In a one step reaction, the activation energy for the forward reaction is 20.0 kJ mol -1, and the enthalpy of the reaction is -30.0 kJ mol-1. Calculate the activation energy for the reverse reaction.

Question

BlackTom AI · Accepted Answer

To tackle this one-step reaction problem, start by recalling the relationship between forward activation energy, reverse activation energy, and the enthalpy change of the reaction. For a single-step reaction, ΔH = E_a,f − E_a,r, which can be rearranged to E_a,r = E_a,f − ΔH.

Option a: -30.0 kJ/mol. This value is not physically reasonable for an activation energy, since activation energies are by definition positive quantities representing an energy barrier that must be overcome. Using the formula with ΔH = -30 and E_a,f = 20 would not yield a negative activation energy.

Option b: 30.0 kJ/mol. If one mistakenly adds the enthalpy change to the forward activation energy as E_a,r = E_a,f + ΔH, you would get 20 + (-30) = -10, not 30. Additionally, this ignores the correct sign convention and the standard derivation ΔH = E_a,f − E_a,r.

Option c: 50.0 kJ/mol. This is the correct result when applying E_a,r = E_a,f − ΔH with E_a,f = 20.0 and ΔH = -30.0: E_a,r = 20 − (-30) = 50 kJ/mol. It reflects the intuitive idea that for an exothermic reaction (ΔH negative), the reverse activation barrier is higher than the forward barrier by the magnitude of the exothermic drop.

Option d: 20.0 kJ/mol. This would imply that E_a,r equals E_a,f, which would correspond to ΔH = 0. Since the reaction has ΔH = -30.0 kJ/mol, this option cannot be correct. It ignores the energy released in going from reactants to products and the resulting change in the energy barrier for the reverse process.

In summary, applying the standard relation ΔH = E_a,f − E_a,r yields E_a,r = 50.0 kJ/mol, making option c the correct choice. The other options fail due to misapplication of the energy-activation relationships or violations of basic energy concepts.

In a one step reaction, the activation energy for the forward reaction is 20.0 kJ mol -1, and the enthalpy of the reaction is -30.0 kJ mol-1. Calculate the activation energy for the reverse reaction.

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