(x+y) and by (3) div (1) "we get, " 2^(y)=2`
`therefore y = 1 , therefore 2^(x+1)=2^(3)" or, " x+1=3 therefore x = 2 `
`therefore " Reaction -rate " = k [A]^(2)[B]`