CHAPTER X

«ALUMINIUM; AMPHOTERIC HYDROXIDES; HYDROLYSIS OF SALTS. THE ALUMINIUM AND ZINC GROUPS»

The chemistry of the analytical reactions of the alkalies and alkaline earths is extremely simple,—it is essentially the chemistry of well-defined bases and their salts,—and the separations and identifications, as we have seen, depend almost entirely on physical differences rather than on chemical contrasts. In the aluminium and zinc groups, which are precipitated together and which will be discussed together, the chemistry of the reactions becomes very much more complex. Therefore, we shall not, as yet, consider the groups as a whole, but shall first discuss the important analytical reactions of some compounds of aluminium.

«Aluminium Hydroxide an Amphoteric Hydroxide.»—Whereas the hydroxides of the alkali and alkaline earth metals are bases, pure and simple, aluminium hydroxide shows the properties both of a base and of an acid; it is an ‹amphoteric› hydroxide, the term "amphoteric" indicating the combination of acid with basic properties in any compound. Aluminium hydroxide dissolves in acids. From its solution in hydrochloric acid, an ‹aluminium› salt, aluminium chloride AlCl_{3}, 6 H_{2}O, is obtained. It also combines with strong bases, dissolving for instance in a solution of sodium hydroxide and forming an ‹aluminate›, NaAlO_{2}. The two salts mentioned are typical representatives of the two series of salts, which aluminium hydroxide is capable of forming. This dual character of the hydroxide raises a number of interesting questions, which one meets with quite frequently in the study of analytical reactions. One may ask, first, how aluminium hydroxide can ionize both as an acid and as a base; second, whether any reason can be given, why it should show the dual nature; and third, if it is both base and acid, why it does not neutralize itself.

According to the best knowledge we have on the subject, the molecule of aluminium hydroxide has the following ‹structure› or arrangement of its atoms: Al(—O—H)_{3}.

It is readily seen that the cleavage of the molecules may produce, [p172] either aluminium and hydroxide ions, characteristic ions of a base, or aluminate[354] and hydrogen ions, characteristic ions of an acid:

Al^{3+} + 3 ^{−}OH ⇄ Al(—0—H)_{3} ⇄ AlO_{2}^{−} + H^{+} + H_{2}O.

The ionization of the hydroxide both as an acid and as a base is, thus, quite possible on the basis of the molecular structure assigned to it. In fact, all of the so-called oxygen acids are considered to be hydroxides—we have sulphuric acid, O_{2}S(OH)_{2}, phosphoric acid, OP(OH)_{3}, etc.,—exactly as the bases, Mg(OH)_{2}, etc., are hydroxides.

That brings us to the second question, why aluminium hydroxide should show this dual character, whereas, for instance, sodium and magnesium hydroxides, which have similar structures, do not show it. The best answer to this question is found when we consider the properties of the elements and their derivatives in connection with their position in the periodic or natural system of elements, which shows the properties as (periodic) functions of the atomic weights. In the second series of the elements,[355] omitting the zero group element neon and taking the elements in the order of increasing atomic weights, we have sodium (23), magnesium (24), aluminium (27), silicon (28), phosphorus (31), sulphur (32), and chlorine (35.5). One of the properties that are shown to be functions dependent on the atomic weight, is the property under discussion, namely the tendency of the (highest) hydroxides of the elements to ionize as bases or acids, respectively. It is clear that the hydroxides of the elements with the lowest atomic weights in the series, sodium and magnesium, show the most pronounced tendency to ionize as bases; the hydroxides of the elements with the highest atomic weights show the most pronounced tendency to ionize as acids—perchloric acid, (HO)ClO_{3}, and sulphuric acid, (HO)_{2}SO_{2}, belong to the strongest acids. In accordance with the underlying principle of the periodic system, the change of [p173] properties, in going from one extreme to the other, is a function of the increase in atomic weight and is not sudden but ‹gradual›. And so the basic function, the tendency to produce the hydroxide-ion, is found to grow ‹weaker› as one goes from sodium to magnesium and then to aluminium, hydroxide; and the acid function, the tendency to produce the hydrogen-ion, grows markedly stronger, as one goes from phosphoric to sulphuric and perchloric acids. It is not surprising to find the two functions existing together, ‹but in rather weak form, in the case of the intermediate hydroxides›, notably in aluminium hydroxide and, to some degree, in silicic acid, ‹the acid character beginning before the basic function has ceased›. In accordance with this view, aluminium hydroxide is found to be only a ‹weak›, slightly ionized base, and a ‹very weak›, even less readily ionizable acid. In the case of silicic acid, which is the next hydroxide one meets as one goes toward the acid end of the series, the conditions are reversed. As the name indicates, it is primarily an acid, but it is a very weak one, and a critical scrutiny of its behavior shows it to have ‹very weak basic› functions, much weaker than those of aluminium hydroxide. The question may, indeed, be raised, whether either the basic or the acid properties really die out altogether in the hydroxides, from one end of the series to the other. In view of the small tendency toward sudden changes found in nature, one might suspect traces of basic character to be preserved right through the series to the strongest acids, like perchloric acid. As a matter of fact, later (see Chapter XV), we shall be obliged to consider possible basic functions of the strongest oxygen acids, such as nitric, perchloric, permanganic acids, and one of their most important properties, their behavior as oxidizing agents, will be found to be probably intimately associated with this remnant of basic ionization. On the other hand, fused sodium hydroxide will dissolve sodium with evolution of hydrogen, sodium oxide, Na—O—Na, being formed; and it can readily be shown,[356] that in the fused hydroxide there must be at least a few ions NaO^{−}, besides HO^{−}, H^{+}, O^{2−}, and Na^{+}. [p174]

The position of aluminium in the periodic system adequately accounts, then, for the amphoteric character of its hydroxide.[357]

«Common Occurrence of Amphoteric Hydroxides.»—If we consider the question of amphoteric behavior a little longer—its consequences are used extensively in analytical work—we find, in the periodic system, two other regular changes concerning acid and basic functions, only one of which we shall discuss here.[358] While in a ‹series› of elements the acid character of the hydroxides increases with the atomic weight, in a family of elements the reverse relation holds. From nitrogen to bismuth, in the nitrogen family of the sixth column of the periodic system, the acid character of the hydroxides grows steadily weaker, the basic character increases, and we find, again, that the intermediate elements, notably arsenic and antimony, produce hydroxides, which show markedly amphoteric character.

