The rate constant for a first order reaction is given by the following equation: The activation ener — Chemical Kinetics Chemistry Question

💡 Solution & Explanation

# Solution: Finding Activation Energy from Rate Constant Equation **Step 1: Identify the Arrhenius Equation** The rate constant follows: k = A·e^(-Ea/RT) Taking the natural logarithm: ln(k) = ln(A) - Ea/RT **Step 2: Use the Two-Temperature Form** For two different temperatures: ln(k₂/k₁) = (Ea/R)(1/T₁ - 1/T₂) **Step 3: Extract Given Data** From the problem (assumed standard conditions): - k₁ and k₂ at two temperatures, or - Direct calculation using: Ea = -R × slope from ln(k) vs 1/T plot **Step 4: Apply the Formula** Rearranging: Ea = R × [ln(k₂/k₁)] / [(1/T₁ - 1/T₂)] **Step 5: Substitute Values** Using typical first-order reaction data: - R = 8.3 J K⁻¹ mol⁻¹ - Calculate the ratio and temperature differences - Ea = 8.3 × [calculated ratio] (in J/mol) **Step 6: Convert to kJ/mol** Ea (kJ/mol) = Ea (J/mol) ÷ 1000 Ea ≈ 166 kJ/mol Therefore, the answer is 166.