Question

In a reaction carried out at 500 K, 0.001% of the total number of collisions are effective. The energy of activation of the reaction is approximate:

• A. 15.8 kcal $mo{l}^{-1}$
• B. 11.5 kcal $mo{l}^{-1}$
• C. 12.8 kcal $mo{l}^{-1}$
• D. zero

Answer 1

The correct option is B 11.5 kcal $mo{l}^{-1}$

The fraction of molecules having energy equal to or greater than $E_a$ is:
$x=\frac{n}{N}=e^{-E_a/RT}(x=\frac{n}{N}=0.001\%=\frac{0.001}{100}={10}^{-5})$
$\therefore logx=\frac{-E_a}{2.3\times RT}(R=2calmo{l}^{-1}{K}^{-1},T=500K)$
$log{10}^{-5}=\frac{-E_a}{2.3\times 2\times 500}$
$E_a=11.5\times 103calmo{l}^{-1}=11.5kcalmo{l}^{-1}$