For a reaction, the potential energy of the reactants is 40 kJ·mol⁻¹ and that of the products is –20 kJ·mol⁻¹. The transition state for the uncatalyzed pathway is at 110 kJ·mol⁻¹, whereas the catalyzed transition state is at 70 kJ·mol⁻¹. Calculate the enthalpy change ΔH and the activation energy for each pathway, and briefly state why ΔH is identical for both.