If, in the second series of the periodic group, one goes back from aluminium to magnesium hydroxide, in accordance with the first general principle laid down a much stronger base is found; and if one then goes, in the magnesium family, to the hydroxide of the element of next lower atomic weight, glucinum or beryllium, one again meets, in accordance with the second principle laid down, a weaker basic and more acidic hydroxide than magnesium hydroxide; in other words, the basic and acid functions revert closely to those exhibited by aluminium hydroxide. Glucinum hydroxide is a pronounced amphoteric hydroxide and resembles aluminium hydroxide so closely that, in the early history of chemistry, it was mistaken for the latter.

If one goes from glucinum back to lithium, in the same series of the periodic system, and from lithium to the element with the next lower atomic weight in the same group, one comes to hydrogen, which forms one of the most important and interesting of the [p175] amphoteric hydroxides, water. The ionization of water, slight as it is, yields hydrogen-ion and hydroxide-ion, the ions characteristic of acids and of bases, and water is placed among the weakest of the acids (see table, p. 104) as well as among the weakest of the bases (table, p. 106). We shall return to these relations, presently, and shall find that the apparent weakness of water, as a base and as an acid, is seemingly very largely due to the fact that water represents only an extremely dilute solution (see p. 66) of the real hydroxide, HOH, or hydrol, and consists very largely of a compound (H_{2}O)_{2}. H_{2}O, or hydrol, is, perhaps, not very much weaker as an acid or as a base, than is aluminium hydroxide.

Lower oxides of elements in the higher (acid-forming) groups show a less pronounced acid-forming character than the higher oxides, and a greater tendency to produce bases as well as acids, and are often amphoteric. Chromium hydroxide is of this type.

In view of all these facts, and in view, also, of the fact that the majority of the seventy-odd elements cannot lie at the ends of the periodic system but are found in the middle, it is not surprising to find that ‹pronounced amphoterism is shown by a large number of metal hydroxides; it is, perhaps, the rule rather than the exception›. A considerable number of the elements in the middle of the system are rare elements and that is perhaps the chief reason why this relation does not stand out more prominently in the consideration of the common acids and bases.

«Amphoteric Character of Hydroxides Considered in Analysis.»—The amphoteric character of hydroxides is frequently made use of in analytical work in the separation and identification of various elements and, when present, it must always be considered, in order to escape possible error. The following hydroxides of the common elements show ‹pronounced amphoteric› character: aluminium, chromic, zinc, lead, stannous, antimonous hydroxides and arsenious, platinic, auric, antimonic and stannic acids. Arsenic acid, ferric hydroxide and silicic acid show exceedingly slight, but perceptible, amphoteric character, sufficient to affect, to a certain degree, their analytical behavior.[359] [p176]

«Self-Neutralization of Amphoteric Substances.»[360]—We may turn now to the third question raised in connection with aluminium hydroxide, to the inquiry (p. 171), why aluminium hydroxide, the acid, does not neutralize aluminium hydroxide, the base. In fact, the base must and does form a salt with the acid. But the salt is formed only to a minimal extent, as the result of the fact that the base is a very weak base, the acid an exceedingly weak acid. Such exceedingly weak bases and acids show little tendency to combine with each other to form salts ‹in the presence of water, especially if one or both are difficultly soluble in water›, as in the present instance. The behavior of aluminium hydroxide, in this respect, is part of a much larger and more general question, growing out of the fact that water is a very weak acid and base, as has been seen, and, to a greater or lesser extent, reacts as such with salts, which are dissolved in it. This action of water plays an important rôle in many analytical reactions, and especially, also, in the reactions of aluminium salts. We shall, first, discuss this larger question of the action of water, as an ionogen, on salts, and then return (p. 187) to the problem of the self-neutralization of an amphoteric hydroxide.

HYDROLYSIS OF SALTS

«Ionization of Water.»—We may first consider, very briefly, the evidence that water is ionized even to the extent indicated by the ionization constants given in our tables. It may be said that the purest water ever prepared[361] shows a minimal conductivity, from which the concentrations of its hydrogen and hydroxide ions and the value of the ionization constant may be calculated. For the ionization of water we have

[H^{+}] × [HO^{−}] / [Nonionized water] = K_{Ion}.

As the concentration of pure water, or of the water in dilute solutions, may be considered nearly a constant, we may put

[H^{+}] × [HO^{−}] = K_{H_{2}O}.

This is the relation most commonly, and most conveniently, used. It is free from all assumptions as to the molecular weight of the nonionized water, the calculation of the concentrations [p177] [H^{+}] and [OH^{−}] being independent of any such assumption. The value of K_{H_{2}O} increases decidedly with an increase in the temperature,[362] whereas the ionization constant of an ordinary acid, such as acetic acid, is affected very little by changes in temperature. This peculiar increase of the ionization of water at higher temperatures is undoubtedly due to the increasing dissociation of the complex water molecules into hydrol molecules (see p. 66), which, presumably, are most easily ionized. Now, the value of the constant K_{H_{2}O}, at any temperature, may be determined in some half a dozen different and independent ways, including the conductivity method mentioned, and one of the most remarkable developments of the theory of ionization is that all of these methods lead to concordant results.[363]

Aside from considerations based on its ionization, water may be shown, by its chemical behavior, to have the functions of an acid and of a base, and the conclusions reached are in complete accord with those reached with the aid of the theory of ionization.

«Water is An Acid.»—If the oxide of a metal such as copper, lead or calcium, is treated with an acid, a salt is formed by the combination of the two; for instance, we have

PbO + HCl → Pb(OH)Cl,

Pb(OH)Cl + HCl → PbCl_{2} + H_{2}O,

PbO + 2 HCl → PbCl_{2} + H_{2}O,

CaO + 2 HCl → CaCl_{2} + H_{2}O.

Water will combine with a number of oxides very much in the same manner and sometimes with such vigor, that considerable heat is evolved, as in the slaking of lime (‹exp.›):

CaO + HOH → Ca(OH)_{2}.

Water in this, and similar actions, takes the place of and plays the rôle of, an ‹acid›, and ‹the metal hydroxides or bases appear as its salts›.[364] It is a ‹very weak› acid, which can easily be driven out of its salts by any stronger acid (neutralization of bases), but that does not alter the conclusions reached. Considered from the point of view of the theory of ionization, the relation [p178] would be expressed by saying that in the common bases the positive hydrogen ion of water has been replaced by some other positive or metal ion. The salt of any acid could be defined in exactly the same way.

«Water as a Base.»—Acid oxides, such as carbon dioxide, silicon dioxide, arsenious oxide, combine more or less readily with bases, such as sodium hydroxide, to form salts:

CO_{2} + NaOH → NaHCO_{3},

As_{2}O_{3} + 2 NaOH → 2 NaAsO_{2} + H_{2}O.

