The activation energies of two raction are `E_(a1)` and `E_(a2)` with `E_(a1)gtE_(a2)` . If the temperature of the reacting systems is increased from `T_(1)` to `T_(2)` predict which of the following alternatives is correct

Options

A. `(k'_(1))/(k_(1)) = (k'_(2))/(k_(2))`
B. `(k'_(1))/(k_(1)) gt (k'_(2))/(k_(2))`
C. `(k'_(1))/(k_(1)) lt (k'_(2))/(k_(2))`
D. `(k'_(1))/(k_(1)) lt 2 (k'_(2))/(k_(2))`

Explanation

We have ln `((k.)/(k)) = (E_(a))/(R) ((1)/(T_(1)) - (1)/(T_(2))) = (E_(a))/(R) (Delta T)/(T_(1)T_(2))`
For `Delta T` positive , k./k increases faster with larger value f activation energy. Hence, `(k._(1)//k_(1)) gt (k._(2)//k_(2))`.