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 ?

Options

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

Answer

B

Explanation

Let rate, `r[A]^(x)[B]^(y)`
`((2a)^(x)(2b)^(y))/((a)^(x)(b)^(y))=(8)/(1)`
`2^(x)+y=2^(3)`
`x+y=3`
`((a)^(x)(2b)^(y))/((a)^(x)(b)^(y))=(2)/(1)`
`2^(y)=2`
y = 1
`therefore x = 2`
`therefore r = [A]^(2)[B]`