Arrhenius Equation Calculator
Free Arrhenius equation Calculator for chemical kinetics. Enter variables to compute results with formulas and detailed steps.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
k = A \u00D7 exp(-Ea / RT)
Where k = rate constant, A = pre-exponential factor (frequency factor), Ea = activation energy (J/mol), R = gas constant (8.314 J/mol/K), T = absolute temperature (K). The exponential term represents the fraction of molecules with sufficient energy to overcome the activation barrier.
Worked Examples
Example 1: First-Order Decomposition Reaction
Problem:A decomposition reaction has A = 1e13 s-1 and Ea = 75 kJ/mol. Calculate the rate constant at 25 C (298.15 K) and 35 C (308.15 K).
Solution:At 298.15 K:\nk = 1e13 x exp(-75000 / (8.314 x 298.15))\nk = 1e13 x exp(-30.26)\nk = 1e13 x 7.31e-14\nk = 0.731 s-1\n\nAt 308.15 K:\nk = 1e13 x exp(-75000 / (8.314 x 308.15))\nk = 1e13 x exp(-29.28)\nk = 1e13 x 1.88e-13\nk = 1.88 s-1\n\nRatio: 1.88 / 0.731 = 2.57x faster
Result:k(298K) = 0.731 s-1 | k(308K) = 1.88 s-1 | 2.57x increase for 10 K rise
Example 2: Determining Activation Energy from Rate Data
Problem:A reaction has k1 = 0.0045 s-1 at 300 K and k2 = 0.087 s-1 at 350 K. Find the activation energy.
Solution:Using: Ea = R x ln(k2/k1) / (1/T1 - 1/T2)\nEa = 8.314 x ln(0.087/0.0045) / (1/300 - 1/350)\nEa = 8.314 x ln(19.33) / (0.003333 - 0.002857)\nEa = 8.314 x 2.962 / 0.000476\nEa = 51,717 J/mol = 51.7 kJ/mol
Result:Ea = 51.7 kJ/mol (12.4 kcal/mol) | A = 2.9e8 s-1
Frequently Asked Questions
What is the Arrhenius equation and what does it describe?
The Arrhenius equation, k = A * exp(-Ea/RT), describes how the rate constant k of a chemical reaction depends on temperature. Svante Arrhenius proposed this relationship in 1889, and it remains one of the most important equations in chemical kinetics. The equation contains three key parameters: A (the pre-exponential or frequency factor) represents the collision frequency and orientation probability of reactant molecules. Ea (activation energy) is the minimum energy barrier that reactant molecules must overcome for the reaction to proceed. R is the universal gas constant (8.314 J/mol/K), and T is the absolute temperature in Kelvin. The exponential term exp(-Ea/RT) represents the fraction of molecules with sufficient energy to react at temperature T.
What is the difference between the Arrhenius equation and the Eyring equation?
The Arrhenius equation is an empirical relationship that describes how rate constants change with temperature using activation energy and a pre-exponential factor. The Eyring equation, derived from transition state theory, provides a more fundamental theoretical framework by relating the rate constant to the Gibbs free energy of activation. The Eyring equation is k = (kB*T/h) * exp(-deltaG_double_dagger/RT), where kB is Boltzmann's constant and h is Planck's constant. While the Arrhenius equation treats the pre-exponential factor as essentially constant, the Eyring equation explicitly accounts for the entropy of activation and has a built-in temperature dependence in the pre-exponential term. For most practical purposes both equations give similar results over moderate temperature ranges.
How do catalysts affect the Arrhenius equation parameters?
Catalysts lower the activation energy Ea by providing an alternative reaction pathway with a lower energy barrier. This means the exponential term exp(-Ea/RT) becomes larger, dramatically increasing the rate constant. For example, reducing Ea from 100 kJ/mol to 50 kJ/mol at 298K increases the rate by a factor of about 500 million. Catalysts may also change the pre-exponential factor A because the alternative pathway may have different geometric and steric requirements for the reacting molecules. Enzymes, which are biological catalysts, can reduce activation energies by 30 to 70 kJ/mol compared to the uncatalyzed reaction. Importantly, catalysts do not change the thermodynamics of the reaction, only the kinetics.
Can the Arrhenius equation be used for non-chemical processes?
Yes, the Arrhenius equation is applied well beyond traditional chemical reactions. It is widely used in semiconductor physics to describe diffusion rates of dopants in silicon and the temperature dependence of electrical conductivity. Food scientists use it to model spoilage rates, vitamin degradation, and microbial growth at different storage temperatures. Materials scientists apply it to creep rates in metals, polymer degradation, and battery aging. The equation describes the temperature dependence of viscosity in some liquids and the rate of corrosion in metals. Even biological aging processes at the cellular level show Arrhenius-type temperature dependence. Any thermally activated process with an energy barrier can potentially be described by the Arrhenius framework.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy