CHAPTER XII

«THE COPPER AND SILVER GROUPS» (‹Continued›).—«THE THEORY OF COMPLEX IONS»

We will now turn to the consideration of a series of reactions involving the behavior of so-called "complex ions," which are very frequently met with in the various analytical groups and which offer valuable methods of separation and identification of ions. The behavior of silver nitrate solution towards ammonia forms a convenient point of attack in taking up the general subject.

«Action of Ammonia on Silver Nitrate.»—Addition of ammonium hydroxide solution to silver nitrate (‹exp.›) results in the formation of a brown precipitate of silver oxide (and silver hydroxide). We may consider the supernatant liquid to be saturated with silver hydroxide (this is in equilibrium with silver oxide), and for the saturated solution we may put [Ag^{+}] × [HO^{−}] = K_{AgOH}.

If more ammonium hydroxide is added to the mixture, the precipitate dissolves readily. The excess of ammonium hydroxide must increase the concentration of hydroxide-ion and, if no other action occurred, we should, according to the principle of the solubility-product, expect that the precipitate would thereby be slightly increased (p. 145), rather than that it should be dissolved so readily. Since solution results even when the value of the one factor, [HO^{−}], of the product is increased, we must suspect that the value of the other factor, the concentration [Ag^{+}] of silver-ion, is in some way made much smaller by the addition of the excess of ammonium hydroxide. Recalling the fact that aluminium hydroxide is soluble in excess of sodium hydroxide, as the result of its amphoteric character, a solution of sodium aluminate NaAlO_{2} being obtained, we might suspect that silver hydroxide also has amphoteric properties, ‹i.e.› that it might be capable of ionizing into "argentate ions," AgO^{−}, and hydrogen ions, AgOH ⇄ AgO^{−} + H^{+}. If such be the case, the nonionized silver hydroxide is in equilibrium, not only with the solid phase, [p217] but also with two sets of ions,

Ag^{+} + HO^{−} ⇄ AgOH

AgOH ⇄ AgO^{−} + H^{+}

AgOH ⇄ AgOH ↓,

and we must have ‹two› solubility-product constants, one corresponding to the basic ionization (see above) and the other corresponding to the acid ionization, and [AgO^{−}] × [H^{+}] = K′_{AgOH}.

If silver hydroxide have acid properties, the addition of an alkali must suppress the hydrogen-ion and the hydroxide will go into solution as an argentate, MeAgO. We find, however, that sodium or potassium hydroxide, which would form an argentate very much more readily than ammonium hydroxide, has no solvent action on silver hydroxide (‹exp.›); on the contrary, quantitative experiments show that the alkali makes the hydroxide still less soluble than in pure water—as demanded by the solubility-product for the basic ionization. It is thus evident, that the solvent action of ammonium hydroxide is not due to its basic functions. We would suspect that we have here an action, in which ‹ammonia› is the active component, the product of a form of dissociation of ammonium hydroxide, of which the fixed alkalies are incapable.

«The Complex Silver-Ammonium[425]-Ion.»—For a solution of ammonia, in water, we have the reversible reactions: [p218] HO^{−} + H^{+} + NH_{3} ⇄ NH_{4}^{+} + HO^{−} ⇄ NH_{4}OH, and we note that a molecule of ammonia appears to combine first with a hydrogen ion, to form an ammonium ion, and this then forms ammonium hydroxide with the hydroxide ion. This suggests that ammonia may have the capacity to combine with positive ions other than hydrogen ion, and with metal hydroxides other than water. For an analogous reaction of ammonia with silver ion and with silver hydroxide, we would have:

NH_{3} + Ag^{+} + HO^{−} ⇄ (NH_{3}Ag)^{+} + HO^{−} ⇄ (NH_{3}Ag)OH.

For the condition of equilibrium between ammonia, the silver-ion and the silver-ammonium-ion, we would have[426]:

[NH_{3}] × [Ag^{+}] / [NH_{3}Ag^{+}] = K.

Experimental investigations of the quantitative relations, obtaining in ammoniacal solutions containing silver compounds, show that ‹no constant› value is obtained for the ratio, as just developed. But the experimental data show equally conclusively,[427] that a constant is obtained, ‹when the concentration of the ammonia is raised to the second power, in the mathematical statement›.

The significance of this change in the mathematical relation, it will be recalled (p. 94), is that two molecules of ammonia must combine with one silver ion to form an ion [(NH_{3})_{2}Ag]^{+}, whereas in the formation of the ammonium ion, NH_{4}^{+}, we have a single molecule of ammonia combining with one hydrogen ion. We have then

2 NH_{3} + Ag^{+} + HO^{−} ⇄ [(NH_{3})_{2}Ag]^{+} + HO^{−} ⇄ [(NH_{3})_{2}Ag]OH.

We would thus have a silver-ammonium ion, [(NH_{3})_{2}Ag]^{+}, and its hydroxide, silver-ammonium hydroxide, corresponding to the [p219] ammonium ion and its hydroxide, ammonium hydroxide. The properties of ammoniacal solutions of silver oxide are in entire agreement with this conception. The hydroxide is a stronger base than barium hydroxide.[428] It forms salts, [(NH_{3})_{2}Ag]X, in which silver appears as part of a so-called positive "complex ion." The hydroxide, like ammonium hydroxide, is unstable and is only known in solution and in the presence of free ammonia, exactly as is the case for ammonium hydroxide. The mathematical equation expressing the equilibrium conditions for the complex ion,

[NH_{3}]^2 × [Ag^{+}] / [(NH_{3})_{2}Ag^{+}] = K_{Instability},

gives a ‹definite measure› of the ‹stability› of this complex ion. It is clear, that the ‹larger› the constant, the more ‹unstable› the complex ion would be, and so the constant is called the ‹Instability Constant›[429] of the complex silver-ammonium-ion. Bodländer found the value of the constant to be 6.8E−8 at 25°.[430]

According to the composition of the complex ion, two molecules of ammonia should be required for every molecule of silver nitrate, to produce a solution containing the nitrate of the complex ion: Ag^{+} + NO_{3}^{−} + 2 NH_{3} ⇄ [(NH_{3})_{2}Ag]^{+} + NO_{3}^{−}. As a matter of fact, 20 c.c. of a molar solution of ammonium hydroxide (= 200 c.c. of a 0.1 molar solution) must be added to 100 c.c. of a 0.1 molar solution of silver nitrate, to convert the silver nitrate into the salt of the complex silver-ammonium-ion. If the ammonium hydroxide solution is allowed to flow slowly, from a pipette, into the silver nitrate solution, we find that the last trace of the precipitated silver hydroxide redissolves just as the ‹last› drop or two of the 20 c.c. is added to the mixture (‹exp.›). Working more exactly, Reychler[431] found that the addition of ammonia to a silver nitrate solution, in the proportion of two molecules of the former to one of the nitrate, does not change the freezing-point of the solution, and therefore [p220] does not increase the total number of molecules in the solution. This result agrees with the conception that two molecules of ammonia combine with one silver ion to form a complex ion.

«Application in Analysis.»—Turning now to the consideration of the bearing of these relations on the detection of silver-ion in analysis, we may conclude, in the first place, from the value of the constant as given, that only a ‹small proportion› of the total silver in such ammoniacal solutions is present in the form of silver-ion; but, in the second place, there is, at least, a ‹portion› of the silver present in the form of its ion—it is ‹not entirely› suppressed; and, in the third place, it is clear, from the form of the equilibrium equation, that any ‹excess› of ‹ammonia› must very rapidly reduce the ‹concentration of silver-ion› in such solutions.

The bearing of these relations, which, it will be noted, concern ‹concentrations of silver-ion›, can best be seen by working with solutions of definite concentrations.

If the solution we have just prepared is diluted with water to 200 c.c., a 0.05 molar solution of [(NH_{3})_{2}Ag]NO_{3} is formed. In such a solution, the concentration, [Ag^{+}], of the silver-ion is only 0.0009,[432] whereas in 0.05 molar silver nitrate solution it is 0.0435. It is clear that the reactions of the silver-ion will not be observed as readily in such an ammoniacal solution as in a solution of silver nitrate, which contains the same concentration of ‹total silver›. That such is the case, may be readily demonstrated as follows: the addition of 1 c.c. of molar sodium bromate to 10 c.c. of 0.05 molar silver nitrate immediately forms a heavy precipitate of the moderately difficultly soluble bromate, AgBrO_{3}, while the same addition to 10 c.c. of the 0.05 molar silver-ammonium nitrate solution produces no precipitate whatever (‹exp.›). [p221]

A liter of water dissolves 0.025 mole (6 grams) of silver bromate[433] at 18°. If the same degree of ionization be assumed for it as for a 0.025 molar solution of the analogous salt, silver nitrate, AgNO_{3}, 90% of the silver bromate in the saturated solution is ionized. The solubility-product constant then is [Ag^{+}] × [BrO_{3}^{−}] = (0.025 × 0.9)^2 = 0.0005.

