Similarly, for the basic ionization,378 Al(OH)3 ⇄ (AlO)+ + HO− + H2O, we have
The formation of traces of nonionized (basic) aluminium aluminate would satisfy the equilibrium requirements for AlO+ + AlO2− ⇄ AlO(AlO2), since the aluminate, like other aluminates, is presumably readily ionizable in aqueous solutions. Aluminium hydroxide, as a base and as an acid, would yield in the first moment greater concentrations of the hydroxide and hydrogen ions than would satisfy the equilibrium constant for water (p. 176); the excess of these ions must combine to form water, until the product of their concentrations is equal to the ionization constant of water. The neutralization of these first quantities of hydrogen and hydroxide ions would destroy the momentary condition of equilibrium between aluminium hydroxide and its ions and would lead to its further ionization, both as a base and as an acid, and to the solution of some aluminium hydroxide (see the above equilibrium equations). However, since AlO+ and AlO2− remain practically uncombined and therefore accumulate in the solution, the concentrations of the hydroxide and hydrogen ions formed grow smaller and smaller; for an increasing excess of the ion AlO+ will allow only smaller and smaller values for [HO−], according to the equilibrium equation for KBase, and, similarly, an increasing excess of the ion AlO2− will permit [H+] to reach only smaller and smaller values, according to the equilibrium equation for KAcid. When the values for [HO−] and [H+] have in this way become small enough to make [HO−] × [H+] = KHOH, equilibrium is reached. It is evident that in such a solution, in the condition of equilibrium, [HO−] is not equal to [AlO+], as it would ordinarily be, according to the ionization equation Al(OH)3 ⇄ AlO+ + HO− + H2O, but is much smaller. Similarly, [H+] is much smaller than [AlO2−].
Just how much aluminium aluminate must be formed by a self-neutralization of the amphoteric hydroxide will depend on the values for KBase and KAcid and on the solubility of aluminium hydroxide (nonionized Al(OH)3). The two equilibrium equations may be combined:
| [AlO+] × [AlO2−] × [H+] × [HO−] | = KBase × KAcid. |
| [Al(OH)3]2 |
Since [H+] × [HO−] = KHOH, and since [AlO+] and [AlO2−] may be taken to represent each the concentration of the practically completely ionized aluminium aluminate AlO(AlO2), we have379
| [Alum. Aluminate]2 | = | KBase × KAcid | , |
| [Alum. Hydroxide]2 | KHOH |
or
| [Alum. Aluminate] | = √ ( | KBase × KAcid | ). |
| [Alum. Hydroxide] | KHOH |
It is clear, that the smaller the ionization constants KBase and KAcid are, and the smaller the solubility of nonionized aluminium hydroxide [Alum. Hydroxide] is, the smaller must be the concentration of the aluminate formed to satisfy the conditions for equilibrium.
Aluminium hydroxide is a typical amphoteric hydroxide, and the relations developed may be applied, mutatis mutandis, to the conditions of equilibrium for analogous amphoteric hydroxides, such as zinc, lead, chromic hydroxides, and so forth. Salt formation or self-neutralization will depend, in every instance, on the strength of the base and the acid formed, and on the solubility of the hydroxide.380
With the aid of the preceding considerations the analytical reactions of aluminium, which are used to separate it from other elements and to identify it, may be readily understood. They will be discussed in connection with the analysis of the "Aluminium and Zinc Groups."
Only one member of this group, zinc, forms an amphoteric hydroxide and advantage is taken of this in identifying zinc.
