sluggishness with which reciprocal transformation of the polymorphic forms
of a substance may occur. In the case of tin, for example, it was found
that the white modification, although apparently possessing permanence, is
in reality in a metastable state, under the ordinary conditions of
temperature and pressure. This great degree of stability is due to the
tardiness with which transformation into the grey form occurs.
What was found in the case of tin, is met with also in the case of all
transformations in the solid state, but the velocity of the change is less
in some cases than in others, and appears to decrease with increase of the
valency of the element.[127] To this fact van't Hoff attributes the great
permanence of many really unstable (or metastable) carbon compounds.
Reference has been made to the fact that the velocity of transformation can
be accelerated by various means. One of the most important of these is the
employment of a liquid which has a solvent action on the solid phases. Just
as we have seen that at any given temperature the less stable form has the
higher vapour pressure, but that at the transition point the vapour
pressure of both forms becomes identical, so also it can be proved
theoretically, and be shown experimentally, that {71} at a given
temperature the solubility of the less stable form is greater than that of
the more stable, but that at the transition point the solubility of the two
forms becomes identical.[128]
If, then, the two solid phases are brought into contact with a solvent, the
less stable phase will dissolve more abundantly than the more stable; the
solution will therefore become supersaturated with respect to the latter,
which will be deposited. A gradual change of the less stable form,
therefore, takes place through the medium of the solvent. In this way the
more rapid conversion of white tin into grey in presence of a solution of
tin ammonium chloride (p. 42) is to be explained. Although, as a rule,
solvents accelerate the transformation of one solid phase into the other,
they may also have a retarding influence on the velocity of transformation,
as was found by Reinders in the case of mercuric iodide.[129]
The velocity of inversion, also, is variously affected by different
solvents, and in some cases, at least, it appears to be slower the more
viscous the solvent;[130] indeed, Kastle and Reed state that yellow
crystals of mercuric iodide, which, ordinarily, change with considerable
velocity into the red modification, have been preserved for more than a
year under vaseline.
Temperature, also, has a very considerable influence on the velocity of
transformation. The higher the temperature, and the farther it is removed
from the equilibrium point (transition point), the greater is the velocity
of change. Above the transition point, these two factors act in the same
direction, and the velocity of transformation will therefore go on
increasing indefinitely the higher the temperature is raised. Below the
transition point, however, the two factors act in opposite directions, and
the more the temperature is lowered, the more is the effect of removal from
the equilibrium point counteracted. A point will therefore be reached at
which the velocity is a maximum. Reduction of the temperature {72} below
this point causes a rapid falling off in the velocity of change. The point
of maximum velocity, however, is not definite, but may be altered by
various causes. Thus, Cohen found that in the case of tin, the point of
maximum velocity was altered if the metal had already undergone
transformation; and also by the presence of different liquids.[131]
Lastly, the presence of small quantities of different substances--catalytic
agents or catalyzers--has a great influence on the velocity of
transformation. Thus, _e.g._, the conversion of white to red phosphorus is
accelerated by the presence of iodine (p. 47).
Greater attention, however, has been paid to the study of the velocity of
crystallization of a supercooled liquid, the first experiments in this
direction having been made by Gernez[132] on the velocity of
crystallization of phosphorus and sulphur. Since that time, the velocity of
crystallization of other supercooled liquids has been investigated; such as
acetic acid and phenol by Moore;[133] supercooled water by Tumlirz;[134]
and a number of organic substances by Tammann,[135] Friedlaender and
Tammann,[136] and by Bogojawlenski.[137]
In measuring the velocity of crystallization, the supercooled liquids were
contained in narrow glass tubes, and the time required for the
crystallization to advance along a certain length of the tube was
determined, the velocity being expressed in millimetres per minute. The
results which have so far been obtained may be summarized as follows. For
any given degree of supercooling of a substance, the velocity of
crystallization is constant. As the degree of supercooling increases, the
velocity of crystallization also increases, until a certain point is
reached at which the velocity is a maximum, which has a definite
characteristic value for each substance. This maximum velocity remains
constant over a certain range of {73} temperature; thereafter, the velocity
diminishes fairly rapidly, and, with sufficient supercooling, may become
zero. The liquid then passes into a glassy mass, which will remain
(practically) permanent even in contact with the crystalline solid.
In ordinary glass we have a familiar example of a liquid which has been
cooled to a temperature at which crystallization takes place with very
great slowness. If, however, glass is heated, a temperature is reached,
much below the melting point of the glass, at which crystallization occurs
with appreciable velocity, and we observe the phenomenon of
devitrification.[138]
When the velocity of crystallization is studied at temperatures above the
maximum point, it is found that the velocity is diminished by the addition
of foreign substances; and in many cases, indeed, it has been found that
the diminution is the same for equimolecular quantities of different
substances. It would hence appear possible to utilize this behaviour as a
method for determining molecular weights.[139] The rule is, however, by no
means a universal one. Thus it has been found by F. Dreyer,[140] in
studying the velocity of crystallization of formanilide, that the
diminution in the velocity produced by equivalent amounts of different
substances is not the same, but that the foreign substances exercise a
specific influence. Further, von Pickardt's rule does not hold when the
foreign substance forms mixed crystals (Chap. X.) with the crystallizing
substance.[141]
Law of Successive Reactions.--When sulphur vapour is cooled at the ordinary
temperature, it first of all condenses to drops of liquid, which solidify
in an amorphous form, and only after some time undergo crystallization; or,
when phosphorus vapour is condensed, white phosphorus is first formed, and
not the more stable form--red phosphorus. It has also been observed that
even at the ordinary temperature (therefore much below the transition
point) sulphur may crystallize out from solution in benzene, alcohol,
carbon disulphide, and other {74} solvents, in the prismatic form, the less
stable prismatic crystals then undergoing transformation into the rhombic
form;[142] a similar behaviour has also been observed in the transformation
of the monotropic crystalline forms of sulphur.[143]
Many other examples might be given. In organic chemistry, for instance, it
is often found that when a substance is thrown out of solution, it is first
deposited as a liquid, which passes later into the more stable crystalline
form. In analysis, also, rapid precipitation from concentrated solution
often causes the separation of a less stable and more soluble amorphous
form.
On account of the great frequency with which the prior formation of the
less stable form occurs, Ostwald[144] has put forward the _law of
successive reactions_, which states that when a system passes from a less
stable condition it does not pass directly into the most stable of the
possible states; but into the next more stable, and so step by step into
the most stable. This law explains the formation of the metastable forms of
monotropic substances, which would otherwise not be obtainable. Although it
is not always possible to observe the formation of the least stable form,
it should be remembered that that may quite conceivably be due to the great
velocity of transformation of the less stable into the more stable form.
From what we have learned about the velocity of transformation of
metastable phases, we can understand that rapid cooling to a low
temperature will tend to preserve the less stable form; and, on account of
the influence of temperature in increasing the velocity of change, it can
be seen that the formation of the less stable form will be more difficult
to observe in superheated than in supercooled systems. The factors,
however, which affect the readiness with which {75} the less stable
modification is produced, appear to be rather various.[145]
Although a number of at least apparent exceptions to Ostwald's law have
been found, it may nevertheless be accepted as a very useful generalization
which sums up very frequently observed phenomena.
* * * * *
{76}
CHAPTER V
SYSTEMS OF TWO COMPONENTS--PHENOMENA OF DISSOCIATION
In the preceding pages we have studied the behaviour of systems consisting
of only one component, or systems in which all the phases, whether solid,
liquid, or vapour, had the same chemical composition (p. 13). In some
cases, as, for example, in the case of phosphorus and sulphur, the
component was an elementary substance; in other cases, however, _e.g._
water, the component was a compound. The systems which we now proceed to
study are characterized by the fact that the different phases have no
longer all the same chemical composition, and cannot, therefore, according
to definition, be considered as one-component systems.
In most cases, little or no difficulty will be experienced in deciding as
to the _number_ of the components, if the rules given on pp. 12 and 13 are
borne in mind. If the composition of all the phases, each regarded as a
whole, is the same, the system is to be regarded as of the first order, or
a one-component system; if the composition of the different phases varies,
the system must contain more than one component. If, in order to _express_
the composition of all the phases present when the system is in
equilibrium, two of the constituents participating in the equilibrium are
necessary and sufficient, the system is one of two components. Which two of
the possible substances are to be regarded as components will, however, be
to a certain extent a matter of arbitrary choice.
The principles affecting the choice of components will best be learned by a
study of the examples to be discussed in the sequel. {77}
Different Systems of Two Components.--Applying the Phase Rule
P + F = C + 2
to systems of two components, we see that in order that the system may be
invariant, there must be four phases in equilibrium together; two
components in three phases constitute a univariant, two components in two
phases a bivariant system. In the case of systems of one component, the
highest degree of variability found was two (one component in one phase);
but, as is evident from the formula, there is a higher degree of freedom
possible in the case of two-component systems. Two components existing in
only one phase constitute a tervariant system, or a system with three
degrees of freedom. In addition to the pressure and temperature, therefore,
a third variable factor must be chosen, and as such there is taken the
_concentration of the components_. In systems of two components, therefore,
not only may there be change of pressure and temperature, as in the case of
one-component systems, but the concentration of the components in the
different phases may also alter; a variation which did not require to be
considered in the case of one-component systems.
[Illustration: FIG. 18.]
Since a two-component system may undergo three possible {78} independent
variations, we should require for the graphic representation of all the
possible conditions of equilibrium a system of three co-ordinates in space,
three axes being chosen, say, at right angles to one another, and
representing the three variables--pressure, temperature, and concentration
of components (Fig. 18). A curve (_e.g._ AB) in the plane containing the
pressure and temperature axes would then represent the change of pressure
with the temperature, the concentration remaining unaltered (_pt_-diagram);
one in the plane containing the pressure and concentration axes (_e.g._ AF
or DF), the change of pressure with the concentration, the temperature
remaining constant (_pc_-diagram), while in the plane containing the
concentration and the temperature axes, the simultaneous change of these
two factors at constant pressure would be represented (_tc_-diagram). If
the points on these three curves are joined together, a surface, ABDE, will
be formed, and any line on that surface (_e.g._ FG, or GH, or GI) would
represent the simultaneous variation of the three factors--pressure,
temperature, concentration. Although we shall at a later point make some
use of these solid figures, we shall for the present employ the more
readily intelligible plane diagram.
The number of different systems which can be formed from two components, as
well as the number of the different phenomena which can there be observed,
is much greater than in the case of one component. In the case of no two
substances, however, have all the possible relationships been studied; so
that for the purpose of gaining an insight into the very varied behaviour
of two-component systems, a number of different examples will be discussed,
each of which will serve to give a picture of some of the relationships.
Although the strict classification of the different systems according to
the Phase Rule would be based on the variability of the systems, the study
of the many different phenomena, and the correlation of the comparatively
large number of different systems, will probably be rendered easiest by
grouping these different phenomena into classes, each of these classes
being studied with the help of one or more typical examples. The order of
treatment adopted here is, of course, quite arbitrary; {79} but has been
selected from considerations of simplicity and clearness.
PHENOMENA OF DISSOCIATION.
Bivariant Systems.--As the first examples of the equilibria between a
substance and its products of dissociation, we shall consider very briefly
those cases in which there is one solid phase in equilibrium with vapour.
Reference has already been made to such systems in the case of ammonium
chloride. On being heated, ammonium chloride dissociates into ammonia and
hydrogen chloride. Since, however, in that case the vapour phase has the
same total composition as the solid phase, viz. NH_{3} + HCl = NH_{4}Cl,
the system consists of only one component existing in two phases; it is
therefore univariant, and to each temperature there will correspond a
definite vapour pressure (dissociation pressure).[146]
If, however, excess of one of the products of dissociation be added, the
system becomes one of two components.
In the first place, analysis of each of the two phases yields as the
composition of each, solid: NH_{4}Cl (= NH_{3} + HCl); vapour: _m_NH_{3} +
_n_HCl. Obviously the smallest number of substances by which the
composition of the two phases can be expressed is two; that is, the number
of components is two. What, then, are the components? The choice lies
between NH_{3} + HCl, NH_{4}Cl + NH_{3}, and NH_{4}Cl + HCl; for the three
substances, ammonium chloride, ammonia, hydrogen chloride, are the only
ones taking part in the equilibrium of the system.
