| Summary: | Solubility may be considered as a measure of the stability of a crystal.
A salt will dissolve when the attraction of its ions for the solvent molecules is stronger than the attraction of its ions for each other, that is, the energy of solvation is greater than the lattice free energy. Quantitatively such information may be obtained from the cycle:-
[Diagram]
A solid MX may be directly dissolved (as in III) to give solvated ions; or it may first be split up into gaseous ions, and then solvated (I and II).
Now [Formula] where K is a measure of the solubility given by K = [Formula]
the molal solubility and [Formula] the mean activity coefficient. That is,[Formula] determines the solubility, and when [Formula] I is large and positive, the solubility will be low.
Also
{Diagram]
where U is the lattice energy as usually defined, viz. the energy of the process ions [Formula] crystal, and hence a negative quantity. [Formula] is then positive, and [Formula] also is positive.
Since[Formula] is always negative, it follows that if it is numerically less than[Formula] , then [Formula] will be positive which leads to a value of K less than unity, that is, to a solubility less than one-molal.
The heat of solvation of a pair of gas ions is given by
[Diagram]
where [Formula] is the near of the solution of the crystal to form an infinity dilute solution and may be determined experimentally.
[Formula] = -U where U is the lattice energy, values of which have been obtained experimentally and by calculation.
From results for alkali halides in water, heats of hydration of ions have been determined.
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