About

The Arrhenius equation quantifies how reaction rate constants depend on temperature through the activation energy barrier E_a. Miscalculating E_a by even 5 kJ/mol can shift predicted rate constants by an order of magnitude at industrial operating temperatures, leading to incorrect reactor sizing, unsafe thermal runaway estimates, or failed pharmaceutical synthesis batches. This tool implements the two-point Arrhenius method using ln(k₂/k₁) = −(E_a/R) ⋅ (1/T₂ − 1/T₁) with the gas constant R = 8.314 J/(mol⋅K). It assumes a single dominant reaction pathway and temperature-independent E_a over the measured range. This assumption breaks down for multi-step mechanisms or temperatures near phase transitions. For enzyme kinetics above denaturation thresholds or catalytic reactions with surface restructuring, treat results as first approximations only.

Formulas

The Arrhenius equation relates the rate constant k to temperature T through the activation energy E_a and the pre-exponential factor A:

k = A ⋅ exp(−E_aR ⋅ T)

Taking the natural logarithm of both sides yields the linearized form:

ln(k) = ln(A) − E_aR ⋅ 1T

For two experimental data points (T₁, k₁) and (T₂, k₂), subtracting the linearized equations eliminates A and isolates E_a:

ln(k₂k₁) = −E_aR ⋅ (1T₂ − 1T₁)

Solving for E_a:

E_a = −R ⋅ ln(k₂/k₁)1T₂ − 1T₁

Where k = rate constant (s⁻¹ or appropriate units), A = pre-exponential (frequency) factor (same units as k), E_a = activation energy (J/mol), R = universal gas constant = 8.314 J/(mol⋅K), and T = absolute temperature (K).

Reference Data

Reaction	E_a (kJ/mol)	A (s⁻¹)	Phase	Notes
2 HI → H₂ + I₂	183	1.0 × 10¹³	(g)	Classic gas-phase bimolecular
CH₃CHO → CH₄ + CO	190	2.0 × 10¹³	(g)	Aldehyde decomposition
C₂H₅Br + OH⁻	89.6	4.3 × 10¹¹	(aq)	S_N2 nucleophilic substitution
H₂ + I₂ → 2 HI	165	2.7 × 10¹¹	(g)	Bimolecular, reversible
NO₂ + CO → NO + CO₂	134	5.0 × 10¹⁰	(g)	Atmospheric chemistry relevant
CH₃I + CH₃O⁻	76.0	2.5 × 10¹⁰	(aq)	S_N2 in methanol
Sucrose hydrolysis (H⁺)	107	1.5 × 10¹⁵	(aq)	Acid-catalyzed, pseudo-first-order
Ethyl acetate + NaOH	47.0	1.1 × 10⁸	(aq)	Saponification, second-order
N₂O₅ decomposition	103	4.9 × 10¹³	(g)	Unimolecular, first-order
C₂H₄ + H₂ (Pt catalyst)	42.0	7.0 × 10⁶	(g)	Heterogeneous catalysis on Pt
H₂O₂ decomposition (I⁻)	56.0	8.0 × 10⁸	(aq)	Homogeneous catalysis
Cyclopropane isomerization	272	1.6 × 10¹⁵	(g)	Ring strain release, thermal
Br₂ + H₂ → 2 HBr	176	1.0 × 10¹²	(g)	Chain reaction mechanism
Diels-Alder (butadiene + ethylene)	115	5.0 × 10⁹	(g)	Concerted pericyclic [4+2]
Fe³⁺ + SCN⁻ complexation	30.0	6.0 × 10⁷	(aq)	Fast, low barrier
Protein denaturation (average)	200-400	10³⁰ - 10⁶⁰	(aq)	Highly cooperative, non-Arrhenius above T_m
CH₄ combustion (uncatalyzed)	218	4.0 × 10¹³	(g)	High barrier, needs ignition
Ozone decomposition (O₃)	95.0	8.0 × 10¹¹	(g)	Stratospheric chemistry
Acetone iodination (acid cat.)	86.0	3.0 × 10¹⁰	(aq)	Zero-order in I₂
Si oxidation (thermal, 1000 °C)	120	3.6 × 10⁶	(s)	Semiconductor fabrication, Deal-Grove model

Frequently Asked Questions

The Arrhenius equation contains the term 1/T, which requires an absolute temperature scale. Using Celsius or Fahrenheit introduces a non-physical offset (e.g., 0 °C = 273.15 K). A calculation at 25 °C using Celsius directly would divide by 25 instead of 298.15, producing an error exceeding 1000%. This calculator performs the conversion internally regardless of your input unit.

A negative E_a indicates the rate constant decreases as temperature rises. This occurs in certain multi-step reactions where an intermediate equilibrium shifts unfavorably at higher temperatures (e.g., some enzyme-catalyzed or radical recombination reactions). It signals non-elementary kinetics. The Arrhenius model assumes a single barrier, so a negative result means the simple model does not capture the mechanism. Consider using the Eyring equation or fitting individual elementary steps.

Highly sensitive when the two temperatures are close together. For T₁ = 300 K and T₂ = 310 K, a 1 K error in either measurement shifts E_a by approximately 10%. For best accuracy, use data points separated by at least 20-30 K. The denominator (1/T₂ − 1/T₁) approaches zero for nearby temperatures, amplifying any noise.

Yes. The Arrhenius equation relates the rate constant k to temperature independent of reaction order. However, the units of k differ by order: first-order uses s⁻¹, second-order uses L/(mol⋅s), etc. Ensure both k₁ and k₂ are in consistent units. The tool computes E_a from their ratio, so units cancel, but the pre-exponential factor A will carry those units.

In collision theory, A represents the product of collision frequency and the steric factor (fraction of collisions with correct orientation). Typical gas-phase values range from 10¹⁰ to 10¹⁴ s⁻¹ for unimolecular reactions. Values outside 10⁶ - 10¹⁸ suggest experimental error or a complex mechanism. In transition state theory, A relates to the entropy of activation ΔS^‡.

A catalyst lowers E_a by providing an alternative reaction pathway. The Arrhenius equation still applies to the catalyzed reaction, but you must use rate constants measured under catalyzed conditions. Comparing E_a values for catalyzed vs. uncatalyzed reactions quantifies the catalyst's effectiveness. For example, platinum reduces the activation energy of H₂ + ethylene from approximately 180 to 42 kJ/mol.