«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]