Kinetics
Arrhenius Equation
How temperature affects reaction rate — k = A·e^(-Ea/RT)
The Arrhenius equation describes how rate constant varies with temperature: k = A × exp(-Ea/RT). A is pre-exponential factor (frequency of collisions). Ea is activation energy. R is gas constant. T is absolute temperature. Higher T or lower Ea → larger k → faster reaction. Linearized: ln(k) = ln(A) - Ea/RT — plotting ln(k) vs 1/T gives straight line with slope -Ea/R, intercept ln(A). Discovered by Svante Arrhenius (1889). Foundation of chemical kinetics; predicts rate for given conditions.
- Equationk = A × exp(-Ea/RT)
- A (pre-exp factor)Frequency of effective collisions
- Ea (activation energy)Minimum energy for reaction (J/mol)
- R (gas constant)8.314 J/mol·K
- Linearized formln(k) = ln(A) - Ea/RT
- DiscoverySvante Arrhenius, 1889 (Nobel 1903)
Interactive visualization
Press play, or step through manually. The visualization is yours to drive — try it before reading on.
Watch the 60-second explainer
A condensed visual walkthrough — narrated, captioned, under a minute.
Why Arrhenius matters
- Industrial. Process design at chosen T.
- Drug stability. Predict shelf life.
- Food. Refrigeration extends shelf.
- Catalysis. Compare catalyzed vs uncatalyzed.
- Atmospheric. Reaction rates with altitude.
- Combustion. Engine kinetics.
- Biology. Enzyme T dependence.
Common misconceptions
- Higher T always doubles rate. Depends on Ea; can be 2× or 100×.
- Arrhenius works for all reactions. Some non-Arrhenius behavior.
- A is just a constant. Depends on collision geometry, kinetic factors.
- Ea is from stoichiometry. Determined experimentally.
- T must be Celsius. Must be Kelvin (absolute).
- Catalysts change A. Mostly change Ea; sometimes A.
Frequently asked questions
What does the Arrhenius equation predict?
Rate constant k as function of temperature. k = A × exp(-Ea/RT). At high T: exponent small (negative number small in magnitude); k closer to A (frequent collisions all effective). At low T: exponent large; k small. Predicts: doubling T might double or 100× rate depending on Ea. Used for: temperature-dependent kinetics across industries.
What's activation energy?
Energy required to reach transition state — bond breaking, rearrangement. Reactants must have ≥ Ea kinetic energy to react. From energy distribution (Boltzmann): fraction with energy ≥ Ea = exp(-Ea/RT). Increases exponentially with T. Catalysts lower Ea (different pathway). Typical Ea: 40-100 kJ/mol for chemistry; can be much higher for difficult reactions.
What's the pre-exponential factor A?
Frequency of collisions (with correct orientation) per unit time. A units same as k (depends on order). Roughly: 10⁹-10¹⁴ s⁻¹ for first-order. Reflects: how often reactants encounter each other in correct orientation. Affected by: concentration, geometry, but mostly inherent to reaction.
How does the equation help measure Ea?
Linearize: ln(k) = -Ea/R × (1/T) + ln(A). Plot ln(k) vs 1/T → straight line. Slope = -Ea/R → multiply by -R for Ea. Intercept = ln(A). Standard method for measuring activation energies experimentally. Just need k at multiple temperatures.
What's the "10°C rule"?
Rule of thumb: rate roughly doubles for every 10°C increase. Applies for Ea ≈ 50 kJ/mol (typical). At 25°C → 35°C: factor ≈ 2. Lower Ea: less T-sensitivity. Higher Ea: more sensitivity (e.g., enzymes can have Q10 of 2-3). Useful for: estimating shelf life, food preservation.
How does it apply to enzymes?
Enzyme kinetics depends on T. Lower Ea (catalyzed): less T sensitive than uncatalyzed. But: enzymes also denature at high T. Combined: optimal T (often 30-40°C for human enzymes). Above: rate increases until denaturation; then decreases. Q10 (rate ratio at 10°C apart) often 2-3 for biological reactions.
What about reactions with zero or negative Ea?
Zero Ea: rate independent of T (rare; e.g., free radical recombination, ion-ion in solution). Negative Ea: rate decreases with T (e.g., 3-body reactions, some enzyme reactions). Suggests: reaction goes through pre-equilibrium step; complex behavior. Arrhenius equation can fail in non-Arrhenius regimes.