Decomposition of a Compound via two Parallel Processes

Question:

A compound can decompose via two parallel processes with rate constants k₁  and k₂ . What is the difference in activation energies for these two reactions if at T=283K, k₁ /k₂ = 10 and at T=313K, k₁ /k₂ = 0.1? Express your answer in kJ/mole.

Solution:
We can use Arrhenius equation for rate constant, i.e.,

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