The first oder rate constant for the decomposition of ethyl iodide
by the reaction
`C_(2)H_(5)l(g)toC_(2)H_(4)(g)+Hl(g)`
at 600k is `1.60xx10^(-5)S^(-1)`.Its energy of activation is 209 kJ/mol. calculate the rate constant at 700k

Explanation

We know that
`log k_(2)-logk_(1)=(E_(a))/(2.303R)[(T_(2)-T_(1))/(T_(1)T_(2))]`
`logk_(2)= logk_(1)+(E_(a))/(2.303R)[(T_(2)-T_1)/(T_(1)T_(2))]`
`= log (1.60xx10^(-5))+(209xx10^(3)Jmol)/(2.303xx8.314mol^(-1)K^(-1))xx[(100)/(600xx700)]K`
`log k_(2)= -4.796+2.599= -2.197`
`k_(2)="Antilog"(-2.197)`
`="Antilog"(-2.197+1-1)`
`="Antilog"(bar(3).803)= 6.36xx10^(-3)s^(-1)`