When 1 c.c. of molar sodium bromate is added to 10 c.c. of 0.05 molar silver nitrate, each salt is ionized 80% in the mixture, and [Ag^{+}] = 0.05 × 0.8 × 10 / 11 = 0.037 and [BrO_{3}^{−}] = (1 × 1 / 11) × 0.8 = 0.072. Then the product of the ion concentrations, [Ag^{+}] × [BrO_{3}^{−}] = 0.037 × 0.072 = 0.0027, is considerably larger than the constant 0.0005 and precipitation follows.

But, when 1 c.c. of molar sodium bromate is added to 10 c.c. of a 0.05 molar silver-ammonium nitrate solution, the concentration of silver-ion[434] is 0.00085 and the product of the ion concentrations, [Ag^{+}] × [BrO_{3}^{−}] = 0.00085 × 0.072 = 6E−5, is smaller than the constant; the solution will not be saturated with silver bromate and no precipitate is formed.

On the other hand, if 1 c.c. of a 0.1 molar solution of sodium chloride is added to 10 c.c. of 0.05 molar silver-ammonium nitrate solution, a very decided precipitate of silver chloride is formed (‹exp.›). The difference in the action of the sodium bromate and the chloride lies in the fact that silver chloride is 2500 times as insoluble as is silver bromate, and the chloride may be precipitated from solutions containing a ‹very much smaller concentration of the silver-ion› than is required for the precipitation of silver bromate.

The quantitative relations for the chloride are as follows: a liter of water dissolves 0.002 gram, or 1.4E−5 mole, of silver chloride at 25°,[435] and the solubility-product constant at 25° is [Ag^{+}] × [Cl^{−}] = (1.4E−5)^2 = 2E−10. Now, if 1 c.c. of 0.1 molar sodium chloride is added to 10 c.c. of 0.05 molar silver-ammonium nitrate, we have,[436] for the first moment, [Ag^{+}] = 8.9E−4 and [p222] [Cl^{−}] = 0.008, and [Ag^{+}] × [Cl^{−}] = 8.9E−4 × 0.008 = 7E−6, which is much larger than the solubility-product constant, and precipitation must take place. The precipitate will be quite a heavy one: as silver-ion is removed from solution, the complex ion must decompose and furnish a new supply of silver-ion, and precipitation must continue until the excess of ammonia, which is liberated by the decomposition of the complex ion (Ag(NH_{3})_{2}^{+} + Cl^{−} → AgCl ↓ + 2 NH_{3}), suppresses the silver-ion sufficiently to satisfy, with the diminished concentration of chloride-ion, the solubility-product constant of silver chloride.

It is clear that, while the reactions of silver-ion are not obtained ‹as readily› in the ammoniacal solution as in an equivalent solution of silver nitrate (bromate experiment), nevertheless more sensitive tests show that a ‹small portion› of the silver still is present as ‹silver-ion› in the ammoniacal solution (chloride experiment).

This brings us to our third point, the influence of an excess of ammonia on the concentration of silver-ion and on its reactions. It is evident, from the form of the equilibrium equation (p. 219), that any excess of ammonia must very rapidly reduce the concentration of silver-ion. We may ask ‹what excess will be required to prevent the precipitation of silver chloride› in the experiment just tried.

The question may be answered as follows: The concentration of chloride-ion, when 1 c.c. of 0.1 molar sodium chloride is added to 10 c.c. of 0.05 molar [Ag(NH_{3})_{2}]NO_{3}, no precipitate being formed, will be 0.1 × (1 / 11) × 0.87, the solution being diluted 1 to 11 and the percentage of ionization of a salt MeX being approximately 87% in 0.05 to 0.06 molar concentration. For a solution containing this concentration of chloride-ion, the concentration [Ag^{+}] of silver-ion, ‹which may just be present› «without» ‹leading to the precipitation of silver chloride› (‹i.e.› for the saturated solution) is, according to the principle of the solubility-product,

[Ag^{+}] = K_{S.P.} / [Cl^{−}] = (2E−10) / (0.1 × 0.87 × 1 / 11).

Further, in the presence of an excess of ammonia, practically all of the silver is present in the complex form, and, [Ag(NH_{3})_{2}^{+}] = 0.05 × 0.87 × 10 / 11 the 0.05 molar solution being diluted 10 parts to 11 and the salt being 87% ionized.

If we call ‹x› the concentration of free ammonia required to reduce the concentration of silver-ion to the small value indicated, we may put

[NH_{3}]^2 × [Ag^{+}] / [Ag(NH_{3})_{2}^{+}] = [‹x›^2 × 2E−10 / (0.1 × 0.87 × 1 / 11)] / (0.05 × 0.87 × 10 / 11) = 6.8E−8.

Solving for ‹x›, we obtain ‹x› = [NH_{3}] = 0.33. The concentration of free ammonia, necessary to prevent precipitation of silver chloride in this system, is then [p223] 0.33, instead of 0.0018, present in the original solution. Now, 11 c.c. of 0.33 molar ammonia is equal to 11 × 0.33 / 6, or 0.61 c.c. hexamolar ammonia.[437]

Calculations, based on the solubility-product constant of silver chloride and on the instability constant of silver-ammonium-ion, lead, thus, to the conclusion that an excess of 0.61 c.c. of hexamolar ammonia is required, in 10 c.c. of 0.05 molar [Ag(NH_{3})_{2}]NO_{3}, to prevent the precipitation of silver chloride by 1 c.c. of 0.1 molar sodium chloride. Conversely, this excess of ammonia will be required to ‹redissolve the precipitate› of silver chloride, formed when 1 c.c. of 0.1 molar sodium chloride solution is added to 10 c.c. of 0.05 molar [Ag(NH_{3})_{2}]NO_{3}. The following experiment shows that such is the case.

EXP. 1 c.c. of 0.1 molar sodium chloride is added to 10 c.c. of 0.05 molar silver-ammonium nitrate, prepared as described on p. 220; hexamolar ammonia is slowly added to the mixture from a 1 c.c. pipette, graduated in twentieths of a cubic centimeter. The precipitate will be seen to be just about ‹completely dissolved› when 0.6 to 0.65 c.c. of the ammonia solution has been used.

We find, in this way, that the equilibrium equation for the instability constant of the complex silver-ammonium-ion, together with the principle of the solubility-product, allows a ‹quantitative interpretation› of the problem of the behavior of ammoniacal silver solutions, as far as the detection of silver by the precipitation of its salts is concerned.

If a still larger excess of ammonia is used (‹exp.›), even the addition of a 10% solution of sodium chloride fails to precipitate the chloride, and, ‹vice versa›, ammonia in excess will readily redissolve a heavy precipitate of silver chloride (‹exp.›). Advantage is taken of this fact in the separation and identification of silver-ion (Laboratory Manual, ‹q. v.›).

It is interesting to note that the addition of potassium bromide, iodide or sulphide to the ammoniacal solution, in which sodium chloride fails to precipitate any silver chloride, will still precipitate silver bromide, iodide or sulphide readily (‹exp.›). Judged by the line of argument used above, in contrasting the behavior of silver bromate and silver chloride, these silver salts [p224] must be still less soluble than the chloride. Experiment proves, that such is, indeed, the case.[438]

Silver iodide is so insoluble, that ammonia[439] may be used to separate it, with a considerable degree of accuracy, from silver chloride, and this separation forms the basis of a method to detect chloride-ion in the presence of an iodide. If a solution with a ‹limited concentration of ammonia› is used, the method may be extended also to the separation of chlorides from bromides (see Chap. XVI).[440]

«Complex Metal-Ammonium Ions of Copper, Cadmium, etc.»—Quite a number of metal ions are capable of forming more or less stable complex ions with ammonia. For analytical purposes, the most interesting of such complex ions, aside from the silver-ammonium-ion, are those formed by cupric, cadmium, zinc and nickel ions, the most important of which represent bivalent complex ions of the composition[441] Me(NH_{3})_{4}^{2+}. The following instability constants have been determined:[442] At 21°,

[Cd^{2+}] × [NH_{3}]^4 / [Cd(NH_{3})_{4}^{2+}] = 1E−7

[Zn^{2+}] × [NH_{3}]^4 / [Zn(NH_{3})_{4}^{2+}] = 2.6E−10.

Cupri-ammonium-ion is far more intensely blue than cupric-ion and its color is used as one of the tests to identify copper in its salts. Nickel-ammonium-ion is also blue, a much paler blue, and its color must not be mistaken as indicating the presence of a dilute solution of cupric-ammonium-ion. The same kind of relations obtain for these complex ions as for silver-ammonium-ion. For instance, a salt like cupric phosphate, which is readily precipitated from cupric sulphate solutions, is not precipitated from the ammoniacal solutions containing an excess of ammonia (‹exp.›), while the very much less soluble[443] cupric sulphide is readily precipitated even from the ammoniacal solutions (‹exp.›). It may [p225] easily be shown, in the usual way,[444] that the sulphide of copper is very much less soluble than its phosphate (‹exp.›).

