Diffusion in a liquid sim

What the sim shows

One crystal of potassium manganate(VII), 0.6 mg, goes into 150 cm³ of still water. It dissolves in about 34 min at 25 °C, and its purple ions spread out by themselves, from where they are crowded (high concentration) to where they are not (low concentration), until the colour is even: 2.53 × 10⁻⁵ mol/dm³ everywhere, a pale purple. Nothing pushes them: each ion moves at random, bumping into water molecules all the time, and on average that carries the ions away from where they are crowded. The colour is worked out from the concentration everywhere in the water (Fick's law, solved exactly for this beaker) and drawn by how much light the purple takes out along each line of sight (Beer-Lambert). The colour spreads about √(2Dt) at first, so four times the time goes only twice as far. D is 0.97, 1.78 and 2.84 × 10⁻⁹ m²/s at 5, 25 and 45 °C (standard data for the K⁺ and MnO₄⁻ ions, and Stokes-Einstein with water's viscosity): warmer water spreads faster. Even so it takes days, not hours: about 5 days at 25 °C. In a gas, D is about 8,990 times larger, and the same beaker would be even in under a minute. Stirring mixes it in seconds, but that is mixing, not diffusion, and proves nothing about the particles. A real beaker often evens out sooner than this, because small temperature differences set up slow convection currents; that is why the water is left still and at one temperature. The crystal's dissolving rate and the stirring time are this desk's estimates. The slider spends its first quarter on the first hour.

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