The Arrhenius equation, k = A·e^(−Ea/RT), is the fundamental relationship between temperature and reaction rate in chemical kinetics. Proposed by Svante Arrhenius in 1889, it explains an everyday observation — chemical reactions speed up when heated — with a precise, testable formula. This article covers where the equation comes from, why temperature has such an outsized effect on rate, how to use the two-temperature shortcut, and where the model's assumptions start to break down.
Why temperature affects reaction rate so strongly
For a reaction to occur, colliding molecules need enough kinetic energy to break existing bonds and form new ones — this energy threshold is the activation energy, Ea. At any given temperature, molecular kinetic energies follow a distribution (the Maxwell–Boltzmann distribution), and only the fraction of molecules with energy above Ea can react on collision. The exponential term e^(−Ea/RT) in the Arrhenius equation is exactly that fraction. Because the relationship is exponential rather than linear, even a modest temperature increase can dramatically increase the fraction of sufficiently energetic molecules, which is why reaction rates are so sensitive to temperature — often described loosely as "doubling every 10 °C," though the real multiplier depends on both Ea and the temperature range.
The pre-exponential factor A
The pre-exponential factor A represents the theoretical rate constant if every collision were successful — no energy barrier at all. It accounts for how frequently molecules collide and the fraction of those collisions with the correct orientation to react (sometimes formalized as the steric factor in collision theory). A is treated as roughly constant over modest temperature ranges in the simple Arrhenius model, which is why the equation can be rearranged to solve for k, A, Ea, or T from just three known quantities, exactly as the Rate Constant tab above does.
The two-temperature method
In the lab, A is rarely known directly, but Ea can be found without it. If the rate constant is measured at two different temperatures, taking the natural log of the Arrhenius equation at each point and subtracting eliminates A entirely, giving ln(k₂/k₁) = −Ea/R·(1/T₂ − 1/T₁). This two-point method is the practical way most activation energies are actually determined — plot ln(k) against 1/T for several temperatures and the slope of the resulting straight line is −Ea/R (an Arrhenius plot). The Two Temperatures tab implements the two-point version of this same idea, and can also run in reverse: given Ea and one rate constant, it predicts the rate constant at a new temperature.
Reading the activation energy
Activation energy is reported in kJ/mol (or sometimes kcal/mol) and is a property of the specific reaction mechanism, not of the reactants alone — a catalyst works by providing an alternative pathway with a lower Ea, which is why catalyzed reactions can proceed quickly even at low temperatures. Small Ea values (under about 40 kJ/mol) describe reactions that are fast and relatively insensitive to temperature; large values (several hundred kJ/mol) describe reactions that are slow at room temperature but accelerate sharply on heating. The dedicated Activation Energy tab is built for the most common real-world question — given a measured rate constant at a known temperature, what energy barrier does that imply?
Limits of the simple Arrhenius model
The basic Arrhenius equation assumes A and Ea are both temperature-independent, which is a good approximation over a narrow temperature range but can break down over wider ones — more advanced treatments (such as the modified Arrhenius equation, k = A·Tⁿ·e^(−Ea/RT)) add a temperature-dependent prefactor to correct for this. The equation also describes an idealized elementary reaction step; for multi-step mechanisms, the measured "activation energy" is really an effective, composite value. Despite these simplifications, the Arrhenius equation remains one of the most useful and widely applied relationships in chemistry, food science (shelf-life modeling), pharmacology, and materials engineering.