🎓 Prepared by students from Boğaziçi University

What is Activation Energy?

Q: What is the relationship between Eₐ and reaction rate?

Eₐ appears in the Arrhenius equation k = Ae^(-Eₐ/RT). Lower Eₐ → higher k → faster rate.

Q: Why do enzymes work so well?

Enzymes lower Eₐ dramatically (often 50+ kJ/mol), speeding reactions by factors of 10⁶–10¹⁷.

Q: Can you measure activation energy?

Yes — by measuring k at two temperatures and using the Arrhenius equation: ln(k₂/k₁) = (Eₐ/R)(1/T₁ − 1/T₂).

Q: Does a spontaneous reaction always happen fast?

No — a reaction can be thermodynamically favourable (ΔG < 0) but kinetically slow due to high Eₐ (e.g. diamond oxidation).

Activation energy (Eₐ) is the minimum energy required for reactants to collide and form products. Even a spontaneous reaction (ΔG < 0) may need a high Eₐ, making it slow. Catalysts speed reactions by lowering Eₐ without being consumed.

Short answer

Activation energy is the energy barrier reactants must overcome. Catalysts lower Eₐ, speeding reactions; higher temperature also increases collision energy, raising the reaction rate.

Energy Profile: With and Without Catalyst

1
Reactants start here
Low potential energy; need Eₐ to reach transition state
↓
2
Transition state (TS)
Highest energy point; bonds partly broken/formed
↓
3
Catalyst lowers barrier
Provides alternative pathway with lower Eₐ
↓
4
Products end here
Final energy (ΔG unchanged)

Step-by-step worked examples

A reaction has Eₐ = 50 kJ/mol. With a catalyst lowering it to 30 kJ/mol, how much faster?

Using Arrhenius: k ∝ e^(-Eₐ/RT)
Ratio: k_cat/k_uncatalysed = e^(-30/RT) / e^(-50/RT) = e^(20/RT)
At T=300 K, R=8.314: e^(20/2494) ≈ e^0.008 ≈ 1.008 × 10^3 ≈ 1000× faster (order-of-magnitude)

Enzyme lowers Eₐ from 80 to 20 kJ/mol (ΔEₐ=60). Compare rates at 37 °C.

k_enzyme/k_uncatalysed = e^(ΔEₐ/RT) = e^(60/(8.314 × 310))
= e^(60/2577) ≈ e^0.0233 ≈ 1.023 × 10^10 ≈ 10 billion× faster

Doubling temperature from 300 to 600 K increases rate 8-fold. Estimate Eₐ.

ln(k₂/k₁) = (Eₐ/R) × (1/T₁ - 1/T₂)
ln(8) = (Eₐ/8.314) × (1/300 - 1/600)
ln(8) ≈ 2.08 = (Eₐ/8.314) × (1/600)
Eₐ ≈ 2.08 × 8.314 × 600 ≈ 10,360 J/mol ≈ 10.4 kJ/mol

Flashcards

Quick quiz

Q1.Eₐ is high but ΔG is negative. The reaction is…

Correct answer: A. ΔG < 0 = spontaneous (favours products). High Eₐ = slow. Both true: spontaneous but slow.

Q2.Lowering Eₐ from 60 to 40 kJ/mol increases rate by…

Correct answer: C. k ∝ e^(-Eₐ/RT); reducing Eₐ by 20 kJ/mol at ~300 K gives ~100-1000× speedup.

Q3.An enzyme-catalysed reaction and uncatalysed reaction have the same…

Correct answer: B. Enzyme lowers Eₐ and increases k, but ΔG and equilibrium constant K remain the same.

Q4.At higher temperature, Eₐ…

Correct answer: C. Activation energy is a fixed property of the reaction pathway, independent of temperature.

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Common mistakes

✗

Confusing ΔG and Eₐ — assuming high ΔG means fast. — Correct: ΔG (spontaneity) and Eₐ (speed) are independent; ΔG < 0 is necessary but not sufficient for fast reaction.

✗

Thinking catalysts provide energy. — Correct: Catalysts lower the energy barrier; the reaction's bonds already contain the energy.

✗

Assuming higher temperature changes Eₐ. — Correct: Eₐ is intrinsic to the reaction pathway. Temperature increases collision frequency, not Eₐ itself.

✗

Believing a catalyst changes the equilibrium. — Correct: Catalyst speeds both directions equally — equilibrium constant K is unchanged.

FAQ

What is the relationship between Eₐ and reaction rate?

Eₐ appears in the Arrhenius equation k = Ae^(-Eₐ/RT). Lower Eₐ → higher k → faster rate.

Why do enzymes work so well?

Enzymes lower Eₐ dramatically (often 50+ kJ/mol), speeding reactions by factors of 10⁶–10¹⁷.

Can you measure activation energy?

Yes — by measuring k at two temperatures and using the Arrhenius equation: ln(k₂/k₁) = (Eₐ/R)(1/T₁ − 1/T₂).

Does a spontaneous reaction always happen fast?

No — a reaction can be thermodynamically favourable (ΔG < 0) but kinetically slow due to high Eₐ (e.g. diamond oxidation).