Question

The rate constant of a reaction at 500k and 700k are 0.02 s-1 and 0.07 s-1 respectively the value of activation energy is (in KJ)​

Answer 1

Concept :- Rate constant (k) is relates to activation energy Ea by the equation :-

$k = A {e}^{ \frac{ - Ea}{RT} }$

where,

A = Arrhenius constant.

SOLUTIONS :-

At 500 K , K = 0.02

=>

$0.02 = A {e}^{ - \frac{Ea}{500R} } .....(1)\\ at \: 700k \\ 0.07 = A {e}^{ - \frac{Ea}{700R} }......(2) \\ divinding \: equation(2) \: by \: (1) \\ \frac{0.07}{0.02} \: = \frac{ \:A {e}^{ - \frac{Ea}{700r} }}{ \:A{e}^{ - \frac{Ea}{500R} }} \\ \\ = > \frac{7}{2} = {e}^{ \frac{Ea}{500R} - \frac{Ea}{700R} } \\ \\ = > \frac{7}{2} = {e}^{ \frac{ 200Ea}{3500R} } \\ \\ = > ln( \frac{7}{2} ) = \frac{ 200Ea}{3500R} \\ \\ = > ln( \frac{7}{2} ) = \frac{2Ea}{35R} \\ \\ = > Ea = \frac{35R}{2} ln( \frac{7}{2} ) \\ \\ = > Ea = 182.27 \\ \\ = > Ea = 0.18227 \: kj$