Activation energy `(E_(a))` and rate constants (`k_(1)` and `k_(2)`) of a chemical reaction at two different temperatures (`T_(1)` and `T_(2)`) are related by

Options

A. `"ln" (k_(2))/(k_(1)) = -(E_)/(R ) ((1)/(T_(1)) - (1)/(T_(2)))`
B. `"ln" (k_(2))/(k_(1)) = -(E_(a))/(R ) ((1)/(T_(2)) - (1)/(T_(1)))`
C. `"ln" (k_(2))/(k_(1)) = (E_(a))/(R ) ((1)/(T_(2)) + (1)/(T_(1)))`
D. `"ln" (k_(2))/(k_(1)) = (E_(a))/(R ) ((1)/(T_(1)) - (1)/(T_(2)))`

Answer

B, D

Explanation

On integrating within limits `k_(1)` to `k_(2)` and `T_(1)` and `T_(2)`
`underset(k_(1))overset(k_(2))(int) ln K = -(E_(a))/(R ) underset(T_(1))overset(T_(2))(int) (1)/(T)`
`"ln" (k_(2))/(k_(1)) = (E_(a))/(R )[(1)/(T_(2)) - (1)/(T_(1))] = (E_(a))/(R ) [(1)/(T_(1)) -(1)/(T_(2))]`
or `"ln" (k_(2))/(k_(1)) = (E_(a))/(k_(1)) [(1)/(T_(1)) - (1)/(T_2)]`
Option (b) and (d) both are one and the same and are correct.