Question

On the basis of Arrhenius equation, how would you determine the energy of activation of a reaction?

Answer 1

Arrhenius equation

\[\ce{k = A e^{−Ea​/(RT)}}\]

Where:

• k = rate constant

• A = frequency factor

• E_a​ = energy of activation (in J/mol or kJ/mol)

• R = gas constant (8.314 J mol⁻¹ K⁻¹)

• T = temperature in Kelvin

Take the logarithm of the Arrhenius equation

\[\ce{ln k = ln A - \frac{E_a}{RT}}\]

or in base 10:

\[\ce{log k = log A - \frac{E_a}{2.303 RT}}\]

Measure the rate constants k₁ and k₂ at two different temperatures T₁ and T₂​.

Use the two-point form of the Arrhenius equation

\[\ce{log (\frac{k_2}{k_1}) = \frac{-E_a}{2.303 R} (\frac{T_2 - T_1}{T_1T_2})}\]

Rearranging the above equation, we get

\[\ce{E_a = \frac{2.303 R * log(k_2/k_1) * T_1T_2}{T_2 - T_1}}\]

Substitute the values of k₁, k₂​, T₁​, T₂​, and R = 8.314 J mol⁻¹ K⁻¹ to calculate E_a.