# Activation Energy

> IB Chemistry SL · Reactivity 2: Energetics and Kinetics
> Source: https://www.owlsprep.com/study/ib-chemistry-sl-u5-activation-energy/

This module covers the definition of activation energy, its role in reaction kinetics, interpretation on reaction profiles, calculation via the Arrhenius equation, and the impact of catalysts on activation energy for IB SL Chemistry.

**Prerequisites:** [Collision theory and reaction rates](https://www.owlsprep.com/study/ib-chemistry-sl-u5-collision-theory/); [Enthalpy and reaction profiles](https://www.owlsprep.com/study/ib-chemistry-sl-u4-reaction-profiles/)

## Learning objectives

- Define activation energy and relate it to successful collisions in reactions
- Interpret activation energy on reaction profile diagrams
- Calculate activation energy using the linear form of the Arrhenius equation
- Explain the effect of catalysts and temperature on activation energy and reaction rate

## Definition and Physical Meaning of Activation Energy

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

*Notation:* E_a

*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.

## Activation Energy and the Arrhenius Equation

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 $y = mx + c$ for plotting:

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

A plot of $
 k$ against $1/T$ gives a straight line with gradient equal to $-E_a/R$.

**Worked example:** An Arrhenius plot of $
 k$ against $1/T$ (in K⁻¹) gives a gradient of $-1.20 \times 10^4$ K. Calculate $E_a$ 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: $m = -1.20 \times 10^4$ 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. $$E_a = 100 \text{ kJ mol}^{-1} \text{ (3 significant figures)}$$

*Calculator:* allowed

## Effect of Temperature and Catalysts

> **Common Misconception**
>
> Changing temperature does not change the activation energy of a reaction. Higher temperature only increases the proportion of particles with energy ≥ Ea, which increases reaction rate.

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 $E_{a(\text{catalyzed})} < E_{a(\text{uncatalyzed})}$. 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.

## Activation Energy and the Maxwell-Boltzmann Distribution

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.

**Check your understanding**

1. 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

   *Why:* 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.

## Common pitfalls

- **Wrong:** Labeling activation energy from the product line to the peak of the reaction profile.
  - Why it fails: Activation energy is the energy required for reactants to form the activated complex, so it is measured starting from reactants.
  - Correct: Always measure and label Ea from the reactant energy level up to the peak of the reaction profile.
- **Wrong:** Claiming increasing temperature decreases activation energy.
  - Why it fails: Temperature does not change the energy threshold for the reaction, only the number of particles that meet the threshold.
  - Correct: State that increasing temperature increases the proportion of particles with energy ≥ Ea, increasing reaction rate, while Ea remains unchanged.
- **Wrong:** Forgetting to convert Ea from J to kJ in Arrhenius calculations.
  - Why it fails: 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: Always divide your calculated Ea by 1000 to convert from J mol⁻¹ to kJ mol⁻¹ before writing your final answer.
- **Wrong:** Claiming catalysts change the overall enthalpy change of a reaction.
  - Why it fails: Catalysts only change the reaction pathway, not the initial energy of reactants or final energy of products.
  - Correct: State that ΔH is identical for catalyzed and uncatalyzed reactions; only activation energy is lower for the catalyzed pathway.
- **Wrong:** Using $E_a = \text{gradient} \times R$ instead of $E_a = -\text{gradient} \times R$ for Arrhenius plots.
  - Why it fails: The gradient of $
 k$ vs $1/T$ is negative, so forgetting the negative sign gives a negative Ea which is physically impossible.
  - Correct: Use $E_a = -(\text{gradient}) \times R$, so a negative gradient gives a positive, physically meaningful value for Ea.

## 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; $\Delta H$ unchanged | n/a |
| Arrhenius Plot Calculation | $E_a = -\text{(gradient)} \times R$ | J mol⁻¹ (convert to kJ) |

## 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.

- [Reactivity 3: Equilibrium and Organic Chemistry](https://www.owlsprep.com/study/ib-chemistry-sl-u6-overview/)
- [Dynamic equilibrium](https://www.owlsprep.com/study/ib-chemistry-sl-u6-dynamic-equilibrium/)
- [Position of equilibrium](https://www.owlsprep.com/study/ib-chemistry-sl-u6-position-of-equilibrium/)

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