Question

The rate of a reaction doubles when the temperature is increased by 10°C. What is the approximate value of the activation energy?

• A. 60 kJ/mol
• B. 100 kJ/mol
• C. 120 kJ/mol
• D. 150 kJ/mol

Hint:

Use the temperature dependence of the rate constant to estimate the activation energy, especially when the rate doubles with a small temperature change.

Answer 1

The Correct Option is A

The Arrhenius equation, \[ k = A \exp\left(-\frac{E_a}{RT}\right), \] describes the relationship between the rate constant (\(k\)), pre-exponential factor (\(A\)), activation energy (\(E_a\)), universal gas constant (\(R\)), and temperature (\(T\)). For a 10°C temperature increase causing the rate to double, the activation energy can be approximated using the two-point form of the Arrhenius equation: \[ \ln \frac{k_2}{k_1} = \frac{E_a}{R} \left(\frac{1}{T_1} - \frac{1}{T_2}\right), \] where \(T_1\) and \(T_2\) represent the initial and final temperatures, respectively. With a 10°C temperature increment, the calculated activation energy (\(E_a\)) is approximately 60 kJ/mol. Therefore, the determined value is: \[ \boxed{60 \, \text{kJ/mol}}. \]