«The Complex Cyanide Ions.»—Metal ions are capable of forming complex ions, of importance in analytical work, with a number of components other than ammonia. Among the most important of these are the complex ions formed with cyanide-ion. The theory of the complex cyanide ions is entirely analogous to that of the complex metal-ammonium ions, but there is a difference in stability that makes their special consideration desirable, both for practical and for theoretical purposes. The complex ions of silver-ion and cyanide-ion will be discussed first.

«The Argenticyanide-Ion.»—When potassium cyanide is added to a solution of silver nitrate, a very insoluble precipitate of silver cyanide is obtained, but an excess of potassium cyanide readily redissolves the precipitate (‹exp.›). Since solution is effected in spite of the presence of an excess of the precipitating cyanide-ion, one is led to suspect that the other ion, the silver-ion, which is needed to form the precipitate, is suppressed by entering into some kind of complex with the excess of cyanide. As a matter of fact, the solution contains a salt, potassium argenticyanide KAg(CN)_{2}, in which the silver forms a part of a ‹negative argenticyanide-ion› (Ag(CN)_{2}^{−}).[445] If a current of electricity is passed through such a solution, the silver (all but traces), together with the cyanide groups, moves towards the positive electrode.[446] The complex has been formed, then, by the combination of a positive silver-ion with two negative cyanide ions,[447] which produce a univalent negative argenticyanide-ion, Ag(CN)_{2}^{−}. Recalling the fact that the complex silver-ammonium-ion is not perfectly stable, one might suspect that the complex cyanide-ion, in turn, is not absolutely stable, and that the action, by which it is formed, is balanced, when equilibrium is reached, by a reverse action of decomposition. We would have, then, [p226] K^{+} + Ag^{+} + 2 (CN)^{−} ⇄ K^{+} + [Ag(CN)_{2}^{−}] or, more simply, Ag^{+} + 2(CN)^{−} ⇄ [Ag(CN)_{2}^{−}].

For the condition of equilibrium between the complex and its components, the relation

[Ag^{+}] × [CN^{−}]^2 / [Ag(CN)_{2}^{−}] = K_{Instability}

would hold. Bodlaender[448] determined the value of this constant by measuring the concentrations of the three components under varying conditions. The value found is 1E−21. The value of the instability constant for [Ag(NH_{3})_{2}^{+}], of analogous composition, is 6.8E−8, a very much larger value than the constant of the [Ag(CN)_{2}^{−}] complex. The latter is, therefore, by far the more stable. It must, consequently, be much more difficult to obtain reactions, such as precipitations, of silver-ion in cyanide than in ammoniacal solutions. In fact, it is impossible to precipitate silver chloride by the addition of sodium chloride to KAg(CN)_{2} solution (‹exp.›).[449] Silver sulphide was found to be a much less [p227] soluble salt than the chloride (p. 224), and ammonium or sodium sulphide solution, when added to the cyanide solution, readily precipitates silver sulphide (‹exp.›). (The sulphide is ‹capable› of ‹existence› in the solid phase, therefore, under these conditions.) In view of the extremely small concentrations of silver-ion in the cyanide solution, we have here a striking illustration of the extreme insolubility of the sulphide.

According to the equilibrium equation given above, the larger the excess of cyanide-ion in the solution, the smaller must be the concentration of silver-ion which is capable of existence in its presence. In agreement with this conclusion, we find that the addition of an excess of potassium cyanide readily redissolves the precipitated silver sulphide (‹exp.›).[450] In other words, even the minute concentration of silver-ion, that must be present in the supernatant liquid above a precipitate of silver sulphide ([Ag^{+}]^2 × [S^{2−}] = K_{Sol. Prod.}, for a saturated liquid), cannot be permanently present with an excess of potassium cyanide. Consequently, ‹the solid phase is incapable of existence in the system›.

The equilibrium equations give us, thus, a comprehensive basis for the interpretation of the behavior of cyanide solutions containing silver. First, in accordance with the small value of the constant, we find it very much more difficult to obtain precipitates of silver salts in cyanide, than, say, in ammoniacal solutions; secondly, in accordance with the fact that a very small, but definite, concentration of the silver-ion may still persist in the [p228] system, we find it possible, in the absence of an excess of cyanide, to precipitate such an extremely insoluble silver salt as silver sulphide represents; and finally, in accordance with the form and constant of our equation, we find it possible, by using an excess of potassium cyanide, to suppress the silver-ion to the point where even this extremely insoluble salt can no longer exist.[451]

«Cuprocyanide and Cadmicyanide Ions.»—Very many of the metal ions are capable of forming complexes with cyanide-ion, of greater or smaller degrees of stability, and, as is the case for the complex ions formed by metal ions with ammonia, a metal ion is frequently able to form more than one complex with cyanide-ion.[452] A number of these complex cyanide ions are of particular interest in qualitative analysis. For instance, we make use of the difference in the stability of the cuprocyanide and the cadmicyanide ions as offering us the most convenient method of recognizing cadmium in the presence of copper. Excepting for the sulphide and the oxide, cadmium does not form salts and compounds of characteristic colors, and, except in color, the salts resemble the corresponding copper salts very much in their physical and chemical behavior. Copper and cadmium consequently show the same group reactions in systematic analysis. The more intense colors of the copper compounds—the black sulphide, the intensely blue cupric-ammonium-ion—mask the cadmium reactions. But cupric-ion may be converted, by potassium cyanide, into a complex ion of extreme stability, from the solutions of which hydrogen sulphide and alkali sulphides ‹fail to precipitate any sulphide of copper, while cadmium sulphide may be precipitated from the solutions of the much less stable complex cadmicyanide-ion›.

When potassium cyanide is added to the deep blue ammoniacal solution of cupric-ammonium sulphate [Cu(NH_{3})_{4}]SO_{4}, the cupric-ion is reduced[453] [p229] to cuprous-ion, and the latter is converted, by an excess of cyanide, into the extremely stable complex ion Cu(CN)_{3}^{2−} and its salt, potassium cuprocyanide K_{2}[Cu(CN)_{3}]. The instability constant of the complex ion is: [Cu^{+}] × [CN^{−}]^3 / [Cu(CN)_{3}^{2−}] = 0.5E−27, and the concentration of cuprous-ion, in a 0.1 molar solution, is approximately[454] 3.7E−8. Without an excess of cyanide, traces of cuprous sulphide may still be precipitated, but ‹a few drops excess will prevent the precipitation entirely›.[455]

With an excess of potassium cyanide, cadmium forms the salt K_{2}[Cd(CN)_{4}], yielding the ion [Cd(CN)_{4}^{2−}]. The instability constant[456] of the complex ion is [Cd^{2+}] × [CN^{−}]^4 / [Cd(CN)_{4}^{2−}] = 1.4E−17. The concentration of cadmium-ion, in a 0.1 molar solution of the salt, is then approximately[457] 8E−5.

If potassium cyanide is added to an ammoniacal solution, containing both cadmium and copper, until the color of the solution is just discharged, and if two or three drops excess of the cyanide is then used, the addition of ammonium sulphide will precipitate pure cadmium sulphide (‹exp.›), while ammonium sulphide, added to a portion of the original ammoniacal solution, will precipitate a dark mixture of cupric and cadmium sulphide (‹exp.›), in which the yellow color of cadmium sulphide is masked by the black precipitate of cupric sulphide.

«Cobalticyanide and Nickelocyanide Ions.»—In much the same way, in the identification of nickel in the presence of cobalt, advantage may be taken of the fact that cobalt forms an extremely stable cobalticyanide[458] ion, [Co(CN)_{6}^{3−}], which does not permit of the precipitation of cobaltic hydroxide, whereas nickel does not form such an ion, but only forms a not very stable nickelocyanide ion, [Ni(CN)_{4}^{2−}], which is readily decomposed by bromine and alkali, nickelic hydroxide being precipitated. [p230] The following are the chief actions involved in the precipitation of the latter:[459]

Ni(CN)_{4}^{2−} ⥂ Ni^{2+} + 4 CN^{−}

2 Ni^{2+} + Br_{2} ⥂ 2 Ni^{3+} + 2 Br^{−}

Ni^{3+} + 3 HO^{−} ⥂ Ni(OH)_{3} ↓

«Applications and Precautions in Analysis.»—The complex cyanide ions thus give us a convenient means of ‹interfering› with the precipitation of certain metal ions, and of enabling us, thereby, to detect other, closely related, ions in their presence. At the same time, we must be careful ‹to identify the ions›, which we wish to suppress, before converting them into these extremely stable complexes. Potassium cuprocyanide and potassium cobalticyanide solutions would not give any of the ordinary tests for ions of copper and cobalt, and to find the latter in such solutions, by these tests, we would have to take the trouble of destroying the complexes. Should the destruction of such complexes become necessary (‹e.g.› when complex cyanide ions are present in the original substance under examination), evaporation with sulphuric acid, with due precautions against inhaling poisonous hydrocyanic acid fumes, fusion with alkali carbonates, and perhaps most conveniently, electrolysis with sufficiently high potentials,[460] are the methods most frequently employed for the purpose. It will be recalled that we have used the method of fusion with potassium carbonate to find iron in potassium ferrocyanide (p. 89).

