chemical potential
Chemical potential is like the 'pressure' that pushes a substance from where there's a lot of it to where there's less. Just as water runs downhill and heat flows from hot to cold, every kind of molecule has a tendency to migrate, react, or change phase from regions of high chemical potential toward regions of low chemical potential. Perfume drifting across a room and sugar spreading through tea are both molecules sliding down their chemical-potential hill.
Precisely, the chemical potential of a substance is how much the system's Gibbs free energy changes when you add one more mole of that substance, keeping temperature, pressure, and the amounts of everything else fixed. Written μ, it is the per-mole 'free energy price tag' of a component. Anything that raises a substance's μ — high concentration, high pressure, the wrong phase — makes it more eager to leave; anything that lowers μ draws it in.
Why it matters: chemical potential is the single quantity that decides the direction of every transfer in chemistry. Reactions run until the chemical potentials of products and reactants balance; phases coexist when a substance has the same μ in each; osmosis, dissolving, evaporation, and diffusion are all just matter equalizing its chemical potential. The honest subtlety is that μ depends on concentration through activity, so it isn't fixed for a substance but shifts with the mixture it's in.
Two sugar solutions, strong and weak, are joined by a membrane water can cross. Water has a higher chemical potential on the dilute side, so it flows toward the strong side until both potentials match — that pull is osmosis.
Matter always slides from high to low chemical potential.
Despite the name, chemical potential isn't only about chemistry — it governs phase changes and diffusion of pure substances too. For a one-component system it equals the molar Gibbs energy; in a mixture it is each component's partial molar Gibbs energy.