Arrhenius equation
/ uh-REE-nee-us /
You already know reactions speed up when you heat them — food cooks faster on a high flame, and cold slows spoilage in a fridge. The Arrhenius equation puts a precise formula behind that everyday feeling: it says exactly how much the rate constant climbs as the temperature rises.
The equation reads k = A·e^(−Eₐ/RT). Here k is the rate constant, T the absolute temperature, R the gas constant, Eₐ the activation energy (the energy hill molecules must clear to react), and A the pre-exponential factor (roughly how often the molecules collide and line up correctly). The exponential term is the fraction of collisions energetic enough to make it over the hill, and because it sits in an exponent, even a modest rise in temperature can multiply the rate.
Its great practical value is that, by measuring k at several temperatures and plotting ln k against 1/T, you get a straight line whose slope reveals the activation energy and whose intercept gives A — letting you predict rates at temperatures you never tested. The honest limits: A and Eₐ are treated as constant, which works well over moderate ranges but can drift for complex or multi-step reactions, and the equation describes how rate depends on temperature without explaining the mechanism itself.
Many reactions roughly double their rate for every 10 °C rise near room temperature — a rule of thumb that falls straight out of the Arrhenius equation for a typical activation energy. It is why bread dough proves faster in a warm kitchen and why milk keeps longer in a cold fridge.
The familiar 'heat it up to speed it up' made quantitative.
Temperature T must be absolute (kelvin), never Celsius — using Celsius in the exponent gives nonsense. A catalyst speeds a reaction by lowering Eₐ, which the equation makes vivid.