difficultly-soluble salt undergo any change if to a saturated solution of the pure salt itself we add a salt having an ion in common? The answer to this is that so far as has been investigated the concentration of the undissociated portion does not seem to vary much, that is, it remains sensibly equal to u. If a salt with no ion in common is added, the same constancy of u holds, provided that the concentration of the added salt is not built up to more than 0.2 molar. If it is built up in excess of this value, then not only does the undissociated portion of the difficultly-soluble salt increase but also the magnitude of its solubility product.

149. Fractional Precipitation. So far we have discussed the solubility product principle in relation to the case where one insoluble salt is formed. Let us now extend the discussion to the case where several difficultly-soluble salts are to be considered, because this is the usual situation which is met with in gravimetric separations. There are two general situations which arise, namely,

I. Those where the salts behave independently, and the solubility product can be applied in a rigid manner to the behavior of each salt the same as it could if the other salts were not present. Only a relatively few number of the cases come under this category.

II. Those where the salts do not behave independently and the solubility product can be applied only in a qualitative way to their behavior. Most of the cases come under this category. 150. As an example coming under the first category we will mention the case of silver chloride and silver chromate. The respective solubility products are

For the condition of equilibrium between the two precipitates and their supernatant liquid, these two relationships must be satisfied simultaneously. Consequently, we have as the equi

The classic method of Mohr for determining chlorides by titration with silver nitrate solution, using sodium or potassium chromate as indicator, is based upon the independence of behavior of silver chloride and silver chromate. The application of the theory works out so beautifully in its detail that the author has deemed it well worth-while for the benefit of the student to present it more fully in § 175.

librium ratio between the concentration of chloride ion and the chromate ion, that

If we start with a solution of a soluble chloride and a soluble chromate in equivalent quantities and add a solution of silver nitrate dropwise, then silver chloride will be precipitated alone? until the chromate ion is in the excess indicated by the equilibrium ratio; after this silver chromate will be precipitated, with traces of silver chloride, the equilibrium ratio between the chloride and chromate ions in the supernatant liquid being maintained. If, on the other hand, we start with a solution containing a concentration of chromate ion greater than that required by the equilibrium ratio, then silver chromate will be precipitated first until the ratio is reached.

The more important cases in elementary analysis where two or more difficultly-soluble salts behave independently are as follows:

Silver chloride and silver chromate

Silver chloride, silver bromide and silver iodide

Antimony sulphide and stannic or stannous sulphide.

151. As an example coming under the second category we will mention the precipitation of copper and zinc as sulphides. If we have a solution of a soluble copper salt and adjust the concentration of hydrogen ion so that it is equivalent to 0.3 M HCl, and then pass in hydrogen sulphide until the solution is saturated, the copper will be quantitatively precipitated as copper sulphide. If on the other hand we have a solution of a soluble zinc salt and adjust the concentration of hydrogen ion so that it likewise is equivalent to 0.3 M HCl, and then pass in hydrogen sulphide, there will be no precipitate of zinc sulphide because the solubility product has not been reached. Suppose now that we have a third solution containing both the soluble copper salt and the soluble zinc salt and adjust the concentration of hydrogen ion to the same value as before and pass in hydrogen sulphide; the copper will be quantitatively precipitated as the

7 If silver chromate is momentarily precipitated at this juncture it will be converted into the chloride.

sulphide and along with it more or less zinc sulphide, even though the solubility product of the latter has not been reached. The zinc sulphide which is thus co-precipitated cannot be dissolved out of or separated away from the rest of the precipitate; apparently it is held by some kind of chemical union and is not present merely as an admixture. This behavior seems characteristic of all cases of co-precipitation.

A few of the more important cases in which one difficultlysoluble salt drags down another are listed herewith:

152. It must also be mentioned that the phenomenon of co-precipitation or dragging down is not limited to the case of one difficultly-soluble salt dragging down another but also extends to the dragging down of salts which are very soluble, as, for instance, the dragging down of ferric sulphate by barium sulphate, or of sodium oxalate by calcium oxalate. It is also true for these cases that the salt which is dragged down, notwithstanding its solubility otherwise, cannot be dissolved out of the precipitate. A list of the more frequent cases which are encountered in regard to the dragging down of soluble salts is given herewith:

153. Theory of Co-precipitation. The phenomenon of coprecipitation is a complex one and at present our insight into its mechanism is but slight. Schneider suggested that the salt which is co-precipitated is taken up by the precipitate as the latter is formed, and remains distributed throughout the interior of the solid particles, that is to say, co-precipitation is the result of the formation of a solid solution in which the precipitate is the solvent and the co-precipitated salt the solute. If this were true it is hard to see why the action is specific, that is, why only certain salts are co-precipitated and others not. Ostwald believes that an attractive or restraining force is exerted by the solid, which tends to hold the molecules of the co-precipitated substance in the immediate neighborhood of its boundary surfaces, and either delays or entirely prevents the removal of these substances by washing. This is the same theory which was advanced by E. du Bois Reymond under the title "adsorption" to characterize the retention of soluble substances by porous or finely-divided solids when the latter are placed in solutions of the former. The well-known property of bone-charcoal of removing coloring matter from solutions is perhaps the best illustration of adsorption. Richards believes that the phenomenon is due to chemical rather than physical forces, and terms it "occlusion." According to this theory, complex basic salts or molecular compounds, which are but slightly soluble, are formed to a greater or less extent along with the desired precipitate. Thus the co-precipitation of ferric salts by barium sulphate is explained on the assumption that the latter precipitate contains small amounts of a double sulphate of the formula BaSO4 · Fe2(SO4)3. H2O. When this compound is ignited the ferric sulphate is decomposed, and three molecules of SO, and one of water are expelled, and one molecule of BaSO4 and Fe2O3 left behind. The results for the determination of SO4 are therefore low even though the precipitate is contaminated with Fe2O3.

The outstanding facts about the phenomenon of co-precipitation, so far as our present-day knowledge goes, are these:

I. The action is specific;

II. The co-precipitation happens at the time of the formation of the precipitate;

III. The amount of co-precipitation is a function of the concentration of the salt dragged down.

154. Specificity of Co-precipitation. This characteristic is represented by the illustrations just cited in § 151. It is not yet possible from theory to say beforehand in the case of two salts whether one will drag down the other, or in the case of several salts how any one of them will influence the others; such information must be supplied by experiment.

155. Concomitant Occurrence of Co-precipitation. — There seems to be scarcely any doubt that co-precipitation takes place simultaneously with the formation of the difficultly-soluble salt which does the dragging down. While the quantitative evidence bearing on this fact is not so extensive as might be desired, such evidence as we have points to its firm establishment. A series of experiments by Blasdales upon the precipitation of barium sulphate is highly corroborative. This investigator carried out experiments in duplicate as follows: 25 c.c. of a solution of sulphuric acid containing exactly 0.425 g. of H2SO4, which should, therefore, yield exactly 1.0118 g. of BaSO4, were used; 1.000 g. KNO, was added, the solution was diluted to exactly 200 c.c., heated to boiling, and the BaSO4 precipitated by the addition of 50 c.c. of a solution containing 1.3 g. of BaCl2; after standing for sixteen hours the precipitate was filtered off, washed thoroughly, ignited and weighed. Another determination in duplicate was made in the same manner as above except that the 1.000 g. of KNO, was added after the precipitant had been added and the mixture had been allowed to stand for ten minutes. A control determination in duplicate was also made without the presence of any potassium nitrate. The several results are given herewith. KNO, added KNO, added Control deter