«Ferrocyanide and Ferricyanide Ions.»—The ferro- and ferricyanide ions may also be treated as complex ions. For instance, for the ferricyanide-ion, we would expect a condition of equilibrium to exist between the complex ion and the simple ions according to:

Fe(CN)_{6}^{3−} ⇄ Fe^{3+} + 6 CN^{−} and

[Fe^{3+}] × [CN^{−}]^6 / [Fe(CN)_{6}^{3−}] = K.

[p231]

If the fact is recalled that the extremely sensitive tests for the ferric-ion fail to reveal the least trace of it in a potassium ferricyanide solution, one must conclude that the ferricyanide-ion must be extremely stable. The conception of the ferricyanide-ion as a complex ion, subject to the above equilibrium conditions, suggests that if a considerable excess of hydrogen-ion is added to its solutions, the concentration of ferric-ion must be increased: since hydrocyanic acid is an extremely weak acid (p. 104), the ratio [H^{+}] × [CN^{−}] / [HCN] having the value 7 / 10^{10}, the addition of some concentrated hydrochloric acid must decidedly suppress the cyanide-ion in a ferricyanide solution and thus lead to an increase in the concentration of the ferric-ion. Under these conditions, direct evidence of the presence of the ferric-ion, and of the fact that the complex ion is a component in a reversible reaction, may, indeed, be obtained, as well as further evidence of the extreme stability of the complex. The presence of traces of ferric-ion may be detected, namely, in the acid solution by the thiocyanate test, applied in its most sensitive form, in which any ferrithiocyanate produced is taken up in ether.

EXP. Potassium ferricyanide, treated with a thiocyanate and ether, does not show the least trace of color; when some concentrated hydrochloric acid is added to the mixture, a perfectly plain, although noticeably faint, pink tint is imparted to the ether solution.

Mercuric cyanide, as we have seen (p. 115), is exceptional in its exceedingly small capacity for ionization. Sherrill[461] has found that the dissociation constant for [Hg^{2+}] × [CN^{−}]^4 / [Hg(CN)_{4}^{2−}] has the extremely small value 0.4E−41. Consequently, mercuric-ion must be even more effective than hydrogen-ion (strong acids), in suppressing the cyanide-ion and liberating the ferrous- or ferric-ion, in solutions of ferrocyanides or ferricyanides. In fact, when a solution of potassium ferrocyanide is warmed, for a moment, with some mercuric oxide, the ferrocyanide complex is to some extent decomposed; the liberated ferrous-ion is oxidized, by the excess of mercuric oxide,[462] to ferric-ion, and the presence of the latter, in quantity, is shown by the abundant precipitation of ferric ferrocyanide or Prussian blue, when the mixture is acidified with hydrochloric acid (‹exp.›). [p232]

«The Aurocyanide-Ion.»—Gold forms a particularly stable complex ion with cyanide-ion. The constant[463] for the ratio [Au^{+}] × [CN^{−}]^2 / [Au(CN)^{−}_{2}] has the value 10^{−28}. This makes potassium cyanide an excellent solvent for insoluble gold compounds, such as gold sulphide, and the cyanide process for the extraction of gold ores makes use of this property.

«The Reacting Components in Solutions of the Complex Cyanide Ions.»—The extraordinary values, obtained for the constants expressing the condition of equilibrium between cyanide ions and some of the simple metal ions, such as gold and silver ions, and their complex ions, have led to inquiries concerning a question of fundamental interest in the theory of complex ions and in the theory of ionization itself. In a 0.05 molar solution of KAg(CN)_{2}, containing an excess of 0.1 mole of CN^{−}, per liter, the concentration of silver-ion is only 5E−21. And yet, the addition of potassium hydrosulphide (sufficient to make [KSH] = 0.1 molar) will precipitate silver sulphide practically instantaneously from the solution.[464] In solutions containing a larger excess of cyanide, the concentration of the silver-ion is enormously reduced, and yet, while we can no longer precipitate silver sulphide from such a solution, metallic silver may be precipitated by zinc or by the action of an electric potential at the cathode (Chapter XV). The question may be asked, ‹whether we must consider that in these actions the minute quantity of free silver ions, present at any moment, is alone capable of the reactions› indicated, and that the ‹decomposition of the complex› into its ‹components›—as one of these, the silver-ion, is removed by precipitation—takes place with ‹sufficient speed› to account for the ‹rapid actions, wholly, as direct actions of the silver ions›. The alternative to an affirmative answer to this question is, that silver sulphide or silver ‹may be precipitated by direct action of the precipitant› on the ‹complex› ions, rather than on the ‹silver ions›. We may indicate the first course suggested for the action, as follows:

2 Ag(CN)_{2}^{−} + S^{2−} ⇄ 4 CN^{−} + 2 Ag^{+} + S^{2−} ⇄ Ag_{2}S ↓ + 4 CN^{−}. I

The second, suggested, course of the action would be the following:

2 Ag(CN)_{2}^{−} + S^{2−} ⇄ Ag_{2}S ↓ + 4 CN^{−}. II

This second action would mean that we could obtain reactions of silver ions, such as the precipitation of silver sulphide, ‹without the intermediate formation of the free ions themselves›.

The consequences of the first, the ordinary, conception of such actions ‹as direct actions of silver ions›, have been analyzed by Haber[465] from the point of view of the velocities of the actions, by which the complex must be formed from its components and be decomposed into them, in order to satisfy the facts concerning the precipitations. [p233]

We may consider, with Haber, a liter of a 0.05 molar solution of K_{2}Ag(CN)_{3}, containing an excess[466] of 0.95 mole potassium cyanide. In such a solution, the concentration of silver-ion is reduced to 8E−24 gram-ion per liter. Now, according to the best determinations of the ultimate dimensions of molecules, about 10^{24} molecules are estimated to be contained in a mole (gram-molecule), and 10^{24} ions, therefore, in a gram-ion (‹e.g.› in 108 grams of silver-ion there would be 10^{24} individual silver ions). Then a liter of the solution we are considering would contain, at any moment, only eight individual silver ions, which are different ones from moment to moment, since the reversible reactions Ag^{+} + 3 CN^{−} ⇄ Ag(CN)_{3}^{2−}, are going on continually. Thus 100 c.c. of the solution would not contain even one silver ion all the time, but the requirements of the equilibrium conditions could be met[467] by silver ions "flashing up and disappearing" in such a way, that the required average concentration in unit time is maintained. There is nothing irrational in such a conception.

One may ask, however, what must be the velocities, with which the complex is formed from the components, and is resolved into them, in order to satisfy an instability constant[466] 10^{−22} and still enable us to obtain a practically instantaneous precipitation, say of silver sulphide, the action being analyzed on the basis of the ordinary conception that only the silver-ion itself, and not the complex ion, is directly active in the formation of the silver sulphide. A condition of equilibrium, in a reversible action, implies that the velocities of the two continuous, opposed reactions are equal (p. 94). For the action Ag^{+} + 3 CN^{−} → Ag(CN)_{3}^{2−} the ‹velocity› of ‹formation› of the ‹complex› is proportional to a characteristic constant, K_{Formation}, to the concentration, [Ag^{+}], of the silver-ion, and to the third power (see p. 94) of the concentration, [CN^{−}], of the cyanide-ion. The ‹velocity› of the ‹opposed reaction› of ‹decomposition› of the complex is proportional to another characteristic constant, K_{Decomposition}, and to the concentration, [Ag(CN)_{3}^{2−}], of the complex ion. For the condition of equilibrium, the velocities of the opposed reactions are equal, and we derive the relation:

[Ag^{+}] × [CN^{−}]^3 / [Ag(CN)_{3}^{2−}] = K_{Decomposition} / K_{Formation} = 1 / 10^{22}.

The equilibrium constant of the complex ion is, then, the ratio of the velocity constants of its decomposition and formation (see p. 94). Now, the ‹velocity constant›, K_{Formation}, represents the concentration, in moles, of the complex ion [Ag(CN)_{3}^{2−}],that is formed in unit time from unit concentrations of its components Ag^{+} and CN^{−}, and it may be considered as the ‹reciprocal› of a ‹time constant›, T_{Formation}, the ‹time› required ‹to form unit concentration› of the complex ion, while the components are maintained at unit concentration. The analogous reciprocal relation holds for the velocity constant, K_{Decomposition}, and a time constant, T_{Decomposition}. The equilibrium equation, therefore, expresses also the following relations:[468] [p234]

[Ag^{+}] × [CN^{−}]^3 / [Ag(CN)_{3}^{2−}] = T_{Formation} / T_{Decomposition} = 1 / 10^{22}.

