Arrhenius Equation: How Temperature Controls Reaction Speed

simulator beginner ~8 min
Loading simulation...
k ≈ 2.0 × 10⁻¹ s⁻¹ at 300 K, Ea = 50 kJ/mol

At 300 K with an activation energy of 50 kJ/mol, the Arrhenius equation predicts a rate constant reflecting the small fraction of molecules with enough kinetic energy to overcome the activation barrier.

Formula

k = A × exp(−Ea / RT) (Arrhenius equation)
ln(k) = ln(A) − Ea/(RT) (linearized Arrhenius)
Q₁₀ = k(T+10) / k(T) = exp(10 × Ea / (R × T × (T+10)))

Temperature: The Universal Reaction Accelerator

In 1889, Svante Arrhenius published an equation that became one of the most important in all of chemistry: k = A × exp(−Ea/RT). This elegant formula captures a profound truth — the rate of virtually every chemical reaction increases exponentially with temperature. From cooking to combustion, from drug metabolism to material degradation, the Arrhenius equation governs the speed of chemistry.

The Energy Barrier

Not every molecular collision leads to a reaction. Molecules must collide with enough kinetic energy to overcome an energy barrier — the activation energy (Ea). At any temperature, the Boltzmann distribution tells us what fraction of molecules exceed this threshold: exp(−Ea/RT). Raising the temperature shifts the distribution, dramatically increasing the fraction of molecules with enough energy to react.

The Arrhenius Plot

Plotting ln(k) versus 1/T gives a straight line with slope −Ea/R. This linearized form is the standard experimental method for determining activation energy. The simulation shows both the exponential curve and the Arrhenius plot, letting you see how changing Ea and temperature affects the rate constant across a wide range of conditions.

Catalysts and Biology

Enzymes are nature's catalysts — they lower activation energy by factors of 10 to 20, accelerating reactions by factors of millions to billions. The Arrhenius equation explains why fever increases metabolic rate (higher T), why food spoils faster in heat, and why cryopreservation works (near-zero reaction rates at very low T). Understanding this equation is essential for drug design, food science, and materials engineering.

FAQ

What is the Arrhenius equation?

The Arrhenius equation k = A × exp(−Ea/RT) describes how the rate constant of a chemical reaction depends on temperature. A is the pre-exponential factor (related to collision frequency), Ea is the activation energy, R is the gas constant, and T is temperature in Kelvin.

Why do reactions speed up with temperature?

Higher temperature means molecules move faster and collide more energetically. The Arrhenius equation shows that the fraction of molecules with energy exceeding the activation barrier (Ea) increases exponentially with temperature. A 10°C increase typically doubles or triples reaction rates.

What is activation energy?

Activation energy (Ea) is the minimum energy molecules must possess to undergo a chemical reaction. It represents the energy barrier between reactants and products. Catalysts work by lowering the activation energy, allowing reactions to proceed faster at the same temperature.

What is the Q₁₀ temperature coefficient?

Q₁₀ is the factor by which a reaction rate increases for every 10°C (or 10 K) rise in temperature. For most chemical reactions, Q₁₀ is between 2 and 3 — meaning the rate doubles or triples per 10°C increase. Biological systems typically have Q₁₀ ≈ 2.

Sources

Embed

<iframe src="https://homo-deus.com/lab/biochemistry/reaction-rate/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub