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. In `(k_2)/(k_1)=-(E_a)/(R)((1)/(T_1)-(1)/(T_2))`
B. In `(k_2)/(k_1)=-(E_a)/(R)((1)/(T_2)-(1)/(T_1))`
C. In `(k_2)/(k_1)=-(E_a)/(R)((1)/(T_1)+(1)/(T_2))`
D. In `(k_2)/(k_1)=(E_a)/(R)((1)/(T_1)-(1)/(T_2))`

Answer

B, D

Explanation

`k_1=Ae^(-E_a//RT_1)`
`k_2=Ae^(-E_a//RT_2)`
In `k_1=In" "A-E_a//RT_1` ….....(i)
`In k_2=In" "A-E_a//RT_2` …......(ii)
From eq. (i) and (ii) ,we have
In `k_2-Ink_1=In" "A-(E_a)/(RT_2)-In" "A+(E_a)/(RT_1)`
`implies" "In (k_2)/(k_1)=(E_a)/(R)(1/T_1-1/T_2)implies" "In(k_2)/(k_1)=-(E_a)/(R)(1/T_2-1/T_1)`