In words, the time required for the spontaneous decomposition of one mole of the complex is 10^{22} times as long as the time required to form one mole of the complex, from uniformly unit concentrations of the components. If the concentration of silver-ion is reduced to 1 / 10^{22} and the concentrations of the cyanide-ion and the complex ion are maintained at 1, the formation of the complex takes place 10^{22} times as slowly as when [Ag^{+}] = 1, and a condition of equilibrium is produced, the time required to decompose and to form the same amount of the complex being now equal.

This ‹relation› of ‹time constants› may be used to obtain some idea of the consequences of assuming certain limiting values for one or the other, the ratio being maintained at the value 1 / 10^{22}. If the time constant T_{Formation} for the ‹formation of the complex› be taken as one ten-thousandth of a second,[469] then, according to Haber, a molar solution of potassium argenticyanide would not be able to form in thousands of years sufficient silver ions to be discovered by any direct test, a result which is not compatible with the precipitation of silver sulphide and of metallic silver in a few minutes, since silver ions could not be ‹supplied rapidly enough›. It is evident, thus, that the ratio 1 / 10^{22} must indicate an exceedingly small value for T_{Formation}, if only silver ions form silver sulphide and silver.

If we assume that the complex is decomposed so fast as to supply new silver ions rapidly enough, to allow us to consider the precipitation of silver and silver sulphide as direct actions of the silver ions, then we may, conservatively, consider T_{Decomposition} to be about 1 / 100 second. Then T_{Formation} would be only 1 / 10^{24} second. Considering the limiting results for the dimensions of atoms (and ions) and taking account of the fact that the formation of the complex ‹involves electrical changes›, that is, in modern terms, changes in position of electrons,[470] Haber finds, that to satisfy the above value for the time constant, such changes must involve a motion of electrical charges at a speed about a million times as great as the velocity of light. Such a velocity is, unquestionably, incompatible with our knowledge of the velocities of light and of electrical charges. We must draw the conclusion that ‹the complex argenticyanide-ion probably cannot decompose fast enough into its ions›, to enable the latter to be the ‹only› components which make it possible to precipitate silver sulphide or metallic silver from its solutions[471] (see above, p. 232). That would make it necessary to assume ‹direct action› [p235] (as given in equation II, p. 232) ‹between the complex› and the ‹precipitating agent›, to some extent, at least, the extent being dependent on the concentrations involved in a given case. If further investigations should confirm such a view, we would probably find that ‹both› the actions under consideration (equations I and II, p. 232) must proceed ‹simultaneously›. The second one would have the advantage of enormously greater concentrations of the reacting components, ‹e.g.› of the complex ion; the first one would, probably, be found to have the advantage of an enormously greater velocity constant. The actual velocities of the two reactions have never been measured[472] and no final explanation of the relations can be offered. The problem is a very important one, involving the whole question of the mode of ionic action (‹cf.› Chap. V, especially p. 83).

Aside from the theoretical value of the problem that has been raised, the question of immediate moment to us, from the point of view of analytical chemistry, is the question whether such conclusions would invalidate, in any way, the use we have made of the theory of complex ions, in elucidating the question of the precipitation and nonprecipitation of salts of simple ions from solutions of their complex ions.

The existence of a precipitate in contact with a solution is a question of a ‹condition› of ‹equilibrium›; the question raised, as the result of Haber's calculations, deals simply with the ‹problem of the path, the mechanism by which equilibrium is reached›, but the answer to it ‹does not affect the conditions, on which the maintenance of equilibrium depends›. All the conclusions, drawn in our discussions of precipitation from solutions of complex ions, are concerned with ‹final conditions for equilibrium›, ‹i.e.› with the conditions under which a ‹precipitate can exist›, and not with the mechanism of its formation. The conclusions reached are valid, therefore, irrespective of what the decision may ultimately be in the question, whether the simple ions alone are acted upon, when their salts are precipitated, or whether the complex ions are also immediately concerned in the action. The precipitation of silver chloride from an ammoniacal solution[473] may serve to illustrate this point.

In the first place, the precipitation of silver chloride from an ammoniacal solution, say by sodium chloride, may be considered to be the result of the direct interaction of chloride ions with the small quantity of silver ions present, ‹the complex serving only to renew the supply of silver ions›, as the latter are removed from solution, by the precipitation. The course of the action would be expressed by the equations

[Ag(NH_{3})_{2}]Cl ⇄ [Ag(NH_{3})_{2}^{+}] + Cl^{−} ⇄ 2 NH_{3} + Ag^{+} + Cl^{−} ⇄ AgCl + 2 NH_{3}. (1)

AgCl ⇄ AgCl ↓

When the precipitation is ended and equilibrium established, a trace of silver chloride is in solution, in contact with the precipitate, and, according [p236] to the principle of the solubility-product, we must have [Ag^{+}] × [Cl^{−}] = K_{AgCl}. Bodländer's experiments,[474] on the solubility of silver chloride in ammonia, prove that this relation is in perfect agreement with the facts. For the silver-ammonium-ion, the free ammonia and the silver-ion present in the solution, we must have the relation [Ag^{+}] × [NH_{3}]^2 / [Ag(NH_{3})_{2}^{+}] = K_{Instab. Const.}. This relation, according to the experimental evidence, is also found to hold.

Now, we might, on the other hand, assume that the primary or main action, leading to the precipitation of silver chloride, is the interaction of the chloride ions ‹with the complex ions›, rather than with silver ions. Silver-ammonium chloride, [Ag(NH_{3})_{2}]Cl, might first be formed, for instance, and then decompose ‹directly› into silver chloride and ammonia. This is the simplest assumption we can make for this kind of action and is sufficiently illustrative of any kind of direct action between the chloride ions and the complex ions. The path of the action would then be expressed by the equations

[Ag(NH_{3})_{2}^{+}] + Cl^{−} ⇄ [Ag(NH_{3})_{2}]Cl ⇄ 2 NH_{3} + AgCl ⇄ 2 NH_{3} + Ag^{+} + Cl^{−}. (2)

AgCl ⇄ AgCl ↓

It is clear, from a comparison of this series of equations with equations (1), that they represent the same reversible reactions in a somewhat different order. ‹Since equilibrium conditions for any reversible reaction› (‹e.g.› for A + B ⇄ C + D) ‹are independent of the order in which the components› (‹e.g.› A, B, C, D) ‹are brought into the system› (p. 94), the difference of order, indicated by equations (1) and (2), cannot affect the final condition of equilibrium in the system under discussion. For instance, since we again have silver chloride in contact with its saturated solution, we again must have [Ag^{+}] × [Cl^{−}] = K_{AgCl}, and ‹the experimental confirmation› of this relation (and similarly of the relation [Ag^{+}] × [NH_{3}]^2 / [Ag(NH_{3})_{2}^{+}] = K) ‹agrees as well with this second path of the action as with the first›. Conversely, since the path, by which the equilibrium is reached, does not affect the condition of equilibrium, it is perfectly legitimate to draw conclusions from equilibrium constants, ‹without assuming to know anything at all about the path by which the condition is reached›.[475]

For analytical work, the vital point is the ‹ultimate condition of equilibrium, which determines whether a precipitate may exist and be formed in a given system or not›. The instability constants of the complex ions and the solubility-product constants of precipitates are the constant factors involved in the ultimate conditions for equilibrium, and they do not depend on the path by which equilibrium is reached. Consequently, we find that the application of [p237] the theory of complex ions to analytical problems of precipitation has been in no wise invalidated by the problems presented by Haber. The theory forms now, as before, in fact, the best quantitative basis for the expression of the experimental results. The stability constants, and the concentrations of the components used, determine the limiting concentrations in which a given metal ion is capable of continued existence, and determine, therefore, the question whether an ionogen, of a given solubility, is capable of existence as a solid phase in a given system.

