Chemistry · General chemistry II · Concept

Potential energy diagrams for reactions

Read a potential energy diagram: where ΔH, the forward and reverse activation energies and the transition state are, how exothermic and endothermic reactions differ, and what a catalyst changes and what it cannot.

What the diagram shows

The horizontal axis is reaction progress: how far the atoms have moved from reactants toward products. It is not time. The vertical axis is potential energy per mole. Reactants and products sit on flat levels, and the path between them climbs over a hump. The top of the hump is the transition state, an arrangement with bonds partly broken and partly formed that cannot be isolated.

Reading a potential energy diagram
Feature	Measured from	To
ΔH	Reactant level	Product level
Ea (forward)	Reactant level	Top of the hump
Ea (reverse)	Product level	Top of the hump
Transition state	—	The top of the hump
Intermediate	—	A valley between two humps

Exothermic and endothermic reactions

If the products sit below the reactants, energy is released and ΔH is negative: exothermic. If the products sit above, energy is absorbed and ΔH is positive: endothermic. Both kinds of reaction must climb a barrier first, so even a strongly exothermic reaction can be slow at room temperature.

The reverse reaction climbs from the product level to the same transition state, so its barrier differs from the forward one by exactly ΔH. For an endothermic reaction, the forward Ea can never be smaller than ΔH, because the transition state must lie above the products too.

E_{a, reverse} = E_{a, forward} - Δ H

What a catalyst changes

A catalyst provides a different pathway with a lower transition state. It lowers the forward and reverse barriers by the same amount, so both directions speed up by the same factor. It does not move the reactant or product levels, so ΔH, the equilibrium constant K and the equilibrium position stay the same; equilibrium is simply reached sooner. The catalyst is used in one step and regenerated in a later one, so a catalyzed pathway often has more than one hump.

\frac{k_{cat}}{k} = e^{(E_{a} - E_{a, cat}) / R T} (same A)

Several humps: mechanisms on the diagram

A mechanism with several elementary steps has one hump per step and a valley for each intermediate. When earlier steps are fast and reversible, the step whose transition state stands highest above the reactants limits the overall rate. That link between the diagram and the rate law is what the mechanisms page tests step by step.

Common mistakes

Reading the horizontal axis as time.
Measuring Ea from the product level for the forward reaction, or from the axis instead of the reactant level.
Saying a catalyst makes a reaction more exothermic or changes ΔH.
Saying a catalyst shifts equilibrium toward products.
Drawing an endothermic reaction with Ea smaller than ΔH.
Calling a transition state an intermediate.

Key terms

Exothermic reaction: A reaction that releases heat to its surroundings (ΔH < 0).
Endothermic reaction: A reaction that absorbs heat from its surroundings (ΔH > 0).
Transition state: The highest-energy arrangement in one elementary step, with bonds partly broken and partly formed. It lasts too briefly to isolate, unlike an intermediate, which sits in an energy valley.
Activated complex: The unstable, high-energy arrangement of atoms at the top of the energy barrier, the transition state. Unlike an intermediate, it can’t be isolated.
Catalyst: A substance that speeds up a reaction by giving it a lower-energy pathway and is not used up. It does not change the equilibrium constant or where equilibrium lies.
Arrhenius equation: k = A·e^(−Ea/RT): how a rate constant grows with temperature. A plot of ln k against 1/T is a line with slope −Ea/R, which gives the activation energy.
Reaction intermediate: A substance made in one step of a mechanism and used up in a later step, so it does not appear in the overall equation.

Work through an example

A reaction has ΔH = −40 kJ/mol and Ea = 50 kJ/mol. A catalyst lowers the forward barrier to 35 kJ/mol. Find the reverse barriers with and without the catalyst, say what happens to ΔH and K, and estimate how much faster the catalyzed reaction is at 298 K.

Read a catalyzed potential energy diagram →

Sources and scope

Authored study material. Tool results depend on the stated inputs and model assumptions.

Tro, Chemistry: A Molecular Approach, 4th ed., §14.5 The Effect of Temperature on Reaction Rate, pp. 642–647 (activation energy and the transition state, p. 643)
Tro, Chemistry: A Molecular Approach, 4th ed., §14.7 Catalysis, pp. 653–657 (catalyzed and uncatalyzed pathways, pp. 653–654)
OpenStax Chemistry 2e — Collision theory
OpenStax Chemistry 2e — Catalysis

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