|MadSci Network: Chemistry|
When a substance such as sodium acetate is dissolved in a solvent, the process is favourable up to saturation because of the Gibbs energy gain in replacing the interionic forces in the crystal with the coordinate bonds in the solution. This gain results mainly from enthalpic terms like the bond energies, and so heat is released.
At saturation a significant proportion of the solvent molecules are already taking part in these bonds, and are not free to devote their electrons entirely to the new molecule; hence the Gibbs energy gain drops to zero, and no further solute can be introduced.
If, through some other method than simply adding solute (normally by changing the temperature), a supersaturated solution is prepared, then the Gibbs energy for further solution is unfavourable. Instead, the reverse process occurs: sodium acetate tends to crystallise out, if it can, and as it does so produces heat.
So, it would be thermodynamically favourable for the sodium acetate to crystallise out of a supersaturated solution--but if the only way it can do it is through an intermediate stage of high energy, it will not be able to. We need to consider the kinetics as well.
In order for the crystallisation to occur, very small particles of crystalline sodium acetate must form, and then aggregate into larger crystals. But when a particle forms it leaves behind a quantity of solvent which is less concentrated--and so those ions near the surface have a tendency to redissolve immediately. This is not a problem for large particles (which have relatively little surface area), but it makes it difficult for a small particle to survive long enough to grow past the critical size where the heat gain outweighs these surface effects.
Small particles therefore face a large energy barrier against crystallisation. The solution is trapped in the metastable, supersaturated state.
Addition of a foreign object helps because particles forming on the surface of the object can only redissolve away from it. Thus the effective surface area of the particle is halved (or reduced even more if the foreign object has cavities). This allows the small particles to grow to a size where surface effects can no longer prevent the formation of the crystal. Once this has happened, the crystal can continue growing and releasing heat until the solution is merely saturated, and the processes of solution and deposition are at equilibrium.
Very similar processes are at work in the formation of bubbles in a liquid, and in the formation in clouds of droplets of water large enough to fall as rain, which are discussed with more mathematical rigour in many text-books, for example, Physical Chemistry by P.W.Atkins (5th ed.), pp.962-5.
As for your last question, the metal discs in hand warmers produce small electrical arcs in the solution, but I do not know how this might cause it to crystallise. Perhaps the localised pulse of energy is enough for small particles in the arc to clump together and overcome the energy barrier; if it lasts long enough this might produce a small crystal larger than the critical size for nucleation, which would immediately allow the rest of the solution to crystallise in the same manner as a foreign object.
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