Question

Consider the reaction 2O3(g) ⟶3O2(g);  Use the following data to calculate the activation energy for the reaction. 

T(°C)                   Rate Constant (M-1s-1)

     527                     3.58 x 105

     727                     5.90 x 106

44.6 kJ/mol

920 J/mol

440 J/mol

93.2 kJ/mol

Answer 1

Eₐ = 44.6 kJ·mol⁻¹

Use the Arrhenius equation

ln(k₂/k₁) = (Eₐ/R)(1/T₁ -1/T₂)

ln(5.90× 10⁶/3.58 × 10⁵) = (Eₐ/8.314 J·K⁻¹mol⁻¹) (1/527 K - 1/727 K)

ln16.48 = (Eₐ/8.314J·mol⁻¹) × 5.220 × 10⁻⁴

2.802 = Eₐ ×6.729 × 10⁻⁵ mol·J⁻¹

Eₐ = 2.802/(6.729 × 10⁻⁵ mol·J⁻¹) = 4.46 × 10⁴ J·mol⁻¹

Eₐ = 44.6 kJ·mol⁻¹