By a comparison of the figures of the second and third columns it is seen that the co-precipitation of the potassium nitrate is very small when this salt is added after the barium sulphate has been precipitated from the solution.

156. Variation of Co-precipitation with the Concentration of the Soluble Salt. For a given weight of precipitate, the amount of co-precipitation varies with the concentration of the soluble salt. The amount, however, is not directly proportional to such concentration but varies as some fractional power 1/n, where n usually has the value two, and in no case apparently has a value less than unity or greater than five. The relationship expressed in the form of an equation is:

Weight of salt dragged down
Weight of precipitate

=

k(concentration of salt) (1)

where the value of k is determined by experiment. Equation (1) is analogous to Freundlich's equation for adsorption," namely, Weight of substance adsorbed Weight of adsorbing agent

=

k(equilibrium conc. of adsorbed substance)

(2)

Equation (1), however, in the light of our present-day knowledge, is only to be regarded as an empirical portrayal of the behavior of co-precipitation and not to follow as a consequence of any

'H. Freundlich, Kapillarchemie. Akademische Verlagsgesellschaft, Leipzig, 1923, 3rd ed., p. 151.

2,

theoretical deductions. In order to visualize the relationship expressed by equation (1) which gives the weight of salt dragged down per unit of precipitate y as a function of the concentration of the salt x, let us plot the curves y 1 and n = 3, and 5; we get the curves given in Fig. 23. All these curves are generalized parabolas.

=

kxn for k

=

A specific example is furnished from the work of Blasdale cited in the preceding paragraph upon the co-precipitation of potassium nitrate by barium sulphate. In addition to the experiments quoted there, this investigator also ran two others under similar conditions, and with the addition of the potassium nitrate beforehand, the results were:

Plotting the results of all four experiments, we see that they

sensibly satisfy the relationship y=kx, where k shown by the graph of Fig. 24.

=

15.6, as

157. Minimization of Co-precipitation. An analysis of the foregoing facts in regard to co-precipitation shows that in order to cut down the amount of co-precipitation which happens at

the time of formation of a precipitate, matters must be so arranged that the concentration of the salt which is co-precipitated shall be as small as practicable. If said salt already exists in the solution and cannot be removed by any ready means like evaporation, or by conversion into an insoluble compound, then the solution should be made as dilute as allowable before adding the precipitant. If the precipitant itself is co-precipitated or leads to the formation of any soluble salt which is co-precipitated, then the precipitant should be diluted and added dropwise, especial care being taken that the solution-where precipitation is being effected-shall be vigorously stirred the meanwhile. In certain cases of co-precipitation recourse is had to the expedient of dissolving the contaminated precipitate and reprecipitating; this procedure, which is known as double precipitation, is invariably followed in rock analysis where most of the salts encountered belong to members of the iron and aluminum or the alkaline earth groups.

As already mentioned in § 42, the amount of co-precipitation which exists after the formation of a precipitate can also be reduced somewhat by the process of digestion. Since we discussed the theory of this process in § 42, we will refer the reader back to it.

158. Separation of Precipitate from Supernatant Solution. The technique of effecting this separation has already been discussed in § 43; the only point to be considered here is the application of the solubility product principle to the selection of the wash solution. Since a precipitate is more soluble in pure water than in a solution which contains an ion in common, it is advisable wherever practicable to employ a wash solution of this description. Thus lead sulphate is washed with a 0.1 molar solution of sulphuric acid;10 copper sulphide with a 0.3 molar solution of hydrochloric acid saturated with hydrogen sulphide; ferric hydroxide with a solution which is 0.1 molar with respect to ammonium nitrate and 0.01 molar with respect to ammonium hydroxide; ammonium phospho-molybdate with a 0.1 molar solution of ammonium nitrate; etc. The use of such solutions, however, is limited by the following considerations: the salt

10 The sulphuric acid is then gotten rid of by washing with 95% alcohol.

which furnishes the ion in common must not leave a non-volatile residue if the precipitate is to be subsequently ignited, nor must it contain an ion that would form an insoluble compound with any of the ions of the supernatant solution from which the precipitate was formed, nor must it contain a complex-forming ion that would enter into combination with either ion of the precipitate. But wherever such restrictions do not apply, the method is desirable one, and it should be mentioned that there are a great many precipitates which can only be washed with a wash solution containing an ion in common, because if the attempt is made to wash them with pure water they will pass into the colloidal condition and run through the filter paper.