Of these three pairs of components, we should obviously choose as the most
simple NH_{3} and HCl, for we can then represent the composition of the two
phases as the _sum_ of the two components. If one of the other two possible
pairs of components be chosen, we should have to introduce negative
quantities of one of the components, in order to represent the composition
of the vapour phase. Although it must be allowed that the introduction of
negative quantities of a component in such cases is quite permissible,
still it will be {80} better to adopt the simpler and more direct choice,
whereby the composition of each of the phases is represented as a sum of
two components in varying proportions (p. 12).
If, therefore, we have a solid substance, such as ammonium chloride, which
dissociates on volatilization, and if the products of dissociation are
added in varying amounts to the system, we shall have, in the sense of the
Phase Rule, a _two-component system existing in two phases_. Such a system
will possess two degrees of freedom. At any given temperature, not only the
pressure, but also the composition, of the vapour-phase, _i.e._ the
concentration of the components, can vary. Only after one of these
independent variables, pressure or composition, has been arbitrarily fixed
does the system become univariant, and exhibit a definite, constant
pressure at a given temperature.
Now, although the Phase Rule informs us that at a given temperature change
of composition of the vapour phase will be accompanied by change of
pressure, it does not cast any light on the relation between these two
variables. This relationship, however, can be calculated theoretically by
means of the Law of Mass Action.[147] From this we learn that in the case
of a substance which dissociates into equivalent quantities of two gases,
the product of the partial pressures of the gases is constant at a given
temperature.
This has been proved experimentally in the case of ammonium hydrosulphide,
ammonium cyanide, phosphonium bromide, and other substances.[148]
Univariant Systems.--In order that a system of two components shall possess
only one degree of freedom, three phases must be present. Of such systems,
there are seven possible, viz. S-S-S, S-S-L, S-S-V, L-L-L, S-L-L, L-L-V,
S-L-V; S denoting solid, L liquid, and V vapour. In the present chapter we
shall consider only the systems S-S-V, _i.e._ those systems in which there
are two solid phases and a vapour phase present.
{81}
As an example of this, we may first consider the well-known case of the
dissociation of calcium carbonate. This substance on being heated
dissociates into calcium oxide, or quick-lime, and carbon dioxide, as shown
by the equation CaCO_{3} <--> CaO + CO_{2}. In accordance with our
definition (p. 9), we have here two solid phases, the carbonate and the
quick-lime, and one vapour phase; the system is therefore univariant. To
each temperature, therefore, there will correspond a certain, definite
maximum pressure of carbon dioxide (dissociation pressure), and this will
follow the same law as the vapour pressure of a pure liquid (p. 21). More
particularly, it will be independent of the relative or absolute amounts of
the two solid phases, and of the volume of the vapour phase. If the
temperature is maintained constant, increase of volume will cause the
dissociation of a further amount of the carbonate until the pressure again
reaches its maximum value corresponding to the given temperature.
Diminution of volume, on the other hand, will bring about the combination
of a certain quantity of the carbon dioxide with the calcium oxide until
the pressure again reaches its original value.
The dissociation pressure of calcium carbonate was first studied by
Debray,[149] but more exact measurements have been made by Le
Chatelier,[150] who found the following corresponding values of temperature
and pressure:--
-------------+-------------------------
|
Temperature. | Pressure in cm. mercury.
-------------+-------------------------
|
547deg | 2.7
610deg | 4.6
625deg | 5.6
740deg | 25.5
745deg | 28.9
810deg | 67.8
812deg | 76.3
865deg | 133.3
-------------+-------------------------
From this table we see that it is only at a temperature of about 812deg
that the pressure of the carbon dioxide becomes equal to atmospheric
pressure. In a vessel open to {82} the air, therefore, the complete
decomposition of the calcium carbonate would not take place below this
temperature by the mere heating of the carbonate. If, however, the carbon
dioxide is removed as quickly as it is formed, say by a current of air,
then the entire decomposition can be made to take place at a much lower
temperature. For the dissociation equilibrium of the carbonate depends only
on the partial pressure of the carbon dioxide, and if this is kept small,
then the decomposition can proceed, even at a temperature below that at
which the pressure of the carbon dioxide is less than atmospheric pressure.
Ammonia Compounds of Metal Chlorides.--Ammonia possesses the property of
combining with various substances, chiefly the halides of metals, to form
compounds which again yield up the ammonia on being heated. Thus, for
example, on passing ammonia over silver chloride, absorption of the gas
takes place with formation of the substances AgCl,3NH_{3} and
2AgCl,3NH_{3}, according to the conditions of the experiment. These were
the first known substances belonging to this class, and were employed by
Faraday in his experiments on the liquefaction of ammonia. Similar
compounds have also been obtained by the action of ammonia on silver
bromide, iodide, cyanide, and nitrate; and with the halogen compounds of
calcium, zinc, and magnesium, as well as with other salts. The behaviour of
the ammonia compounds of silver chloride is typical for the compounds of
this class, and may be briefly considered here.
It was found by Isambert[151] that at temperatures below 15deg, silver
chloride combined with ammonia to form the compound AgCl,3NH_{3}, while at
temperatures above 20deg the compound 2AgCl,3NH_{3} was produced. On
heating these substances, ammonia was evolved, and the pressure of this gas
was found in the case of both compounds to be constant at a given
temperature, but was greater in the case of the former than in the case of
the latter substance; the pressure, further, was independent of the amount
decomposed. The behaviour of these two substances is, therefore, exactly
analogous to that shown by calcium carbonate, and the explanation is also
similar.
{83}
Regarded from the point of view of the Phase Rule, we see that we are here
dealing with two components, AgCl and NH_{3}. On being heated, the
compounds decompose according to the equations:--
2(AgCl,3NH_{3}) <--> 2AgCl,3NH_{3} + 3NH_{3}.
2AgCl,3NH_{3} <--> 2AgCl + 3NH_{3}.
There are, therefore, three phases, viz. AgCl,3NH_{3}; 2AgCl,3NH_{3}, and
NH_{3}, in the one case; and 2AgCl,3NH_{3}; AgCl, and NH_{3} in the other.
These two systems are therefore univariant, and to each temperature there
must correspond a definite pressure of dissociation, quite irrespective of
the amounts of the phases present. Similarly, if, at constant temperature,
the volume is increased (or if the ammonia which is evolved is pumped off),
the pressure will remain constant so long as two solid phases, AgCl,3NH_{3}
and 2AgCl,3NH_{3}, are present, _i.e._ until the compound richer in ammonia
is completely decomposed, when there will be a sudden fall in the pressure
to the value corresponding to the system 2AgCl,3NH_{3}--AgCl--NH_{3}. The
pressure will again remain constant at constant temperature, until all the
ammonia has been pumped off, when there will again be a sudden fall in the
pressure to that of the system formed by solid silver chloride in contact
with its vapour.
The reverse changes take place when the pressure of the ammonia is
gradually increased. If the volume is continuously diminished, the pressure
will first increase until it has reached a certain value; the compound
2AgCl,3NH_{3} can then be formed, and the pressure will now remain constant
until all the silver chloride has disappeared. The pressure will again
rise, until it has reached the value at which the compound AgCl,3NH_{3} can
be formed, when it will again remain constant until the complete
disappearance of the lower compound. _There is no gradual change of
pressure_ on passing from one system to another; but the changes are
abrupt, as is demanded by the Phase Rule, and as experiment has
conclusively proved.[152]
The dissociation pressures of the two compounds of silver {84} chloride and
ammonia, as determined by Isambert,[153] are given in the following
table:--
-------------------------+-------------------------
|
AgCl,3NH_{3}. | 2AgCl,3NH_{3}.
-------------+-----------+--------------+----------
| | |
Temperature. | Pressure. | Temperature. | Pressure.
-------------+-----------+--------------+----------
| | |
0deg | 29.3 cm. | 20.0deg | 9.3 cm.
10.6deg | 50.5 " | 31.0deg | 12.5 "
17.5deg | 65.5 " | 47.0deg | 26.8 "
24.0deg | 93.7 " | 58.5deg | 52.8 "
28.0deg | 135.5 " | 69.0deg | 78.6 "
34.2deg | 171.3 " | 71.5deg | 94.6 "
48.5deg | 241.4 " | 77.5deg | 119.8 "
51.5deg | 413.2 " | 83.5deg | 159.3 "
54.0deg | 464.1 " | 86.1deg | 181.3 "
| | 88.5deg | 201.3 "
-------------+-----------+--------------+----------
The conditions for the formation of these two compounds, by passing ammonia
over silver chloride, to which reference has already been made, will be
readily understood from the above tables. In the case of the triammonia
mono-chloride, the dissociation pressure becomes equal to atmospheric
pressure at a temperature of about 20deg; above this temperature,
therefore, it cannot be formed by the action of ammonia at atmospheric
pressure on silver chloride. The triammonia dichloride can, however, be
formed, for its dissociation pressure at this temperature amounts to only 9
cm., and becomes equal to the atmospheric pressure only at a temperature of
about 68deg; and this temperature, therefore, constitutes the limit above
which no combination can take place between silver chloride and ammonia
under atmospheric pressure.
Attention may be here drawn to the fact, to which reference will also be
made later, that _two_ solid phases are necessary in order that the
dissociation pressure at a given temperature shall be definite; _and for
the exact definition of this pressure it is necessary to know, not merely
what is the substance undergoing dissociation, but also what is the solid
product of dissociation formed_. For the definition of the equilibrium, the
latter is as important as the former. We shall presently find proof of this
in the case {85} of an analogous class of phenomena, viz. the dissociation
of salt hydrates.
Salts with Water of Crystallization.--In the case of the dehydration of
crystalline salts containing water of crystallization, we meet with
phenomena which are in all respects similar to those just studied. A salt
hydrate on being heated dissociates into a lower hydrate (or anhydrous
salt) and water vapour. Since we are dealing with two components--salt and
water[154]--in three phases, viz. hydrate _a_, hydrate _b_ (or anhydrous
salt), and vapour, the system is univariant, and to each temperature there
will correspond a certain, definite vapour pressure (the dissociation
pressure), which will be independent of the relative or absolute amounts of
the phases, _i.e._ of the amount of hydrate which has already undergone
dissociation or dehydration.
[Illustration: FIG. 19.]
The constancy of the dissociation pressure had been proved experimentally
by several investigators[155] a number of years before the theoretical
basis for its necessity had been given. In the case of salts capable of
forming more than one hydrate, we should obtain a series of dissociation
curves (_pt_-curves), as in the case of the different hydrates of copper
sulphate. In Fig. 19 there are represented diagrammatically the
vapour-pressure curves of the following univariant systems of copper
sulphate and water:--
Curve OA: CuSO_{4},5H_{2}O <--> CuSO_{4},3H_{2}O + 2H_{2}O.
Curve OB: CuSO_{4},3H_{2}O <--> CuSO_{4},H_{2}O + 2H_{2}O.
Curve OC: CuSO_{4},H_{2}O <--> CuSO_{4} + H_{2}O.
Let us now follow the changes which take place on {86} increasing the
pressure of the aqueous vapour in contact with anhydrous copper sulphate,
the temperature being meanwhile maintained constant. If, starting from the
point D, we slowly add water vapour to the system, the pressure will
gradually rise, without formation of hydrate taking place; for at pressures
below the curve OC only the anhydrous salt can exist. At E, however, the
hydrate CuSO_{4},H_{2}O will be formed, and as there are now three phases
present, viz. CuSO_{4}, CuSO_{4},H_{2}O, and vapour, the system becomes
_univariant_; and since the temperature is constant, the pressure must also
be constant. Continued addition of vapour will result merely in an increase
in the amount of the hydrate, and a decrease in the amount of the anhydrous
salt. When the latter has entirely disappeared, _i.e._ has passed into
hydrated salt, the system again becomes _bivariant_, and passes along the
line EF; the pressure gradually increases, therefore, until at F the
hydrate 3H_{2}O is formed, and the system again becomes univariant; the
three phases present are CuSO_{4},H_{2}O, CuSO_{4},3H_{2}O, vapour. The
pressure will remain constant, therefore, until the hydrate 1H_{2}O has
disappeared, when it will again increase till G is reached; here the
hydrate 5H_{2}O is formed, and the pressure once more remains constant
until the complete disappearance of the hydrate 3H_{2}O has taken place.
