State that a catalyst decreases the activation energy, $E_a$, of a reaction

Chemical Reactions – Rate of Reaction (Cambridge IGCSE 0620 §6.2)

Learning Objective

State that a catalyst decreases the activation energy, \(E_{a}\), of a reaction.

Factors that Influence Reaction Rate

All five factors required by the syllabus are listed below. Tick each box when revising.

• Concentration (or pressure for gases)
• Temperature
• Surface area of a solid
• Catalyst (homogeneous or heterogeneous)
• Pressure (for gases only)

Factor	How it influences the rate
Concentration (or pressure for gases)	Higher concentration → more frequent collisions → larger number of effective collisions per unit time → faster rate.
Temperature	Raises the average kinetic energy of particles. A larger fraction have kinetic energy ≥ \(E_{a}\) (see Arrhenius equation), so the rate increases sharply.
Surface area of a solid	Grinding or spreading a solid increases the area that is exposed to reactants, providing more active sites for collisions and therefore a higher rate.
Catalyst (homogeneous or heterogeneous)	Provides an alternative pathway with a lower \(E_{a}\); more particles can overcome the barrier at the same temperature, so the rate constant \(k\) becomes larger. The catalyst is not consumed.
Pressure (gases only)	Increasing pressure compresses gas molecules together, increasing collision frequency and thus the reaction rate.

Collision Theory – Qualitative Basis for the Arrhenius Equation

• Reactions occur when particles collide with:
  • sufficient kinetic energy (≥ \(E_{a}\)), and
  • the correct orientation.
• The **frequency factor** \(A\) represents the number of collisions per unit time that have the proper orientation.
• Mathematically, the temperature‑dependence of the rate constant is expressed by the Arrhenius equation: \[ k = A\,\exp\!\left(-\frac{E_{a}}{RT}\right) \] where A = frequency factor (s⁻¹), Eₐ = activation energy (J mol⁻¹), R = 8.314 J mol⁻¹ K⁻¹, T = absolute temperature (K).

Quantitative illustration

For the decomposition of hydrogen peroxide, suppose the activation energy falls from 75 kJ mol⁻¹ (no catalyst) to 45 kJ mol⁻¹ (with MnO₂) at 298 K. The ratio of the rate constants is

\[ \frac{k_{\text{cat}}}{k_{\text{uncat}}} = \exp\!\left(\frac{E_{a,\text{uncat}}-E_{a,\text{cat}}}{RT}\right) = \exp\!\left(\frac{30\,000\ \text{J mol}^{-1}}{8.314\times298}\right) \approx \exp(12.1) \approx 1.8\times10^{5}. \]

Thus the catalyst makes the reaction roughly 180 000 times faster at the same temperature.

How a Catalyst Works

• Offers an **alternative reaction pathway** with a lower activation energy.
• Because \(E_{a}\) is lower, a larger proportion of molecules possess enough kinetic energy to form the activated complex at a given temperature.
• The rate constant \(k\) increases, so the reaction proceeds faster.
• The overall enthalpy change, \(\Delta H\), is unchanged – the catalyst does not affect the thermodynamics, only the kinetic pathway.
• For solid (heterogeneous) catalysts, increasing the **surface area** (e.g., grinding) exposes more active sites and further accelerates the reaction.

Potential‑Energy Profile (Illustrative)

Comparison of Activation Energies

Reaction	Without Catalyst \(E_{a}\) (kJ mol⁻¹)	With Catalyst \(E_{a}\) (kJ mol⁻¹)	Effect on Rate
Decomposition of hydrogen peroxide (2 H₂O₂ → 2 H₂O + O₂)	75	45	≈ 10‑fold increase (MnO₂ solid catalyst)
Formation of ammonia (Haber process) (N₂ + 3 H₂ → 2 NH₃)	200	130	Rate increases dramatically (Fe + K₂O + Al₂O₃)
Esterification of acetic acid (CH₃COOH + C₂H₅OH ⇌ CH₃COOC₂H₅ + H₂O)	95	60	Equilibrium reached faster (H₂SO₄ homogeneous catalyst)

Examples of Catalysts

• Homogeneous catalyst – sulfuric acid in the esterification of acetic acid (same liquid phase as reactants).
• Heterogeneous catalyst – manganese(IV) oxide (MnO₂) for the decomposition of hydrogen peroxide (solid surface).
• Industrial catalyst – iron with promoters (K₂O, Al₂O₃) in the Haber process for ammonia synthesis.
• Biological catalyst (enzyme) – amylase in starch breakdown (useful for extended study, not required for the core syllabus).

Practical Investigation (AO3 Skill)

Summary

A catalyst accelerates a chemical reaction by providing an alternative pathway with a lower activation energy, \(E_{a}\). This reduction increases the fraction of reacting particles that can overcome the energy barrier at a given temperature, giving a larger rate constant \(k\) and a faster reaction. The catalyst is not consumed, does not alter the overall enthalpy change (\(\Delta H\)), and its effectiveness can be enhanced by increasing the surface area of solid catalysts.