Question

Decomposition of a hydrocarbon follows the equation} \[ k = (5.5 \times 10^{11}\, s^{-1})\, e^{\frac{-28000}{T}} \] The activation energy of reaction is _____ kJ mol\(^{-1}\). (Nearest Integer)} Given: \(R = 8.3\, J\,K^{-1}\,mol^{-1}\)}

Answer 1

Correct Answer: 233

Step 1: Understanding the Question:
We need to extract the activation energy (\(E_{a}\)) from the given Arrhenius equation.
Step 2: Key Formula or Approach:
Compare the given equation with the standard Arrhenius equation:
\[ k = A e^{\frac{-E_{a}}{RT}} \]
Step 3: Detailed Explanation:
Given equation: \(k = (5.5 \times 10^{11}) e^{\frac{-28000}{T}}\).
By direct comparison of the exponential terms:
\[ \frac{-E_{a}}{RT} = \frac{-28000}{T} \]
\[ \frac{E_{a}}{R} = 28000 \text{ K} \]
Given \(R = 8.3 \text{ J K}^{-1} \text{ mol}^{-1}\):
\[ E_{a} = 28000 \times 8.3 \text{ J/mol} \]
\[ E_{a} = 232400 \text{ J/mol} \]
Convert to kJ/mol:
\[ E_{a} = 232.4 \text{ kJ/mol} \]
The nearest integer value is 232.
Step 4: Final Answer:
The activation energy is 232 kJ/mol.