A number of acid oxides combine with water in exactly the same manner, and sometimes with such tremendous vigor, that great care must be taken in bringing the two together, as is the case when sulphur trioxide or phosphorus pentoxide are added to water (‹Exp.›).

We have P_{2}O_{5} + HOH → 2 HPO_{3}.

It is evident that in such actions water may take the place of, and play the rôle of, an ordinary base, forming the ‹acids›, which may well be defined as hydrogen salts.[365] It is true that the basic properties of water are so weak, that the metal ion of even a weak base, like ammonium hydroxide, will replace the hydrogen-ion in its salts, the acids, quite readily (HCl + NH_{4}OH ⥂ NH_{4}Cl + H_{2}O). But such a weak base, in turn, will have to give way, of course, to still stronger bases; for instances, NH_{4}Cl + NaOH ⥂ NaCl + NH_{4}OH. From the point of view of the theory of ionization, the hydrogen-ion is positive, like all the other metals ions whose hydroxides are bases.

There should be no difficulty, therefore, in considering water to have the chemical properties of a base as well as of an acid. Its chemical activities as such, weak as they may be, must be satisfied whenever it is present. These activities lead to the hydrolysis or the decomposition of salts by water, in greater or lesser degree, whenever water is used as a solvent for salts.

«Action of Water on a Salt of a Strong Base and a Strong Acid.»—If sodium chloride, a typical salt formed from a strong base and a strong acid, is dissolved in water, it is ionized to a considerable extent. Considering the solution from a mechanical point of view, we would expect that the sodium ions, moving in all directions, would collide occasionally with hydroxide ions, which are formed from the water and are present in minute but definite quantity. Some of the collisions must result in the formation of sodium hydroxide, as we have no reason to suppose that the result would differ from that in other cases where positively charged particles meet with negatively charged ones. However, since sodium hydroxide is an ionogen, with a very great tendency to ionize, and since there is present only a minute concentration of the hydroxide-ion, the [p179] equilibrium conditions will be satisfied when only traces of the nonionized hydroxide are formed. In a similar manner, we must expect to have traces, and only traces, of nondissociated hydrochloric acid formed by the union of chloride ions with some of the hydrogen ions of the water. Since hydrogen chloride and sodium hydroxide show practically the same tendency to ionize (tables, pp. 104 and 106), the two kinds of ions which water forms, the hydrogen-ion and the hydroxide-ion, will be used up ‹to a very slight› and practically ‹equal› extent to form nonionized sodium hydroxide and hydrogen chloride, but the ions will be immediately regenerated, and in equal concentrations, from the nonionized water which is present. All the equilibrium requirements will be satisfied when ‹traces› of sodium chloride have been converted into nonionized sodium hydroxide and hydrogen chloride. Such a solution, containing no excess of the hydrogen- or the hydroxide-ion, would react ‹neutral›. The action may be expressed by the equation[366]

«NaCl» ⇄ «Na»^{+} + «Cl»^{−}

«H_{2}O» ⇄ HO^{−} + H^{+}

Na^{+} + HO^{−} ⇄ NaOH

Cl^{−} + H^{+} ⇄ HCl.

The decomposition of sodium chloride by water, which one may predict on the basis of these theoretical considerations, may be demonstrated, slight as it is, by the following experiment.[367]

EXP. A pinch of sodium chloride is brought into a platinum crucible, which is previously heated in a blast lamp to a bright yellow heat (1100°); then 1 c.c. of water is introduced, drop by drop. A steam cushion is formed at once (Leidenfrost's phenomenon). After about half of the water has been evaporated (half a minute), the water is poured into a solution colored with blue litmus; it is changed to red by an excess of hydrochloric acid in the water. The crucible is cooled, and the salt remaining in it is dissolved in a little water and the solution poured into a red litmus solution; the latter turns blue.

The sodium chloride has obviously been partially decomposed, by the water, into its base and its acid; the decomposition is favored by the high temperature and by the fact that the hydrogen chloride [p180] formed can pass through the steam cushion into the water, while the sodium hydroxide is left behind. The removal of a product of the decomposition would favor its progress (see. p. 114).

The conclusions concerning salts of the type of sodium chloride may then be summarized in the statement, that ‹salts formed by the union of a very strong base with an equally strong acid are only very slightly decomposed by water and their solutions show a neutral reaction›.

The decomposition of a salt by water into its component base and acid is called ‹hydrolysis› and the salt is said to be ‹hydrolyzed› in the action.

«Action of Water on the Salt of a Strong Base with a Weak Acid.»—The relations are similar in principle, but quite different in degree and in net result, when the salt of a very strong base, combined with a weak acid, is dissolved in water. Potassium cyanide is a typical salt of this kind, and the study of its hydrolysis will illustrate the behavior of this class of salts. The hydrolysis takes place according to the equations

«KCN» ⇄ «K»^{+} + «CN»^{−}

«HOH» ⇄ «HO»^{−} + H^{+}

K^{+} + HO^{−} ⇄ KOH

CN^{−} + H^{+} ⇄ «HCN».

When the cyanide is dissolved in water, we must obtain, for the same reasons as were developed in the discussion of the hydrolysis of sodium chloride, a ‹little› nonionized potassium hydroxide, from the union of potassium ions with hydroxide ions, formed by the water. Potassium hydroxide being a strong, easily ionizable base, there will be only a ‹slight tendency› towards this union. Hydrocyanic acid, on the other hand, is an exceedingly weak acid. The value of its ionization constant K_{HCN} = [H^{+}] × [CN^{−}] / [HCN] is only 7E−10, as compared with a similar ratio approximating 1 for potassium hydroxide ([K^{+}] × [HO^{−}] / [KOH] = 1; see the tables, p. 104 and p. 106 and see pp. 106–7). The hydrogen-ion, formed from the water, must therefore combine with cyanide-ion, ‹to form nonionized hydrocyanic acid›, much more completely than the hydroxide-ion combines with potassium-ion. With the disappearance of the ions of water, in this case notably of its hydrogen ions, more water must ionize to satisfy the ionization constant [p181] for water (p. 176), and the formation of hydrocyanic acid will continue, towards the satisfying of its own constant. It is important to note that, for the reasons given, the hydrogen-ion of water ‹is used up to a far greater extent› than is the hydroxide-ion; ‹the latter therefore accumulates›, and this accumulation results in the formation of smaller and smaller concentrations of the hydrogen-ion, by the water. Since [H^{+}] × [HO^{−}] = 1.2E−14 (at 25°; p. 104), as [HO^{−}] grows larger, [H^{+}] must grow ‹proportionally smaller›. The ‹suppression of the hydrogen-ion by the accumulation of the hydroxide ion› will, ultimately, make [H^{+}] so small, that the equilibrium ratio [H^{+}] × [CN^{−}] / [HCN] will equal the equilibrium constant. Since the union of the hydrogen-ion with the cyanide-ion, to form little ionized hydrocyanic acid, is the main moving cause for the changes, the latter will then come to a standstill and equilibrium will be established. The net result of the action of water on potassium cyanide may be said to consist in the formation of practically nonionized hydrocyanic acid and the liberation of (chiefly) ionized potassium hydroxide, ‹until all the equilibrium constants› of the system are satisfied. We note that potassium cyanide solution must react strongly alkaline (‹exp.›) and that a free acid (‹e.g.› HCN) may well exist in the presence of a free base (‹e.g.› KOH), provided the acid is present in a nonionized, and therefore chemically inactive, condition (inactive as an ‹acid›).

