The first order rate constant for the decomposition of ethyl iodide by the reaction, `C_(2)H_(5)I(g) rarr 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. Calculate the rate constant of the reaction at 700 K.

Explanation

`E_(a) = (2.303 RT_(1)T_(2))/(T_(2)-T_(1))"log"(k_(2))/(k_(2))`
`k_(2)` is rate constant at temperature `T_(1)`
`k_(2)` is rate constant at temperature `T_(2)`
`k_(1) = 1.60 xx 10^(-5) s^(-1)`
`T_(1) = 600 K`
`k_(2) = ?`,
`T_(2) = 700 K`
`E_(a)` = Activation energy = 209 kJ
`R = 8.3143 xx 10^(-3)"kJ mol"^(-1)K^(-1)`
`"log" (k_(2))/(k_(1)) = (E_(a)(T_(2)-T_(1)))/(2.303RT_(1)T_(2))`
`= (209 xx (700 - 600))/(2.303 xx 8.3143 xx 10^(-3) xx 600 xx 700)`
`log((k_(2))/(k_(1))) = 2.5988`
`(k_(2))/(k_(1))` = Antilog of 2.5988 = 397.009
`therefore" "k_(2) = 397.009 xx k_(1)`
`k_(2) = 397.009 xx 1.60 xx 10^(-5)s^(-1)`
`= 6.35 xx 10^(-3)s^(-1)`