[C12H22O11]aq. : [C12H22O11]solid = k.
Since a pure solid like sugar at a given temperature has a definite specific gravity, the concentration of the sugar in the solid condition should also be a definite one. Consequently, according to the law under discussion, the first term, [C12H22O11]aq., of the ratio, the concentration of the sugar in its saturated solution in contact with the solid phase, must also have a definite value. This is in agreement with fact, the concentration of the sugar in the saturated solution, termed its solubility, being a definite one for a given temperature. (See below, p. [123], in regard to the solubility of fine powders.)
Supersaturated Solutions.
Exp. Supersaturated solutions of sodium sulphate and sodium thiosulphate, into which crystals of the salts are dropped, show how the crystal starts crystallization. The crystals develop as branches from the crystal first introduced and from the new crystals formed.
This phenomenon of supersaturation is one which analytical chemists must always take into consideration. Tests which involve the precipitation of substances that are merely difficultly soluble, rather than exceedingly insoluble, or of substances present only in very small quantities, may well lead to entirely wrong conclusions, if precautions are not taken against the possibility of the failure of a precipitate to appear as a consequence of persistent supersaturation. For instance, a common test for the presence of potassium salts consists in the precipitation of potassium acid tartrate by the addition of tartaric acid to the solution of a potassium salt (exp.). The tartrate is somewhat soluble and tends to form supersaturated solutions; if we proceed without due regard for this phenomenon, we may readily have a quantity of potassium salt present and fail to obtain the test for it. Simply mixing tartaric acid and potassium chloride solutions (exp.) may fail to [p123] give any precipitate, and if the test is thrown away and potassium reported absent, a glaring blunder is committed. To insure against the error of supersaturation, we try to start crystallization by the common devices of shaking the solution or "scratching" the walls of the vessel, the object being to facilitate the formation of the first crystal. The surest method is to inoculate a small portion of the mixture with a minute crystal of the substance we expect to be formed. If no precipitate results in a short time, the solution is not supersaturated—it may be too dilute and may require further concentration, but the error of supersaturation has been excluded.
The relation between supersaturated solutions and crystals brings out sharply the fact that physical equilibrium is essentially a condition of equilibrium between the substance at the surface of the solid and the substance in its dissolved state. In terms of the molecular theory, equilibrium is established when the molecules of the crystal surface dissolve as rapidly as molecules from the solution are deposited on the surface. If the concentration of the dissolved molecules is reduced below the point required for equilibrium, the velocity of deposition is diminished. The velocity of solution will then be greater than the velocity of deposition and solution will result. The reversed relations hold when the concentration of the solution is greater than that demanded by equilibrium: the velocity of deposition will be the greater than that of solution and precipitation follows.[231]
Solubility of Fine Powders.
The application of these relations to analysis is as follows: If a crystalline precipitate is in contact with a solvent, e.g. if barium sulphate is in contact with the liquid from which it has been precipitated, then this liquid must be continually in a state of change, not of equilibrium, with respect to the solution and the deposited barium sulphate. The more minute crystals, being a little more soluble than the larger ones, will supersaturate the solution in respect to the larger crystals and the excess will be deposited on these larger crystals and make them grow still larger. This deposition will make the solution unsaturated with respect to the smaller crystals and more of these will dissolve. The process is obviously a continuous one, and must lead in time to the disappearance of the minute crystals and the growth of the larger ones. That is a result which analysts aim to attain,—which in quantitative work it is in fact necessary to attain, since the more minute crystals are likely to pass through filters and be lost in the analysis. The views expressed, and the experimental confirmation of the conclusion reached, form the theory of what is called the "digesting" of precipitates before they are brought on filters. It is clear that every condition facilitating contact between solvent and solid will accelerate the desired change and continuous stirring is therefore desirable. Heating is, as a rule, also to be desired for very insoluble precipitates, as it will, in the majority of cases, facilitate the solution of the undesirable, finer crystals.
In conclusion, these considerations will also indicate the precautions to be observed in the precipitation of difficultly soluble substances. If this is not properly carried out, endless trouble in [p125] the analytical laboratory results. Except when heating is, for some special reason, undesirable—as inducing a chemical change (like hydrolysis) that is not wanted—solutions are brought to the boiling-point, and the precipitant added drop by drop, in order not to supersaturate the solution too strongly. The solution is thus allowed time to deposit its excess as far as possible on the first crystals formed, which it will do rather than to form new, minute ones (see supersaturation, p. [121]). Constant stirring is prescribed in order to bring older crystals, as far as possible, into contact with all parts of the slightly supersaturated solution. After the precipitation is complete, it is usually desirable to allow the mixture to "digest" for some time, for the reasons given above—stirring and a high temperature during the process being desirable. (See further Chap. VIII, p. [147], in regard to the use of an excess of precipitant.)