Conversely, on dehydrating CuSO_{4},5H_{2}O at constant temperature, we
should find that the pressure would maintain the value corresponding to the
dissociation pressure of the system
CuSO_{4},5H_{2}O--CuSO_{4},3H_{2}O--vapour, until all the hydrate 5H_{2}O
had disappeared; further removal of water would then cause the pressure to
fall _abruptly_ to the pressure of the system
CuSO_{4},3H_{2}O--CuSO_{4},H_{2}O--vapour, at which value it would again
remain constant until the tri-hydrate had passed into the monohydrate, when
a further sudden diminution of the pressure would occur. This behaviour is
represented diagrammatically in Fig. 20, the values of the pressure being
those at 50deg.
Efflorescence.--From Fig. 19 we are enabled to predict the conditions under
which a given hydrated salt will effloresce when exposed to the air. We
have just learned that copper {87} sulphate pentahydrate, for example, will
not be formed unless the pressure of the aqueous vapour reaches a certain
value; and that conversely, if the vapour pressure falls below the
dissociation pressure of the pentahydrate, this salt will undergo
dehydration. From this, then, it is evident that a crystalline salt hydrate
will effloresce when exposed to the air, if the partial pressure of the
water vapour in the air is lower than the dissociation pressure of the
hydrate. At the ordinary temperature the dissociation pressure of copper
sulphate is less than the pressure of water vapour in the air, and
therefore copper sulphate does not effloresce. In the case of sodium
sulphate decahydrate, however, the dissociation pressure is greater than
the normal vapour pressure in a room, and this salt therefore effloresces.
[Illustration: FIG. 20.]
Indefiniteness of the Vapour Pressure of a Hydrate.--Reference has already
been made (p. 84), in the case of the ammonia compounds of the metal
chlorides, to the importance of the solid product of dissociation for the
definition of the dissociation pressure. Similarly also in the case of a
hydrated salt. A salt hydrate in contact with vapour constitutes only a
bivariant system, and can exist therefore at different values of
temperature and pressure of vapour, as is seen from the diagram, Fig. 19.
Anhydrous copper sulphate can exist in contact with water vapour at all
values of temperature and pressure lying in the field below the curve OC;
and the hydrate CuSO_{4},H_{2}O can exist in contact with vapour at all
values of temperature and pressure in the field BOC. Similarly, each of the
other hydrates can exist in contact with vapour at different values of
temperature and pressure.
From the Phase Rule, however, we learn that, in order that at a given
temperature the pressure of a two-component system {88} may be constant,
there must be three phases present. Strictly, therefore, we can speak only
of the vapour pressure of a _system_; and since, in the cases under
discussion, the hydrates dissociate into a solid and a vapour, any
statement as to the vapour pressure of a hydrate has a definite meaning
_only when the second solid phase produced by the dissociation is given_.
The everyday custom of speaking of the vapour pressure of a hydrated salt
acquires a meaning only through the assumption, tacitly made, that the
second solid phase, or the solid produced by the dehydration of the
hydrate, is the _next lower_ hydrate, where more hydrates than one exist.
That a hydrate always dissociates in such a way that the next lower hydrate
is formed is, however, by no means certain; indeed, cases have been met
with where apparently the anhydrous salt, and not the lower hydrate (the
existence of which was possible), was produced by the dissociation of the
higher hydrate.[156]
That a salt hydrate can exhibit different vapour pressures according to the
solid product of dissociation, can not only be proved theoretically, but it
has also been shown experimentally to be a fact. Thus CaCl_{2},6H_{2}O can
dissociate into water vapour and either of two lower hydrates, each
containing four molecules of water of crystallization, and designated
respectively as CaCl_{2},4H_{2}O[alpha], and CaCl_{2},4H_{2}O[beta].
Roozeboom[157] has shown that the vapour pressure which is obtained differs
according to which of these two hydrates is formed, as can be seen from the
following figures:--
-------------+----------------------------------------------------------
| Pressure of System.
Temperature. +-----------------------------+----------------------------
| CaCl_{2},6H_{2}O; CaCl_{2}, | CaCl_{2},6H_{2}O; CaCl_{2},
| 4H_{2}O[alpha]; vapour. | 4H_{2}O[beta]; vapour.
-------------+-----------------------------+----------------------------
-15deg | 0.027 cm. | 0.022 cm.
0 | 0.092 " | 0.076 "
+10 | 0.192 " | 0.162 "
20 | 0.378 " | 0.315 "
25 | 0.508 " | 0.432 "
29.2 | -- | 0.567 "
29.8 | 0.680 " | --
-------------+-----------------------------+---------------------------
{89}
By reason of the non-recognition of the importance of the solid
dissociation product for the definition of the dissociation pressure of a
salt hydrate, many of the older determinations lose much of their value.
Suspended Transformation.--Just as in systems of one component we found
that a new phase was not necessarily formed when the conditions for its
existence were established, so also we find that even when the vapour
pressure is lowered below the dissociation pressure of a system,
dissociation does not necessarily occur. This is well known in the case of
Glauber's salt, first observed by Faraday. Undamaged crystals of
Na_{2}SO_{4},10H_{2}O could be kept unchanged in the open air, although the
vapour pressure of the system Na_{2}SO_{4},10H_{2}O--Na_{2}SO_{4}--vapour
is greater than the ordinary pressure of aqueous vapour in the air. That is
to say, the possibility of the formation of the new phase Na_{2}SO_{4} was
given; nevertheless this new phase did not appear, and the system therefore
became metastable, or unstable with respect to the anhydrous salt. When,
however, a trace of the new phase--the anhydrous salt--was brought in
contact with the hydrate, transformation occurred; the hydrate effloresced.
The possibility of suspended transformation or the non-formation of the new
phases must also be granted in the case where the vapour pressure is raised
above that corresponding to the system hydrate--anhydrous salt (or lower
hydrate)--vapour; in this case the formation of the higher hydrate becomes
a possibility, but not a certainty. Although there is no example of this
known in the case of hydrated salts, the suspension of the transformation
has been observed in the case of the compounds of ammonia with the metal
chlorides (p. 82). Horstmann,[158] for example, found that the pressure of
ammonia in contact with 2AgCl,3NH_{3} could be raised to a value higher
than the dissociation pressure of AgCl,3NH_{3} without this compound being
formed. We see, therefore, that even when the existence of the higher
compound in contact with the lower became possible, the higher compound was
not immediately formed.
Range of Existence of Hydrates.--In Fig. 19 the vapour {90} pressure curves
of the different hydrates of copper sulphate are represented as maintaining
their relative positions throughout the whole range of temperatures. But
this is not necessarily the case. It is possible that at some temperature
the vapour pressure curve of a lower hydrate may cut that of a higher
hydrate. At temperatures above the point of intersection, the lower hydrate
would have a higher vapour pressure than the higher hydrate, and would
therefore be metastable with respect to the latter. The range of stable
existence of the lower hydrate would therefore end at the point of
intersection. This appears to be the case with the two hydrates of sodium
sulphate, to which reference will be made later.[159]
Constancy of Vapour Pressure and the Formation of Compounds.--We have seen
in the case of the salt hydrates that the continued addition of the vapour
phase to the system caused an increase in the pressure until at a definite
value of the pressure a hydrate is formed; the pressure then becomes
constant, and remains so, until one of the solid phases has disappeared.
Conversely, on withdrawing the vapour phase, the pressure remained constant
so long as any of the dissociating compound was present, independently of
the degree of the decomposition (p. 86). This behaviour, now, has been
employed for the purpose of determining whether or not definite chemical
compounds are formed. Should compounds be formed between the vapour phase
and the solid, then, on continued addition or withdrawal of the vapour
phase, it will be found that the vapour pressure remains constant for a
certain time, and will then suddenly assume a new value, at which it will
again remain constant. By this method, Ramsay[160] found that no definite
hydrates were formed in the case of ferric and aluminium oxides, but that
two are formed in the case of lead oxide, viz. 2PbO,H_{2}O and 3PbO,H_{2}O.
The method has also been applied to the investigation of the so-called
palladium hydride,[161] and the results obtained appear to show that no
compound is formed. Reference will, however, be made to this case later
(Chap. X.).
{91}
Measurement of the Vapour Pressure of Hydrates.--For the purpose of
measuring the small pressures exerted by the vapour of salt hydrates, use
is very generally made of a differential manometer called the
_Bremer-Frowein tensimeter_.[162]
This apparatus has the form shown in Fig. 21. It consists of a U-tube, the
limbs of which are bent close together, and placed in front of a millimetre
scale. The bend of the tube is filled with oil or other suitable liquid,
_e.g._ bromonaphthalene. If it is desired to measure the dissociation
pressure of, say, a salt hydrate, concentrated sulphuric acid is placed in
the flask _e_, and a quantity of the hydrate, well dried and powdered,[163]
in the bulb d. The necks of the bulbs _d_ and _e_ are then sealed off.
Since, as we have learned, suspended transformation may occur, it is
advisable to first partially dehydrate the salt, in order to ensure the
presence of the second solid product of dissociation; the value of the
dissociation pressure being independent of the degree of dissociation of
the hydrate (p. 86). The small bulbs _d_ and _e_ having been filled, the
apparatus is placed on its side, so as to allow the liquid to run from the
bend of the tube into the bulbs _a_ and _b_; it is then exhausted through
_f_ by means of a mercury pump, and sealed off. The apparatus is now placed
in a perpendicular position in a thermostat, and kept at constant
temperature until equilibrium is established. Since the vapour pressure on
the side containing the sulphuric acid may be regarded as zero, the
difference in level of the two surfaces of liquid in the U-tube gives
directly the dissociation pressure of the hydrate in terms of the
particular liquid employed; if the density of the latter is known, the
pressure can then be calculated to cm. of mercury.
[Illustration: FIG. 21.]
* * * * *
{92}
CHAPTER VI
SOLUTIONS
Definition.--In all the cases which have been considered in the preceding
pages, the different phases--with the exception of the vapour
phase--consisted of a single substance of definite composition, or were
definite chemical individuals.[164] But this invariability of the
composition is by no means imposed by the Phase Rule; on the contrary, we
shall find in the examples which we now proceed to study, that the
participation of phases of variable composition in the equilibrium of a
system is in no way excluded. To such phases of variable composition there
is applied the term _solution_. A solution, therefore, is to be defined as
_a homogeneous mixture, the composition of which can undergo continuous
variation within certain limits_; the limits, namely, of its
existence.[165]
From this definition we see that the term solution is not restricted to any
particular physical state of substances, but includes within its range not
only the liquid, but also the gaseous and solid states. We may therefore
have solutions of gases in liquids, and of gases in solids; of liquids in
liquids or in solids; of solids in liquids, or of solids in solids.
Solutions of gases in gases are, of course, also possible; since, however,
gas solutions never give rise to more than one phase, their {93} treatment
does not come within the scope of the Phase Rule, which deals with
heterogeneous equilibria.
It should also be emphasized that the definition of solution given above,
neither creates nor recognizes any distinction between solvent and
dissolved substance (solute); and, indeed, a too persistent use of these
terms and the attempt to permanently label the one or other of two
components as the solvent or the solute, can only obscure the true
relationships and aggravate the difficulty of their interpretation. In all
cases it should be remembered that we are dealing with equilibria between
two components (we confine our attention in the first instance to such),
the solution being constituted of these components in variable and varying
amounts. The change from the case where the one component is in great
excess (ordinarily called the solvent) to that in which the other component
predominates, may be quite gradual, so that it is difficult or impossible
to say at what point the one component ceases to be the solvent and becomes
the solute. The adoption of this standpoint need not, however, preclude one
from employing the conventional terms solvent and solute in ordinary
language, especially when reference is made only to some particular
condition of equilibrium of the system, when the concentration of the two
components in the solution is widely different.
SOLUTIONS OF GASES IN LIQUIDS.
As the first class of solutions to which we shall turn our attention, there
may be chosen the solutions of gases in liquids, or the equilibria between
a liquid and a gas. These equilibria really constitute a part of the
equilibria to be studied more fully in Chapter VIII.; but since the
two-phase systems formed by the solutions of gases in liquids are among the
best-known of the two-component systems, a short section may be here
allotted to their treatment.
When a gas is passed into a liquid, absorption takes place to a greater or
less extent, and a point is at length reached when the liquid absorbs no
more of the gas; a condition of equilibrium is attained, and the liquid is
said to be saturated {94} with the gas. In the light of the Phase Rule,
now, such a system is bivariant (two components in two phases); and two of
the variable factors, pressure, temperature, and concentration of the
components, must therefore be chosen in order that the condition of the
system may be defined. If the concentration and the temperature are fixed,
then the pressure is also defined; or under given conditions of temperature
and pressure, the concentration of the gas in the solution must have a
definite value. If, however, the temperature alone is fixed, the
concentration and the pressure can alter; a fact so well known that it does
not require to be further insisted on.
