Dynamic equilibrium: both directions at once

Put a little nitrogen dioxide in a sealed flask and it is red-brown at room temperature. Leave it all day and the colour does not change — nothing seems to happen. Yet $\ce{NO2}$ molecules keep pairing up into colourless $\ce{N2O4}$, and $\ce{N2O4}$ keeps splitting back into $\ce{NO2}$. The colour holds only because the two directions run at exactly the same rate.

Isotope tracers give the same evidence. Drop a few crystals containing radioactive iodide into a saturated solution of the same salt: the concentration does not change, yet the radioactivity soon turns up in the solution — crystals keep dissolving while an equal amount of ions crystallises.

Take the simplest case, an isomerisation $\ce{A} \mathrel{\ce{<=>}} \ce{B}$, and assume both directions are single elementary steps. The forward rate is proportional to the concentration of A, the reverse rate to that of B. At the start there is only A: the forward reaction is fast and the reverse is zero. As A is used up the forward reaction slows; as B builds up the reverse reaction speeds up. The two rates must meet — and from then on, as much B forms each second as is used up, so the concentrations stop changing.

That is dynamic equilibrium: the macroscopic properties (concentrations, colour, pressure) are constant, while at the molecular level both reactions carry on at the same rate.

The simulation has only a hundred or so molecules, so the number of B keeps hopping a few above and below its average. Random fluctuations scale roughly as $1/\sqrt{N}$: about 10 % for 100 molecules, but only about $1.3\times10^{-12}$ for a mole ($6.0\times10^{23}$ molecules) — far below anything an instrument can detect. That is why a macroscopic equilibrium looks perfectly still, and the equilibrium constant describes the average of countless random events.