Use of a Saturated Solution of the Precipitate Itself as Wash Solution.11 "It has sometimes been recommended to wash a precipitate with a saturated aqueous solution of the precipitate itself, in place of with pure water. It was reasoned that the solution, being already saturated with the salt, would not be able to dissolve any of the precipitate obtained. That is true; but if a saturated solution of a salt, MeX, is placed on a filter still holding an excess of the precipitant, i.e. one of the ions, say X, of the precipitate, then this excess may cause supersaturation of the saturated washing fluid and some of the salt may be precipitated out of the washing fluid. The method, as commonly employed, has therefore the inherent fault, theoretically at least, of being liable to give too high results. If it is to be employed without error, precautions must be taken first to remove, from the precipitate and filter, the mother liquor (containing the excess of precipitant) as completely as possible. If in a given case this can be accomplished, then the danger of precipitating any of the salt (MeX) from the saturated solution is avoided, and the precipitate (MeX ↓) may then be further washed with a saturated solution of the same salt (MeX), with advantage, in certain cases. Thus, in the Lindo-Gladding method12 of determining potassium in the form of potassium chloroplatinate, the source of error, just discussed, has been avoided in the following way: the excess of precipitant, chloroplatinic acid H¿PtCl6, which has the ion PtCl in common with the precipitate, is first removed from the precipitate by thorough washing of the precipitate with alcohol: subsequently, other impurities, e.g. sulphates, soluble in water but not in alcohol, are washed out with an aqueous solution of ammonium chloride13 that has been saturated with potassium chloroplatinate. The method gives good results."

11 This paragraph quoted verbatim from Stieglitz, loc. cit., § 13, p. 149.

12 Official Methods of Analysis, Bulletin 107, p. 11, U. S. Dept. of Agriculture.

13 The excess of chloroplatinic acid is first washed out of the precipitate primarily to avoid subsequent precipitation of ammonium chloroplatinate, but its removal also avoids the error discussed in the text.

159. Rôle of Hydrogen Ion Concentration. It will be found in almost every case where we are dealing with the solubility product principle that the hydrogen ion concentration of the solution enters into matters as a very important factor. This situation arises from the fact that the concentrations of anions which we use to bring about precipitation as well as those which we use to form complexes are very greatly influenced by the concentration of hydrogen ion. Taking up for our consideration first the more common examples of the anions used for precipitation, we have for the case of hydroxyl ion that its concentration varies inversely as the concentration of hydrogen ion by virtue of the relationship that сH+ X Cон-10-14. The concentration of the divalent anions, such as the sulphide ion, the carbonate ion, the sulphate ion, are affected by virtue of the equilibrium that in a solution containing such an ion there is always present not only the divalent anion but also the corresponding monovalent ion and the undissociated acid, the particular distribution of the respective concentrations depending on the concentration of hydrogen ion. Thus if we take the case of sulphide ion we have the equilibrium represented by the scheme:

If now we alter the concentration of hydrogen ion, then the components toward the left-hand end of the equilibrium will predominate if the solution is made increasingly acid; while the components toward the right-hand end will predominate if the solution is made increasingly alkaline.

In the case of the anions of the weak acids, we are able by an extension of Ostwald's Dilution Law to calculate the distribution of the various components involved in the equilibrium as a function of the concentration of hydrogen ion. Thus for the equilibrium between sulphide ion, hydrosulphide ion, and undissociated hydrogen sulphide, it has been shown by Auerbach14

14 Z. physik. Chem. 49, 220 (1904).