Reaction pathway diagrams with and without a catalyst

7 minAS Level8.3.1

AI-drafted, independently checked · not yet teacher-reviewed

By the end of this lesson

By the end you can draw a reaction pathway diagram for a reaction with and without a catalyst, label reactants, products, $E_a$ and $\Delta H$ , and explain every difference between the two curves.

What the diagram shows

A reaction pathway diagram plots energy (y-axis) against reaction progress (x-axis). Left to right is the story of the reaction: reactants on the left, products on the right, anything in between happening as the atoms rearrange.

The reactants sit at one energy level, the products at another.
The difference between those two levels is $\Delta H$ : negative if the products are lower.
The highest point on the path is the transition state, and the climb from the reactants to that point is the activation energy $E_a$ .

Without a catalyst there is one hill. With a catalyst the reaction usually goes through an intermediate, so the profile has two smaller humps with a dip between them.

Definition

Reaction pathway diagram

A graph of energy against reaction progress for a reaction. The height of the highest energy point above the reactants is the activation energy $E_a$ ; the energy difference between the reactants and the products is $\Delta H$ .

On a catalysed pathway the highest point is lower and the route may pass through one or more intermediates — species formed in one step and used up in the next, sitting in dips between the humps.

Two humps, each lower than the single uncatalysed hump: a two-step mechanism through an intermediate. The start and finish are unchanged, so ΔH is unchanged.

Why two humps?

A catalyst does not wave the reaction through in one step. It reacts with a reactant to make an intermediate, and the intermediate then reacts on to give the products, regenerating the catalyst:

$\text{A} + \text{cat} \rightarrow \text{A–cat} \rightarrow \text{P} + \text{cat}.$

Each of those steps is a small journey with its own barrier. The diagram shows the energy along that two-step route, which is why there are two humps instead of one.

The important comparison is not the number of humps but the height of the highest hump: it is lower than the single hump of the uncatalysed route, so $E_a$ is smaller.

Worked example: Reading the numbers off a profile

For a reaction, the reactants are at $60\ \text{kJ mol}^{-1}$ and the products at $20\ \text{kJ mol}^{-1}$ . Without a catalyst the highest point is at $210\ \text{kJ mol}^{-1}$ ; with a catalyst it is at $130\ \text{kJ mol}^{-1}$ .

Find $E_a$ with and without the catalyst, and $\Delta H$ .

Have a go first?

Worked example: Sketching the pair

Sketch, on the same axes, the reaction pathway for an exothermic reaction with and without a catalyst.

Have a go first?

Common mistakes

The catalysed curve starts at a lower energy than the uncatalysed one.

Both start at the same reactant energy. Only the top of the route is lower.

The catalysed curve ends at a lower energy, so more energy is released.

Both finish at the same product energy. $\Delta H$ is identical.

Having two humps means the catalysed reaction is slower, because there are two barriers.

The rate depends on the highest barrier on the route. Both catalysed humps are lower than the single uncatalysed hump.

In the exam

When you are asked to draw the catalysed pathway:

start and finish on the same levels as the uncatalysed curve;
make the highest point lower, not higher;
label $E_a$ on the uncatalysed curve and $E_a'$ (or "lower $E_a$ ") on the catalysed one;
if you draw two humps, put an intermediate in the dip and label it.

When interpreting, remember that the reverse reaction's activation energy is measured from the products up to the highest point, and that a catalyst lowers that too.

Check yourself

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