Question

Arrhenius equations for two chemical reactions are $k_1 = A_1e^{- E_1 /RT} , k_2 = A_2e^{-E_2/RT} $ . If $ E_1 > \, E_2 $ then at a given temperature $ T, $

• A. $\frac{k_1}{k_2} <\, \frac{A_1}{A_2} $
• B. $.\frac {k_2}{k_1} < \, \frac {A_2}{A_1} $
• C. $k_1k_2 >\, A _1A_2 $
• D. $k_1 + k_2 > \, A_1 + A_2 $

Answer 1

Answer: (A)

$ \frac{k_1}{A_1} = e^{-E1/RT} $
$\frac{k_2}{k_2} =e^{-E_2/RT} $
Dividing eqn. $(ii)$ by eqn. $(i), $
$ \frac{k_2}{A_2} \times \frac{A_1}{k_1} = e ^{(E_1-E_2)/RT} $
$\frac{k_2}{k_1} \times \frac{A_1}{A_2} >\, 1 \Rightarrow \frac {A_1}{A_2} > \, \frac{k_1}{k_2} $