We have, therefore, a certain degree of control over the precipitation and solution of electrolytes, the control depending upon, and being limited by, the fact that the factors of the product of ion concentrations are variables.
On the other hand, we have little control, in a given solvent, over the question of solution or precipitation as affected by the value of the ion product constant, the remaining term in the equation of the solubility-product for saturated solutions. These constants cover a very wide range of values for the various salts, which are most frequently used in analytical work for the precipitation of the common ions.[319] They are subject to variation with the temperature, and, as a rule, as most salts are more soluble at higher than at lower temperatures, the values of the constants increase with the temperature. For exceedingly difficultly soluble salts, the increase is commonly of no practical moment in analytical work, when, by an excess of the precipitant, the ion, which is to be precipitated, can be precipitated quantitatively; the solubility of the nonionized salt, that is precipitated, is so minute (see p. [148]) in this case, even at high temperatures, that it is altogether negligible for ordinary purposes.[320] On the other hand, precipitates are often used which are not at all extremely insoluble but merely rather difficultly soluble; they are used in spite of their relatively slight insolubility because they are the best available forms for our purposes. Such salts are, for instance, lead chloride, magnesium-ammonium phosphate, potassium chloroplatinate. When these are precipitated, not only must the fact that they are appreciably soluble at ordinary temperature be taken into account, but also the fact that they are very much more soluble at higher temperatures. Lead chloride and potassium chloroplatinate are, for instance, quite soluble in hot water.
As a rule, we select for the form in which a given ion is to be precipitated, a form which, in a saturated aqueous solution, shows the smallest concentration of the ion in question. But if no form is [p154] known which is sufficiently insoluble to give satisfactory quantitative results, then we have recourse to a change in the solvent.
Solubility and Solvent.
If this relation is combined with that discussed on page [63], according to which the degree of ionization of a given salt, in different solvents, is the same, when the cube roots of its concentrations are directly proportional to the dielectric constants of the solvents (e1 : ∛c1 = e2 : ∛c2 = a constant), then we find, that in saturated solutions of a given salt, in different solvents, the cube roots of the concentrations, or solubilities, are directly proportional to the dielectric constants of the solvents, or, the solubilities are proportional to the third powers of the dielectric constants.
e1 : ∛c1 = e2 :∛c2 = a constant, or e13 : e23 = c1 : c2,
c1 and c2 representing the solubilities, in molar concentrations, in two solvents of dielectric constants e1 and e2.
The following table illustrates the relations for a salt examined by Walden, a derivative of ammonium iodide, namely tetraethyl ammonium iodide (C2H5)4NI. The first column gives the name of the solvent, the second the solubility or concentration in the saturated solution, in terms of the proportion of moles of the solute to the total number of moles present[324] [p155] (solute + solvent); the third column gives the dielectric constant, under comparable conditions, and the last column gives the relation e : ∛c.
| Solvent. | Solubility. | e5 | e : ∛c |
|---|---|---|---|
| Water | 0.0332 | 75.0 | 50.5 |
| Nitrobenzene | 0.0020 | 32.2 | 54.8 |
| Ethyl alcohol | 0.00201 | 26.6 | 45.5 |
| Acetone | 0.00072 | 21.8 | 52.8 |
| Amyl alcohol | 0.00031 | 15.0 | 48. |
In view of the difficulties in determining the values for the dielectric constant, the agreement in the values of the last column must be considered satisfactory.[325]