Ignoring the (practically) unimportant formation of small quantities of nonionized potassium hydroxide, we may summarize the action in a single equation, which shows the main action:

CN^{−} + HOH ⇄ HCN + HO^{−}.

Whereas water, as an acid and as a base, is so exceedingly weak, that it can form but traces of its own salts, sodium hydroxide and hydrochloric acid, when acting on sodium chloride and competing for the base with such a strong acid as hydrochloric acid and for the acid with such a strong base as sodium hydroxide (see p. 179), the result, evidently, is quite different when water competes for a base with so weak an acid as hydrocyanic acid. In this case, we note that a considerable quantity of (ionized) potassium hydroxide, the salt of water in its rôle of an acid, is formed as a result of the action of water on potassium cyanide. [p182]

The theory of ionization, with the aid of the law of chemical equilibrium, gives us the means for ‹accurately defining the relative concentrations of the products, in the final condition of equilibrium›.[368] For the weak acid, hydrocyanic acid, we have the condition of equilibrium

[H^{+}] × [CN^{−}] / [HCN] = K_{HCN} = 7E−10.

The symbols [H^{+}], [CN^{−}] and [HCN] denote the final concentrations for the condition of equilibrium, indicated in the equations on p. 180; in such a mixture [H^{+}] is ‹not equal to› [CN^{−}], as it is in pure solutions of hydrocyanic acid in water. [CN^{−}], representing the total concentration of the cyanide-ion, is very much larger than [H^{+}], since the salt, potassium cyanide, produces the cyanide-ion in large concentrations.

For water, we have [H^{+}] × [HO^{−}] = K_{HOH} = 1.2E−14, at 25°. Here, again, the symbols represent the final, total concentrations of the ions in the mixture and [HO^{−}] is much larger than [H^{+}], since hydroxide-ion is formed in large quantities, as described above.

Combining the two equations, we have:

[CN^{−}] / ([HCN] × [HO^{−}]) = K_{HCN} / K_{HOH} = K_{Hydrolysis}.

The cyanide-ion, whose concentration is expressed by [CN^{−}], is formed practically altogether by the ionization of potassium cyanide, which is an easily ionizable and almost entirely ionized salt; the hydroxide-ion, whose concentration is expressed by [HO^{−}], is formed by the ionization of potassium hydroxide, which is an easily ionizable base, ionized to practically the same degree as is the potassium cyanide in the solution. If we represent the ‹total› concentration of the potassium cyanide, ionized and nonionized, at the point of equilibrium, by [KCN] and its degree of ionization by α_{1}, and if we represent, similarly, the total concentration of potassium hydroxide by [KOH] and its degree of ionization by α_{2}, the equilibrium equation may be written:

α_{1}[KCN] / ([HCN] × α_{2}[KOH]) = K_{HCN} / K_{HOH} = K_{Hydrolysis}.

Since the degrees of ionization of the two strong electrolytes are practically the same, we have further simply

[KCN] / ([HCN] × [KOH]) = K_{HCN} / K_{HOH} = K_{Hydrolysis}.

The mathematical equations give us a measure of the extent to which water must decompose or ‹hydrolyze› the salt in question, as expressed in the chemical equations (p. 180). The ‹extent› of the hydrolysis, clearly, depends on the relative ionization constants of hydrocyanic acid and water, the ‹two acids competing for the base›.

From the known values of the constants, one may calculate that, at 25°, in a solution of 6.5 grams potassium cyanide in a liter (0.1 molar), almost 1.3% of the cyanide is decomposed into potassium hydroxide and hydrocyanic acid. Since every molecule of hydrolyzed salt forms one molecule of [p183] the hydroxide and one molecule of the acid, we may put [KOH] = [HCN] = ‹x› and [KCN] = 0.1 − ‹x›. The ionization constant, K_{HCN} = 7E−10, and K_{HOH} = 1.2E−14, at 25°. Inserting these values into the equation [KCN] / ([HCN] × [KOH]) = K_{HCN} / K_{HOH} we have: (0.1 − ‹x›) / ‹x›^2 = 7E−10 / 1.2E−14. Here ‹x› = 0.0013. This is 1.3% of the 0.1 mole of cyanide used.

One may convince himself, as follows, that the constants are satisfied when the decomposition of the cyanide has proceeded to this point: the degrees of ionization of the potassium cyanide and potassium hydroxide, α_{1} and α_{2}, may be taken as 85% (the same as the degree of ionization of the similar electrolyte KCl in 0.1 molar solution). Then [HO^{−}] = 0.85 × 0.0013 = 0.0011; [CN^{−}] = 0.85 × (0.1 − 0.0013) = 0.083; [H^{+}] = 1.2E−14 / [HO^{−}] = 1.1E−11. For [H^{+}] × [CN^{−}] / [HCN] we have then: (1.1E−11 × 0.083) / (0.0013) or 7E−10, the value for the ionization constant of hydrocyanic acid. It should be noted that, whereas in pure water at 25° [H^{+}] = [HO^{−}] = √(1.2E−14) = 1.1E−7, in the solution under consideration [HO^{−}] has increased to the value 0.0011 and [H^{+}] is only 1.1E−11.

The relation developed for the ‹hydrolysis› of potassium cyanide is a general one, holding for the hydrolysis of salts, of the type MeX, of a weak acid with a strong base. It may be expressed in general as follows: for the hydrolysis of a salt according to MeX + HOH ⇄ MeOH + HX, where HX is a weak acid and MEOH a strong base, we have:[369]

[Salt] / ([Acid] × [Base]) = K_{Acid} / K_{HOH}.