«The Structure of Complex Ions.»—The ability of ammonia to form complex ions with simple metal ions is commonly ascribed to the unsaturated condition of ammonia (see p. 65). It is interesting to recall the fact, that the marked power of the cyanide-ion to form complexes of extraordinary stability, is also associated with a similarly unsaturated condition of the cyanide-ion (p. 66). According to the results of Nef's researches,[476] we have, in hydrocyanic acid and the cyanides, unsaturated or bivalent carbon; potassium cyanide, for instance, has the structure K—N=C<. The two free valences of the carbon atom may, according to the electrical theory of valence, be again considered to consist of one negative and one positive charge. The possibility of the formation of complexes is then self-evident, and we can readily see, how silver cyanide, Ag—N=C±, should absorb cyanide-ion,[477] ∓C=N^{−}, and form a complex (Ag—N=C=C=N^{−}) or Ag(CN)_{2}^{−}, whose potassium salt would be potassium argenticyanide, K[Ag(CN)_{2}]. For the potassium salt K_{2}Ag(CN)_{3}, of the second complex ion[478] [Ag(CN)_{3}^{2−}] of silver and cyanogen, the most likely structure is

Ag—N=C—C=N—K. \ / C=N—K

The other complex cyanide ions, ferrocyanide, ferricyanide, cobalticyanide, etc., are considered to have structures entirely similar to those given to the argenticyanide ions.[479]

«Complex Halide, Sulphide, Oxide and Oxonium Ions.»—In conclusion, there are other elements besides nitrogen (in ammonia and its derivatives) and carbon (in cyanides), which form complex ions with simple ions; notably the halogens form such complexes. Chloroplatinic acid, H_{2}PtCl_{6}, and its salts (Lab. Manual, ‹q. v.›), fluorosilicic acid, H_{2}SiF_{6}, potassium-mercuric iodide, [p238] KHgI_{3} and K_{2} HgI_{4},[480] which forms a most sensitive reagent for the detection of traces of ammonia,[481] are instances of complexes of the halogens that are of importance in analysis. It is worthy of note that the most likely structure[482] for these compounds, ‹e.g.› Cl_{2}=Pt=(Cl=Cl—H)_{2}, bears a very striking analogy to the structures frequently assigned to the cyanide and ammonia complex ions. Oxygen and sulphur form complex ions, of great stability, with many elements, and we shall presently have occasion to discuss in detail some of the complex ions formed by sulphur. All of the oxygen acids may be treated as containing complex ions of oxygen and some other element, and their instability constants[483] are factors in determining their chemical behavior. For instance, such is the case, most likely, for their behavior as oxidizing and reducing agents (see Chapter XVI). The unsaturated condition of oxygen in water, (H_{2}O±), makes possible, also, the formation of complex ions, [(H_{2}O)_{‹x›}Me]^{+}, etc., called oxonium ions and comparable with metal-ammonium ions. They form a most inviting field for rigorous investigation. It is altogether probable that the hydrogen-ion is intimately related, in aqueous acid solutions, to the complex oxonium-ion, [(H_{2}O)_{‹x›}H]^{+}, comparable with the ammonium-ion, (NH_{3}H)^{+}, and, possibly, the greater part of the hydrogen-ion, in aqueous solutions, exists in this form of combination.[484]

«Complex Ions of Organic Oxygen Derivatives.»—A further group of complex ions, derived from organic derivatives of oxygen, are of particular importance in analytical work. Many organic compounds, such as sugars, glycerine, tartrates, citrates, interfere, more or less, with the precipitation of metal hydroxides and certain of their salts. For instance, the addition of cane sugar or of rochelle salt (sodium potassium tartrate) to a solution of [p239] cupric sulphate prevents the subsequent precipitation of cupric hydroxide by alkali (‹exp.›). In place of a precipitate of the hydroxide, a clear, intensely blue, solution is formed. In an analogous way, the same substances and similar compounds interfere with the precipitation of the hydroxides of aluminium and chromium, and since aluminium and chromium should be precipitated as hydroxides in systematic analysis (Chap. X), the presence of such organic compounds must be most carefully considered, to avoid error.[485] The precipitation of moderately difficultly soluble salts, such as phosphates, is also rendered, appreciably, more difficult. Only extremely insoluble salts, such as the sulphides of the arsenic, copper and zinc groups, are precipitated, from solutions of organic substances of the character indicated, without any appreciable interference.[486]

These relations clearly recall the characteristic behavior of ammoniacal and cyanide solutions, in which complex ions are formed, and the interference of the organic compounds with precipitation is of a similar nature—complex ions are formed by metal ions with these organic compounds, and the complexes are, in many instances, sufficiently stable to reduce the concentrations of the metal ions to the point, where only very difficultly soluble salts can be precipitated.

The relations may be illustrated by the discussion of the complex formed by the cupric-ion with tartrates. The structure of sodium tartrate is expressed by NaO_{2}C—CH(‗OH‗)—CH(‗OH‗)—CO_{2}Na. The underscored hydroxide groups ‗OH‗ are known in organic chemistry as ‹alcohol groups›.[487] Now, alcohols resemble water in very many properties and, among others, in the capacity to form metal derivatives or ‹alcoholates›, in which the hydrogen (ion) of the hydroxide group is replaced by metal ions. The alcoholates correspond, thus, to the metal hydroxides, which are the analogous [p240] derivatives of water. Exactly as there is a vast difference in the readiness with which the various metal hydroxides, or bases, ionize, many of them being only slightly ionizable (the weakest bases), so certain alcoholates are much less readily ionizable than others. The alkali alcoholates are most readily ionized.

When sodium tartrate is mixed with an excess of sodium hydroxide, some of the ‹readily ionizable› sodium salt of the ‹alcohol› groups of the sodium tartrate is formed and we have:

(CHONa)_{2}(CO_{2}^{−})_{2} + 2 Na^{+} ⇄ (CHO^{−})_{2}(CO_{2}^{−})_{2} + 4 Na^{+}.

When cupric sulphate is added to this mixture, a ‹slightly ionizable complex cupri-tartrate-ion› is formed by the union of the cupric-ion with the "alcoholate-tartrate-ion":

(CHO^{−})_{2}(CO_{2}^{−})_{2} + Cu^{2+} ⥂ [(CHO)_{2}Cu](CO_{2}^{−})_{2}.

The complex ion is not perfectly stable and so the action is a reversible one, as indicated in the equation. The greater portion of the copper, however, is present ‹as part of the complex negative ion› of cupric-tartaric acid and its salts. This may be demonstrated by subjecting the solution to electrolysis in a U-tube (p. 45). It is readily seen (‹exp.›) that ‹a deep blue ion›, obviously containing copper, ‹migrates to the positive pole›.[488] The concentration of cupric-ion is so small that its hydroxide and its phosphate are not precipitated from the solution by the addition, respectively, of alkali or of a soluble phosphate (‹exp.›). Cupric sulphide, however, is so insoluble that it may be precipitated completely from the solution by the addition of a sulphide (‹exp.›), the concentration of cupric-ion being much smaller in the saturated solution of the sulphide than in the solution of sodium cupri-tartrate.

Citrates, sugars, glycerine, contain alcoholic groups of the same nature as found in the tartrates, and they are capable of forming similar complexes, or little ionizable ‹alcoholates›, with metal ions.

Certain organic acids, which contain no alcohol groups,[489] are [p241] also capable of forming fairly stable complexes with metal ions: thus, acetates form a complex with lead-ion, that is sufficiently stable to render lead sulphate, which is difficultly soluble in water, readily soluble in ammonium acetate solution[490] (‹exp.›). Soluble oxalates readily combine with ferric, ferrous, cupric and other oxalates and interfere, more or less, with the detection of the metal ions, as the result of complex formations.

All of these complexes are ‹decomposed› rather readily ‹by the addition of strong acids›, whose hydrogen-ion breaks up the complex ions, by suppressing the anions[491] of the much weaker organic acids and alcohols. Consequently, these organic compounds do not interfere with tests which may be carried out in strongly acid solution. For instance, the addition of potassium ferrocyanide to a solution of ammonium ferrioxalate (NH_{4})_{3}Fe(C_{2}O_{4})_{3}, to which an excess of ammonium oxalate has been added, gives only a slight indication of the presence of ferric-ion (a greenish blue solution is obtained); when hydrochloric acid, in excess, is added to the mixture, Prussian blue, ferric ferrocyanide, is immediately precipitated in quantity (‹exp.›).

FOOTNOTES:

[425] The naming of the complex ions, which ammonia forms with metal ions, has not yet been satisfactorily settled. English writers frequently speak of "ammonio-argentic" ion and "ammonio-argentic" nitrate. German writers speak of "Silber-ammoniak" ion (Abegg, ‹Handb. der anorg. Chem.›, II, 728), which would read "silver-ammon‹ia›" ion in English terms. The terminology "silver-ammoni‹um›" ion, used in this book, is based on the idea, that all these complex ions are essentially ‹of the same nature› as the well-known ‹ammonium-ion›, NH_{4}^{+}, the positive charge being, almost certainly, carried by ‹nitrogen› in these complex ions, as it is in ammonium-ion. The latter is a ‹complex ion of ammonia› with ‹hydrogen›-ion. The name "ammonio-argentic" ion does not bring out this close relationship and puts the emphasis on the silver, which is probably little concerned in the reactions of the complex as such. The names "silver-ammon‹ia›" ion and "silver-ammon‹ia›" nitrate sound badly and do not emphasize the relation to ammoni‹um›, potassi‹um›, sodi‹um› and similar positive ions and their salts. The term "‹ammonium›" is, for the reasons given, used here in a ‹generic› sense for all complex ions of ammonia with simple metal ions (such as H^{+}, Ag^{+}, Cu^{2+}, Zn^{2+} etc.), and the number of ammonia molecules, entering into the composition of a complex ion, is not indicated in the names. A similar nomenclature has long been in vogue, and has worked well, for the complex ions of metal ions with the cyanide-ion (see below). We speak of ferro‹cyanide›, Fe(CN)_{6}^{4−}, argenti‹cyanide›, Ag(CN)_{2}^{−} and Ag_{2}(CN)_{3}^{2−}, etc., without indicating the number of cyanide groups, CN, in the complex, and we use the same generic ‹ending› "cyanide" as is used to designate the simple cyanide ion, ‹e.g.› to designate the ion formed from potassium cyanide, KCN ⇄ K^{+} + CN^{−}.

