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 relationship between the rate constant and temperature is given by the Arrhenius equation: \[ k = A \exp\left(-\frac{E_a}{RT}\right), \] where: - \(k\) is the rate constant, - \(A\) is the pre-exponential factor, - \(E_a\) is the activation energy, - \(R\) is the universal gas constant, and - \(T\) is the temperature. The rate doubles when the temperature increases by 10°C, which can be approximated using the formula: \[ \ln \frac{k_2}{k_1} = \frac{E_a}{R} \left(\frac{1}{T_1} - \frac{1}{T_2}\right), \] where \(T_1\) and \(T_2\) are the initial and final temperatures. Using a temperature increase of 10°C, the activation energy \(E_a\) can be found to be approximately 60 kJ/mol. Thus, the correct answer is: \[ \boxed{60 \, \text{kJ/mol}}. \]