Activation Energy and Energy Profiles

Introduction

An energy profile places reactants, a transition-state region and products along a reaction coordinate. The vertical difference from reactants to the peak is the forward barrier; from products to the same peak is the reverse barrier. The product-minus-reactant difference is the reaction energy change. These are related but not interchangeable quantities.

Core explanation

For a one-step profile with reactant energy ER, product energy EP and peak energy E‡, the forward activation energy is Ea,f=E‡−ER, while the reverse activation energy is Ea,r=E‡−EP. Their difference is Ea,f−Ea,r=EP−ER=ΔE for that schematic energy surface. If products lie lower, the forward reaction is exothermic in the simple diagram and the reverse barrier is larger than the forward barrier.

Reaction enthalpy ΔH uses enthalpies at specified conditions, while a graph may show potential energy or Gibbs free energy. One should read the axis label before equating an energy difference with ΔH. In basic diagrams the vertical axis is often called energy loosely; an exam answer can say “energy change shown” and use ΔH only when the graph or question specifies enthalpy.

For a multistep mechanism, the profile has multiple peaks and valleys. Peaks correspond to transition-state regions, and valleys between them to intermediates. The highest peak measured from initial reactants is not always the only relevant activation barrier for the observed rate, because intermediate concentrations and preceding equilibria matter. A simple “tallest hill is always the slow step” rule can mislead when starting levels differ.

A catalyst changes the pathway, often introducing several lower barriers. It does not lower the energy of only the products while leaving reactants fixed as a way to accelerate the reaction. For a fixed-temperature catalytic comparison, reactant and product state energies and the equilibrium constant remain unchanged, although the path between them differs.

An activation energy estimated from an Arrhenius plot is an apparent temperature-sensitivity parameter. It may not exactly equal a single geometric peak difference in a complex reaction, especially when multiple steps, temperature-dependent prefactors or equilibria contribute. Introductory energy diagrams are qualitative models; their main strength is separating barrier height from overall energy change.

Exothermicity does not guarantee rapid reaction. A strongly downhill product can sit behind a high peak, making the uncatalyzed path slow. Conversely, a modestly endothermic reaction can proceed quickly if supplied with energy and a low barrier. Thermodynamic direction and kinetic accessibility answer different questions.

Step-by-step reasoning

1. Read the vertical-axis quantity and identify reactant and product levels. 2. Find the peak for a specified pathway. 3. Subtract reactant level from peak for forward barrier. 4. Subtract product level from peak for reverse barrier. 5. Subtract reactant from product for reaction energy change; keep it separate from barriers.

Visual explanation

Draw a hump with reactants at 40 kJ mol⁻¹, peak at 100 and products at 10. Mark forward rise 60, reverse rise 90 and product-minus-reactant change −30. Add a second lower-hump catalytic route sharing the same endpoints.

Real-world analogy

Two valleys separated by a mountain can differ in altitude. The climb from each valley to the pass is its direction-specific barrier, while the difference between valley floors is the overall energy change. A tunnel changes the path but not the valleys' heights.

Real-world example

Hydrogen and oxygen can form energetically favorable water, but a mixture can persist until a spark or catalyst supplies an accessible initiation pathway. The energy release of products does not remove the initial activation barrier.

Why?

Why is the reverse barrier larger for a downhill exothermic forward profile with one shared peak? Products start lower, so they must climb farther to reach the same transition-state region.

Common misconception

“Activation energy equals the heat released.” The barrier is a peak-minus-starting-level difference, while heat or reaction energy is product-minus-reactant; they can have very different magnitudes.

Worked example

A diagram shows reactants at 40, transition state at 100 and products at 10 kJ mol⁻¹ on a consistent axis. Ea,f=100−40=60 kJ mol⁻¹. Ea,r=100−10=90 kJ mol⁻¹. Product-minus-reactant energy is 10−40=−30 kJ mol⁻¹. Check: 60−90=−30, matching the overall change in the one-step profile.

Quick check

1. What two points determine a forward activation barrier? Answer: The reactant energy level and the transition-state peak for that pathway.

Exam focus

Label all energy levels and calculate both barriers and reaction change separately. Distinguish one-step diagrams from multistep profiles and use ΔH only when the axis supports it.

Advanced insight

Free-energy profiles include entropy and are temperature dependent. A lower free-energy barrier, rather than a potential-energy peak alone, is often more directly connected to solution reaction rates.

Summary

Forward and reverse activation energies are measured from different starting levels to a transition-state region. Reaction energy is the difference between product and reactant levels. Catalysts change the route without changing endpoint equilibrium energies.

Practice questions

1. If reactants are at 20, a peak at 80 and products at 50 kJ mol⁻¹, what is Ea,f? Answer: 60 kJ mol⁻¹. 2. What is Ea,r for the same profile? Answer: 30 kJ mol⁻¹, from 80−50. 3. Is the forward process exothermic in that example? Answer: No. Products are 30 kJ mol⁻¹ above reactants on the stated energy axis.