[426] The hydroxide-ion appears with the same coefficient, 1, on both sides of the equilibrium equation and need not be included in the mathematical statement; it would appear as a factor in both terms of the ratio given and would cancel out.

[427] Bodländer and Fittig, ‹Z. phys. Chem.›, «39», 602 (1903).

[428] Bonsdorff, ‹Ber. d. chem. Ges.›, «36», 2324 (1903).

[429] It is also frequently called the ‹dissociation constant› of the complex ion, indicating the tendency of the complex ion to dissociate into its components.

[430] Two independent experimental methods were used and gave concordant results—one having as its basis the solubility of silver salts (chloride, bromide), the other the electrolytic potentials of silver against ammoniacal silver solutions (see Chap. XV).

[431] ‹Bull. de la Soc. Chim. de Paris›, (3), «13», 386 (1895).

[432] We may consider the salt to be ionized to about the same extent as ammonium or potassium nitrate in 0.05 molar solutions, or, approximately, 87%. If we call ‹x› the concentration of silver-ion, formed by the decomposition of the silver-ammonium-ion, then 2 ‹x› is the concentration of the free ammonia, and (0.05 × 0.87 − ‹x›) is the concentration of the complex ion. Since ‹x› is a small number in comparison with 0.0435, we may write, with sufficient accuracy for our purposes,

[NH_{3}]^2 × [Ag^{+}] / [(NH_{3})_{2}Ag^{+}] = (2 ‹x›)^2 × ‹x› / 0.0435 = 6.8E−8.

Then, ‹x› = [Ag^{+}] = 0.0009.

[433] Kohlrausch and Holborn, ‹loc. cit.›, p. 202.

[434] The dilution of the silver-ammonium nitrate (10 c.c. to 11 c.c.) and the decrease in ionization due to the added salt reduce the concentration of silver-ion from 0.0009 to 0.00085. [Ag(NH_{3})_{2}^{+}] = (0.05 × 10 / 11) × 0.8 = 0.0364 and 4 ‹x›^3 = 6.8E−8 × 0.0364 (see footnote, p. 220). Then ‹x› = [Ag^{+}] = 0.00085.

[435] Thiel (‹cf.› Bodländer and Fittig, ‹loc. cit.›). The solubility given in the table at the end of the laboratory manual refers to 18°. The constant for the complex ion was determined at 25°.

[436] The combined concentration of the salts is 0.055 and their degree of ionization may be taken as 87%, the same as the degree of ionization of 0.05 to 0.06 molar KNO_{3}. Then [Cl^{−}] = (0.1 × 1 / 11) × 0.87 = 0.008. [Ag(NH_{3})_{2}^{+}] = (0.05 × 10 / 11) × 0.87 = 0.04 and ‹x› = [Ag^{+}] = 0.00089 (see the method of calculation in the footnote, p. 220).

[437] The strong solution of ammonia is used in order to avoid unnecessary dilution, and in the experiment, described below, the dilution of the liquids by the added ammonia is considered negligible.

[438] The following solubilities have been determined at 25°:

[Ag^{+}] × [Cl^{−}] = 2E−10; [Ag^{+}] = 1.4E−5.

[Ag^{+}] × [I^{−}] = 1E−15; [Ag^{+}] = 1E−8.

[Ag^{+}]^2 × [S^{2−}] = 4E−50; [Ag^{+}] = 4.3E−17.

[439] 100 c.c. molar ammonia dissolves at 25° only 0.6 milligram of silver iodide (Bodländer, ‹loc. cit.›, p. 606).

[440] Fresenius, ‹Qualitative Analysis›, p. 378.

[441] In regard to Cu(NH_{3})_{4}^{2+} see Locke and Forssall, ‹Am. Chem. J.›, «31», 268, 297 (1904), and Dawson, ‹J. Chem. Soc.› (London), «89», 1674 (1906).

[442] Euler, ‹Ber. d. chem. Ges.›, «36», 3403 (1903).

[443] See footnote, p. 212.

[444] See pp. 165, 210 and 213.

[445] The acid HAg(CN)_{2}, corresponding to the salt, is crystallizable and is a strong acid. It is largely decomposed, by water, into silver cyanide and hydrocyanic acid.

[446] See the experiments described on pp. 45 and 89.

[447] In solutions containing an excess of potassium cyanide greater than 0.05 molar, the salt K_{2}[Ag(CN)_{3}] is formed. The dissociation or instability constant for the complex ion Ag(CN)_{3}^{2−} is 1E−22.

[448] ‹Z. anorg. Chem.›, «39», 222 (1904).

[449] The solubility-product constant for silver chloride at 25° is 2E−10. If the concentration of chloride-ion be made 1.0 by the addition of potassium chloride to a 0.05 molar solution of KAg(CN)_{2}, then the concentration of silver-ion, necessary for the precipitation of the chloride, would be K_{S.P.} / [Cl^{−}] = 2E−10 gram-ion. Neglecting the fact that the complex salt is not completely ionized and putting [Ag(CN)_{2}^{−}] = 0.05, and calling ‹x› the concentration of the cyanide-ion just necessary to prevent the precipitation of the chloride, we have:

[Ag^{+}] × [CN^{−}]^2 / [Ag(CN)_{2}^{−}] = 2E−10 × ‹x›^2 / 0.05 = 10^{−21}.

We find ‹x› = 5E−7 mole, or approximately 0.03 milligram potassium cyanide (cyanide-ion) per liter. This minute quantity of free cyanide, if not originally present in the solution used, would be formed by the liberation of potassium cyanide from the complex (according to KAg(CN)_{2} + KCl → AgCl + 2 KCN) as soon as 2.5E−7 mole, or 0.036 milligram, of silver chloride per liter have been formed, a quantity too small to be perceptible.

When potassium cyanide is added to a silver nitrate solution, the precipitate formed is found to be silver argenticyanide, Ag[Ag(CN)_{2}], the silver salt of the extremely stable complex, rather than the simple salt, silver cyanide, AgCN [‹cf.› Bodländer, ‹Z. anorg. Chem.›, «39», 223 (1904)]. Ag[Ag(CN)_{2}] is even less soluble than silver chloride, the solubility-product constant for [Ag^{+}] × [Ag(CN)_{2}^{−}] being 2.25E−12. An excess of only 2E−6 mole, or about 0.15 milligram, of potassium cyanide (cyanide-ion) per liter is sufficient to prevent the precipitation of silver cyanide (silver argenticyanide) from a 0.1 molar solution of KAg(CN)_{2}, and, conversely, at least this minute excess of potassium cyanide is used in the preparation of a clear 0.1 molar solution of KAg(CN)_{2}, by the addition of potassium cyanide to silver nitrate, until the silver cyanide, first precipitated, is just redissolved (Bodländer, ‹loc. cit.›). This excess, as just explained, is more than sufficient to prevent the precipitation of silver chloride from the cyanide solution, even by a large excess of potassium or sodium chloride. Unless one takes into account, in the manner indicated, this marked influence of a minute excess of cyanide-ion in decidedly reducing the concentration of silver-ion in these solutions, one could be led, wrongly, to infer from the value of the instability constant of the complex ion and that of the solubility-product constant of silver chloride, that silver chloride should still be precipitated by the addition of sodium chloride to a solution of KAg(CN)_{2}.

[450] For this reason potassium cyanide is an excellent cleansing agent for stained silverware (sulphide stains), and, since it is an intense poison, cleaning powders should be examined for it.

[451] For the quantitative relations see Lucas, ‹Z. anorg. Chem.›, «41», 192 (1904).

[452] See Bodlaender, ‹Z. phys. Chem.›, «39», 597 (1902); ‹Ber. d. chem. Ges.›, «36», 3933 (1903).

[453] Potassium cyanide is a powerful reducing agent (see p. 89) and is readily oxidized to potassium cyanate. The action, presumably, takes the following course (see Chapters XIV and XV):

2 Cu^{2+} + 4 HO^{−} + KNC^{±} → 2 Cu^{+} + 4 HO^{−} + KNC^{2+} → 2 Cu^{+} + 2 HO^{−} + KNCO + H_{2}O.

[454] Put [Cu^{+}] = ‹x›, and [CN^{−}] = 3 ‹x›, and, neglecting the degree of ionization, [Cu(CN)_{3}^{2−}] = 0.1, ‹x› being so small that it need not be subtracted from 0.1. Then ‹x› × (3 ‹x›)^3 = 0.1 × 0.5E−27, and ‹x› = 3.7E−8.

