Practice question

Given: The rate constant of a reaction is 5.0 × 10⁻⁵ s^{-1 at 290 K and 1.5 × 10⁻⁴ s^{-1 at 300 K. What is the activation energy in kJ mol^{-1 ? (R = 8.314 J/mol · K) These values define the system as per NCERT data. Formula: log k_2/k_1 = E_a/2.303R ( T_2 - T_1/T_1 T_2 ). This is the standard NCERT relation for this phenomenon. Substitution & Calculation: log frac1.5 × 10⁻⁴⁵.0 × 10⁻⁵= log 3 = 0.477 . 0.477 = E_a/2.303 × 8.314 ( 10/290 × 300 ), E_a approx 51.5 kJ mol^{-1 . Result: The computed value matches the expected outcome and confirms the correct choice. Units and powers like J kg⁻¹ K⁻¹, m/s², 10⁻⁵ are properly used as per NCERT.