First order rate constant for the decomposition of ethyl iodide, `C_(2)H_(5)I(g)rarrC_(2)H_(4)(g)+HI(g)` at 600K is `1.60xx10^(-5)s^(-1)` . Its activation energy is `209kJ."mol"^(-1)` . Calculate rate constant of the reaction at 700K.

Explanation

`E_(a)=2.303R[(T_(1)T_(2))/(T_(2)-T_(1))]log.(k_(2))/(k_(1))`
or`logk_(2)-logk_(1)=(E_(a))/(2.303R)[(1)/(T_(1))-(1)/(T_(2))]`
or,`logk_(2)=logk_(1)+(E_(a))/(2.303R)[(1)/(T_(1))-(1)/(T_(2))]`
or, `logk_(2)=log(1.6xx10^(-5))+(209000)/(2.303xx8.314)[(1)/(600)-(1)/(700)]`
or, `log_(2)=-2.197 thereforek_(2)=6.35xx10^(-3)s^(-1)`