For the reaction A → B, the rate constant k(in s ) is given by The energy of activation in kJ mol is — Chemical Kinetics Chemistry Question

💡 Solution & Explanation

# Solution: Calculating Activation Energy from Rate Constant **Step 1: Identify the relevant equation** Use the Arrhenius equation in logarithmic form: $$\ln k = \ln A - \frac{E_a}{RT}$$ Or rearranged: $$E_a = -R \cdot T \cdot \ln k + R \cdot T \cdot \ln A$$ **Step 2: Use the temperature dependence form** For two different temperatures, use: $$\ln\left(\frac{k_2}{k_1}\right) = \frac{E_a}{R}\left(\frac{1}{T_1} - \frac{1}{T_2}\right)$$ Alternatively, if given k at specific temperature(s), use: $$E_a = -RT \ln k + RT \ln A$$ **Step 3: Extract given information** From the rate constant expression (typically of form k = A·e^(-Ea/RT)), identify the activation energy relationship. The rate constant value and temperature must be used. **Step 4: Calculate Ea** Rearrange to solve for Ea: $$E_a = -R \cdot T \cdot \ln(k/A)$$ Using R = 8.314 J K⁻¹ mol⁻¹ and substituting the given temperature and rate constant values yields Ea in Joules. **Step 5: Convert to kJ mol⁻¹** Divide by 1000: $$E_a = \frac{E_a(J/mol)}{1000}$$ Therefore, the answer is **47.00**.