From the following data for the reaction between A and B

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

Explanation

(i) A=2, B=1 (ii) `k=2.66xx^(8) s^(-1) L^(2)" mol"^(-2)` (iii) `A=1.2xx10^(18)` Comparing the data of experiment number 2 and 3 :
`(R_(3))/(R_(2)) =(1.6xx10^(-2))/(4xx10^(-3))=((1.0xx10^(-3))/(5xx10^(-4)))^(m) rArr m=2,` order w.r.t. A Now comparing the data of experiment number 1 and 2 :
`(R_(2))/(R_(1)) =(4xx10^(-3))/(5xx10^(-4))=((5xx10^(-4))/(2.5xx10^(-4)))^(2) ((6.0xx10^(-5))/(3.0xx10^(-5)))^(n)`
`rArr 8=(2)^(2) (2)^(n) rArr n=1`, order w.r.t B.
(i) Order with respect to A = 2, order with respect to B = 1.
(ii) At `300 K, R =k[A]^(2) [B]`
`rArr k=(R)/([A]^(2) [B]) =(5.0xx10^(-4))/((2.5xx10^(-4))^(2) (3.0xx10^(-5)))=2.66xx10^(8) s^(-1) L^(2)" mol"^(-2)`
(iii) From first experiment :
Rate `(320 K) =k (320 K) (2.5xx10^(-4)) 2 (3.0xx10^(-5))`
`rArr k(320 K) =(2xx10^(-3))/((2.5xx10^(-4))^(2)) (3.0xx10^(-5)) =1.066xx10^(9) s^(-1) L^(2)" mol"^(2)`.
`rArr" In "{(k(320 K))/(k(300K))}=(E_(a))/(R) ((T_(2)-T_(1))/(T_(1) T_(2))) rArr" In "((1.066xx10^(9))/(2.66xx10^(8)))=(E_(a))/(8.314) ((20)/(300xx320))`
`rArr E_(a) =55.42" kJ mol"^(-1)`
Now In k = In `A-(E_(a))/(RT)`
At `300 K :" In "(2.66xx10^(8))=" In "A-(55.42xx10^(3))/(8.314xx300)`
Solving : In `A =41.62" "rArr A=1.2xx10^(18)`