Question

The rate of a reaction quadruples when the temperature changes from 293 K to 313 K. Calculate the energy of activation of the reaction assuming that it does not change with temperature.

Answer 1

T₁ = 293K,

T₂ = 313K 

According to Arrhenius equation,

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

∴ E_a = 2.303 R x \([\frac{T_1\,T_2}{T_2\,-\,T_1}]log\frac{k_2}{k_1}\) 

∴ E_a = 2.303 R x 8.314 JK^-1mol^-1 x \([\frac{293\,\times\,313}{313\,-\,293}]log\frac{4}{1}\)

2.303 × 8.314 J K^-1 mol^-1 × 4585.45 K × 0.6021 

= 52863.33 J mol^-1

= 52.86 kJ mol^-1