Activation Energy

IB Chemistry SL· 35 min read

1. Definition and Physical Meaning of Activation Energy★★☆☆☆⏱ 10 min

📘 Definition

Activation Energy

E_a

The minimum total kinetic energy that colliding reactant particles must have to form an activated complex and proceed to form products.

Example:

For the reaction of hydrogen and oxygen, E_a ≈ 25 kJ mol⁻¹, so a spark provides enough energy to initiate the reaction.

Activation energy exists because chemical bonds in reactants must be broken before new bonds can form in products. Breaking bonds requires an input of energy, so this minimum energy threshold must be overcome even for exothermic reactions.

📐 Worked Example

Explain why activation energy is always positive, and describe how to label it on a reaction profile for an endothermic reaction.

1
Draw the reaction profile with reactants at a lower enthalpy than products, and a peak (hump) between them representing the activated complex.
2
Activation energy is the vertical difference between the reactant enthalpy level and the peak of the hump:
3
$E_a = H_{\text{activated complex}} - H_{\text{reactants}}$
4
Activation energy is always positive because energy is always required to break reactant bonds, so the activated complex always has higher enthalpy than reactants.

Exam tip:

Always label Ea starting from the reactant energy line, not the product line, even for exothermic reactions.

2. Activation Energy and the Arrhenius Equation★★★☆☆⏱ 15 min

✓ Calculator OK

The Arrhenius equation relates the rate constant $k$ of a reaction to activation energy $E_{a}$ and absolute temperature $T$ . The equation is provided in the IB data booklet, so you do not need to memorize it.

k = A e^{-\frac{E_a}{RT}}

To calculate $E_{a}$ from experimental data, the equation is rearranged into linear form $y = m x + c$ for plotting:

\ln k = -\frac{E_a}{R} \left(\frac{1}{T}\right) + \ln A

A plot of $ k $a g ain s t$ 1/T $g i v es a s t r ai g h tl in e w i t h g r a d i e n t e q u a l t o$ -E_a/R$.

📐 Worked Example

An Arrhenius plot of $ k $a g ain s t$ 1/T $(in K^{- 1}) g i v es a g r a d i e n t o f$ -1.20 \times 10^4 $K . C a l c u l a t e$ E_a$ in kJ mol⁻¹.

1
Rearrange the linear equation to solve for $E_{a}$ , using gradient $m = - E_{a} / R$ :
2
$E_a = -m \times R$
3
Substitute values: $m = - 1.20 \times 1 0^{4}$ K, $R = 8.31$ J K⁻¹ mol⁻¹:
4
$E_a = -(-1.20 \times 10^4) \times 8.31 = 99720 \text{ J mol}^{-1}$
5
Convert to kJ mol⁻¹ by dividing by 1000:
6
$E_a = 100 \text{ kJ mol}^{-1} \text{ (3 significant figures)}$

3. Effect of Temperature and Catalysts★★☆☆☆⏱ 12 min

Catalysts increase reaction rate by providing an alternative reaction mechanism (different reaction pathway) with a lower activation energy than the uncatalyzed reaction. Lower Ea means more particles have enough energy to react, so rate increases.

📐 Worked Example

Compare the activation energy of a catalyzed vs uncatalyzed exothermic reaction on the same reaction profile.

1
Draw reactants at a higher enthalpy than products, consistent with an exothermic reaction.
2
Draw a higher, wider energy hump for the uncatalyzed reaction, and a lower hump for the catalyzed reaction (different pathway, lower Ea). Both start at reactant energy and end at product energy.
3
Label Ea(uncatalyzed) from reactants to the higher peak, and Ea(catalyzed) from reactants to the lower peak, showing $E_{a (catalyzed)} < E_{a (uncatalyzed)}$ . The overall enthalpy change ΔH is identical for both pathways.

Exam tip:

Catalysts never change the overall enthalpy change ΔH of a reaction, only the activation energy.

