Reaction rates

Thermodynamics says whether a reaction can go; kinetics says how fast. The rate is how quickly a concentration changes, in mol/(L·s). For molecules to react they must collide, hard enough and the right way round. More concentration, higher temperature, more surface area (powders react faster than lumps) and a catalyst all speed things up.

A rate law ties the rate to concentrations: rate = k[A]ⁿ, where k is the rate constant and n the order, found by experiment, not from the equation. First order (n = 1): double [A] and the rate doubles. Second order: double [A] and the rate goes up four times. Zero order: the rate doesn't depend on [A] at all.

First-order reactions have a fixed half-life, the time for half of what's left to react: t½ = ln 2 ÷ k ≈ 0.693 ÷ k. After one half-life 50% is left, after two 25%, after three 12.5%, whatever you started with. Radioactive decay works the same way.

To react, molecules have to get over an energy hill, the activation energy, Ea. The Arrhenius equation, k = A·e^(−Ea/RT), shows the rate constant rising steeply with temperature, because more molecules have enough energy. Comparing two temperatures: ln(k₂/k₁) = (Ea/R) × (1/T₁ − 1/T₂). With Ea = 50 kJ/mol, going from 25 °C to 35 °C multiplies k by about 1.9, the old rule that rates roughly double every 10 °C.

A catalyst gives the reaction a different route with a lower activation energy, so it speeds it up without being used up. It speeds the forward and reverse reactions alike, so it doesn't change where the equilibrium lies, only how quickly you get there. Enzymes are biology's catalysts; car exhausts use platinum, and most industrial processes rely on one.