Question

Consider the reaction.
$B\stackrel{k_1}{\leftarrow }A\stackrel{k_2}{\to }C$
The rate constant for two parallel reactions were found to be ${10}^{–2}{\text{dm}}^3{\text{mol}}^{–1}{\text{s}}^{–1}\left(k_1\right)$ and $4\times {10}^{–2}{\text{dm}}^3{\text{mol}}^{–1}{\text{s}}^{–1}\left(k_2\right)$. If the corresponding energies of activation of the parallel reactions are $80$ and $100\text{kJ}$, respectively. What is the apparent (net) overall energy of activation (in kJ/mol) of a given reaction?

Answer 1

Overall energy of activation $=\frac{k_1\left(E{a}_1\right)}{k_1+k_2}+\frac{k_2\left(E{a}_2\right)}{k_1+k_2}$
On substituting the all values in formula,
$E_{\text{net}}=\frac{80\times {10}^{-2}+4\times {10}^{-2}\times 100}{{10}^{-2}+4\times {10}^{-2}}=\frac{0.8+4}{5\times {10}^{-2}}=96\text{kJ/mol}$