In a reactio between A and B, the initial rate of reaction `(r_(0))` was measured for different initial concentrations of A and B as given below :

What is the order of the reaction with respect to A and B?

Explanation

Rate law states that
`(Rate)=k[A]^(x)[B]^(y)` m
`(Rate)_(1)=k[0.20]^(x)[0.30]^(y) =5.07xx10^(-5)-(i)`
`(Rate)_(2) =k [0.20] ^(x) [0.10]^(y)=5.07 xx10^(-5)-(ii)`
`(Rate)_(3)=k[0.40]^(x)[0.05]^(y)=1.43xx10^(-4)-(iii)`
Dividing equation (i) by equation (ii)
`((Rate)_(1))/((Rate)_(2))=(k[0.20]^(x))/(k[0.20]^(x))([0.30]^(y))/([0.10]^(y))=(5.07xx10^(-5))/(5.07xx10^(-5))=1`
`[3]^(y)=[3]^(0)=1,y=0`
Dividing equation (ii) by equation (iii) `((Rate)_(2))/((Rate)_(3))=(k[0.20]^(x)[0.10]^(0))/(k[0.40]^(x)[0.05]^(0))=(5.07xx10^(-5))/(1.43xx10^(-4))`
`[(1)/(2)]^(x) =(1)/(2.82),2^(x) =2.82`
`x log 2 = log 2.82`
`x=1.4957=1.5` ltbgt `therefore` order with respect to `A=1.5`
order with respect to `B=0.`