From the following data for the reaction between A and B

Calculate the following
(i) The order of the reaction with respect to A and with respect to B
(ii) The rate constant at 300K
(iii) The energy of activation and
(iv) The pre-exponential factor.

Explanation

(i) Let the rat law be :
Rate= `k[A]^(x)[B]^(y)`
`"From expt".(1),5.0xx10^(-4)=k[2.5xx10^(-4)]^(x)[3.0xx10^(-5)]^(y)" "....(i)`
`"From expt".(2),4.0xx10^(-4)=k[5.0xx10^(-4)]^(x)[6.0xx10^(-5)]^(y)" "....(ii)`
Dividing by eq. (i), `(4.0xx10^(-3))/(5.0xx10^(-4))=2^(x)*2^(y)=8`
`"From expt".(3),1.6xx10^(-2)=k[1.0xx10^(-3)]^(x)[6.0xx10^(-5)]^(y)" "....(iii)`
`"From expt".(1),5xx10^(-4)=k[2.5xx10^(-4)]^(2)[3.0xx10^(-5)]`
or `k=(5xx10^(-4))/([2.5xx10^(-4)]^(2)[3.0xx10^(-5)])=2.67xx10^(8)L^(2)"mol"^(-2)s^(-1)`
(iii) From Arrhenius eqauation,
`log_(10).(2.0xx10^(-3))/(5.0xx10^(4))=(E_(a))/(2.3030xx8.314)xx(20)/(300xx320)`
`E_(a)=(2.303xx8.314xx300xx320)/(20)xxlog_(10)4`
(iv) Applying `log_(10) k=log_(10) A-(E_(a))/(2.3030RT)`
`log_(10).(A)/(k)=(55333)/(2.3030xx8.314xx300)=9.633`
or `(A)/(k)=4.29xx10^(9)`
or `A=4.29xx10^(9)xx2.67xx10^(8)`
`=1.145xx10^(18)`