«Precipitation.»—We see thus that ‹precipitation› of a difficultly soluble ionogen ‹will result when the product of the ion concentrations› [p146] ‹is made greater than the value of the solubility-product constant for that substance›. In the second place, it is seen that the concentration of an ion of an insoluble salt, which can be present in the saturated solution of the salt, ‹is dependent on the concentration of the other ion (or ions) of the salt›. This fact is a very important one in analytical chemistry and it is taken advantage of in many ways, as we shall presently see. It is clear that a corresponding result should be obtained when, to the saturated aqueous solution of silver acetate, an excess of the silver-ion is added—for instance by the addition of solid silver nitrate or of a little of a concentrated solution of this salt (‹exp.›). Here again, the product of the ion concentrations is greater than the constant, ‹i.e.› [CH_{3}COO^{−}] × ‹y› [Ag^{+}] > K_{S.P.}, and precipitation results. Silver acetate therefore crystallizes out, until ([CH_{3}COO^{−}] / ‹y′›) × ‹y′› [Ag^{+}] = K_{S.P.}. The following table shows the relations when sodium acetate is added to the saturated solution of silver acetate. Column 1 gives the concentration of the sodium acetate in the solution saturated with silver acetate, column 2 the percentage of the sodium acetate that is ionized, column 3 the total concentration of silver acetate in the saturated solution, column 4 the percentage of it which is ionized, column 5 the concentration of the acetate-ion, column 6 the concentration of the silver-ion and column 7 the value of the solubility-product. 1 2 3 4 5 6 7 Na-Acet. 100 p. Ag-Acet. 100 p′. acetate. [Ag^{+}]. K_{S.P.}. 0 .... 0.0603 70.8 0.0427 0.0427 0.00182 0.061 78.6 0.0392 64.5 0.0735 0.0258 0.00185 0.119 75.8 0.028 59.7 0.1065 0.0167 0.00179 0.239 70.8 0.0208 52.3 0.1727 0.0109 0.00188 The second table shows the relations when an excess of the silver-ion is present, silver nitrate having been added to the saturated silver acetate solution. The columns have the same significance as in the first table, excepting that the first column gives the concentration of silver nitrate present and the second column its degree of ionization.[306] It is clear from these results that a difficultly soluble salt is rendered less soluble (see column 3 of the tables) by the presence of another salt, when the [p147] latter has an ‹ion in common with the former›. This conclusion has been well established[307] for a considerable number of salts.[308]