As to the way in which the solubility of a gas in a liquid varies with the
pressure, the Phase Rule of course does not state; but guidance on this
point is again yielded by the theorem of van't Hoff and Le Chatelier. Since
the absorption of a gas is in all cases accompanied by a diminution of the
total volume, this process must take place with increase of pressure. This,
indeed, is stated in a quantitative manner in the law of Henry, according
to which the amount of a gas absorbed is proportional to the pressure. But
this law must be modified in the case of gases which are very readily
absorbed; the _direction of change_ of concentration with the pressure
will, however, still be in accordance with the theorem of Le Chatelier.
If, on the other hand, the pressure is fixed, then the concentration will
vary with the temperature; and since the absorption of gases is in all
cases accompanied by the evolution of heat, the solubility is found, in
accordance with the theorem of Le Chatelier, to diminish with rise of
temperature.
In considering the changes of pressure accompanying changes of
concentration and temperature, a distinction must be drawn between the
total pressure and the partial pressure of the dissolved gas, in cases
where the solvent is volatile. In these cases, the law of Henry applies not
to the total pressure of the vapour, but only to the partial pressure of
the dissolved gas. {95}
SOLUTIONS OF LIQUIDS IN LIQUIDS.
When mercury and water are brought together, the two liquids remain side by
side without mixing. Strictly speaking, mercury undoubtedly dissolves to a
certain extent in the water, and water no doubt dissolves, although to a
less extent, in the mercury; the amount of substance passing into solution
is, however, so minute, that it may, for all practical purposes, be left
out of account, so long as the temperature does not rise much above the
ordinary.[166] On the other hand, if alcohol and water be brought together,
complete miscibility takes place, and one homogeneous solution is obtained.
Whether water be added in increasing quantities to pure alcohol, or pure
alcohol be added in increasing amount to water, at no point, at no degree
of concentration, is a system obtained containing more than one liquid
phase. At the ordinary temperature, water and alcohol can form only two
phases, liquid and vapour. If, however, water be added to ether, or if
ether be added to water, solution will not occur to an indefinite extent;
but a point will be reached when the water or the ether will no longer
dissolve more of the other component, and a further addition of water on
the one hand, or ether on the other, will cause the formation of two liquid
layers, one containing excess of water, the other excess of ether. We
shall, therefore, expect to find all grades of miscibility, from almost
perfect immiscibility to perfect miscibility, or miscibility in all
proportions. In cases of perfect immiscibility, the components do not
affect one another, and the system therefore remains unchanged. Such cases
do not call for treatment here. We have to concern ourselves here only with
the second and third cases, viz. with cases of complete and of partial
miscibility. There is no essential difference between the two classes, for,
as we shall see, {96} the one passes into the other with change of
temperature. The formal separation into two groups is based on the
miscibility relations at ordinary temperatures.
Partial or Limited Miscibility.--In accordance with the Phase Rule, a pure
liquid in contact with its vapour constitutes a univariant system. If,
however, a small quantity of a second substance is added, which is capable
of dissolving in the first, a bivariant system will be obtained; for there
are now two components and, as before, only two phases--the homogeneous
liquid solution and the vapour. At constant temperature, therefore, both
the composition of the solution and the pressure of the vapour can undergo
change; or, if the composition of the solution remains unchanged, the
pressure and the temperature can alter. If the second (liquid) component is
added in increasing amount, the liquid will at first remain homogeneous,
and its composition and pressure will undergo a continuous change; when,
however, the concentration has reached a definite value, solution no longer
takes place; two liquid phases are produced. Since there are now three
phases present, two liquids and vapour, the system is univariant; at a
given temperature, therefore, the concentration of the components in the
two liquid phases, as well as the vapour pressure, must have definite
values. Addition of one of the components, therefore, cannot alter the
concentrations or the pressure, but can only cause a change in the relative
amounts of the phases.
The two liquid phases can be regarded, the one as a solution of the
component I. in component II., the other as a solution of component II. in
component I. If the pressure is maintained constant, then to each
temperature there will correspond a definite concentration of the
components in the two liquid phases; and addition of excess of one will
merely alter the relative amounts of the two solutions. As the temperature
changes, the composition of the two solutions will change, and there will
therefore be obtained two solubility curves, one showing the solubility of
component I. in component II., the other showing the solubility of
component II. in component I. Since heat may be either evolved or absorbed
when one liquid dissolves in another, the solubility may diminish or
increase {97} with rise of temperature. The two solutions which at a given
temperature correspond to one another are known as _conjugate solutions_.
The solubility relations of partially miscible liquids have been studied by
Guthrie,[167] and more especially by Alexejeff[168] and by Rothmund.[169] A
considerable variety of curves have been obtained, and we shall therefore
discuss only a few of the different cases which may be taken as typical of
the rest.
Phenol and Water.--When phenol is added to water at the ordinary
temperature, solution takes place, and a homogeneous liquid is produced.
When, however, the concentration of the phenol in the solution has risen to
about 8 per cent., phenol ceases to be dissolved; and a further addition of
it causes the formation of a second liquid phase, which consists of excess
of phenol and a small quantity of water. In ordinary language it may be
called a solution of water in phenol. If now the temperature is raised,
this second liquid phase will disappear, and a further amount of phenol
must be added in order to produce a separation of the liquid into two
layers. In this way, by increasing the amount of phenol and noting the
temperature at which the two layers disappear, the so-called solubility
curve of phenol in water can be obtained. By noting the change of the
solubility with the temperature in this manner, it is found that at all
temperatures below 68.4deg, the addition of more than a certain amount of
phenol causes the formation of two layers; at temperatures above this,
however, two layers cannot be formed, no matter how much phenol is added.
At temperatures above 68.4deg, therefore, water and phenol are miscible in
all proportions.
On the other hand, if water is added to phenol at the ordinary temperature,
a liquid is produced which consists chiefly of phenol, and on increasing
the amount of water beyond a certain point, two layers are formed. On
raising the temperature these two layers disappear, and a homogeneous
solution is again obtained. The phenomena are exactly analogous to those
already described. Since, now, in the second {98} case the concentration of
the phenol in the solution gradually decreases, while in the former case it
gradually increases, a point must at length be reached at which the
composition of the two solutions becomes the same. On mixing the two
solutions, therefore, one homogeneous liquid will be obtained. But the
point at which two phases become identical is called a critical point, so
that, in accordance with this definition, the temperature at which the two
solutions of phenol and water become identical may be called the _critical
solution temperature_, and the concentration at this point may be called
the _critical concentration_.
[Illustration: FIG. 22.]
From what has been said above, it will be seen that at any temperature
below the critical solution temperature, two conjugate solutions containing
water and phenol in different concentration can exist together, one
containing excess of water, the other excess of phenol. The following table
gives the composition of the two layers, and the values are represented
graphically in Fig. 22.[170]
PHENOL AND WATER.
C_{1} is the percentage amount of phenol in the first layer.
C_{2} " " " second layer.
-------------+--------+--------
Temperature. | C_{1}.| C_{2}.
-------------+--------+--------
20deg | 8.5 | 72.2
30deg | 8.7 | 69.9
40deg | 9.7 | 66.8
50deg | 12.0 | 62.7
55deg | 14.2 | 60.0
60deg | 17.5 | 56.2
65deg | 22.7 | 49.7
68.4deg | 36.1 | 36.1
-------------+--------+--------
{99}
The critical solution temperature for phenol and water is 68.4deg, the
critical concentration 36.1 per cent. of phenol. At all temperatures above
68.4deg, only homogeneous solutions of phenol and water can be obtained;
water and phenol are then miscible in all proportions.
At the critical solution point the system exists in only two phases--liquid
and vapour. It ought, therefore, to possess two degrees of freedom. The
restriction is, however, imposed that the composition of the two liquid
phases, coexisting at a point infinitely near to the critical point,
becomes the same, and this disposes of one of the degrees of freedom. The
system is therefore univariant; and at a given temperature the pressure
will have a definite value. Conversely, if the pressure is fixed (as is the
case when the system is under the pressure of its own vapour), then the
temperature will also be fixed; that is, the critical solution temperature
has a definite value depending only on the substances. If the vapour phase
is omitted, the temperature will alter with the pressure; in this case,
however, as in the case of other condensed systems, the effect of pressure
is slight.
From Fig. 22 it is easy to predict the effect of bringing together water
and phenol in any given quantities at any temperature. Start with a
solution of phenol and water having the composition represented by the
point _x_. If to this solution phenol is added at constant temperature, it
will dissolve, and the composition of the solution will gradually change,
as shown by the dotted line _xy_. When, however, the concentration has
reached the value represented by the point _y_, two liquid layers will be
formed, the one solution having the composition represented by _y_, the
other that represented by _y'_. The system is now univariant, and on
further addition of phenol, the composition of the two liquid phases will
remain unchanged, but their relative amounts will alter. The phase richer
in phenol will increase in amount; that richer in water will decrease, and
ultimately disappear, and there will remain the solution _y'_. Continued
addition of phenol will then lead to the point _x'_, there being now only
one liquid phase present.
Since the critical solution point represents the highest temperature at
which two liquid phases consisting of phenol and {100} water can exist
together, these two substances can be brought together in any amount
whatever at temperatures higher than 68.4deg, without the formation of two
layers. It will therefore be possible to pass from a system represented by
_x_ to one represented by _x'_, without at any time two liquid phases
appearing. Starting with _x_, the temperature is first raised above the
critical solution temperature; phenol is then added until the concentration
reaches the point _x__{2}. On allowing the temperature to fall, the system
will then pass into the condition represented by _x'_.
[Illustration: FIG. 23.]
Methylethylketone and Water.--In the case just described, the solubility of
each component in the other increased continuously with the temperature.
There are, however, cases where a maximum or minimum of solubility is
found, _e.g._ methylethylketone and water. The curve which represents the
equilibria between these two substances is given in Fig. 23, the
concentration values being contained in the following table:[171]--
METHYLETHYLKETONE AND WATER.
--------------+-----------------+-----------------
Temperature. | C_{1} per cent. | C_{2} per cent.
--------------+-----------------+-----------------
-10deg | 34.5 | 89.7
+10deg | 26.1 | 90.0
30deg | 21.9 | 89.9
50deg | 17.5 | 89.0
70deg | 16.2 | 85.7
90deg | 16.1 | 84.8
110deg | 17.7 | 80.0
130deg | 21.8 | 71.9
140deg | 26.0 | 64.0
151.8deg | 44.2 | 44.2
--------------+-----------------+-----------------
{101}
These numbers and Fig. 23 show clearly the occurrence of a minimum in the
solubility of the ketone in water, and also a minimum (at about 10deg) in
the solubility of water in methylethylketone. Minima of solubility have
also been found in other cases.
[Illustration: FIG. 24.]
Triethylamine and Water.--Although in most of the cases studied the
solubility of one liquid in another increases with rise of temperature,
this is not so in all cases. Thus, at temperatures below 18deg,
triethylamine and water mix together in all proportions; but, on raising
the temperature, the homogeneous solution becomes turbid and separates into
two layers. In this case, therefore, the critical solution temperature is
found in the direction of lower temperature, not in the direction of
higher.[172] This behaviour is clearly shown by the graphic representation
in Fig. 24, and also by the numbers in the following table:--
TRIETHYLAMINE AND WATER.
-------------+-----------------+----------------
Temperature. | C_{1} per cent. | C_{2} per cent.
-------------+-----------------+----------------
70deg | 1.6 | --
50deg | 2.9 | --
30deg | 5.6 | 96
25deg | 7.3 | 95.5
20deg | 15.5 | 73
+/-18.5deg | +/-30 | +/-30
-------------+-----------------+----------------
General Form of Concentration-Temperature Curve.--From the preceding
figures it will be seen that the general {102} form of the solubility curve
is somewhat parabolic in shape; in the case of triethylamine and water, the
closed end of the curve is very flat. Since for all liquids there is a
point (critical point) at which the liquid and gaseous states become
identical, and since all gases are miscible in all proportions, it follows
that there must be some temperature at which the liquids become perfectly
miscible. In the case of triethylamine and water, which has just been
considered, there must therefore be an upper critical solution temperature,
so that the complete solubility relations would be represented by a closed
curve of an ellipsoidal aspect. An example of such a curve is furnished by
nicotine and water. At temperatures below 60deg and above 210deg, nicotine
and water mix in all proportions.[173] Although it is possible that this is
the general form of the curve for all pairs of liquids, there are as yet
insufficient data to prove it.
