The rate constant k for the first order gas phase decomposition of ethyl iodide, `C_(2)H_(5)I rarr C_(2)H_(4)+HI` is `1.60xx10^(-5)s^(-1)` at 600 k and `6.36xx10^(-3)s^(-1)` at 700 K. Calculate the energy of activation for this reaction.

Explanation

Given
`K_(1)=1.60xx10^(-5)s^(-1) , T_(1)=600 K`
`K_(2)=6.36xx10^(-3)s^(-1) , T_(2) = 700 K`
We know that log `(K_(2))/(K_(1))=(E_(a))/(2.303R)[(1)/(T_(1))-(1)/(T_(2))]`
Substituting the values of `K_(1), K_(2)` and `R(=8.314 JK^(-1)mol^(-1))`, we get,
`"log"(6.36xx10^(-3))/(1.60xx10^(-5))=(E_(a))/(2.303xx8.314)[(1)/(600)-(1)/(700)]`
`log(3.98xx10^(2))=(E_(a))/((19.15)xx(4200))`
`therefore E_(a)=2.6xx19.15xx4200 J mol^(-1)`
`= 2.09xx10^(5)J mol^(-1)`
`= 209"kJ mol"^(-1)`