It is clear, from the equation, that the weaker the acid of the salt (measured by the ionization constant K_{Acid}, the numerator on the right), the more will water, ‹ceteris paribus›, be able to drive it out of its salt and form its own salt, ‹the base› (the smaller the numerator on the right, the larger must be the denominator on the left).

The conclusions may be summarized in the statement that the salts of strong bases with weak acids are more or less decomposed by water (hydrolyzed) and the resulting solutions must react ‹alkaline›. We find, as a matter of fact, that aqueous solutions of potassium cyanide, sodium carbonate, sodium sulphide, borax (see the table, p. 104), all react strongly alkaline to litmus (‹exp.›). Conversely, it may be said, that if the sodium or potassium salt of an acid dissolves in water with a ‹decidedly› alkaline reaction, it is the salt of a weak, poorly ionized acid.[370] [p184]

«Action of Water on a Salt of a Strong Acid with a Weak Base.»—Exactly similar relations obtain in the case of salts of strong acids with weak bases:[1] they are decomposed, to a greater or less extent, into the free, strong, largely ionized acid and the free, scarcely ionized weak base, ‹the decomposition being stopped by the accumulation of the free strong acid› (more exactly, of the ‹hydrogen-ion›). Such solutions react strongly ‹acid›, as in the case of the chloride, nitrate, sulphate of aluminium, of iron (ferric), of chromium, and of similar salts of weak bases.

For MeX + HOH ⇄ MeOH + HX, where MeOH ‹is a weak base› and HX a strong acid, we have as before:[371]

[Me^{+}] / ([H^{+}] × [MeOH]) = [Salt] / ([Acid] × [Base]) = K_{Base} / K_{HOH}.

«Action of Water on a Salt of a Base and an Acid, Both of which are Weak.»—We will now turn to the consideration of the action of water on the fourth class of salts, the salts of a weak base with a weak acid.[372]

Like all salts, such a salt, say MeX, would ionize very readily, when dissolved in water (the few exceptions to readily ionizable salts are not under consideration), and, in this case, both the positive and the negative ions would have to combine respectively with the hydroxide and the hydrogen ions of water to form the ‹nonionized weak base› and the ‹nonionized weak acid›, and satisfy ‹two very small constants›, K_{Base} and K_{Acid}:

[Me^{+}] × [HO^{−}] / [MeOH] = K_{Base}

and [H^{+}] × [X^{−}] / [HX] = K_{Acid}.

Both the hydrogen and the hydroxide ions of water would disappear, and in approximately equal quantity, if the base and acid were approximately equally weak, and the ions would be regenerated from water ‹with no accumulation of either one to suppress the other›, as in the two previous cases considered. Under these circumstances, the decomposition by water ‹must proceed very much further than in the previous cases›. For instance, in the hydrolysis of potassium cyanide in 0.1 molar solution, at 25°, we find the concentration of the hydrogen-ion [H^{+}] reduced[373] from 1.1E−7, its [p185] value in pure water, to 1.1E−11, as a result of the accumulation of potassium hydroxide (the hydroxide-ion), and only ‹this small value› for [H^{+}] appears in the equation for the formation of the free acid, HCN (first equation, p. 182; ‹vide› the calculation, p. 183). But, in the present case, the factors [HO^{−}] and [H^{+}], in the equations on p. 184, maintain practically their original value, about the same as in pure water, and the formation of nonionized MeOH and HX must go correspondingly further to satisfy the constants K_{Base} and K_{Acid}. Just how far the action must proceed, can be formulated with the aid of the theory of ionization and the law of chemical equilibrium,[374] much in the same way as for the hydrolysis of potassium cyanide.

The final equation, as developed by Arrhenius, reads:

[Me^{+}] × [X^{−}] / ([HX] × [MeOH]) = α^2 [Salt]^2 / ([Acid] × [Base]) = (K_{Acid} × K_{Base}) / K_{HOH} = K,

in which K_{Acid} and K_{Base} represent the ionization constants of the acid and the base, as given in the tables (pp. 104 and 106), and α is the degree of ionization of the salt.

For the cyanide of a base, which is as weak a base as hydrocyanic acid is an acid, we find that the decomposition by water, at 25° in a 0.1 molar solution, must comprise 99.35%[375] of the salt, in order to establish equilibrium. In the case of potassium cyanide, in 0.1 molar solution, only 1.3% of the salt is decomposed (p. 182).

Now, if both the free base and the free acid are very ‹difficultly soluble›, then the concentrations [MeOH] and [HX], respectively, in the solution ‹cannot go beyond a certain minute limit›. In view,[376] then, of the very small value, K_{Base}, of the ratio [Me^{+}] × [HO^{−}] / [MeOH] and the minute value that the second term [MeOH] has under these conditions, the first term [Me^{+}] × [HO^{−}] must have a correspondingly smaller value. It is clear, therefore, that in such a solution neither the nonionized base, MeOH, nor its ion, Me^{+}, can exist in more than minute quantities when the equilibrium constants are satisfied. The same conclusion is reached regarding the [p186] possibility of the existence of the difficultly soluble acid HX and its ion X^{−}, in more than minimal quantities. Since, then, neither the ion Me^{+} nor the ion X^{−} can be present in more than traces, their salt, MeX, which is considered readily ionizable, also ‹cannot exist in aqueous solutions›, except in traces.

The ‹quantitative relations› are evident from the equilibrium equation (p. 185): [Me^{+}] × [X^{−}] / ([HX] × [MeOH]) = α^2 [Salt]^2 / ([Acid] × [Base]) = (K_{Acid} × K_{Base}) / K_{HOH} = K. It is evident that the concentration of the salt, [Salt], which is capable of existence in aqueous solution, is, in the first place, ‹the smaller the smaller the values› for K_{Acid} and K_{Base} are, ‹i.e. the weaker the acid and the base are›; and, in the second place, it is the smaller the smaller the values for [Acid] and [Base] are, which, in the present instance, represent the concentrations of the difficultly soluble acid and base in saturated solution, ‹i.e. their solubilities›.