With regard to the closed end of the curve it may be said that it is
continuous; the critical solution point is not the intersection of two
curves, for such a break in the continuity of the curve could occur only if
there were some discontinuity in one of the phases. No such discontinuity
exists. The curve is, therefore, not to be considered as two solubility
curves cutting at a point; it is a curve of equilibrium between two
components, and so long as the phases undergo continuous change, the curve
representing the equilibrium must also be continuous. As has already been
emphasized, a distinction between solvent and solute is merely conventional
(p. 93).
Pressure-Concentration Diagram.--In considering the pressure-concentration
diagram of a system of two liquid components, a distinction must be drawn
between the total pressure of the system and the partial pressures of the
components. On studying the total pressure of a system, it is found that
two cases can be obtained.[174]
So long as there is only one liquid phase, the system is bivariant. The
pressure therefore can change with the concentration and the temperature.
If the temperature is maintained {103} constant, the pressure will vary
only with the concentration, and this variation can therefore be
represented by a curve. If, however, two liquid phases are formed, the
system becomes univariant: and if one of the variables, say the
temperature, is arbitrarily fixed, the system no longer possesses any
degree of freedom. _When two liquid phases are formed, therefore, the
concentrations and the vapour pressure have definite values, which are
maintained so long as the two liquid phases are present_; the temperature
being supposed constant.
In Fig. 25 is given a diagrammatic representation of the two kinds of
pressure-concentration curves which have so far been obtained. In the one
case, the vapour pressure of the invariant system (at constant temperature)
lies higher than the vapour pressure of either of the pure components; a
phenomenon which is very generally found in the case of partially miscible
liquids, _e.g._ ether and water.[175] Accordingly, by the addition of water
to ether, or of ether to water, there is an increase in the _total_ vapour
pressure of the system.
[Illustration: FIG. 25.]
With regard to the second type, the vapour pressure of the systems with two
liquid phases lies between that of the two single components. An example of
this is found in sulphur dioxide and water.[176] On adding sulphur dioxide
to water there is an increase of the total vapour pressure; but on adding
water to liquid sulphur dioxide, the total vapour pressure is diminished.
The case that the vapour pressure of the system with two {104} liquid
phases is _less_ than that of each of the components is not possible.
With regard to the _partial pressure_ of the components, the behaviour is
more uniform. The partial pressure of one component is in all cases lowered
by the addition of the other component, the diminution being approximately
proportional to the amount added. If two liquid phases are present, the
partial pressure of the components, as well as the total pressure, is
constant, and is the same for both phases. That is to say, in the case of
the two liquids, saturated solution of water in ether, and of ether in
water, the partial pressure of the ether in the vapour in contact with the
one solution is the same as that in the vapour over the other
solution.[177]
Complete Miscibility.--Although the phenomena of complete miscibility are
here treated under a separate heading, it must not be thought that there is
any essential difference between those cases where the liquids exhibit
limited miscibility and those in which only one homogeneous solution is
formed. As has been already pointed out, the solubility relations alter
with the temperature; and liquids which at one temperature can dissolve in
one another only to a limited extent, are found at some other temperature
to possess the property of complete miscibility. Conversely, we may expect
that liquids which at one temperature, say at the ordinary temperature, are
miscible in all proportions, will be found at some other temperature to be
only partially miscible. Thus, for example, it was found by Guthrie that
ethyl alcohol and carbon disulphide, which are miscible in all proportions
at the ordinary temperature, possess only limited miscibility at
temperatures below -14.4deg.[178] Nevertheless, it is doubtful if the
critical solution temperature is in all cases experimentally realizable.
Pressure-Concentration Diagram.--Since, in the cases of complete
miscibility of two liquid components, there are never more than two phases
present, the system must always be bivariant; and two of the variables
pressure, temperature or concentration of the components, must be
arbitrarily chosen {105} before the system becomes defined. For this reason
the Phase Rule affords only a slight guidance in the study of such
equilibria; and we shall therefore not enter in detail into the behaviour
of these homogeneous mixtures. All that the Phase Rule can tell us in
connection with these solutions, is that at constant temperature the vapour
pressure of the solution varies with the composition of the liquid phase;
and if the composition of the liquid phase remains unchanged, the pressure
also must remain unchanged. This constancy of composition is exhibited not
only by pure liquids, but also by liquid solutions in all cases where the
vapour pressure of the solution reaches a maximum or minimum value. This is
the case, for example, with mixtures of constant boiling point.[179]
* * * * *
{106}
CHAPTER VII
SOLUTIONS OF SOLIDS IN LIQUIDS, ONLY ONE OF THE COMPONENTS BEING VOLATILE
General.--When a solid is brought into contact with a liquid in which it
can dissolve, a certain amount of it passes into solution; and the process
continues until the concentration reaches a definite value independent of
the amount of solid present. A condition of equilibrium is established
between the solid and the solution; the solution becomes _saturated_. Since
the number of components is two, and the number of phases three, viz.
solid, liquid solution, vapour, the system is univariant. If, therefore,
one of the factors, pressure, temperature, or concentration of the
components (in the solution[180]), is arbitrarily fixed, the state of the
system becomes perfectly defined. Thus, at any given temperature, the
vapour pressure of the system and the concentration of the components have
a definite value. If the temperature is altered, the vapour pressure and
also, in general, the concentration will undergo change. Likewise, if the
pressure varies, while the system is isolated so that no heat can pass
between it and its surroundings, the concentration and the temperature must
also undergo variation until they attain values corresponding to the
particular pressure.
That the temperature has an influence, sometimes a very considerable
influence, on the amount of substance passing into solution, is
sufficiently well known; the effect of pressure, although less apparent, is
no less certain. If at any given temperature the volume of the vapour phase
is diminished, {107} vapour will condense to liquid, in order that the
pressure may remain constant, and so much of the solid will pass into
solution that the concentration may remain unchanged; for, so long as the
three phases are present, the state of the system cannot alter. If,
however, one of the phases, _e.g._ the vapour phase, disappears, the system
becomes bivariant; at any given temperature, therefore, there may be
different values of concentration and pressure.
The direction in which change of concentration will occur with change of
pressure can be predicted by means of the theorem of Le Chatelier, if it is
known whether solution is accompanied by increase or diminution of the
total volume. If diminution of the total volume of the system occurs on
solution, increase of pressure will increase the solubility; in the reverse
case, increase of pressure will diminish the solubility.
This conclusion has also been verified by experiment, as is shown by the
following figures.[181]
---------------------------------------------------------------
|Change of | Solubility (at 18deg) (grams salt
|volume by | in 1 gram of solution).
|dissolving 1 gm.|---------------------------
Salt. |of salt in the | |
|saturated | Pressure | Pressure
|solution. | = 1 atm. | = 500 atm.
------------------+----------------+----------+----------------
Sodium chloride | -0.07 | 0.264 | 0.270
Ammonium chloride | +0.10 | 0.272 | 0.258
Alum | -0.067 | 0.115 | 0.142
| | |(_p_ = 400 atm.)
-------------------------------------------------------------
As can be seen, a large increase of the pressure brings about a no more
than appreciable alteration of the solubility; a result which is due, as in
the case of the alteration of the fusion point with the pressure, to the
small change in volume accompanying solution or increase of pressure. For
all practical purposes, therefore, the solubility as determined under
atmospheric pressure may be taken as equal to the true {108} solubility,
that is, the solubility when the system is under the pressure of its own
vapour.
The Saturated Solution.--From what has been said above, it will be seen
that the condition of saturation of a solution can be defined only with
respect to a certain solid phase; if no solid is present, the system is
undefined, for it then consists of only two phases, and is therefore
bivariant. Under such circumstances not only can there be at one given
temperature solutions of different concentration, all containing less of
one of the components than when that component is present in the solid
form, but there can also exist solutions containing more of that component
than corresponds to the equilibrium when the solid is present. In the
former case the solutions are _unsaturated_, in the latter case they are
_supersaturated with respect to a certain solid phase_; in themselves, the
solutions are stable, and are neither unsaturated nor supersaturated.
Further, if the solid substance can exist in different allotropic
modifications, the particular form of the substance which is in equilibrium
with the solution must be known, in order that the statement of the
solubility may be definite; for each form has its own solubility, and, as
we shall see presently, the less stable form has the greater solubility
(cf. p. 47). In all determinations of the solubility, therefore, not only
must the concentration of the components in the solution be determined, but
equal importance should be attached to the characterisation of the solid
phase present.
In this connection, also, one other point may be emphasised. For the
production of the equilibrium between a solid and a liquid, time is
necessary, and this time not only varies with the state of division of the
solid and the efficiency of the stirring, but is also dependent on the
nature of the substance.[182] Considerable care must therefore be taken
that sufficient time is allowed for equilibrium to be established. Such
care is more especially needful when changes may occur in the solid phase,
and neglect of it has greatly diminished the value of many of the older
determinations of solubility.
Form of the Solubility Curve.--The solubility curve--that {109} is, the
curve representing the change of concentration of the components in the
solution with the temperature--differs markedly from the curve of vapour
pressure (p. 63), in that it possesses no general form, but may vary in the
most diverse manner. Not only may the curve have an almost straight and
horizontal course, or slope or curve upwards at varying angles; but it may
even slope downwards, corresponding to a decrease in the solubility with
rise of temperature; may exhibit maxima or minima of solubility, or may, as
in the case of some hydrated salts, pass through a point of maximum
temperature. In the latter case the salt may possess two values of
solubility at the same temperature. We shall consider these cases in the
following chapter.
[Illustration: FIG. 26.]
The great variety of form shown by solubility curves is at once apparent
from Fig. 26, in which the solubility curves of various substances (not,
however, drawn to scale) are reproduced.[183]
Varied as is the form of the solubility curve, its _direction_,
nevertheless, can be predicted by means of the theorem of van't Hoff and Le
Chatelier; for in accordance with that theorem (p. 57) increase of
solubility with the temperature must occur in those cases where the process
of solution is accompanied by an _absorption_ of heat; and a decrease in
the solubility with rise of temperature will be found in cases where
solution occurs with _evolution_ of heat. Where there is no heat effect
accompanying solution, {110} change of temperature will be without
influence on the solubility; and if the sign of the heat of solution
changes, the direction of the solubility curve must also change, _i.e._
must show a maximum or minimum point. This has in all cases been verified
by experiment.[184]
In applying the theorem of Le Chatelier to the course of the solubility
curve, it should be noted that by heat of solution there is meant, not the
heat effect produced on dissolving the salt in a large amount of solvent
(which is the usual signification of the expression), but the heat which is
absorbed or evolved when the salt is dissolved in the almost saturated
solution (the so-called last heat of solution). Not only does the heat
effect in the two cases have a different value, but it may even have a
different sign. A striking example of this is afforded by cupric chloride,
as the following figures show:[185]--
-----------------------------------------------------------
Number of gram-molecules of |
CuCl_{2}, 2H_{2}O dissolved in 198 | Heat effect.
gram-molecules of water. |
-----------------------------------+-----------------------
1 | +37 K
2.02 | +66 "
4.15 | +105 "
7.07 | +117 "
9.95 | +117 "
11 | +91 "
18.8 | -10 "
19.6 | -31 "
24.75 | -198 "
------------------------------------------------------------
In the above table the positive sign indicates evolution of heat, the
negative sign, absorption of heat; and the values of the heat effect are
expressed in centuple calories. Judging from the heat effect produced on
dissolving cupric chloride in a large bulk of water, we should predict that
the solubility of that salt would diminish with rise of temperature; as a
matter of fact, it increases. This is in accordance with the fact that
{111} the last heat of solution is _negative_ (as expressed above), _i.e._
solution of the salt in the almost saturated solution is accompanied by
absorption of heat. We are led to expect this from the fact that the heat
of solution changes sign from positive to negative as the concentration
increases; experiment also showed it to be the case.
Despite its many forms, it should be particularly noted that the solubility
curve of any substance is _continuous_, so long as the solid phase, or
solid substance in contact with the solution, remains unchanged. If any
"break" or discontinuous change in the direction of the curve occurs, it is
a sign that the _solid phase has undergone alteration_. Conversely, if it
is known that a change takes place in the solid phase, a break in the
solubility curve can be predicted. We shall presently meet with examples of
this.[186]
A.--ANHYDROUS SALT AND WATER.
