The rate constants for a reaction at 400 K and 500 K are `2 . 60 xx 10^(-5) s^(-1) and 2.60 xx 10^(-3) s^(-1)` respectively. The activation energy of the reaction in kJ `mol^(-1)` is

Options

A. 38.3
B. 57.4
C. 114.9
D. 76.6

Answer

D

Explanation

Given, `k_(1) = 2 . 60 xx 10^(-5) s^(-1)`
`k_(2) = 2 . 60 xx 10^(-3) s^(-1)`
`T_(1) = 400 K`
`T_(2) = 500 K`
According to Arrhenius equation,
`"log" (k_(2))/(k_(1))= (E_(a))/(2.30 3R) [(T_(2) - T_(1))/(T_(1)T_(2))]`
`rArr "log" (2 . 60 xx 10^(-3))/(2 . 60 xx 10^(-5))= (E_(0))/(2 . 303 xx 8.314)[(500- 400)/(500xx 400)]`
`E_(a) = (2 xx 2,303 xx 8.314 xx 2 xx 10^(5))/(100)`
`E_(a) = 76.6 xx 10^(3) J //mol`
`:. E_(a) = 76.6 kJ //mol`