For the reaction `A+B rarr C`. The following data were obtained. In the first experiment, when the initial concentrations of both `A` and `B` are `0.1 M`, the observed initial rate of formation of `C` is `1xx10^(-4) mol litre^(-1) minute^(-1)`. In the second experiment when the initial concentrations of `A` and `B` are `0.1 M` and `0.3 M`, the initial rate is `9.0xx10^(-4) mol liter^(-1) "minute"^(-1)`. In the third experiment when the initial concentrations of both `A` and `B` are `0.3M` the initial rate is `2.7xx10^(-3) mol litre^(-1) "minute"^(-1)`.
(a) Write rate law for this reaction.
(b) Calculate the value of specific rate constant for this reaction.

Explanation

Let `" Rate "=K[A]^(m)[B]^(n)`
`r_(1)=1xx10^(-4) =K[0.1]^(m)[0.1]^(n)" ….(1)"`
`r_(2)=9xx10^(-4)=K[0.1]^(m)[0.3]^(n)" ….(2)"`
`r_(3)=2.7xx10^(-3)=K[0.3]^(m)[0.3]^(m)" ….(3)"`
By Eqs. (1) and (2),
`(r_(1))/(r_(2))=(1xx10^(-4))/(9xx10^(-4))=((1)/(3))^(n)`
`therefore" "n=2`
By Eqs. (2) and (3),
`(r_(2))/(r_(3))=(9xx10^(-4))/(27xx10^(-4))=((1)/(3))^(m)`
`m=1`
`therefore" Rate "=K[A]^(1)[B]^(2)`