Question

The rate of a reaction quadruples when the temperature changes from $300$ to $310K$ . The activation energy of this reaction is:
(Assume Activation energy and pre-exponential factor are independent of temperature; $ln(2)=0.693;R=8.314J{\left(mol\right)}^{-1}{K}^{-1}$ )

• A. $53.6kJmo{l}^{-1}$
• B. $214.4kJmo{l}^{-1}$
• C. $107.2kJmo{l}^{-1}$
• D. $53.7kJmo{l}^{-1}$

Answer 1

Answer: (C)

The activation energy, rate constant and temperature can be related using Arrhenius equation.
$k=A{e}^{-\frac{E_a}{RT}}$
$ln\left(\frac{k_2}{k_1}\right)=\frac{E_a}{R}\left(\frac{1}{T_1}-\frac{1}{T_2}\right)$
$ln\left(4\right)=\frac{E_a}{R}\left(\frac{1}{300}-\frac{1}{310}\right)$
$2\times 0.693=\frac{E_a}{R}\left(\frac{10}{300\times 310}\right)$
${\text{E}}_{\text{a}}=\frac{2\times 0.693\times 300\times 310\times 8.314}{10}=107.2\text{kJ/mol}$