The members of the aluminium group form hydroxides, which are much weaker bases than are the hydroxides of the bivalent group just considered. Their salts with strong acids are considerably hydrolyzed and react strongly acid, and their salts with very weak acids, like carbonic acid and hydrogen sulphide, are decomposed so readily by water, that only ferric sulphide is capable of existence in its presence. When the sulphide, Al2S3, prepared by heating aluminium with sulphur, is added to water, it is totally decomposed into the hydroxide and hydrogen sulphide (p. 186); and if aluminium chloride is treated with ammonium sulphide in aqueous solution, aluminium hydroxide, and not its sulphide, is precipitated. The latter result may be interpreted in two ways, both of which, in the ultimate analysis, mean that hydrogen sulphide is too weak an acid to form a stable sulphide with aluminium hydroxide in the presence of water, the difficult solubility of aluminium hydroxide and the limited solubility of hydrogen sulphide being favoring factors (see p. 186). In a solution of aluminium chloride, the salt of a very weak base with a strong [p190] acid, more or less of the salt is hydrolyzed, and we have a condition of equilibrium as expressed in the equation AlCl3 + 3 H2O ⇄ Al(OH)3 + 3 HCl. The addition of ammonium sulphide to such a solution would neutralize the free hydrochloric acid, and the action would proceed to completion towards the right, hydrogen sulphide being liberated, by the action of the acid on the ammonium sulphide. As hydrogen sulphide is too weak an acid to combine, appreciably, with aluminium hydroxide, and as the latter is difficultly soluble, the hydroxide is precipitated. According to the degree of dilution, more or less of the hydrogen sulphide also escapes. Besides this interpretation of the precipitation of aluminium hydroxide under these conditions, we may also consider the following: any aluminium sulphide, formed the first moment, would remain largely ionized and would be immediately converted, by the ions of water, into aluminium hydroxide and hydrogen sulphide. The net result of the action is the precipitation of aluminium hydroxide and the evolution of hydrogen sulphide:
A similar result is obtained when the solution of a chromium salt is treated with a solution of ammonium sulphide. Only ferric hydroxide is capable of forming a sulphide, ferric sulphide, Fe2S3, which is precipitated when solutions of ferric salts are treated with ammonium sulphide.382
Ammonium sulphide will, consequently, precipitate aluminium and chromium hydroxides and ferric, ferrous, nickel, cobalt, manganese and zinc sulphides, from a solution of the chlorides of the metals.
Now, both the sulphides and the hydroxides of the alkaline earths and alkalies are sufficiently soluble not to be precipitated by ammonium sulphide, or by a mixture of it with ammonium hydroxide, if ammonium chloride be added to the mixture to prevent the precipitation of magnesium hydroxide (see p. 168), which is the least soluble of the hydroxides of the alkaline earth group. [p191] A mixture of ammonium sulphide, ammonium hydroxide and ammonium chloride will, therefore, precipitate the aluminium and zinc groups together, separating them from the alkaline earth and alkali groups.383
Aluminium Group: Fe2S3, Al(OH)3, Cr(OH)3.
Zinc Group: NiS, CoS, FeS, MnS,385 ZnS.
If such a precipitate is treated, in the cold, for a short time with quite dilute (1 to 1.2 molar) hydrochloric acid, all of the hydroxides and sulphides dissolve, excepting the greater part of the nickel and cobalt sulphides, which dissolve very much more slowly than do the other compounds. Advantage is taken of this fact, to separate these two elements from the remaining members of these groups, and if the treatment is carried out with care, the separation is usually satisfactory. In all cases, however, since it is a question of delayed solution only, at least traces, and sometimes considerably more than traces, of the sulphides of nickel and cobalt go into solution with the other compounds. No sacrifice of analytical accuracy is involved, if this possible loss is kept in mind and provision made for the later detection of these small quantities of nickel and cobalt.
The question of the slow solution, or apparent lack of solubility, of nickel and cobalt sulphides in dilute hydrochloric acid has formed an interesting problem for investigation. While nickel and cobalt sulphides are precipitated by ammonium sulphide, these sulphides, in common with those of all the other members of the zinc group, are not precipitated by hydrogen sulphide in the presence of a small excess of hydrochloric acid.386 We would have [p193]
as representing the condition of equilibrium, if we start with nickel chloride, hydrochloric acid and hydrogen sulphide; the amount of sulphide NiS, formed, is insufficient to supersaturate the solution and form a precipitate. In reversible reactions the final condition of equilibrium must be independent of the order in which components are mixed (p. 91), a conclusion which is borne out by experience. One should expect, then, that nickel sulphide, when treated with dilute hydrochloric acid, would dissolve and give nickel chloride, hydrogen sulphide and an excess of acid, and thus produce the same system, found to be in equilibrium, when one starts with the chloride, hydrogen sulphide and hydrochloric acid. As a matter of fact, the same condition of equilibrium is finally reached, only it is reached slowly,387 much more slowly than ordinarily in such cases, much more slowly, for instance, than with ferrous sulphide, hydrochloric acid and hydrogen sulphide (exp.). By taking advantage of this slow return to equilibrium and by working with the system during the process of slow change (collecting the undissolved nickel and cobalt sulphides on a filter), one can separate the sulphides of nickel and cobalt from the other components of the mixed precipitate, which dissolve much more rapidly.
When zinc chloride, which may be taken as a representative of the bivalent group, is treated with sodium carbonate, a difficultly soluble carbonate is precipitated, since zinc hydroxide, like the remaining bivalent hydroxides, is a sufficiently strong base to form a fairly stable carbonate.388 When ferric chloride, a representative of the trivalent group, is treated with a solution of sodium carbonate, ferric hydroxide, mixed with some basic ferric carbonate389 Fe2(OH)4CO3, is precipitated and carbon dioxide escapes (exp.). The trivalent hydroxides are too weak bases390 to form stable salts with so weak an acid as carbonic acid.
