This Arrhenius equation calculator connects temperature, activation energy and reaction rate: compute k from A and Ea, or how much a rate multiplies between two temperatures.
k = A · e^(−Ea ÷ RT) — Temperature’s Exponential Lever
Rates respond to temperature exponentially because the population of molecules above the Ea threshold sits on the Maxwell–Boltzmann tail — small T changes swing that tail’s area hugely. The two-temperature form eliminates A: ln(k₂/k₁) = −Ea/R × (1/T₂ − 1/T₁). Part of our Chemistry Calculators collection.
Worked Examples (Verified)
- Ea = 50 kJ/mol, 300 K → 310 K (defaults): k₂/k₁ = 1.909 — the “doubles every 10 degrees” rule, exact at these values
- Food spoilage (Ea ≈ 60–100 kJ/mol for many degradation reactions): fridge at 277 K vs counter at 298 K slows rates ~4–10× — refrigeration is applied Arrhenius
- k-mode: A = 10⁷, Ea 50 kJ/mol at 310 K → k ≈ 10⁷ × e^(−19.4) ≈ 0.037 — watch how a modest exponent annihilates the huge prefactor; kinetics lives in exponentials
- Cooking: pressure-cooker +20 K at Ea ~80 kJ/mol (protein/starch transformations) multiplies rates ≈ 5× — the quantitative story behind “pressure cooking is faster” beyond mere boiling point
Reading Arrhenius Plots & Limits
- ln k vs 1/T linear = single mechanism, constant Ea. Kinks mean mechanism changes (or diffusion taking over at high rates).
- Extrapolating shelf life from accelerated (hot) aging assumes the same mechanism dominates at use temperature — the assumption behind, and sometimes the failure of, accelerated-aging claims.
- A (pre-exponential) carries reaction-order units with k; Ea from ratios is unit-clean, which is why ratio mode leads here.
- Enzymes break Arrhenius above their denaturation temperature — biology’s ceiling on the lever.
Related Tools
- Gibbs Free Energy Calculator — whether reaction goes, vs how fast
- Half-Life Calculator — first-order decay kinetics
- Chemistry Calculators — the full collection
Frequently Asked Questions
What is the Arrhenius equation?
k = A·e^(−Ea/RT): the rate constant equals a pre-exponential factor times the Boltzmann probability that a collision carries at least the activation energy Ea. R = 8.314 J/(mol·K), T in kelvin. Its two-temperature ratio form cancels A — used by this calculator’s default mode.
Why do reaction rates roughly double per 10 °C?
Only coincidentally: at Ea ≈ 50 kJ/mol near 300 K, the ratio form evaluates to ≈ 1.9 per 10 K. Change Ea to 25 or 100 kJ/mol and the multiplier becomes 1.4 or 3.6. The rule of thumb is the equation wearing typical values, not a law of nature.
How is activation energy measured?
Measure k at several temperatures, plot ln k vs 1/T: the slope is −Ea/R. This calculator gives the forward predictions; experimentalists run it in reverse on their data lines. Two temperatures suffice arithmetically, but more points expose mechanism changes.
How do catalysts fit the Arrhenius picture?
They lower Ea by providing an alternative mechanism — same A-ballpark, smaller barrier, exponentially larger k at the same temperature. That’s why catalysis beats heating when selectivity matters: heat accelerates everything over its own barrier; a catalyst lowers one chosen barrier.
Does Arrhenius apply to shelf life and spoilage?
It’s the working model of accelerated aging (pharma, food science): measure degradation hot, extrapolate cold. Valid while one mechanism dominates; phase changes, microbial growth dynamics and enzyme denaturation set its boundaries — which is why extrapolated shelf lives carry safety margins.
Is this Arrhenius calculator free?
Yes — free, instant, no sign-up.