1 A. E. Hill, J. A. C. S. 30, 14 (1908). 2 G. Bodländer & O. Storbeck, Z. anorg. Chem. 31, 465 (1902). 3 L. W. McCoy & H. J. Smith, J. A. C. S. 33, 473 (1911). 4 G. Bodländer, Z. physik. Chem. 35, 31 (1900). 5 M. Pleissner, Arb. Gesundh. 26, 30 (1907). 6 H. M. Goodwin, Z. physik. Chem. 13, 645 (1894). 7 M. S. Sherrill, Z. physik. Chem. 43, 732 (1903). 8 K. Beck, Z. Elektroch. 17, 846 (1911). 9 F. Kohlrausch, Z. physik. Chem. 64, 158 (1908). 10 A. A. Noyes & D. A. Kohr, Z. physik. Chem. 42, 342 (1903). 11 R. E. Slade, Z. Elektroch. 17, 262 (1911). 12 E. Müller, Z. Elektroch. 14, 77 (1908). 13 F. Kohlrausch & F. Rose, Z. physik. Chem. 12, 24 (1893). 14 O. Sackur & E. Fritzmann, Z. Elektroch. 15, 845 (1909). 15 T. W. Richards, C. F. McCaffrey & H. Bisbee, Z. anorg. Chem. 28, 85 (1901). 16 K. Bube, Zeit. anal. Chem. 49, 557 (1910). 17 A. C. Melcher, J. A. C. S. 32, 54 (1910). 18 J. Knox, Z. Elektroch. Ch. 12, 480 (1906). 19 L. Bruner & J. Zawadski, Z. anorg. Chem. 67, 455 (1910). 20 G. Trümpler, Z. physik. Chem. 99, 49 (1921). 21 F. W. Küster & A. Thiel, Z. anorg. Chem. 33. 139 (1903). 143. Solubility Product an Ultimate Value of Equilibrium.— The solubility product is in reality an ultimate value which is attained by the ionic product when equilibrium has been established between the solid phase of a difficultly-soluble salt and the solution. If affairs so happen or can be so arranged in any given case that the ionic product is different from the solubility product, then the system will seek to adjust itself in such a way that the ionic product will attain the value of the solubility product. Thus, if the ionic product is arbitrarily made greater than the solubility product, as for instance through the addition of another salt with an ion in common, the adjustment of the system results in the precipitation of the solid salt. Conversely, if the ionic product is of itself smaller than the solubility product or can arbitrarily be made smaller, as, for instance, by the repression of the concentration of one of the ions, the adjustment of the system results in the solid salt going into solution. 144. To illustrate the ideas of the preceding paragraph we will now give two examples. As our first example let us consider the case of silver chloride to show the formation of a precipitate. If we add a solution of potassium chloride to a solution of silver nitrate, the chloride ion is momentarily present in such concentration that its ionic product with the silver ion exceeds the solubility product of silver chloride, and consequently the insoluble silver chloride is precipitated according to the reaction: Ag++ Cl AgCl ↓ = At the point at which we have added an equivalent amount of potassium chloride, granting that the system has reached equilibrium, the concentration of the silver ion will be equal to that of the chloride ion and the actual concentrations will then be: CAg+ = 10-5, ccr10-5. These values follow at once from the application of the solubility product of silver chloride Cag+ X CC 10-10 and the equality of the concentration of the two ions. If now, starting with such a saturated solution of silver chloride, we add either a soluble silver salt or a soluble chloride, we find that a slight further precipitation of silver chloride takes place, and if after equilibrium has been attained we measure the concentrations of the respective ions we will find that although the CCI = concentration of the one has been increased and the concentration of the other decreased, nevertheless their product has sensibly the same value as before. Thus to take the results of Jahn1 who employed potassium chloride and worked at 18°, we have: 145. As our second case let us consider the behavior of silver argenticyanide (silver cyanide) in order to show the solution of a precipitate by the repression of one of the ions (in this case the silver ion), the silver ion being repressed by virtue of its uniting with excess cyanide ion to form the complex argenticyanide ion.5 The mechanism of the process is as follows: silver argenticyanide ionizes according to the scheme (I) Ag [Ag (CN)2] → Ag+ + [Ag (CN)2] ̄ H so that we have the following ions present in its saturated solution: silver ion, cyanide ion and argenticyanide ion. If we add a solution of potassium cyanide to a solution of silver nitrate, the cyanide ion combines with some of the silver ion to form the complex argenticyanide ion and this latter reacts with more silver ion to form the difficultly-soluble salt silver argenticyanide. There are two equilibriums involved in this process: that existing between the cyanide ion, the silver ion and the complex argenticyanide ion, the instability constant for which is 10-21, i.e., (II) 4 Z. physik. Chem. 33, 545 (1900). CAg+ X (CCN-)2 = 10-21 5 Complex ions may