Activation energy vs reaction enthalpy:\nFor an endothermic reaction, what is the minimum possible value of the forward activation energy relative to ΔH (reaction enthalpy)?

Introduction / Context:
Activation energy (Ea) measures the energy barrier that must be overcome for reactants to reach the transition state. For endothermic reactions, products lie at a higher enthalpy level than reactants (ΔH > 0). Understanding the relationship between Ea and ΔH is fundamental to interpreting Arrhenius kinetics and energy profiles.

Given Data / Assumptions:

• Elementary viewpoint using a single transition state.
• Forward reaction is endothermic: ΔH > 0.
• Classical energy profile (reactants → barrier → products).

Concept / Approach:
Let Ea,f be forward activation energy and Ea,r be reverse activation energy. The energy diagram gives Ea,f − Ea,r = ΔH. Since activation energies are non-negative (barriers cannot be negative in classical terms), the smallest Ea,f occurs when the reverse barrier approaches zero, yielding Ea,f(min) = ΔH.

Step-by-Step Solution:
Use relation: Ea,f = Ea,r + ΔH.Minimum Ea,r is 0 (limiting case), so Ea,f(min) = ΔH.Therefore, the least possible Ea for an endothermic forward reaction equals ΔH.

Verification / Alternative check:
Transition-state theory gives the same qualitative picture: for larger ΔH, the forward barrier must be at least ΔH to place products above reactants.

Why Other Options Are Wrong:
“Greater than ΔH” can be true but is not the minimum. “Less than ΔH” or “zero/negative” violate the barrier relation for endothermic profiles.

Common Pitfalls:
Confusing thermodynamic uphill (ΔH) with kinetic barrier (Ea); they are distinct but related by the reverse barrier.

Final Answer:
Equal to ΔH