The first order rate constant for the decomposition of ethyl iodide by the reaction `C_2 H_5 I_((g)) to C_2 H_4 (g) + HI_((g))` at 600 K is `1.60 xx 10^(-5) s^(-1)` . Its energy of activation is 209 kJ/mol. Calculate the rate constant of the reaction at 700 K.

Answer

`k_2 = 6.35 xx 10^(-3) s^(-1)`

Explanation

`log (k_2)/(k_1) = (E_a)/(2.303 R) xx ([T_2 -T_1])/( T_1 T_2) `
` or log k_2 = log k_1 +(E_a)/(2.303 R) xx (100)/(700 xx 600 )`
` = log ( 1.6 xx 10^(-5)) +(209000 )/( 2.303 xx 8.314 ) xx ( 100)/(700 xx 600 )`
` = 0.2041 -5 +2.5989 `
` or log k_2 = -2.1970 `
` k_2 = ` antilog ` -2.1970 = 6.35 xx 10^(-3) s^(-1)`