The Solubility Curve.--In studying the equilibria in those systems of two
components in which the liquid phase is a solution or phase of varying
composition, we shall in the present chapter limit the discussion to those
cases where no compounds are formed, but where the components crystallise
out in the pure state. Since some of the best-known examples of such
systems are yielded by the solutions of anhydrous salts in water, we shall
first of all briefly consider some of the results which have been obtained
with them.
For the most part the solubility curves have been studied only at
temperatures lying between 0deg and 100deg, the solid phase in contact with
the solution being the anhydrous salt. For the representation of these
equilibria, the concentration-temperature {112} diagram is employed, the
concentration being expressed as the number of grams of the salt dissolved
in 100 grams of water, or as the number of gram-molecules of salt in 100
gram-molecules of water. The curves thus obtained exhibit the different
forms to which reference has already been made. So long as the salt remains
unchanged the curve will be continuous, but if the salt alters its form,
then the solubility curve will show a break.
[Illustration: FIG. 27.]
Now, we have already seen in Chapter III. that certain substances are
capable of existing in various crystalline forms, and these forms are so
related to one another that at a given temperature the relative stability
of each pair of polymorphic forms undergoes change. Since each crystalline
variety of a substance must have its own solubility, there must be a break
in the solubility curve at the temperature of transition of the two
enantiotropic forms. At this point the two solubility curves must cut, for
since the two forms are in equilibrium with respect to their vapour, they
must also be in equilibrium with respect to their solutions. From the table
on p. 63 it is seen that potassium nitrate, ammonium nitrate, silver
nitrate, thallium nitrate, thallium picrate, are capable of existing in two
or more different enantiotropic crystalline forms, the range of stability
of these forms being limited by definite temperatures (transition
temperature). Since the transition point is not altered by a solvent
(provided the latter is not absorbed by the solid phase), we should find on
studying the solubility of these substances in water that the solubility
curve would exhibit a change in direction at the temperature of transition.
As a matter of fact this has been verified, more especially in the case of
ammonium nitrate[187] {113} and thallium picrate.[188] The following table
contains the values of the solubility of ammonium nitrate obtained by
Mueller and Kaufmann, the solubility being expressed in gram-molecules
NH_{4}NO_{3} in 100 gram-molecules of water. In Fig. 27 these results are
represented graphically. The equilibrium point was approached both from the
side of unsaturation and of supersaturation, and the condition of
equilibrium was controlled by determinations of the density of the
solution.
SOLUBILITY OF AMMONIUM NITRATE.
------------------------------------------------------------
Temperature. | Solubility. | Temperature. | Solubility.
--------------+-------------+--------------+----------------
12.2deg | 34.50 | 32.7deg | 57.90
20.2deg | 43.30 | 34.0deg | 58.89
25.05deg | 48.19 | 35.0deg | 59.80
28.0deg | 51.86 | 36.0deg | 61.00
30.0deg | 54.40 | 37.5deg | 62.90
30.2deg | 54.61 | 38.0deg | 63.60
31.9deg | 57.20 | 39.0deg | 65.09
32.1deg | 57.60 | 40.0deg | 66.80
------------------------------------------------------------
From the graphic representation of the solubility given in Fig. 27, there
is seen to be a distinct change in the direction of the curve at a
temperature of 32deg; and this break in the curve corresponds to the
transition of the [beta]-rhombic into the [alpha]-rhombic form of ammonium
nitrate (p. 63).
Suspended Transformation and Supersaturation.--As has already been learned,
the transformation of the one crystalline form into the other does not
necessarily take place immediately the transition point has been passed;
and it has therefore been found possible in a number of cases to follow the
solubility curve of a given crystalline form beyond the point at which it
ceases to be the most stable modification. Now, it will be readily seen
from Fig. 27 that if the two solubility curves be prolonged beyond the
point of intersection, the solubility of the less stable form is greater
than that of the more stable. A solution, therefore, which is saturated
with respect to the less stable form, _i.e._ which is in equilibrium with
that form, is _supersaturated with respect to the more stable
modification_. If, {114} therefore, a small quantity of the more stable
form is introduced into the solution, the latter must deposit such an
amount of the more stable form that the concentration of the solution
corresponds to the solubility of the stable form at the particular
temperature. Since, however, the solution is now _unsaturated_ with respect
to the less stable variety, the latter, if present, must pass into
solution; and the two processes, deposition of the stable and solution of
the metastable form, must go on until the latter form has entirely
disappeared and a saturated solution of the stable form is obtained. There
will thus be a conversion, through the medium of the solvent, of the less
stable into the more stable modification. This behaviour is of practical
importance in the determination of transition points (_v._ Appendix).
From the above discussion it will be seen how important is the statement of
the solid phase for the definition of saturation and supersaturation.[189]
Solubility Curve at Higher Temperatures.--On passing to the consideration
of the solubility curves at higher temperatures, two chief cases must be
distinguished.
(1) The two components in the fused state can mix in all proportions.
(2) The two components in the fused state cannot mix in all
proportions.
1. _Complete Miscibility of the Fused Components._
[Illustration: FIG. 28.]
The best example of this which has been studied, so far as anhydrous salts
and water are concerned, is that of silver nitrate and water. The
solubility of this salt at temperatures {115} above 100deg has been studied
chiefly by Etard[190] and by Tilden and Shenstone.[191] The values obtained
by Etard are given in the following table, and represented graphically in
Fig. 28.
SOLUBILITY OF SILVER NITRATE.
---------------------------------------------------
Temperature. |Parts of dry salt in 100 parts
| of solution.
--------------------+------------------------------
-7deg | 46.2
-1deg | 52.1
+5deg | 56.3
10deg | 61.2
20deg | 67.8
40.5deg | 76.8
73deg | 84.0
135deg | 92.8
182deg | 96.9
---------------------------------------------------
In this figure the composition of the solution is expressed in parts of
silver nitrate in 100 parts by weight of the solution, so that 100 per
cent. represents pure silver nitrate. As can be seen, the solubility
increases with the temperature. At a temperature of about 160deg there
should be a break in the curve due to change of crystalline form (p. 63).
Such a change in the direction of the solubility curve, however, does not
in any way alter the essential nature of the relationships discussed here,
and may for the present be left out of account. On following the solubility
curve of silver nitrate to higher temperatures, therefore, the
concentration of silver nitrate in the solution gradually increases, until
at last, at a temperature of 208deg,[192] the melting point of pure silver
nitrate is reached, and the concentration of the water has become zero. The
curve throughout its whole extent represents the equilibrium between silver
nitrate, solution, and vapour. Conversely, starting with pure silver
nitrate in contact with the fused salt, addition of water will lower the
melting point, _i.e._ will lower the temperature at which the solid salt
can exist in contact with the liquid; {116} and the depression will be all
the greater the larger the amount of water added. As the concentration of
the water in the liquid phase is increased, therefore, the system will pass
back along the curve from higher to lower temperatures, and from greater to
smaller concentrations of silver nitrate in the liquid phase. The curve in
Fig. 28 may, therefore, be regarded either as the solubility curve of
silver nitrate in water, or as the freezing point curve for silver nitrate
in contact with a solution consisting of that salt and water.
As the temperature of the saturated solution falls, silver nitrate is
deposited, and on lowering the temperature sufficiently a point will at
last be reached at which ice also begins to separate out. Since there are
now four phases co-existing, viz. silver nitrate, ice, solution, vapour,
the system is invariant, and the point is a _quadruple point_. This
quadruple point, therefore, forms the lower limit of the solubility curve
of silver nitrate. Below this point the solution becomes metastable.
Ice as Solid Phase.--Ice melts or is in equilibrium with water at a
temperature of 0deg. The melting point, will, however, be lowered by the
solution of silver nitrate in the water; and the greater the concentration
of the salt in the solution the greater will be the depression of the
temperature of equilibrium. On continuing the addition of silver nitrate, a
point will at length be reached at which the salt is no longer dissolved,
but remains in the solid form along with the ice. We again obtain,
therefore, the invariant system ice--salt--solution--vapour. The
temperature at which this invariant system can exist has been found by
Middelberg[193] to be -7.3deg, the solution at this point containing 47.1
per cent. of silver nitrate.
The same general behaviour will be found in the case of all other systems
of two components belonging to this class; that is, in the case of systems
from which the components crystallise out in the pure state, and in which
the fused components are miscible in all proportions. In all such cases,
therefore, the solubility curves (curves of equilibrium) can be represented
diagrammatically as in Fig. 29. In this figure OA represents the solubility
curve of the salt, and OB the freezing {117} point curve of ice. O is the
quadruple point at which the invariant system exists, and may be regarded
as the point of intersection of the solubility curve with the
freezing-point curve. Since this point is fixed, the condition of the
system as regards temperature, vapour pressure, and concentration of the
components (or composition of the solution), is perfectly definite. From
the way, also, in which the condition is attained, it is evident that the
quadruple point is the lowest temperature that can be obtained with
mixtures of the two components in presence of vapour. It is known as the
_cryohydric point_, or, generally, the _eutectic point_.[194]
[Illustration: FIG. 29.]
Cryohydrates.[195]--On cooling a solution of common salt in water to a
temperature of -3deg, Guthrie observed that the hydrate NaCl,2H_{2}O
separated out. This salt continued to be deposited until at a temperature
of -22deg opaque crystals made their appearance, and the liquid passed into
the solid state without change of temperature. A similar behaviour was
found by Guthrie in the case of a large number of other salts, a
temperature below that of the melting point of ice being reached at which
on continued withdrawal of heat, the solution solidified at a constant
temperature. When the system had attained this minimum temperature, it was
found that the composition of the solid and the liquid phases was the same,
and remained unchanged throughout the period of solidification. This is
shown by the following figures, which give the composition of different
samples of the solid phase deposited from the solution at constant
temperature.[196]
{118}
---------------------------------
No. | Temperature of | NaCl.
| solidification. | Per cent.
----|-----------------|----------
1 |-21deg to -22deg | 23.72
2 | -22deg | 23.66
3 | -22deg | 23.73
4 | -23deg | 23.82
5 | -23deg | 23.34
6 | -23deg | 23.35
---------------------------------
Mean 23.6
---------------------------------
Conversely, a mixture of ice and salt containing 23.6 per cent. of sodium
chloride will melt at a definite and constant temperature, and exhibit,
therefore, a behaviour supposed to be characteristic of a pure chemical
compound. This, then, combined with the fact that the solid which was
deposited was crystalline, and that the same constant temperature was
attained, no matter with what proportions of water and salt one started,
led Guthrie to the belief that the solids which thus separated at constant
temperature were definite chemical compounds, to which he gave the general
name _cryohydrate_. A large number of such cryohydrates were prepared and
analysed by Guthrie, and a few of these are given in the following table,
together with the temperature of the cryohydric point:[197]--
CRYOHYDRATES.
------------------------------------------------------------------
Salt. | Cryohydric point. | Percentage of anhydrous
| | salt in the cryohydrate.
------------------------------------------------------------------
Sodium bromide | -24deg | 41.33
Sodium chloride | -22deg | 23.60
Potassium iodide | -22deg | 52.07
Sodium nitrate | -17.5deg | 40.80
Ammonium sulphate | -17deg | 41.70
Ammonium chloride | -15deg | 19.27
Sodium iodide | -15deg | 59.45
Potassium bromide | -13deg | 32.15
Potassium chloride | -11.4deg | 20.03
Magnesium sulphate | -5deg | 21.86
Potassium nitrate | -2.6deg | 11.20
Sodium sulphate | -0.7deg | 4.55
------------------------------------------------------------------
{119}
The chemical individuality of these cryohydrates was, however, called in
question by Pfaundler,[198] and disproved by Offer,[199] who showed that in
spite of the constancy of the melting point, the cryohydrates had the
properties, not of definite chemical compounds, but of mixtures; the
arguments given being that the heat of solution and the specific volume are
the same for the cryohydrate as for a mixture of ice and salt of the same
composition; and it was further shown that the cryohydrate had not a
definite crystalline form, but separated out as an opaque mass containing
the two components in close juxtaposition. The heterogeneous nature of
cryohydrates can also be shown by a microscopical examination.
