Debye-Huckel equation
/ duh-BYE HUK-uhl /
We know that ions in a salty solution behave as if weaker than their numbers, but how much weaker? You need an actual formula to put a number on it. The Debye-Huckel equation is that formula: it predicts an ion's activity coefficient from just two things — the solution's ionic strength and the ion's charge.
Its picture is physical and intuitive. Each ion drifts inside a faint cloud of oppositely charged neighbours, which shields it and dulls its chemical effectiveness. The equation captures how this shielding grows with ionic strength and with the ion's charge: more salt and more charge mean a stronger cloud and a smaller activity coefficient. From it you can compute the correction needed to turn concentrations into activities.
The equation is the everyday workhorse for accurate equilibrium calculations in dilute solutions. Its honest and important caveat is range: the simplest form is reliable only at very low ionic strength, and an extended version (which also uses the ion's size) stretches it to roughly 0.1 molar. Beyond that — in seawater or concentrated brines — Debye-Huckel breaks down, and chemists turn to more elaborate models or to directly measured activity coefficients.
Plugging an ionic strength of 0.01 and a charge of +2 into the extended Debye-Huckel equation gives a calcium-ion activity coefficient near 0.67 — meaning that calcium acts as if only about two-thirds of its counted concentration is present.
Charge and ionic strength go in; an activity coefficient comes out.
It is named for Peter Debye and Erich Huckel, who derived it in 1923. The plain 'limiting law' form works only in extremely dilute solutions; the 'extended' form, which includes an estimate of the hydrated ion's diameter, is what is actually used for most practical analytical work.