Question

Calculate the Activation Energy (\(E_a\)) given rate constants at two different temperatures.

Hint:

Always convert temperatures to Kelvin before applying the formula.

Answer 1

Concept: Activation energy is calculated using the Arrhenius equation, which relates rate constant with temperature.
Answer:
The Arrhenius equation is: \[ k = A e^{-\frac{E_a}{RT}} \] Taking logarithm for two temperatures: \[ \log \frac{k_2}{k_1} = \frac{E_a}{2.303R} \left( \frac{1}{T_1} - \frac{1}{T_2} \right) \] Formula for Activation Energy: \[ E_a = \frac{2.303R \log (k_2/k_1)}{\left( \frac{1}{T_1} - \frac{1}{T_2} \right)} \] where:

• \(k_1, k_2\) = rate constants
• \(T_1, T_2\) = temperatures in Kelvin
• \(R = 8.314 \, J\,mol^{-1}K^{-1}\)

Example:
If \(k_1 = 2 \times 10^{-3}\), \(k_2 = 4 \times 10^{-3}\), \(T_1 = 300K\), \(T_2 = 310K\), substitute values to calculate \(E_a\).