Chemistry · General chemistry II · Worked example

Read an energy diagram with and without a catalyst

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.

Δ H = - 40 kJ/mol, E_{a} = 50 kJ/mol, E_{a, cat} = 35 kJ/mol

Place the levels

ΔH is negative, so the products sit 40 kJ/mol below the reactants: the reaction is exothermic. The uncatalyzed transition state is 50 kJ/mol above the reactants; the catalyzed one is 35 kJ/mol above.

Reverse barriers

Each reverse barrier is measured from the product level up to the same transition state.

E_{a, rev} = 50 - (- 40) = 90 kJ/mol, E_{a, rev,cat} = 35 - (- 40) = 75 kJ/mol

What the catalyst leaves alone

Both barriers fall by 15 kJ/mol, so the forward and reverse rates rise by the same factor. The reactant and product levels do not move: ΔH is still −40 kJ/mol and K is unchanged.

How much faster

Assuming the same frequency factor A, the rate constants differ by the Arrhenius factor for the 15 kJ/mol drop.

\frac{k_{cat}}{k} = e^{15000 / (8.314 \times 298)} = e^{6.05} \approx 4.3 \times 10^{2}

Result

Reverse barriers: 90 kJ/mol uncatalyzed and 75 kJ/mol catalyzed. ΔH (−40 kJ/mol) and K are unchanged. Both directions run about 430 times faster at 298 K.

Your turn

An endothermic reaction has ΔH = +30 kJ/mol and Ea = 80 kJ/mol. What is the reverse activation energy, and could a catalyst lower the forward Ea to 25 kJ/mol?

Show the answer and explanation

50 kJ/mol; no.

Ea,rev = 80 − 30 = 50 kJ/mol. The transition state must lie above the products, which are 30 kJ/mol above the reactants, so no pathway can have a forward barrier below 30 kJ/mol.

E_{a, rev} = 80 - 30 = 50 kJ/mol

Keep exploring

Open the diagram in Energy diagrams, then make ΔH positive and see which barrier the transition state must clear.

Return to the concept →

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