Question

For a reaction taking place in three steps, the rate constants are $k_1{k}_{2}and{k}_3$. The overall rate constant
$k=\frac{k_1,k_2}{k_3}$
If the energy of activation values for the first, second and third stages are respectively 40, 50 and 60 KJ $mo{l}^{-1}$ then the overall energy of activation in
kJ $mo{l}^{-1}$ is

• A. 30
• B. 40
• C. 60
• D. 50
• E. 150

Answer 1

Answer: (A)

$Given,K=\frac{k_1{k}_2}{k_3}$
On taking log both sides
$logk=log{k}_1+log{k}_2-log{k}_3$ ..( i )
We know that
log k = log A $-\frac{E_a}{2.303RT}$
On putting values of log k, $log{k}_{1}log{k}_{2}andlog{k}_3$ in Eq. (i)
and solving, we get
$E_a=E_{a_1}+E_{a_2}-E_{a-3}$
=40 + 50 - 60
= 30 KJ $mo{l}^{-1}$