4. Activation Energy and the Maxwell-Boltzmann Distribution★★★☆☆⏱ 8 min

The Maxwell-Boltzmann distribution shows the spread of kinetic energies among reactant particles at a given temperature. The area under the curve beyond the Ea threshold equals the fraction of particles with enough energy to react successfully.

✓ Quick check

Which of the following changes lowers the activation energy of a reaction?
- A. Increasing temperature
- B. Adding a catalyst
- C. Increasing reactant concentration
- D. Increasing pressure
Reveal answer
B —
Increasing temperature, concentration, and pressure all increase reaction rate by increasing the fraction of collisions with energy ≥ Ea, but do not change the Ea threshold itself. Only catalysts provide an alternative reaction pathway with lower Ea.

5. Common Pitfalls

Wrong move:

Labeling activation energy from the product line to the peak of the reaction profile.

Why:

Activation energy is the energy required for reactants to form the activated complex, so it is measured starting from reactants.

Correct move:

Always measure and label Ea from the reactant energy level up to the peak of the reaction profile.

Wrong move:

Claiming increasing temperature decreases activation energy.

Why:

Temperature does not change the energy threshold for the reaction, only the number of particles that meet the threshold.

Correct move:

State that increasing temperature increases the proportion of particles with energy ≥ Ea, increasing reaction rate, while Ea remains unchanged.

Wrong move:

Forgetting to convert Ea from J to kJ in Arrhenius calculations.

Why:

R has units of J K⁻¹ mol⁻¹, so initial calculations give Ea in J, but exam questions almost always ask for kJ.

Correct move:

Always divide your calculated Ea by 1000 to convert from J mol⁻¹ to kJ mol⁻¹ before writing your final answer.

Wrong move:

Claiming catalysts change the overall enthalpy change of a reaction.

Why:

Catalysts only change the reaction pathway, not the initial energy of reactants or final energy of products.

Correct move:

State that ΔH is identical for catalyzed and uncatalyzed reactions; only activation energy is lower for the catalyzed pathway.

Wrong move:

Using $E_{a} = gradient \times R$ instead of $E_{a} = - gradient \times R$ for Arrhenius plots.

Why:

The gradient of $ k $v s$ 1/T$ is negative, so forgetting the negative sign gives a negative Ea which is physically impossible.

Correct move:

Use $E_{a} = - (gradient) \times R$ , so a negative gradient gives a positive, physically meaningful value for Ea.

6. Quick Reference Cheatsheet

Concept	Key Fact	Standard Unit
Activation Energy ( $E_{a}$ )	Minimum energy for successful reaction	kJ mol⁻¹
Arrhenius Linear Form	$ln k = (- E_{a} / R) (1/ T) + ln A$	n/a
Effect of Temperature	No change to $E_{a}$ ; increases fraction of particles ≥ $E_{a}$	n/a
Effect of Catalyst	Alternative lower $E_{a}$ pathway; $Δ H$ unchanged	n/a
Arrhenius Plot Calculation	$E_{a} = - (gradient) \times R$	J mol⁻¹ (convert to kJ)

When this came up on past exams

AI-estimated based on syllabus patterns — cross-check with official past papers for accuracy. Use only as revision-focus signals.

2022 · 1
Identify Ea from a reaction profile
2021 · 2
Calculate Ea from Arrhenius plot gradient
2023 · 1
Effect of catalyst on activation energy

Going deeper

syllabusOfficial IB Chemistry SL SyllabusFull topic 5 learning outcomes

What's Next

Activation energy is a core foundational concept for all kinetics topics in IB SL Chemistry, and is regularly tested in both Paper 1 and Paper 2 exams. Mastering the interpretation of reaction profiles and calculation of Ea from Arrhenius plots will help you tackle more complex kinetics questions, including those about catalysis and rate mechanisms. This topic also connects closely to enthalpy changes and collision theory, so reviewing these concepts alongside activation energy will help you build a cohesive understanding of chemical reactivity.