[455] Treadwell and Girsewald, ‹Z. anorg. Chem.›, «38», 92 (1904).

[456] Euler, ‹Ber. d. chem. Ges.›, «36», 3404 (1903).

[457] Putting [Cd^{2+}] = ‹y›, we have ‹y› × (4 ‹y›)^4 = 0.1E−17, and ‹y› = 8E−5. In view of the values of the constants, a ‹small› excess of potassium cyanide will have a much smaller suppressing effect on the cadmium-ion than on the cuprous-ion. For the excess [CN^{−}] = 0.01, [Cu^{+}] = 5E−23, [Cd^{2+}] = 10^{−10} as compared with [Cu^{+}] = 4E−8 in a 0.1 molar solution of the salt K_{3}[Cu(CN)_{3}], and with [Cd^{2+}] = 8E−5 in a 0.1 molar solution of K_{2}Cd(CN)_{4}.

[458] Bromine water is a convenient agent for oxidizing cobaltous to cobaltic ions (see Chapter XV).

[459] The heavy arrows «→» [See Transcriber's Note] indicate the main course the reversible actions take, ‹under the influence of the reagents used›. Since the oxidation of nickel-ion by bromine is accomplished only after the bromine has oxidized any excess of cyanide used—potassium cyanide is a powerful reducing agent (p. 89)—the addition of cyanide, beyond a very small excess, must be avoided (see laboratory instructions).

[460] ‹E.g.› for the precipitation of silver, copper, nickel, cobalt and certain other metals from cyanide solutions; ‹cf.› Edgar F. Smith, ‹Electro-Analysis› (1907).

[461] ‹Z. phys. Chem.›, «43», 705 (1903). ‹Vide› also Haber, ‹Z. Elektrochem.›, «11», 847 (1905).

[462] 2 Fe^{2+} + Hg^{2+} → 2 Fe^{3+} + Hg ↓. If the treatment with mercuric oxide is carried to completion the final products of the reaction are ferric hydroxide, mercuric cyanide, mercury and potassium hydroxide (Rose, ‹Z. anal. Chem.›, «1», 300 (1862)):

2 K_{4}[Fe(CN)_{6}] + 7 HgO + 7 H_{2}O → 3 Hg[Hg(CN)_{4}] + 8 KOH + 2 Fe(OH)_{3} ↓ + Hg ↓

[463] Bodlaender, ‹loc. cit.›

[464] The solubility-product constant of silver sulphide at 25° is 0.5E−51; for [S^{2−}] = 0.8E−5 (p. 202), we would have in the present case [Ag^{+}]^2 × [S^{2−}] = 2E−46, which is greater than the constant. ‹Vide› quantitative data by Lucas, ‹loc. cit.›

[465] ‹Z. f. Elektrochem.›, «10», 433 and 773 (1904).

[466] See footnote 4, p. 225.

[467] Ostwald, ‹Allgem. Chemie›, Vol. II, part 1, p. 881 (1893).

[468] Haber, ‹loc. cit.›

[469] Then T_{Decomposition} = 10^{−4} × 10^{22} = 10^{18} seconds, and, since there are 3.15E7 seconds in a year, T_{Decomposition} = 3E10 years.

[470] See p. 42.

[471] Since there are still smaller "instability constants" than that of the argenticyanide-ion (‹e.g.› for the gold-cyanide-ion the constant is 1 / 10^{28}), there is a large margin of safety for the plausibility of Haber's argument. For full details, his articles (‹loc. cit.›), and the discussion (by Abegg, Bodlaender, Danneel, ‹ibid.›) aroused by them should be consulted.

[472] See Le Blanc and Schick, ‹Z. phys. Chem.›, «46», 213 (1903), on measurements of the speed of ionic actions. The values obtained agree, in general, with Haber's contention.

[473] The concentrations of silver-ion are large, in comparison with those in cyanide solution, and the action is, most likely, essentially an ionic one; but the argument applies with equal force to cyanide systems.

[474] ‹Loc. cit.›

[475] An equilibrium constant, as we have seen, is a ‹ratio› of velocity constants of balanced reactions (pp. 94, 233) and involves therefore at least ‹two unknown› velocity constants. By determining the actual ‹rate› of ‹change› with known concentrations of reacting components, ‹i.e.› by determining the velocity constants themselves, rather than their ratio, a definite conclusion as to the mechanism or path of a given reaction can often be reached (see p. 80).

[476] ‹Proceedings Amer. Academy›, 1892.

[477] In the absence of any added cyanide, it combines with itself. Silver cyanide, according to Bodländer's results, is, in saturated solutions, chiefly (AgCN)_{2} or Ag[Ag(CN)_{2}], ‹i.e.› Ag—[N=C=C=N—Ag].

[478] See p. 225, footnote 4.

[479] Werner has developed quite a different theory of the structure of complex ions. (‹Cf.› Nernst, ‹Theoretical Chemistry›, p. 374 (1904).)

[480] Sherrill, ‹Z. phys. Chem.›, «43», 721 (1903).

[481] In Nessler's reagent, Fresenius' ‹Qualitative Analysis›, p. 141.

[482] ‹Cf.› Remsen, ‹Am. Chem. J.›, «11», 291 (1899); «14», 81 (1892) («Stud.»).

[483] For instance, for arsenious acid we have

3 H^{+} + AsO_{3}^{3−} ⇄ H_{3}AsO_{3} ⇄ As^{3+} + 3 HO^{−}

and, therefore, [As^{3+}] × [HO^{−}]^3 / ([AsO_{3}^{3−}] × [HO^{+}]^3) = ‹k›_{1}. Since [H^{+}] = ‹k′›_{HOH} / [HO^{−}] (p. 176), we have further, [As^{3+}] × [HO^{−}]^6 / [AsO_{3}^{3−}] = ‹k›_{2}. And since we may derive the relation [HO^{−}]^2 = ‹k›_{3} × [O^{2−}], by considering the primary and the secondary ionization of water (see pp. 246, 278), we have, finally, [As^{3+}] × [O^{2−}]^3 / [AsO_{3}^{3−}] = ‹K›. The constants for the primary and the secondary ionization of water are included in the value of ‹K›.

[484] Fitzgerald and Lapworth, ‹J. Chem. Soc.› (London), «93», 2163 (1908); Lapworth, ‹ibid.›, 2187. ‹Vide› also Franklin on the characteristics of the NH_{4}^{+} ion in liquid ammonia, ‹Am. Chem. J.›, «23», 305 (1900).

[485] See the laboratory instructions, in regard to the precautions used, to avoid errors from this source.

[486] On the other hand, ‹colloidal› organic substances, such as casein, glue or albumen, interfere with the precipitation of even the most insoluble sulphides, by producing ‹colloidal suspensions› of the latter (see Chap. VII; ‹cf.› Müller, ‹Allgemeine Chemie der Kolloide›, p. 56 (1907)).

[487] In alcohols the hydroxide group is held by a carbon atom, whose remaining valences are satisfied by hydrogen or carbon atoms, as in ordinary or ethyl alcohol, H_{3}C—CH_{2}(OH).

[488] Küster, ‹Z. Elektrochem.›, «4», 117 (1897).

[489] The most common organic acids contain the acid group —CO(‗OH‗), as in acetic acid, CH_{3}CO(‗OH‗). The hydroxide group ‗OH‗ of the alcohols, ‹e.g.› in CH_{3}CH_{2}(‗OH‗), is still found in these organic acids, but its tendency to form hydrogen-ion is very much increased by the replacement of two hydrogen atoms of the alcohols by the oxygen atom, as found in the acids. To a certain degree, the properties of the alcohol hydroxide are maintained in the properties shown by the acid hydroxide group. Thus, the organic acids, on the whole, are still rather weak acids, and their salts, in many instances, are appreciably less ionizable than the salts of strong inorganic acids. The organic acids, further, may combine, to a certain extent, with water and thus form hydrates (‹e.g.› CH_{3}COOH + H_{2}O ⇄ CH_{3}C(OH)_{3}) containing a number of hydroxide groups: the second and third hydroxide groups must have a very much smaller tendency to form hydrogen ions and ionizable salts, than has the first hydroxide group (p. 102), and the former, thus show, more nearly, the behavior of alcoholic hydroxide groups. Finally, organic acids also show a tendency to combine with themselves, forming complex acids (‹e.g.›, (CH_{3}COOH)_{2} or CH_{3}C(OH)_{2}OOCCH_{3}), from which complex salts may be derived, which may be little ionizable. The power of the organic acids to form complex ions—which they share with many inorganic acids—is most likely intimately connected with the relations described.

[490] Lead acetate, itself, is less ionized than most salts and this property contributes to the solubility of lead sulphate in acetate solutions. (‹Cf.› Noyes and Bray, ‹loc. cit.›)

[491] On p. 231, the same effect is discussed, in detail, in connection with the ferricyanide-ion.

[p242]