Within an energetic parallel reaction scheme featuring and , the respective pure activation energies — Chemical Kinetics Chemistry Question
Question
Within an energetic parallel reaction scheme featuring $A \xrightarrow{k_1} B$ and $A \xrightarrow{k_2} C$, the respective pure activation energies are cleanly mapped as $E_{a1} = 20 \text{ kJ/mol}$ and $E_{a2} = 40 \text{ kJ/mol}$. If the chemical reaction is thermally carried out at an exact precise temperature where $k_1$ coincidentally equals $k_2$, what is the overall effective combined activation energy $E_a$ for the gross destruction of reactant A, natively expressed in $\text{kJ/mol}$?
💡 Solution & Explanation
The master formula for the composite activation energy of simultaneous parallel reactions is $E_a = \frac{k_1 E_{a1} + k_2 E_{a2}}{k_1+k_2}$. The prompt dictates that at the operating temperature, $k_1 = k_2$. Substituting $k_1$ for $k_2$ collapses the equation exactly to $E_a = \frac{k_1(20) + k_1(40)}{k_1 + k_1} = \frac{60 k_1}{2 k_1} = \frac{60}{2} = 30 \text{ kJ/mol}$.