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),(1.0xx10^(-2),0.010,0.010,0.010),(1.25xx10^(-3),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`

Explanation

Suppose order w.r.t. A, B and C are `alpha, beta and gamma` respectively. Then
`5*0 xx 10^(-3) = (0*010)^(alpha) (0.005)^(beta) (0.010)^(gamma)" "…(i)`
`5*0 xx 10^(-3) = (0*10)^(alpha)(0.005)^(beta) (0*015)^(gamma)" "…(ii)`
`1*0 xx 10^(-2) = (0*010)^(alpha) (0*010)^(beta) (0.010)^(gamma) " "...(iii)`
`1*25 xx 10^(-3) = (0*005)^(alpha)(0.005)^(beta) (0.010)^(gamma)" "...(iv)`
Dividing (i) by (ii)
1=((0*010)/(0*015))^(gamma)or((2)/(3))^(gamma)=1=((2)/(3))^(0)thereforegamma=0`
Dividing (iii) by (ii),
`(1*0 xx 10^(-2))/(5*0 xx 10^(-3)) = (2)^(beta) ((2)/(3))^(gamma) or 2 = (2)^(beta) ((2)/(3))^(0) = 2^(beta)`
or `2^(beta) = 2 or beta =1.`
Dividing (i) by (iv), 4 = `(2)^(alpha) or alpha = 2 `
`therefore` Orders w.r.t. A , B and C are 2, 1, 0.