Since the bivalent metal ions are precipitated by sodium carbonate as carbonates and the trivalent ones as hydroxides, the reagent, obviously, cannot be used to separate the two groups. But barium carbonate is so little soluble in water that it will not precipitate manganous, zinc, nickel, cobalious and ferrous carbonates391 from solutions of their chlorides or nitrates. We have, for instance, ZnCl2 + BaCO3 ↓ ⥃ BaCl2 + ZnCO3. Barium carbonate has, however, the same effect on ferric chloride (exp.) and on the other chlorides of the trivalent group, as has sodium carbonate, i.e. it precipitates their hydroxides. By means of barium carbonate [p195] we can, therefore, precipitate the hydroxides of the aluminium group without precipitating the ions of the zinc group. The separation is carried out in a, practically, neutral medium (free carbonic acid in excess is evolved; barium carbonate alone, when treated with water, is slightly alkaline) and thus avoids the error of facilitating the precipitation of the bivalent metals in the shape of salts of the acidic forms of the trivalent metals, i.e. as aluminates, chromites, and so forth. Manganous salts are liable to oxidation to manganic salts, when exposed to the air, especially in alkaline, neutral or slightly acid solutions, and prolonged exposure of the barium carbonate mixture to the air may result in the precipitation of manganic hydroxide, Mn(OH)3, with the other trivalent hydroxides. Provision is made for its detection in the systematic analysis.
We have, in this instance, the case of a very weak, difficultly soluble acid, aluminium hydroxide, forming a salt with a weak, soluble base, ammonium hydroxide. The conditions determining the solubility of aluminium hydroxide in ammonium hydroxide, as an aluminate NH4AlO2, may be shown as follows: for the acid ionization of aluminium hydroxide, Al(OH)3 ⇄ AlO2− + H+ + H2O (p. 172); the solubility-product for a saturated solution is [AlO2−] × [H+] = KAc.S.P.. Further, from [H+] × [HO−] = KHOH, we find [H+] = KHOH / [HO−]. Then [AlO2−] = [HO−] × KAc.S.P. / KHOH, which shows that the solubility of aluminium hydroxide, as aluminate, is proportional to the concentration [HO−] of the hydroxide-ion in the solution. For NH4OH we have [NH4+] × [HO−] / ([NH3] + [NH4OH]) = 0.000,018 (p. 161), and consequently, [HO−] = 0.000,018 × ([NH3] + [NH4OH]) / [NH4+]. Then [HO−] is the smaller, the smaller the excess of ammonium hydroxide used (which is approximately equal to ([NH3] + [NH4OH])) and the greater the concentration [NH4+] of the ammonium-ion, i.e. of the added ammonium salt. The solubility of Al(OH)3, as aluminate, in ammonium hydroxide and ammonium chloride is, therefore, directly proportional to the excess of ammonium hydroxide, and indirectly proportional to the concentration of the ammonium salt present.392
For the sake of a certain simplicity in the result, we will, for the moment, consider aluminium hydroxide to ionize as an acid according to Al(HO)3 ⇄ AlO33− + 3 H+, which would resemble the basic ionization. Then we would have [AlO33−] × [H+]3 = K′Ac.S.P., and, using the relation [H+] = KHOH / [HO−], we have
Adding equations I and II we find
Aluminium hydroxide will be most completely precipitated when [Al3+] + [AlO33−] is a minimum, the values [Al3+] and [AlO33−] measuring the solubility of aluminium as aluminium-ion and as aluminate-ion. If we put [Al3+] + [AlO33−] = y and [HO−] = x, we can find the value x (the concentration of the hydroxide-ion) for which y is a minimum. We have y = KBas.S.P. × x−3 + x3 × K′Ac.S.P. × KHOH−3, and find, by means of the calculus,393 that y is a minimum, when x = +(KHOH3 × KBas.S.P. / K′Ac.S.P.)1/6.
