Question

A reaction takes place in various steps. The rate constant for first, second, third and fifth steps are $k_1,k_2,k_3$ and $k_5$ respectively. The overall rate constant is given by:$k=\frac{k_2}{k_3}\times (\frac{k_1}{k_5}{)}^{0.5}$
If the activation energies are 40, 60, 50 and 10 kJ/mol respectively, the overall activation energy (kJ/mol) is:

• A. 10
• B. 20
• C. 25
• D. None of the above

Answer 1

The correct option is C 25

We know that Arrhenius equation:
$k=A{e}^{-\frac{E_a}{RT}}$
Since we know that rate constant is given as:
$k=\frac{k_2\times {k_1}^{0.5}}{k_3\times {k_5}^{0.5}}$
activation energy can be given by:
$E_a=(E_2+0.5\times E_1)-(E_3+0.5\times E_5)$
$E_a=25$