be defined as the combination of two or more different varieties of ions to give a new variety of ion which shows to a very slight extent, if any, the characteristic properties of the original ions. The definition of complex ions by words is not very satisfactory and it is usual to define them by illustration. Thus we have the complexes formed between the metal ions and the following ions: cyanides, fluorides, tartrates, citrates, etc.; the complexes formed between the metal ions and ammonia; also the more stable complex ions like ferricyanide, ferrocyanide, permanganate, dichromate, chlorate, etc. and that existing between the silver ion, the complex argenticyanide ion and the solid silver argenticyanide, the solubility product for which is 2.25 X 10-12, i.e., (III) CAg+ X C[Ag(CN)2] = 2.25 X 10-12 At the point at which an equivalent amount of potassium cyanide has been added the concentration of silver ion will be sensibly equal to that of the complex argenticyanide ion by virtue of (I) and (III), or specifically by further virtue of (III) equal to 1.5 X 10-6, while the concentration of cyanide ion will be but a minute fraction of this by virtue of (II), namely 3.16 X 10-10. If now we add an excess of potassium cyanide and seek to build up the concentration of cyanide ion, the system will adjust itself so that (I) and (II) must still be satisfied. This means that the cyanide ion will combine with silver ion to form more complex argenticyanide ion; this silver ion, however, must be furnished by some of the solid silver argenticyanide going into solution. Thus while we cut down the concentration of silver ion in conformity with (III) the process results in the solution of our precipitate, whereas in the case of silver chloride excess of chloride ion results in further precipitation of silver chloride. 146. Solubility Product Makes No Mention of Rate of Attainment of Equilibrium. It is to be noticed that the solubility product defines a state of equilibrium but makes no mention of the rate at which equilibrium is attained; so that while it is a necessary condition that the solubility product be exceeded in order to bring about precipitation, it is no guarantee that precipitation will happen at once, and in point of fact in the formation of small amounts (say up to 5 mg.) of a great many of our insoluble salts, such as barium sulphate, ammonium phosphomolybdate, magnesium ammonium phosphate, copper sulphide, etc., it takes from 14 to 48 hours before precipitation is ended and equilibrium reached. Hence the statement so often made that exceeding the solubility product causes precipitation must be taken with the important qualification that for small amounts of precipitates a certain time must elapse before precipitation begins, and then a further and often considerable period must elapse before precipitation is completed. 147. Complete Precipitation Impossible. It should be pointed out at this juncture that while we can precipitate almost all of a difficultly-soluble salt, complete precipitation is impossible because no matter how much we arbitrarily increase the concentration of the one ion we cannot decrease the concentration of the other to zero, by virtue of the fact that the solubility product is a constant. This idea can perhaps best be brought out if we depict the relationship graphically, using the respective ionic concentrations as coördinates. The graph will be an equilateral hyperbola for simple salts of the 1:1 type like that for silver chloride, and there will be very similar curves for the other types of salts 1:2, 1:3, 2:3, etc. From the properties of the equilateral CCI hyperbola we know that it never intersects the coördinate axes but becomes sensibly parallel to them. This idea can be visualized from Fig. 22. An important corollary that follows as a result of the above is that after a certain point, further excess of precipitant accomplishes no material benefit in the further throwing out of the precipitate. CAg+x CC-Constant CA8+ FIG. 22 148. Undissociated Portion of a Difficultly-Soluble Salt. The solubility product treats only of the ionized portion of a salt, and as the salt exists in solution not only in the ionized form but also in the un-ionized form, we have still to consider the un-ionized portion. Let us designate by u the concentration of the undissociated portion of a difficultly-soluble salt existing in a saturated solution of the salt when just the salt itself is present in the solution. Under these conditions the undissociated portion u is, in general, only a small fractional part of the total concentration of the dissolved salt since most difficultly-soluble salts are ionized to the extent of 98% or thereabouts. The question next arises, does the concentration of the undissociated portion of a |