For the elementary reaction `aA+bBrarr` product, the initial reaction-rate is `r_(0)` if the initial concentration of A is doubled and that of B is held constant, the reaction-rate becomes `4r_(0)` On doubling the initial concentration of both A and B, the reaction-rate become `8r_(0)` Which one of A and B , the disappears to a larger extent at a given time?

Explanation

As the given reaction is an elementary reaction , its rate equation can be written from the balanced equation
Rate , `r=k[A]^(a)[B]^(b)`
If the initial concentrations of A and B are `[A]_(0) and [B]_(0)`
respectively, then `r_(0)=k[A]_(0)^(a)[B]_(0)^(b)" "....[1]`
Given , `4r_(0)=k[2A]_(0)^(a)[B]_(0)^(b)=2axxk[A]_(0)^(a)[B]_(0)^(b) " "....[2]`
and `8r_(0)=k[2A]_(0)^(a)[2B]_(0)^(b)=2^(a)xx2^(b)xxk[A]_(0)^(a)[B]_(0)^(b) " "....[3]`
Dividing equation [2] by equation [1] gives , `2^(a)=4=2^(2) `
`therefore` a = 2
Dividing equation [3] by equation [2] gives , `2^(b)=2=2^(1) `
`therefore b = 1 `
Hence , the balanced equation for the reaction:
`2A+Brarr` product
Reaction -rate = `-(1)/(2) (d[A])/(dt)=-(d[B])/(dt)=k[A]^(2)[B]`
`therefore` The rate of disappearance of A
`(-(d[A])/(dt))=2xx` the rate of disappearance of B `(-(d[B])/(dt))`
Hence , A disappears at a faster rate than B.