Activation Energy
Activation energy (Eₐ) is the minimum amount of energy that reacting molecules must possess for a collision to result in a chemical reaction — effectively the energy barrier that must be overcome to convert reactants into products. It determines how fast a reaction proceeds: reactions with low activation energies are generally fast (explosions, acid-base), while those with high activation energies are slow (rusting, digestion). The concept was introduced by Svante Arrhenius in 1889 and is central to the Arrhenius equation and transition state theory.
Key Formula
k = A × exp(-Ea / RT)
LaTeX: k = A e^{-E_a / (RT)}
| Symbol | Meaning | Unit |
|---|---|---|
| k | Rate constant | varies (mol⁻¹ L s⁻¹ for second order) |
| A | Pre-exponential (frequency) factor | same as k |
| E_a | Activation energy | J/mol or kJ/mol |
| R | Universal gas constant | 8.314 J/(mol·K) |
| T | Absolute temperature | K |
Worked Example
Problem
The activation energy of a reaction is 50 kJ/mol. At 300 K the rate constant k₁ = 2.0 × 10⁻³ s⁻¹. Calculate the rate constant k₂ at 350 K using the Arrhenius equation.
Solution
Step 1: Use the two-temperature form of the Arrhenius equation: ln(k₂/k₁) = (Eₐ/R) × (1/T₁ − 1/T₂) Step 2: Substitute values: Eₐ = 50,000 J/mol, R = 8.314 J/(mol·K), T₁ = 300 K, T₂ = 350 K Step 3: Calculate the exponent: (1/300 − 1/350) = (350 − 300)/(300 × 350) = 50/105,000 = 4.762 × 10⁻⁴ K⁻¹ Step 4: ln(k₂/k₁) = (50,000 / 8.314) × 4.762 × 10⁻⁴ = 6014.4 × 4.762 × 10⁻⁴ = 2.864 Step 5: k₂/k₁ = e^2.864 = 17.53 k₂ = 17.53 × 2.0 × 10⁻³ = 3.51 × 10⁻² s⁻¹
Answer
k₂ ≈ 3.51 × 10⁻² s⁻¹ at 350 K
Activation Energies of Typical Reactions
| Reaction | Type | Eₐ (kJ/mol) | Rate at 25°C |
|---|---|---|---|
| H₂ + Cl₂ → 2HCl (catalyzed) | Halogenation | ≈ 0 | Explosive |
| Decomposition of N₂O₅ | Decomposition | 103 | Slow |
| Hydrolysis of sucrose | Biological | 107 | Very slow (uncatalyzed) |
| Combustion of CH₄ | Combustion | ~125 | Requires ignition |
| Fe corrosion (rusting) | Oxidation | ~80 | Very slow |
Interactive Tools
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Related Terms
Reaction Rate
The reaction rate is the change in concentration of a reactant or product per unit time in a chemical reaction, expressed in units of mol/(L·s) or mol·L⁻¹·s⁻¹. It quantifies how quickly reactants are consumed and products are formed, and is influenced by factors including concentration, temperature, surface area, catalysts, and the nature of the reactants. Understanding reaction rates is fundamental to chemical engineering (designing reactors), pharmacology (drug metabolism), and environmental chemistry (pollutant breakdown).
Chemical Catalysis
Chemical catalysis is the process by which a catalyst — a substance that participates in a reaction and increases its rate without being consumed or permanently altered — provides an alternative reaction pathway with a lower activation energy. Catalysts can be homogeneous (same phase as reactants, e.g., H⁺ in acid hydrolysis), heterogeneous (different phase, e.g., Pt in catalytic converters), or biological (enzymes). Catalysis is fundamental to industrial chemistry: approximately 85-90% of all industrial chemical processes rely on catalysts, including the Haber-Bosch ammonia synthesis (Fe catalyst) and petroleum cracking (zeolites).
Rate Constant
The rate constant (k) is the proportionality constant in the rate law that relates the reaction rate to the concentrations of reactants; it is a characteristic value for a given reaction at a specific temperature. Unlike the reaction rate itself, k does not depend on concentrations but is strongly temperature-dependent, following the Arrhenius equation k = A·e^(−Eₐ/RT). The units of k vary with the overall reaction order, and a larger k indicates a faster inherent reaction speed.
From Latin "activus" (active, energetic) and Greek "energeia" (activity, operation). The term was formalized by Swedish chemist Svante Arrhenius in 1889 when he derived the exponential relationship between temperature and reaction rate to explain why reaction rates increase with temperature.