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An exothermic reaction $X \to Y$ has an activation energy 30 kJ mol$^{-1}$. If energy change $\Delta E$ during the reaction is $-20$ kJ, then the activation energy for the reverse reaction in kJ is:
$\Delta H = E_{a_f} - E_{a_b}$. $-20 = 30 - E_{a_b}$. $E_{a_b} = 50,\text{kJ/mole}$.
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