We reach the conclusion that ‹salts of very weak bases and very weak acids are very considerably decomposed by water›, and, if both the acid and the base are difficultly soluble in water, the decomposition is ‹practically complete›. ‹Conversely, such a very weak, difficultly soluble base will not combine with a very weak, difficultly soluble acid to form a salt in the presence of water.› An instance of the first kind is found in the case of aluminium sulphide, the salt of a very weak, difficultly soluble base, aluminium hydroxide, with a rather little soluble, weak acid, hydrogen sulphide (see table, p. 104). We find that when a piece of aluminium sulphide, prepared by dry methods, is dropped into water (‹exp.›), a precipitate of aluminium hydroxide is immediately formed and evolution of hydrogen sulphide occurs. We have

Al_{2}S_{3} ⇄ 2 Al^{3+} + 3 S^{2−},

«6 HOH» ⇄ 6 HO^{−} + 6 H^{+}

2 Al^{3+} + 6 HO^{−} ⇄ «2 Al(OH)_{3} ↓»

3 S^{2−} + 6 H^{+} ⇄ «3 H_{2}S ↑».

An instance where a very weak insoluble acid will not combine, appreciably, with a very weak insoluble base, is found in the case of ‹aluminium hydroxide›. A development of the equilibrium equations for its ionization as a base and its ionization as an acid would show, that all the constants would be readily satisfied, when a very minute quantity of dissolved ionized aluminium aluminate is formed. [p187]

«Self-Neutralization of Amphoteric Hydroxides.»—We may consider a saturated solution of aluminium hydroxide, in contact with the solid hydroxide. For the ‹acid ionization›,[377] Al(OH)_{3} ⇄ AlO_{2}^{−} + H^{+} + H_{2}O, we have

[AlO_{2}^{−}] × [H^{+}] / [Al(OH)_{3}] = K_{Acid}.

Similarly, for the ‹basic ionization›,[378] Al(OH)_{3} ⇄ (AlO)^{+} + HO^{−} + H_{2}O, we have

[AlO^{+}] × [HO^{−}] / [Al(OH)_{3}] = K_{Base}.

The formation of ‹traces of nonionized› (basic) aluminium aluminate would satisfy the equilibrium requirements for AlO^{+} + AlO_{2}^{−} ⇄ AlO(AlO_{2}), 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 AlO_{2}^{−} 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 K_{Base}, and, similarly, an increasing excess of the ion AlO_{2}^{−} will permit [H^{+}] to reach only smaller and smaller values, according to the equilibrium equation for K_{Acid}. When the values for [HO^{−}] and [H^{+}] have in this way become small enough to make [HO^{−}] × [H^{+}] = K_{HOH}, 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^{−} + H_{2}O, but is much ‹smaller›. Similarly, [H^{+}] is much smaller than [AlO_{2}^{−}].

Just how much aluminium aluminate must be formed by a self-neutralization of the amphoteric hydroxide will depend on the values for K_{Base} and K_{Acid} and on the solubility of aluminium hydroxide (nonionized Al(OH)_{3}). The two equilibrium equations may be combined:

[AlO^{+}] × [AlO_{2}^{−}] × [H^{+}] × [HO^{−}] / [Al(OH)_{3}]^2 = K_{Base} × K_{Acid}.

[p188]

Since [H^{+}] × [HO^{−}] = K_{HOH}, and since [AlO^{+}] and [AlO_{2}^{−}] may be taken to represent ‹each› the concentration of the practically completely ionized aluminium aluminate AlO(AlO_{2}), we have[379]

[Alum. Aluminate]^2 / [Alum. Hydroxide]^2 = (K_{Base} × K_{Acid}) / K_{HOH},

or

[Alum. Aluminate] / [Alum. Hydroxide] = √[(K_{Base} × K_{Acid}) / K_{HOH}].

It is clear, that the smaller the ionization constants K_{Base} and K_{Acid} 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."

«The Analysis of the Aluminium and Zinc Groups.»—The groups of metals which are here called the [p189] "‹Aluminium and Zinc Groups›" consist of two groups, which ordinarily are precipitated together in qualitative analysis, and which are then separated from each other. We may distinguish the "‹Aluminium Group›" of trivalent metal ions, including aluminium, ferric and chromium ions, and the "‹Zinc Group›" of bivalent metal ions, including zinc, nickelous, cobaltous, manganous and ferrous ions. Of the two groups, the ions of the second group, in agreement with their lower valence (see p. 172), form the ‹stronger bases›, and, as such, they are all capable of forming ‹comparatively stable salts› even with such very weak acids as hydrogen sulphide and carbonic acid. Ammonium sulphide, added to a solution of a salt of any one of the ions of the zinc group, precipitates the corresponding sulphide, sodium or ammonium carbonate precipitates the corresponding carbonate.[381] We have, for instance:

FeCl_{2} + (NH_{4})_{2}S → FeS ↓ + 2 NH_{4}Cl,

FeCl_{2} + Na_{2}CO_{3} → FeCO_{3} ↓ + 2 NaCl.

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, Al_{2}S_{3}, 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 AlCl_{3} + 3 H_{2}O ⇄ 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:

2 AlCl_{3} + 3 (NH_{4})_{2}S + 6 H_{2}O → 2 Al(OH)_{3} ↓ + 6 NH_{4}Cl + 3 H_{2}S ↑

or 2 Al^{3+} + 3 S^{2−} + 6 HOH → 2 Al(OH)_{3} ↓ + 3 H_{2}S ↑.

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, Fe_{2}S_{3}, 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]

«Separation of the Aluminium Group from the Zinc Group by Means of Ammonium Chloride and Ammonium Hydroxide.»—The precipitation of the two groups together makes their subsequent separation necessary. Some analysts attempt to avoid the extra operations involved, by making use of the fact that the hydroxides of the bivalent group, although difficultly soluble, are, like magnesium hydroxide, still sufficiently soluble not to be precipitated by ammonium hydroxide in the presence of sufficient ammonium chloride, while the hydroxides of the trivalent metals of this group are so insoluble that they may be precipitated quantitatively by such a mixture (p. 170). The trivalent hydroxides may be first precipitated by ammonium hydroxide, in the presence of ammonium chloride, and, subsequently, the sulphides of the bivalent metals may be precipitated by ammonium sulphide, the two precipitates being collected separately. The method has the disadvantage that it is not always accurate. The acid character of aluminium and chromium hydroxides (and even of ferric hydroxide, see p. 195), as well as of zinc hydroxide, leads, to a certain extent, to the precipitation, from such ‹alkaline› solutions, of ‹salts› of these amphoteric hydroxides with the basic hydroxides of the bivalent group; the latter are thus liable to be ‹lost› in the analysis. It will be recalled, that the equilibrium conditions in alkaline solutions ‹favor› the ‹ionization› of amphoteric substances in the acid form (Part III), and ‹alkaline› solutions would favor the precipitation of aluminates, chromites, etc., of the ions of the zinc group. Methods have, therefore, been devised to separate the two groups in neutral, or very slightly acid, media, and they give quantitative separations and are preferable to the method just described. The separation by means of suspended ‹barium carbonate›, in which carbonic acid is liberated and the solution is practically neutral, will be discussed below on page 193. A second method, frequently used in quantitative analysis, is based on the [p192] ‹decomposition› of the ‹acetates› of the aluminium group by boiling water, acetic acid being liberated.[384]

«Separation of Cobalt and Nickel from the Other Members of the Zinc and Aluminium Groups.»—When the aluminium and zinc groups are precipitated together, by means of a mixture of ammonium sulphide, hydroxide and chloride, the precipitate, obtained from a solution containing, say, the chlorides of all the ions of the groups, would consist of the following compounds:

‹Aluminium Group›: Fe_{2}S_{3}, 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]

NiCl_{2} + ‹x› HCl + H_{2}S ⥃ NiS + (‹x› + 2) HCl

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.