If aluminium hydroxide were as strong an acid as it is a base, i.e. if KBas.S.P. = K′Ac.S.P., we would have, simply, x = [HO−] = ((1.2E−14)3)1/6 = √(1.2E−14) (at 25°), which is the concentration of the hydroxide-ion in pure water at 25° (p. 176). In other words, a perfectly neutral solution would then give us the conditions for as complete a precipitation as possible. But aluminium hydroxide is a stronger base than acid, KBas.S.P. > K′Ac.S.P., and consequently we find for x = [HO−] = (KHOH3 × KBas.S.P. / K′Ac.S.P.)1/6, a value somewhat greater than the concentration of the hydroxide-ion in pure water, i.e. we must use a slightly alkaline medium—which agrees with common practice. In other words, there is less danger of losing aluminium hydroxide in the form of aluminate, owing to the weaker acid character of the hydroxide, than there is of losing it in the form of aluminium-ion. The most favorable degree of alkalinity for the precipitation would depend on the relation of KBas.S.P.. and K′Ac.S.P..
The exact values for KBas.S.P. and K′Ac.S.P., the two solubility-product constants, and for the corresponding ionization constants, which would show the same ratio, are still not known. But, if, for the sake of an illustration, we take recourse to assumed values for these constants, we find that the solubility of aluminium, as aluminium-ion and as aluminate-ion, is, by calculation, as anticipated, a minimum for a solution, which contains the concentration of HO− calculated (for x) in the manner indicated above. And the further interesting conclusion is reached that this minimum loss of aluminium [p198] hydroxide would occur when [Al3+] = [AlO33−]—which would correspond to a saturated solution of aluminium aluminate, Al(AlO3).
When the ionization of aluminium hydroxide, as an acid, is considered to take place according to Al(OH)3 ⇄ AlO2− + H+ + H2O, which agrees best with its real behavior (p. 172), we can find, similarly, that [Al3+] + [AlO2−] is a minimum, when aluminium hydroxide is precipitated in such a way, that an excess x of the hydroxide-ion is used, and x = [HO−] = (3 KHOH × KBas.S.P. / KAc.S.P.)0.25,—where KAc.S.P. represents the solubility-product constant for [AlO2−] × [H+]. That a minimum loss of aluminium hydroxide would be suffered when the favorable excess of the hydroxide-ion (x) is calculated on the basis of the equation as given, may readily be seen by again assuming definite values for KBas.S.P. and KAc.S.P.. It also appears that this minimum loss394 of aluminium includes one-third as many Al3+ ions, as AlO2− ions—a relation corresponding, again, to a saturated solution of aluminium aluminate, Al(AlO2)3.
[354] When all three of the hydrogen atoms in the hydroxide are ionized, an aluminate ion, AlO33− is formed: Al(OH)3 ⇄ AlO33− + 3 H+. But, as in the case of other weak polybasic acids, a single hydrogen atom is far more readily ionized than are the remaining two (p. 102), and the ion Al(OH)2O−, which is formed by the primary ionization, readily loses water and forms the anhydride ion AlO2−. The most important aluminates are derivatives of this ion.
[355] See the table at the back of Smith's Inorganic Chemistry, or p. 149 of Remsen's Inorganic Chemistry.
[356] The displacement of hydrogen by a metal, like sodium, is the result of the displacement of the hydrogen-ion (see Chapters XIV and XV). The hydrogen-ion in fused sodium hydroxide is probably formed chiefly by the secondary ionization of the hydroxide-ion (HO− ⇄ H+ + O2−) (see Chap. XIII). We cannot have positive ions, Na+, with negative ions, O2−, without having some ions NaO−. (O2− + Na+ ⥂ NaO−), NaOH, undoubtedly, is much too weak an acid to form salts with bases in the presence of water. Such salts would be decomposed by water (see below, p. 180), as sodium oxide, indeed, is decomposed; we have Na─O─Na + HOH ⇄ 2 NaOH (see Chapter XIII for a detailed discussion of this action). These relations sufficiently account for the fact that salts of sodium hydroxide, in which it has the functions of an acid, are not commonly formed. (Cf. Abegg, Anorganische Chemie, II, (1) p. 247.)
[357] See J. J. Thomson, Corpuscular Theory of Matter, pp. 103–141.
[358] See Mendeléeff, Principles of Chemistry, I, 22 (1891), in regard to the rôle of "even" and "uneven" series in the system.
[359] In regard to the indications of the amphoteric character of stronger acids, see Chapter XV.
[360] An elaborate treatment of this problem is given by Walker, Z. phys. Chem., 49, 82 (1904), 51, 706 (1905).
[361] Kohlrausch and Heydweiller, Z. phys. Chem., 14, 317 (1894).
[364] This suggests a much broader, natural definition of a base than the conventional one. All salts of very weak acids, to a certain degree, which is determined by the weakness of their acids, do exactly what the ordinary bases do, e.g. neutralize acids. Metal derivatives of acids weaker than water, metal amides, like Zn(NH2)2, metal alkyls, like zinc methyl, Zn(CH3)2, react more vigorously than the hydroxides do, e.g. in neutralizing acids, and water attacks them and acts upon them, exactly as ordinary acids interact with metal hydroxides. We have, for instance, Zn(CH3)2 + 2 HOH → Zn(OH)2 + 2 CH4.
