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.
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 aluminate354 and hydrogen ions, characteristic ions of an acid:
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, O2S(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)ClO3, and sulphuric acid, (HO)2SO2, 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+, O2−, and Na+. [p174]
The position of aluminium in the periodic system adequately accounts, then, for the amphoteric character of its hydroxide.357
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 (H2O)2. H2O, 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.
As the concentration of pure water, or of the water in dilute solutions, may be considered nearly a constant, we may put
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 KH2O 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 KH2O, 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 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.):
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.
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.).
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 + NH4OH ⥂ NH4Cl + H2O). But such a weak base, in turn, will have to give way, of course, to still stronger bases; for instances, NH4Cl + NaOH ⥂ NaCl + NH4OH. 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.
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.
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 KHCN = [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:
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
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−] = KHOH = 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:
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 α1, and if we represent, similarly, the total concentration of potassium hydroxide by [KOH] and its degree of ionization by α2, the equilibrium equation may be written:
Since the degrees of ionization of the two strong electrolytes are practically the same, we have further simply
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, KHCN = 7E−10, and KHOH = 1.2E−14, at 25°. Inserting these values into the equation [KCN] / ([HCN] × [KOH]) = KHCN / KHOH we have: (0.1 − x) / x2 = 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, α1 and α2, 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
It is clear, from the equation, that the weaker the acid of the salt (measured by the ionization constant KAcid, 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]
For MeX + HOH ⇄ MeOH + HX, where MeOH is a weak base and HX a strong acid, we have as before:371
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, KBase and KAcid:
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+] reduced373 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 KBase and KAcid. 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−] | = | α2 [Salt]2 | = | KAcid × KBase | = K, |
| [HX] × [MeOH] | [Acid] × [Base] | KHOH |
in which KAcid and KBase 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, KBase, 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]) = α2 [Salt]2 / ([Acid] × [Base]) = KAcid × KBase / KHOH = 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 KAcid and KBase 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
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]