«Separation of the Aluminium and Zinc Groups by Means of Barium Carbonate.»—The solution, obtained by treating the mixture of the sulphides and hydroxides of the aluminium and zinc groups with dilute hydrochloric acid (p. 192), contains aluminium, chromium, manganous, zinc and ferrous chlorides, all the iron being now present in the ferrous condition because of the reducing action of hydrogen sulphide on the ferric-ion (Part III). The chlorides of nickel and cobalt are also present in small quantities (see above). The further treatment of the solution is directed toward a ‹separation› of the ‹bivalent› ions of the zinc group from the ‹trivalent› ions of the aluminium group, and the intention is to have all the iron go with the trivalent metals. The ferrous is, therefore, oxidized to the ferric-ion. After a part of the solution has been tested to show the presence or absence of ferric salts, the two groups are separated by means of a suspension, in water, of finely [p194] divided barium carbonate. ‹The theory of the separation› may be developed as follows:

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 carbonate[389] Fe_{2}(OH)_{4}CO_{3}, is precipitated and carbon dioxide escapes (‹exp.›). The trivalent hydroxides are too weak bases[390] to form stable salts with so weak an acid as carbonic acid.

2 FeCl_{3} + 3 Na_{2}CO_{3} + 6 H_{2}O ⥂ 2 Fe(OH)_{3} ↓ + 3 H_{2}CO_{3} + 6 NaCl

3 H_{2}CO_{3} ⇄ 3 H_{2}O + 3 CO_{2} ↑.

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 carbonates›[391] from solutions of their chlorides or nitrates. We have, for instance, ZnCl_{2} + BaCO_{3} ↓ ⥃ BaCl_{2} + ZnCO_{3}. 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.

«Analysis of the Aluminium Group.»—The precipitate of the aluminium group may contain aluminium, chromium and ferric hydroxides (possibly traces of manganic hydroxide) and their basic carbonates. A color test for ferric-ion has already been made (see p. 193) and chromium (and manganese) is readily found and identified by oxidation to the intensely colored salts of chromic (and manganic) acid (Part III, ‹q.v.›). In ascertaining whether aluminium hydroxide is present or not, advantage is taken of its ‹amphoteric character›. Chromium hydroxide, like aluminium hydroxide, is amphoteric; but, in agreement with the greater atomic weight of chromium, it is an even weaker acid than is aluminium hydroxide. Its sodium salt, sodium chromite, is completely decomposed by boiling water, chromium hydroxide being precipitated in a less hydrated, insoluble form. Ferric hydroxide, whose metal has the highest atomic weight of the three elements under consideration, has so little acid character, that it is not perceptibly soluble in solutions of potassium or sodium hydroxide. (That it has slight acidic properties is shown by its capacity to form ferrites, ‹e.g.› Me(FeO_{2})_{2}, which may best be obtained by dry methods, and of which ferrous ferrite or magnetic iron ore, Fe_{3}O_{4} or Fe(FeO_{2})_{2}, is the most important representative.) Of the three hydroxides, aluminium hydroxide is, therefore, the only one that will dissolve in boiling sodium hydroxide. In this solution we can best identify it, by converting the aluminate into an aluminium salt, by means of an excess of acid, [p196] and by a final precipitation of aluminium hydroxide with ammonium hydroxide. Aluminium hydroxide is too weak an acid to form a stable aluminate with so weak a base as ammonium hydroxide, when the latter is used only in slight excess (p. 186). If we attempt to prepare ammonium aluminate, by adding ammonium chloride to a solution of sodium aluminate, a precipitate of aluminium hydroxide is obtained (‹exp.›). For exact work, an excess of ammonium hydroxide is to be avoided and ‹its strength as a base should be weakened› by the addition of some ammonium chloride or nitrate (pp. 114, 169 and Lab. Manual, p. 9, § 6).

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 NH_{4}AlO_{2}, may be shown as follows: for the acid ionization of aluminium hydroxide, Al(OH)_{3} ⇄ AlO_{2}^{−} + H^{+} + H_{2}O (p. 172); the solubility-product for a saturated solution is [AlO_{2}^{−}] × [H^{+}] = K_{Ac.S.P.}. Further, from [H^{+}] × [HO^{−}] = K_{HOH}, we find [H^{+}] = K_{HOH} / [HO^{−}]. Then [AlO_{2}^{−}] = [HO^{−}] × K_{Ac.S.P.} / K_{HOH}, which shows that the solubility of aluminium hydroxide, as aluminate, is proportional to the concentration [HO^{−}] of the hydroxide-ion in the solution. For NH_{4}OH we have [NH_{4}^{+}] × [HO^{−}] / ([NH_{3}] + [NH_{4}OH]) = 0.000,018 (p. 161), and consequently, [HO^{−}] = 0.000,018 × ([NH_{3}] + [NH_{4}OH]) / [NH_{4}^{+}]. Then [HO^{−}] is the smaller, the smaller the excess of ammonium hydroxide used (which is approximately equal to ([NH_{3}] + [NH_{4}OH])) and the greater the concentration [NH_{4}^{+}] 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]

«The Favorable Conditions for a Maximum Precipitation of an Amphoteric Hydroxide.»—The precipitation of aluminium hydroxide depends also on the solubility-product of aluminium hydroxide, ionized as a base. For Al(HO)_{3} ⇄ Al^{3+} + 3 HO^{−}, in a saturated solution, [Al^{3+}] × [HO^{−}]^3 = K_{Bas.S.P.}. It is evident, that an excess of the precipitating hydroxide-ion would be favorable to the precipitation in this form, and that the reduction of the concentration of the hydroxide-ion, ‹while acting favorably›, as just shown, ‹in preventing the solution of the hydroxide as an aluminate, must be, to some extent, detrimental to a maximum precipitation of the hydroxide as a base›. One may ask, therefore, ‹what the most favorable concentration of the hydroxide-ion› must be for a quantitative precipitation of aluminium hydroxide. The problem may be treated as follows: According to the solubility-product relation for the basic ionization, we have, in a solution saturated with aluminium hydroxide, [p197]

