Question

The rate constant of a reaction increases by five times on increase in temperature from 27°C to 52°C. The value of activation energy in kJ mol⁻¹ is ________. (Rounded-off to the nearest integer) [R=8.314 JK⁻¹ mol⁻¹]

Hint:

The Arrhenius equation is fundamental for problems involving temperature dependence of reaction rates. Ensure temperatures are always converted to Kelvin. The term $(\frac{1}{T_1} - \frac{1}{T_2})$ can be rewritten as $(\frac{T_2 - T_1}{T_1 T_2})$ which is sometimes easier for calculation.

Answer 1

Correct Answer: 52

Q57. Rate constant increases five times when temperature changes from 27°C to 52°C. Step 1: Convert temperatures to Kelvin \[ T_1 = 300\text{ K}, \quad T_2 = 325\text{ K} \] Step 2: Arrhenius equation \[ \ln\left(\frac{k_2}{k_1}\right) = \frac{E_a}{R}\left(\frac{1}{T_1}-\frac{1}{T_2}\right) \] \[ \ln(5) = \frac{E_a}{8.314}\left(\frac{25}{300 \times 325}\right) \] Step 3: Solve \[ E_a = 1.609 \times 8.314 \times 3900 \approx 5.21 \times 10^4\text{ J mol}^{-1} \] \[ E_a \approx 52\text{ kJ mol}^{-1} \] \[ \boxed{52} \]