For a solution containing one or two drops (0.1 c.c.) of saturated potassium chromate solution per 100 c.c., a proportion frequently used in quantitative analysis, the concentration of the chromate-ion is approximately 2.5E−3 and the chloride-ion will consequently be precipitated until [Cl−] = 3E−6. The chief source of error in the method, then, will not be due to the incompleteness of the prior precipitation of the chloride, but rather to the use of the small excess of silver nitrate required to precipitate sufficient chromate to be visible. This error may be avoided, and is avoided in very accurate work (e.g. in water analysis), by determining, in a blank test, the amount of silver nitrate required to show the change of tint of a pure chromate solution of the concentration to be used in the titration and by titrating to this tint in the determination of the chloride: the volume of silver nitrate (e.g. 0.2 c.c. of a 0.01 molar solution), required to produce the tint in the blank test, is subtracted from the total volume of silver nitrate used in the chloride determination.
We find thus, that the order of precipitation of difficultly soluble salts, which contain a common ion (fractional precipitation), is subject to the equilibrium conditions derived from the application of the principle of the solubility-product to the salts in question.[341]
It should be further noted that the condition of equilibrium between two precipitates, containing a common ion, and a supernatant liquid, depends on the concentrations in the supernatant liquid, in the liquid phase, and not on the quantities of the solids [p167] present. This conclusion was first reached by Guldberg and Waage, to whom we owe the law of mass action, and was fully confirmed by them. The modern treatment of the subject substitutes ion concentrations, i.e. the concentrations of the active components,[342] for the total concentrations used by these investigators.[343]
That the condition of equilibrium is dependent on the liquid phase can easily be demonstrated if mercurous chloride and mercurous hydroxide are selected as the two precipitates, in order that we may follow changes of concentration in the liquid phase by color changes. For the condition of equilibrium between the two precipitates and the supernatant liquid we may develop the relation
[OH−] / [Cl−] = KHgOH / KHgCl = K.
Exp. A few drops of phenolphthaleïn are added to 100 c.c. of a very dilute solution of potassium hydroxide (1 / 500 molar); the usual indication of the presence of the hydroxide-ion is shown and the intensity of the color will be a measure of its concentration. Three identical solutions are prepared and then a pinch of calomel is added to two of the solutions,—their pink color fades decidedly.
Some of the calomel is decomposed into dark-colored mercurous oxide, which is precipitated, and sufficient potassium chloride is formed to bring the ratio [OH−] / [Cl−], in the solution, down to the value required by the constant K. Since no chloride-ion is present at the start, this result can be brought about only by the change indicated. Now, some chloride, say a little of a concentrated solution of potassium chloride, which reacts perfectly neutral, is added to one of the mixtures of the hydroxide and chloride. The concentration of the chloride-ion is increased in the solution, the ratio [OH−] / [Cl−] is made much too small and the condition of equilibrium is disturbed. Consequently, mercurous oxide reacts with potassium chloride, as expressed in the equation HgOH ↓ + KCl → HgCl ↓ + KOH, until the ratio [OH−] / [Cl−] [p168] has the value required by the constant K. The phenolphthaleïn is colored by the increased concentration of the hydroxide-ion and shows the direction of the change.[344]
Precipitation by a Weak Base in the Presence of its Salts.
The fact that ammonium salts prevent the precipitation of magnesium hydroxide was formerly explained as being due to the formation of "double salts," such as MgCl2,NH4Cl. It is true that such double salts exist, but, if their formation should prevent the precipitation of magnesium hydroxide, possibly by including the magnesium as part of a negative ion or radical,[347] MgCl3, then the corresponding double salts of magnesium chloride with potassium and sodium chloride (e.g. MgCl2,KCl), which are just as stable as the ammonium salts, should show the same behavior; but, as a matter of fact, the addition of potassium chloride does not interfere with the precipitation of the hydroxide by either [p169] potassium hydroxide or ammonium hydroxide (exp.). So the explanation is untenable. Obviously, a specific interference of ammonium salts with the precipitating power of ammonium hydroxide is involved. But that is exactly what the law of chemical equilibrium, applied to the ionization of ammonium hydroxide, would demand: As a weak base, which is little ionized in pure aqueous solutions, it is very much weaker as a base, produces a far smaller concentration of the hydroxide-ion, when readily ionizable salts of ammonium are added to the solution,[348] and the precipitation of magnesium hydroxide, and of metal hydroxides in general, depends on the concentration of the hydroxide-ion, which is a factor in the solubility-products of bases.
The precipitation of magnesium hydroxide, in particular, depends on the relation of the product [Mg2+] × [HO−]2 to the solubility-product constant of magnesium hydroxide. For the saturated aqueous solution, the product [Mg2+] × [HO−]2 is equal to the solubility-product constant, and from the solubility of magnesium hydroxide (see the table) the value of the constant is found to be 15E−12 at 18°. The concentration of magnesium-ion is 0.000,154 in this solution. In a 0.1 molar solution of magnesium sulphate, which is ionized to the extent of 37.3%, the concentration of magnesium-ion is 0.0373, and it would require a concentration greater than 2E−5 of hydroxide-ion to precipitate any magnesium hydroxide.[349] Now, the concentration of the hydroxide-ion, in an ammoniacal solution, can easily be reduced far below this value by the addition of ammonium chloride, nitrate, sulphate or other readily ionizable ammonium salt to the solution, and then magnesium hydroxide will not be precipitated.