The initial rates of reaction `3 A+ 2B +C rarr` products at different initial concentration are given below
`{:("Initial rate, MS"^(-1),|A_(0)|M,|B_(0)|M,|C_(0)|M),(5.0xx10^(-3),0.010,0.005,0.010),(5.0xx10^(-3),0.010,0.005,0.015),(10xx10^(-2),0.010,0.010,0.010),(1.25xx10^(-2),0.005,0.005,0.010):}`
The order of reaction with respect to the reacts A, B and C are respectively.

Options

A. 3,2,0
B. 3,2,1
C. 2,2,0
D. 2,1.0

Answer

D

Explanation

Suppose order of reaction w.r.t. A, B, and C are `alpha, beta and gamma` respetively, Then
`5.0 xx10^(-3)=(0.010)^(alpha)(0.005)^(beta)(0.010)^(gamma)`....(i)
`5.0xx10^(-3)=(0.010)^(alpha)(0.0105)^(beta)(0.015)^(gamma)` ....(ii)
`1.0xx10^(-2)=(0.010)^(alpha)(0.010)^(beta)(0.010)^(gamma)`....(iii)
`1.25xx10^(-3)=(0.015)^(alpha)(0.010)^(beta)(0.010)^(gamma)`....(iv)
Dividing (i) by (ii)
`1=((0.010)/(0.015))^(alpha)=(2)^(beta)((2)/(3))^(gamma)or 2=(2)^(beta)((2)/(3))`
or `2^(beta)=or B=X`
Dividing (i) by (iv) `4 = (2)alpha or alpha =2`
`:.` order w.r.t. A,B and C are `2,1,0`