The first order rate constant for the decomposition of ethyl iodide by the reaction `C_2H_5I(g) rarr C_2H_4 (g) + HI(g)` at 600K is `1.60 x 10^(-5) s^(-1)`. Its energy of activation is 209 kJ/mol. Calculate the rate constant of the reaction at 700K.

Explanation

`k_1=1.60xx10^(-5)s^(-1),T_1=600K` `E_aimplies,R=8.314" J "K^(-1)mol^(-1)`
`log(k_2)/(k_1)=(E_a)/(2.303R)[(T_2-T_1)/(T_1T_2)]`
`log(6.36xx10^(-3))/(1.60xx10^(-5))=(E_a)/(2.303xx8.314JK^(-1)mol^(-1))`
`[(700-600)/(700xx600K)]`
`log397.9=(E_a)/(19.15J mol^(-1))xx(100)/(420000)`
`2.5997=(E_a)/(19.15xx4200Jmol^(-1))`
`E_a=2.5997xx19.15xx4200" J mol"^(-1)`
`=209093.87" J mol"^(-1)`
`=209.1" k J mol"^(-1)`