Question

A reaction takes place in three steps with activation energy $E_{a_{1}}=180$ kJ/mol, $E_{a_{2}}=80$ kJ/mol and $E_{a_{3}}=50$ kJ/mol respectively.

Overall rate constant of the reaction is $k=\left[\frac{k_{1} k_{2}}{k_{3}}\right]^{2 / 3}$ .

The activation energy of the reaction will be

• A. 140 kJ/mol
• B. 150 kJ/mol
• C. 43.44 kJ/mol
• D. 100 kJ/mol

Answer 1

Answer: (A)

The rate of constant of the reaction is

$k=\left[\frac{k_{1} k_{2}}{k_{3}}\right]^{2 / 3}$

Activation energy of the reaction will be

$E_{a}=\frac{2}{3}\left[\right.E_{a_{1}}+E_{a_{2}}-E_{a_{3}}\left]\right.$

$=\frac{2}{3}\left[\right.180+80-50\left]\right.$

$=140$ kJ/mol.