[Al^{3+}] = K_{Bas.S.P.} × [HO^{−}]^{−3}. I

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} ⇄ AlO_{3}^{3−} + 3 H^{+}, which would resemble the basic ionization. Then we would have [AlO_{3}^{3−}] × [H^{+}]^3 = K′_{Ac.S.P.}, and, using the relation [H^{+}] = K_{HOH} / [HO^{−}], we have

[AlO_{3}^{3−}] = [HO^{−}]^3 × K′_{Ac.S.P.} × K_{HOH}^{−3}. II

Adding equations I and II we find

[Al^{3+}] + [AlO_{3}^{3−}] = K_{Bas.S.P.} × [HO^{−}]^{−3} + [HO^{−}]^3 × K′_{Ac.S.P.} × K_{HOH}^{−3} III

Aluminium hydroxide will be most completely precipitated when [Al^{3+}] + [AlO_{3}^{3−}] is a ‹minimum›, the values [Al^{3+}] and [AlO_{3}^{3−}] measuring the solubility of aluminium as aluminium-ion and as aluminate-ion. If we put [Al^{3+}] + [AlO_{3}^{3−}] = ‹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› = K_{Bas.S.P.} × ‹x›^{−3} + ‹x›^3 × K′_{Ac.S.P.} × K_{HOH}^{−3}, and find, by means of the calculus,[393] that ‹y› is a minimum, when ‹x› = +(K_{HOH}^3 × K_{Bas.S.P.} / K′_{Ac.S.P.})^{1/6}.

If aluminium hydroxide were as strong an acid as it is a base, ‹i.e.› if K_{Bas.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, K_{Bas.S.P.} > K′_{Ac.S.P.}, and consequently we find for ‹x› = [HO^{−}] = (K_{HOH}^3 × K_{Bas.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 K_{Bas.S.P.}. and K′_{Ac.S.P.}.

The exact values for K_{Bas.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 [Al^{3+}] = [AlO_{3}^{3−}]—which would correspond to a saturated solution of aluminium aluminate, Al(AlO_{3}).

When the ionization of aluminium hydroxide, as an acid, is considered to take place according to Al(OH)_{3} ⇄ AlO_{2}^{−} + H^{+} + H_{2}O, which agrees best with its real behavior (p. 172), we can find, similarly, that [Al^{3+}] + [AlO_{2}^{−}] 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 K_{HOH} × K_{Bas.S.P.} / K_{Ac.S.P.})^{0.25},—where K_{Ac.S.P.} represents the solubility-product constant for [AlO_{2}^{−}] × [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 K_{Bas.S.P.} and K_{Ac.S.P.}. It also appears that this minimum loss[394] of aluminium includes one-third as many Al^{3+} ions, as AlO_{2}^{−} ions—a relation corresponding, again, to a saturated solution of aluminium aluminate, Al(AlO_{2})_{3}.

FOOTNOTES:

[354] When all three of the hydrogen atoms in the hydroxide are ionized, an aluminate ion, AlO_{3}^{3−} is formed: Al(OH)_{3} ⇄ AlO_{3}^{3−} + 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)_{2}O^{−}, which is formed by the ‹primary› ionization, readily loses water and forms the anhydride ion AlO_{2}^{−}. 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^{+} + O^{2−}) (see Chap. XIII). We cannot have positive ions, Na^{+}, with negative ions, O^{2−}, without having some ions NaO^{−}. (O^{2−} + 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).

[362] See the table, p. 104.

[363] See p. 53 and van 't Hoff's remarks, ‹ibid.›

[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(NH_{2})_{2}, metal alkyls, like zinc methyl, Zn(CH_{3})_{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(CH_{3})_{2} + 2 HOH → Zn(OH)_{2} + 2 CH_{4}.

[365] See footnote, p. 177. Similar considerations apply to the conventional definition of an acid.

[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, K_{2}SO_{4}, 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: K_{2}SO_{4} + HOH ⇄ KHSO_{4} + KOH or SO_{4}^{2−} + HOH ⇄ HSO_{4}^{−} + HO^{−}.

[371] Walker, ‹Z. phys. Chem.›, 4, 319, (1889); Arrhenius, ‹loc. cit.›; Bredig, ‹ibid.›, «13», 321 (1894).

[372] Arrhenius, ‹loc. cit.›

[373] See p. 183.

[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 / ‹x›^2 = (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%.

[376] See the equations for K_{Base} and K_{Acid}, on p. 184, and their premises.

[377] See p. 172. The concentration of water may be considered a constant and is included in K_{Acid} (and K_{Base}, 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(AlO_{2}).

[379] See the similar equation, p. 185.

[380] Amphoteric substances of a different class are also known, which have, at the same time, moderately ‹strong› acid and moderately ‹strong› basic functions. Glycocoll, H_{2}N.CH_{2}COOH, a derivative of acetic acid and ammonia, contains an acid group, the —COOH group, the hydrogen of which is approximately as ionizable as the hydrogen in the corresponding group in acetic acid, CH_{3}COOH. The ammonia residue, H_{2}N—, in glycocoll, forms with water a hydroxide, corresponding to ammonium hydroxide, which likewise is approximately as ionizable as is ammonium hydroxide. In the hydroxide of glycocoll we have, consequently, both a moderately strong acid, and a moderately strong basic, group. In this, and in similar cases, ‹salt formation between the acid and the basic groups of the amphoters takes place to as great an extent as if the functions were attributes of distinct compounds›. Glycocoll in aqueous solution is present, then, chiefly in the form of a salt, for instance, H_{3}N^{+}.CH_{2}.COO^{−}, corresponding to ammonium acetate, CH_{3}COONH_{4}. For an elaborate discussion of the equilibrium conditions in solutions of amphoteric compounds ‹vide› Walker, ‹Z. phys. Chem.›, «49» and «51».

[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).

[388] See footnote, p. 189.

[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 Fe^{3+} + 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).

[394] Losses due to the tendency of aluminium hydroxide to assume the colloidal condition (p. 136) must be guarded against by other precautions (‹loc. cit.›).

[p199]