At the cryohydric point, therefore, we are not dealing with a single solid
phase, but with two solid phases, ice and salt; the cryohydric point,
therefore, as already stated, is a quadruple point and represents an
invariant system.
Although on cooling a solution to the cryohydric point, separation of ice
may occur, it will not necessarily take place; the system may become
metastable. Similarly, separation of salt may not take place immediately
the cryohydric point is reached. It will, therefore, be possible to follow
the curves BO and AO beyond the quadruple point,[200] which is thereby
clearly seen to be the point of intersection of the solubility curve of the
salt and the freezing-point curve of ice. At this point, also, the curves
of the univariant systems ice--salt--vapour and ice--salt--solution
intersect.
Changes at the Quadruple Point.--Since the invariant system
ice--salt--solution--vapour can exist only at a definite temperature,
addition or withdrawal of heat must cause the disappearance of one of the
phases, whereby the system will become univariant. So long as all four
phases are present the temperature, pressure, and concentration of the
components in the solution must remain constant. When, therefore, heat is
added to or withdrawn from the system, mutually compensatory changes will
take place within the system whereby the {120} condition of the latter is
preserved. These changes can in all cases be foreseen with the help of the
theorem of van't Hoff and Le Chatelier; and, after what was said in Chap.
IV., need only be briefly referred to here. In the first place, addition of
heat will cause ice to melt, and the concentration of the solution will be
thereby altered; salt must therefore dissolve until the original
concentration is reached, and the heat of fusion of ice will be
counteracted by the heat of solution of the salt. Changes of volume of the
solid and liquid phases must also be taken into account; an alteration in
the volume of these phases being compensated by condensation or
evaporation. All four phases will therefore be involved in the change, and
the final state of the system will be dependent on the amounts of the
different phases present; the ultimate result of addition or withdrawal of
heat or of change of pressure at the quadruple point will be one of the
four univariant systems: ice--solution--vapour; salt--solution--vapour;
ice--salt--vapour; ice--salt--solution. If the vapour phase disappear,
there will be left the univariant system ice--salt--solution, and the
temperature at which this system can exist will alter with the pressure.
Since in this case the influence of pressure is comparatively slight, the
temperature of the quadruple point will differ only slightly from that of
the cryohydric point as determined under atmospheric pressure.
Freezing Mixtures.--Not only will the composition of a univariant system
undergo change when the temperature is varied, but, conversely, if the
_composition_ of the system is caused to change, corresponding changes of
temperature must ensue. Thus, if ice is added to the univariant system
salt--solution--vapour, the ice must melt and the temperature fall; and if
sufficient ice is added, the temperature of the cryohydric point must be at
length reached, for it is only at this temperature that the four phases
ice--salt--solution--vapour can coexist. Or, on the other hand, if salt is
added to the system ice--solution--vapour, the concentration of the
solution will increase, ice must melt, and the temperature must thereby
fall; and this process also will go on until the cryohydric point is
reached. In both cases ice melts and there is a change in the {121}
composition of the solution; in the former case, salt will be
deposited[201] because the solubility diminishes as the temperature falls;
in the latter, salt will pass into solution. This process may be
accompanied either by an evolution or, more generally, by absorption of
heat; in the former case the effect of the addition of ice will be
partially counteracted; in the latter case it will be augmented.
These principles are made use of in the preparation of _freezing mixtures_.
The lowest temperature which can be reached by means of these (under
atmospheric pressure) is the cryohydric point. This temperature-minimum is,
however, not always attained in the preparation of a freezing mixture, and
that for various reasons. The chief of these are radiation and the heat
absorbed in cooling the solution produced. The lower the temperature falls,
the more rapid does the radiation become; and the rate at which the
temperature sinks decreases as the amount of solution increases. Both these
factors counteract the effect of the latent heat of fusion and the heat of
solution, so that a point is reached (which may lie considerably above the
cryohydric point) at which the two opposing influences balance. The
absorption of heat by the solution can be diminished by allowing the
solution to drain off as fast as it is produced; and the effect of
radiation can be partially annulled by increasing the rate of cooling. This
can be done by the more intimate mixing of the components. Since, under
atmospheric pressure, the temperature of the cryohydric point is constant,
the cryohydrates are very valuable for the production of baths of constant
low temperature.
2. _Partial Miscibility of the Fused Components._
On passing to the study of the second class of systems of two components
belonging to this group, namely, those in which the fused components are
not miscible in all proportions, we find that the relationships are not
quite so simple as {122} in the case of silver nitrate and water. In the
latter case, only one liquid phase was possible; in the cases now to be
studied, two liquid phases can be formed, and there is a marked
discontinuity in the solubility curve on passing from the cryohydric point
to the melting point of the second (non-volatile) component.
Paratoluidine dissolves in water, and the solubility increases as the
temperature rises.[202] At 44.2deg, however, paratoluidine in contact with
water melts, and two liquid phases are formed, viz. a solution of water in
fused paratoluidine and a solution of fused paratoluidine in water. We
have, therefore, the phenomenon of _melting under the solvent_. This
melting point will, of course, be lower than the melting point of the pure
substance, because the solid is now in contact with a solution, and, as we
have already seen, addition of a foreign substance lowers the melting
point. Such cases of melting under the solvent are by no means rare, and a
review of the relationships met with may, therefore, be undertaken here. As
an example, there may be chosen the equilibrium between succinic nitrile,
C_{2}H_{4}(CN)_{2} and water, which has been fully studied by
Schreinemakers.[203]
[Illustration: FIG. 30.]
If to the system ice--water at 0deg succinic nitrile is added, the
temperature will fall; and continued addition of the nitrile will lead at
last to the cryohydric point _b_ (Fig. 30), at which solid nitrile, ice,
solution, and vapour can coexist. The temperature of the cryohydric point
is -1.2deg, and the composition of the solution is 1.29 mol. of nitrile in
100 mol. of solution. From _a_ to _b_ the solid phase in contact with the
solution is ice. {123} If the temperature be now raised so as to cause the
disappearance of the ice, and the addition of nitrile be continued, the
concentration of the nitrile in the solution will increase as represented
by the curve _bc_. At the point _c_ (18.5deg), when the concentration of
the nitrile in the solution has increased to 2.5 molecules per cent., the
nitrile melts and two liquid phases are formed; the concentration of the
nitrile in these two phases is given by the points _c_ and _c'_. As there
are now four phases present, viz. solid nitrile, solution of fused nitrile
in water, solution of water in fused nitrile, and vapour, the system is
_invariant_. Since at this point the concentration, temperature, and
pressure are completely defined, addition or withdrawal of heat can only
cause a change in the relative amounts of the phases, _but no variation of
the concentrations_ of the respective phases. As a matter of fact,
continued addition of nitrile and addition of heat will cause an increase
in the amount of the liquid phase containing excess of nitrile (_i.e._ the
solution of water in fused nitrile), whereas the other liquid phase, the
solution of fused nitrile in water, will gradually disappear. When it has
completely disappeared, the system will be represented by the point _c'_,
where the molecular concentration of nitrile is now 75 per cent., and again
becomes univariant, the three phases being solid nitrile, liquid phase
containing excess of nitrile, and vapour; and as the amount of the water is
diminished the temperature of equilibrium rises, until at 54deg the melting
point of the pure nitrile is reached.
Return now to the point c. At this point there exists the invariant system
solid nitrile, two liquid phases, vapour. If heat be added, the solid
nitrile will disappear, and there will be left the univariant system,
consisting of two liquid phases and vapour.[204] Such a system will exhibit
relationships similar to those already studied in the previous chapter. As
the temperature rises, the mutual solubility of the two fused components
becomes greater, until at _d_ (55.5deg) the critical solution temperature
is reached, and the fused components become miscible in all proportions.
At all temperatures and concentrations lying to the right {124} of the
curve _abcdc'e_ there can be only one liquid phase; in the field _cdc'_
there are two liquid phases.
From the figure it will be easy to see what will be the result of bringing
together succinic nitrile and water at different temperatures and in
different amounts. Since _b_ is the lowest temperature at which liquid can
exist in stable equilibrium with solid, ice and succinic nitrile can be
mixed in any proportions at temperatures below _b_ without undergoing
change. Between _b_ and _c_ succinic nitrile will be dissolved until the
concentration reaches the value on the curve _bc_, corresponding to the
given temperature. On adding the nitrile to water at temperatures between
_c_ and _d_, it will dissolve until a concentration lying on the curve _cd_
is attained; at this point two liquid phases will be formed, and further
addition of nitrile will cause the one liquid phase (that containing excess
of nitrile) to increase, while the other liquid phase will decrease, until
it finally disappears and there is only one liquid phase left, that
containing excess of nitrile. This can dissolve further quantities of the
nitrile, and the concentration will increase until the curve _c'e_ is
reached, when the concentration will remain unchanged, and addition of
solid will merely increase the amount of the solid phase.
If a solution represented by any point in the field lying below the curve
_bcd_ is heated to a temperature above _d_, the critical solution
temperature, then the concentration of the nitrile can be increased to any
desired amount without at any time two liquid phases making their
appearance; the system can then be cooled down to a temperature represented
by any point between the curves _dc'e_. In this way it is possible to pass
continuously from a solution containing excess of one component to
solutions containing excess of the other, as represented by the dotted line
_xxxx_ (_v._ p. 100). At no point is there formation of two liquid phases.
Supersaturation.--Just as suspended transformation is rarely met with in
the passage from the solid to the liquid state, so also it is found in the
case of the melting of substances under the solvent that suspended fusion
does not occur; but that when the temperature of the invariant point is
reached at which, therefore, the formation of two liquid layers is
possible, {125} these two liquid layers, as a matter of fact, make their
appearance. Suspended transformation can, however, take place from the side
of the liquid phase, just as water or other liquid can be cooled below the
normal freezing point without solidification occurring. The question,
therefore, arises as to the relative solubilities of the solid and the
supercooled liquid at the same temperature.
[Illustration: FIG. 31.]
The answer to this question can at once be given from what we have already
learned (p. 113), if we recollect that at temperatures below the point of
fusion under the solvent, the solid form, at temperatures above that point,
the liquid form, is the more stable; at this temperature, therefore, the
relative stability of the solid and liquid forms changes. Since, as we have
already seen, the less stable form has the greater solubility, it follows
that the supercooled liquid, being the less stable form, must have the
greater solubility. This was first proved experimentally by Alexejeff[205]
in the case of benzoic acid and water, the solubility curves for which are
given in Fig. 31. As can be seen from the figure, the prolongation of the
curve for liquid--liquid, which represents the solubility of the
supercooled liquid benzoic acid, lies above that for the solubility of the
{126} solid benzoic acid in water; the solution saturated with respect to
the supercooled liquid is therefore supersaturated with respect to the
solid form. A similar behaviour has been found in the case of other
substances.[206]
Pressure-Temperature Diagram.--Having considered the changes which occur in
the concentration of the components in a solution with the temperature, we
may conclude the discussion of the equilibrium between a salt and water by
studying the variation of the vapour pressure.
Since in systems of two components the two phases, solution and vapour,
constitute a bivariant system, the vapour pressure is undefined, and may
have different values at the same temperature, depending on the
concentration. In order that there may be for each temperature a definite
corresponding pressure of the vapour, a third phase must be present. This
condition is satisfied by the system solid--liquid (solution)--vapour; that
is, by the saturated solution (p. 108). In the case of a saturated
solution, therefore, the pressure of the vapour at any given temperature is
constant.
Vapour Pressure of Solid--Solution--Vapour.--It has long been known that
the addition of a non-volatile solid to a liquid in which it is soluble
lowers the vapour pressure of the solvent; and the diminution of the
pressure is approximately proportional to the amount of substance dissolved
(Law of Babo). The vapour-pressure curve, therefore, of a solution of a
salt in water must lie below that for pure water. Further, in the case of a
pure liquid, the vaporization curve is a function only of the temperature
(p. 63), whereas, in the case of a solution, the pressure varies both with
the temperature and the _concentration_. These two factors, however, act in
opposite directions; for although the vapour pressure in all cases
increases as the temperature rises, increase of concentration, as we have
seen, lowers the vapour pressure. Again, since the concentration itself
varies with the temperature, two cases have to be considered, viz. where
the concentration increases with rise of {127} temperature, and where the
concentration diminishes with rise of temperature.
