Arrhenius equation

The Arrhenius equation is the rule that turns up the speed of chemistry when you turn up the heat. It is the quantitative version of everyday experience: food spoils faster in summer than in a fridge, and a reaction's rate constant climbs steeply as temperature rises.

Mathematically it states that the rate constant k equals a frequency factor A times the exponential of minus the activation energy divided by the gas constant times absolute temperature. Plotting the natural logarithm of k against the reciprocal of absolute temperature gives a straight line whose slope reveals the activation energy. Measure k at a few elevated temperatures, fit that line, and you can extrapolate down to room temperature.

This is precisely why accelerated stability testing works: degradation rates measured at, say, 40, 50 and 60 degrees Celsius are extrapolated along the Arrhenius line to predict the much slower rate at 25 degrees, and hence the shelf life, long before a real-time study finishes.

Caveats matter. The equation assumes a single, temperature-independent degradation mechanism over the whole range. It fails if a new pathway switches on at high temperature, if the physical state changes (melting, phase transition), or if humidity rather than temperature drives the reaction — situations where Arrhenius extrapolation can be dangerously optimistic.