For the reaction `A+Brarr` product , (a) the rate of reaction doubles on doubling the concentration of A. (b) the rate of reaction increases by four times on doubling the concentration of B. Determine the overall order of the reaction ?

Explanation

Reaction -rate , `r=k[A]^(x)[B]^(y)" "…[1]`
When the concentration of A gets double, the reaction -rate,
`2r=k[2A]^(x)[B]^(y)=2^(x)k[A]^(x)[B]^(y)" "...[2]`
When the concentration of B gets double , the reaction-rate
`4r=k[A]^(x)[2B]^(y)=2^(y)k[A]^(x)[B]^(y)" "...[3]`
By `(2)div(1)" we get," 2^(x)=2therefore x = 1 and (3) div(1) " we get, " 4 = 2^(y)`
`4=2^(y)`
`therefore y= 2 `
`therefore ` Overall order of the reaction = x + y = 1 + 2 = 3