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 $ mol^{ - 1} $ then the overall energy of activation in
kJ $ mol^{ - 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
$log k = log k_1 + log k_2 - log k_3 $ $ $ ..( i )
We know that
log k = log A $ - \frac{ E_a }{ 2.303 RT } $
On putting values of log k, $log k_1 \, log \, k_2 \, and \, log \, 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 $ mol^{ - 1} $