For the non-stoichiometric reaction `2A+BrarrC+D`
The following kinetic data were obtained in theee separate experiment, all at `98 K`
`|{:("Initial concentration (A)","Initial concentration (B)","Initial rate of formation of C" (molL^(-1) s^(-1))),(0.1 M,0.1 M,1.2 xx 10^(-3)),(0.1 M,0.2 M,1.2 xx 10^(-3)),(0.2 M,0.1 M,2.4 xx 10^(-3)):}|`
The rate law for the formation of `C` is:

Options

A. `(dc)/(dt)=k[A][B]^(2)`
B. `(dc)/(dt)=k[A]`
C. `(dc)/(dt)=k[A][B]`
D. `(dc)/(dt)=k[A]^(2)[B]`

Answer

B

Explanation

Let order with respect to A and B are `alpha and beta` resepecitvely
`:. (dc)/(dt)=k[A]^(alpha)[B]^(beta)`
`1.2xx10^(-3)=k[0.1]^(alpha)[0.1]^(beta)" ".....(i)`
`1.2xx10^(-3)=k[0.1]^(alpha)[0.2]^(beta)" ".....(ii)`
`2.4xx10^(-3)=k[0.2]^(alpha)[0.1]^(beta)" ".....(iii)`
`{:("Dividing (ii) by (i)":,2^(beta),:.beta=0),("Dividing (ii)by(i)":,2^(alpha)=2,:.alpha1),("Rate law will be ":,,):}`
`(dc)/(dt)=k[A]`