[366] The symbols in heavy type indicate the chief components of the final system. Vide Smith's General Chemistry for Colleges and Inorganic Chemistry, for the form of equations used.
[367] Emich, Ber. d. chem. Ges. 40, 1482 (1901).
[368] Arrhenius, Z. phys. Chem., 5, 16 (1890); Shields, ibid., 12, 167 (1893).
[369] See below for the corresponding equation, developed by Walker for a salt of a weak base and a strong acid.
[370] Potassium sulphate, K2SO4, reacts faintly alkaline in aqueous solution, the secondary ionization of sulphuric acid (table, p. 104) being somewhat weaker than the ionization of potassium hydroxide. We have: K2SO4 + HOH ⇄ KHSO4 + KOH or SO42− + HOH ⇄ HSO4− + HO−.
[371] Walker, Z. phys. Chem., 4, 319, (1889); Arrhenius, loc. cit.; Bredig, ibid., 13, 321 (1894).
[372] Arrhenius, loc. cit.
[374] Arrhenius developed the relation for aniline acetate, loc. cit.
[375] Putting x = [Acid] = [Base], we have [Salt] = (0.1 − x), and (0.1 − x)2 / x2 = (7E−10)2 / 1.2E−14. Then (0.1 − x) / x = 0.0064 and x = .09935, which is 99.35% of the total salt used. The degree of ionization, α, of the salt, in the extremely dilute solution, is taken to be 100%.
[377] See p. 172. The concentration of water may be considered a constant and is included in KAcid (and KBase, below).
[378] Only the primary ionization (of aluminium hydroxide) is considered in the text, because only that is involved, as a rule, in the neutralization of very weak bases by very weak acids (see footnote 2, p. 194). The relations are also simpler and clearer, if we limit the discussion to the formation of a salt AlO(AlO2).
| H3 | N | .CH2.CO | O |
| └ | ─────── | ┘ |
[381] The carbonates are occasionally partially hydrolyzed to basic carbonates.
[382] Stokes, J. Am. Chem. Soc., 29, 304 (1907).
[383] A complication, which leads to the precipitation of alkaline earths, along with these groups, as phosphates and similar insoluble salts (not as hydroxides or sulphides), when phosphate or certain other acid ions are present, is treated in Part IV (q.v.) under the systematic analysis of the groups.
[384] Cf. Fresenius, Quantitative Analysis.
[385] Ammonium sulphide usually precipitates a pink hydrated sulphide of manganese, probably Mn(SH)(OH). Under certain conditions of concentration and temperature, the dark green sulphide MnS is precipitated. In quantitative work the chemist aims to precipitate this green sulphide, which is more easily collected on a filter. (Cf. Fresenius, Quantitative Analysis.)
[386] We shall find that this property of the whole zinc group makes it possible to separate the following groups, the copper and arsenic groups, from the zinc group (see p. 158). The theory of the separation will be discussed in detail in Chapter XI.
[387] Vide Noyes, Bray and Spear, J. Am. Chem. Soc., 30, 483 (1908).
[389] The comparative stability of this basic salt represents an instance of the different ionizing power, or basic strength, of the three hydroxide groups of a trivalent base (see p. 106). The hydrolysis of ferric chloride seems to involve, primarily, only the third or least ionizable of the hydroxide groups of ferric hydroxide, and the hydrolysis, except in extreme dilution, proceeds chiefly according to Fe3+ + 3 Cl− + HOH ⇄ Fe(OH)2+ + 3 Cl− + H+. Vide Goodwin, Z. phys. Chem., 21, 1 (1896). In the case of the salt of the much weaker acid, carbonic acid, the hydrolysis goes further, involving two hydroxide groups of ferric hydroxide and, to some extent, all three.
[390] The extreme insolubility of Al(OH)3, Fe(OH)3 and Cr(OH)3, together with their weakness as bases, facilitates their precipitation (see pp. 185–6).
[391] There is a small degree of hydrolysis (see footnote, p. 189), but the hydroxides of the zinc group are not sufficiently insoluble to be precipitated under these conditions.
[392] Cf. A. A. Noyes, Bray and Spear, J. Am. Chem. Soc., 30, 496 (1908).
[393] Cf. The Elements of the Differential and Integral Calculus, based on Nernst and Schönflies's Lehrbuch, etc., by Young and Linebarger, pp. 363 and 364 (1900).