An exothermic reaction X → Y has an activation energy 30 kJ mol⁻¹. If energy change ΔE during the reaction is -20 kJ, then the activation energy for the reverse reaction in kJ is ___________. (Integer answer)

Solution

Chemistry ma’am · 4 steps

Picture the energy hill: going back, Y has to climb the forward barrier plus the 20 kJ it lost.

1. Read the profile. In an exothermic reaction, the product Y sits 20 kJ below the reactant X. Both directions pass over the same transition state at the top of the hill.
2. Relate the barriers. Forward, X climbs E_(a,f) to reach the top. Backward, Y starts lower, so it must climb that same height plus the extra |Δ E|.

   E_(a,f) - E_(a,b) = Δ E

3. Put in numbers. 30 - E_(a,b) = -20, so E_(a,b) = 30 + 20 = 50 kJ.
4. So. The activation energy for the reverse reaction is 50 kJ.

The common slip: 10. Subtracting the energy change from the forward barrier gives 30 - 20 = 10. Y sits lower than X, so the reverse climb is taller, not shorter.

The idea to keep. Δ E = E_(a,f) - E_(a,b) always. For an exothermic reaction the reverse barrier is the bigger one, so a negative Δ E makes E_(a,b) larger than E_(a,f).

Answer from the NTA final answer key. Solution by PrepWiser.