The relations which are found here will be best understood with the help of
Fig. 32.[207] In this figure, OB represents the sublimation curve of ice,
and BC the vaporization curve of water; the curve for the solution must lie
below this, and must cut the sublimation curve of ice at some temperature
below the melting point. The point of intersection A is the cryohydric
point. If the solubility increases with rise of temperature, the increase
of the vapour pressure due to the latter will be partially annulled. Since
at first the effect of increase of temperature more than counteracts the
depressing action of increase of concentration, the vapour pressure will
increase on raising the temperature above the cryohydric point. If the
elevation of temperature is continued, however, to the melting point of the
salt, the effect of increasing concentration makes itself more and more
felt, so that the vapour-pressure curve of the solution falls more and more
below that of the pure liquid, and the pressure will ultimately become
equal to that of the pure salt; that is to say, practically equal to zero.
The curve will therefore be of the general form AMF shown in Fig. 32. If
the solubility should diminish with rise of temperature, the two factors,
temperature and concentration, will act in the same direction, and the
vapour-pressure curve will rise relatively more rapid than that of the pure
liquid; since, however, the pure salt is ultimately obtained, the
vapour-pressure curve must in this case also finally approach the value
zero.
[Illustration: FIG. 32.]
Other Univariant Systems.--Besides the univariant system {128}
salt--solution--vapour already considered, three others are possible, viz.
ice--solution--vapour, ice--salt--solution, and ice--salt--vapour.
The fusion point of a substance is lowered, as we have seen, by the
addition of a foreign substance, and the depression is all the greater the
larger the quantity of substance added. The vapour pressure of the water,
also, is lowered by the solution in it of other substances, so that the
vapour pressure of the system ice--solution--vapour must decrease as the
temperature falls from the fusion point of ice to the cryohydric point.
This curve is represented by BA (Fig. 32), and is coincident with the
sublimation curve of ice.
This, at first sight, strange fact will be readily understood when we
consider that since ice and solution are together in equilibrium with the
same vapour, they must have the same vapour pressure. For suppose at any
given temperature equilibrium to have been established in the system
ice--solution--vapour, removal of the ice will not alter this equilibrium.
Suppose, now, the ice and the solution placed under a bell-jar so that they
have a common vapour, but are not themselves in contact; then, if they do
not have the same vapour pressure, distillation must take place and the
solution will become more dilute or more concentrated. Since, at the
completion of this process, the ice and solution are now in equilibrium
when they are not in contact, they must also be in equilibrium when they
are in contact (p. 32). But if distillation has taken place the
concentration of the solution must have altered, so that the ice will now
be in equilibrium with a solution of a different concentration from before.
But according to the Phase Rule ice cannot at one and the same temperature
be in equilibrium with two solutions of different concentration, for the
system ice--solution--vapour is univariant, and at any given temperature,
therefore, not only the pressure but also the _concentration of the
components in the solution must be constant_. Distillation could not,
therefore, take place from the ice to the solution or _vice versa_; that is
to say, the solution and the ice must have the same vapour pressure--the
sublimation pressure of ice. The reason of the coincidence is the
non-volatility of the salt: had {129} the salt a measurable vapour pressure
itself, the sublimation curve of ice and the curve for
ice--solution--vapour would no longer fall together.
The curve AO represents the pressures of the system ice--salt--vapour. This
curve will also be coincident with the sublimation curve of ice, on account
of the non-volatility of the salt.
The equilibria of the fourth univariant system ice--salt--solution are
represented by AE. Since this is a condensed system, the effect of a small
change of temperature will be to cause a large change of pressure, as in
the case of the fusion point of a pure substance. The direction of this
curve will depend on whether there is an increase or diminution of volume
on solidification; but the effect in any given case can be predicted with
the help of the theorem of Le Chatelier.
Since the cryohydric point is a quadruple point in a two-component system,
it represents an invariant system. The condition of the system is,
therefore, completely defined; the four phases, ice, salt, solution,
vapour, can co-exist only when the temperature, pressure, and concentration
of the solution have constant and definite values. Addition or withdrawal
of heat, therefore, can cause no alteration of the condition of the system
except a variation of the relative amounts of the phases. Addition
of heat at constant volume will ultimately lead to the system
salt--solution--vapour or the system ice--solution--vapour, according as
ice or salt disappears first. This is readily apparent from the diagram
(Fig. 32), for the systems ice--salt--solution and ice--salt--vapour can
exist only at temperatures below the cryohydric point (provided the curve
for ice--salt--solution slopes towards the pressure axis).
Bivariant Systems.--Besides the univariant systems already discussed,
various bivariant systems are possible, the conditions for the existence of
which are represented by the different areas of Fig. 32. They are as
follows:--
_Area._ _System._
OAMF Salt--vapour.
CBAMF Solution--vapour; salt--solution.
EABD Salt--solution; ice--solution.
EAO Ice--salt.
{130}
Deliquescence.--As is evident from Fig. 32, salt can exist in contact with
water vapour at pressures under those represented by OAMF. If, however, the
pressure of the vapour is increased until it reaches a value lying on this
curve at temperatures above the cryohydric point, solution will be formed;
for the curve AMF represents the equilibria between salt--solution--vapour.
From this, therefore, it is clear that if the pressure of the aqueous
vapour in the atmosphere is greater than that of the saturated solution of
a salt, that salt will, on being placed in the air, form a solution; it
will _deliquesce_.
Separation of Salt on Evaporation.--With the help of Fig. 32 it is possible
to state in a general manner whether or not salt will be deposited when a
solution is evaporated under a constant pressure.[208]
The curve AMF (Fig. 32) is the vapour-pressure curve of the saturated
solutions of the salt, _i.e._ it represents, as we have seen, the maximum
vapour pressure at which salt can exist in contact with solution and
vapour. The dotted line _aa_ represents atmospheric pressure. If, now, an
unsaturated solution, the composition of which is represented by the point
_x_, is heated in an open vessel, the temperature will rise, and the vapour
pressure of the solution will increase. The system will, therefore, pass
along a line represented diagrammatically by _xx'_. At the point _x'_ the
vapour pressure of the system becomes equal to 1 atm.; and as the vessel is
open to the air, the pressure cannot further rise; the solution boils. If
the heating is continued, water passes off, the concentration increases,
and the boiling point rises. The system will therefore pass along the line
_x'm_, until at the point _m_ solid salt separates out (provided
supersaturation is excluded). The system is now univariant, and continued
heating will no longer cause an alteration of the concentration; as water
passes off, solid salt will be deposited, and the solution will evaporate
to dryness.
If, however, the atmospheric pressure is represented not by _aa_ but by
_bb_, then, as Fig. 32 shows, the maximum vapour {131} pressure of the
system salt--solution--vapour never reaches the pressure of 1 atm. Further,
since the curve _bb_ lies in the area of the bivariant system
solution--vapour there can at no point be a separation of the solid form;
for the system solid--solution--vapour can exist only along the curve AMF.
On evaporating the solution of a salt in an open vessel, therefore, salt
can be deposited only if at some temperature the pressure of the saturated
solution is equal to the atmospheric pressure. This is found to be the case
with most salts. In the case of aqueous solutions of sodium and potassium
hydroxide, however, the vapour pressure of the saturated solution never
reaches the value of 1 atm., and on evaporating these solutions, therefore,
in an open vessel, there is no separation of the solid. Only a homogeneous
fused mass is obtained. If, however, the evaporation be carried out under a
pressure which is lower than the maximum pressure of the saturated
solution, separation of the solid substance will be possible.
General Summary.--The systems which have been discussed in the present
chapter contained water as one of their components, and an anhydrous salt
as the other. It will, however, be clear that the relationships which were
found in the case of these will be found also in other cases where it is a
question of the equilibria between two components, which crystallize out in
the pure state, and only one of which possesses a measurable vapour
pressure. A similar behaviour will, for example, be found in the case of
many pairs of organic substances; and in all cases the equilibria will be
represented by a diagram of the general appearance of Fig. 29 or Fig. 30.
That is to say: Starting from the fusion point of component I., the system
will pass, by progressive addition of component II., to regions of lower
temperature, until at last the cryohydric or eutectic point is reached. On
further addition of component II., the system will pass to regions of
higher temperature, the solid phase now being component II. If the fused
components are miscible with one another in all proportions a continuous
curve will be obtained leading up to the point of fusion of component II.
Slight changes of direction, it is true, due to changes in the crystalline
form, may be found along this curve, {132} but throughout its whole course
there will be but one liquid phase. If, on the other hand, the fused
components are not miscible in all proportions, then the second curve will
exhibit a marked discontinuity, and two liquid phases will make their
appearance.
* * * * *
{133}
CHAPTER VIII
SOLUTIONS OF SOLIDS IN LIQUIDS, ONLY ONE OF THE COMPONENTS BEING VOLATILE
B.--HYDRATED SALT AND WATER.
In the preceding chapter we discussed the behaviour of systems formed of
two components, only one of which was volatile, in those cases where the
two components separated from solution in the pure state. In the present
chapter we shall consider those systems in which combination between the
components can occur with the formation of definite compounds; such as are
found in the case of crystalline salt hydrates. Since a not inconsiderable
amount of study has been devoted to the systems formed by hydrated salts
and water, systems which are of great chemical interest and importance, the
behaviour of these will first call for discussion in some detail, and it
will be found later that the relationships which exist in such systems
appear also in a large number of other two-component systems.
The systems belonging to this group may be divided into two classes
according as the compounds formed possess a definite melting point, _i.e._
form a liquid phase of the same composition, or do not do so. We shall
consider the latter first.
1. _The Compounds formed do not have a Definite Melting Point._
Concentration-Temperature Diagram.--In the case of salts which can form
crystalline hydrates, the temperature-concentration diagram, representing
the equilibria of the {134} different possible systems, must necessarily be
somewhat more complicated than where no such combination of the components
occurs. For, as has already been pointed out, each substance has its own
solubility curve; and there will therefore be as many solubility curves as
there are solid phases possible, _the curve for each particular solid phase
being continuous so long as it remains unchanged in contact with the
solution_. As an example of the relationships met with in such cases, we
shall first of all consider the systems formed of sodium sulphate and
water.
[Illustration: FIG. 33.]
Sodium Sulphate and Water.--At the ordinary temperatures, sodium sulphate
crystallises from water with ten molecules of water of crystallisation,
forming Glauber's salt. On determining the solubility of this salt in
water, it is found that the solubility increases as the temperature rises,
the values of the solubility, represented graphically by the curve AC (Fig.
33), being given in the following table.[209] The numbers denote grams of
sodium sulphate, calculated as anhydrous salt, dissolved by 100 grams of
water.
SOLUBILITY OF Na_{2}SO_{4},10H_{2}O.
--------------------------
Temperature. | Solubility.
--------------------------
0deg | 5.02
10deg | 9.00
15deg | 13.20
18deg | 16.80
20deg | 19.40
25deg | 28.00
30deg | 40.00
33deg | 50.76
34deg | 55.00
--------------------------
{135}
On continuing the investigation at higher temperatures, it was found that
the solubility no longer increased, but _decreased with rise of
temperature_. At the same time, it was observed that the solid phase was
now different from that in contact with the solution at temperatures below
33deg; for whereas in the latter case the solid phase was sodium sulphate
decahydrate, at temperatures above 33deg the solid phase was the anhydrous
salt. The course of the solubility curve of anhydrous sodium sulphate is
shown by BD, and the values of the solubility are given in the following
table:--[210]
SOLUBILITY OF ANHYDROUS SODIUM SULPHATE.
--------------------------
Temperature. | Solubility.
--------------------------
18deg | 53.25
20deg | 52.76
25deg | 51.53
30deg | 50.37
33deg | 49.71
34deg | 49.53
36deg | 49.27
40.15deg | 48.78
50.40deg | 46.82
--------------------------
As is evident from the figure, the solubility curve which is obtained when
anhydrous sodium sulphate is present as the solid phase, cuts the curve
representing the solubility of the decahydrate, at a temperature of about
33deg.
If a solution of sodium sulphate which has been saturated at a temperature
of about 34deg be cooled down to a temperature below 17deg, while care is
taken that the solution is protected against access of particles of
Glauber's salt, crystals of a second hydrate of sodium sulphate, having the
composition Na_{2}SO_{4},7H_{2}O, separate out. On determining the
composition of the solutions in equilibrium with this hydrate at different
temperatures, the following values were obtained, these values being
represented by the curve FE (Fig. 33):--
{136}
SOLUBILITY OF Na_{2}SO_{4},7H_{2}O.
--------------------------
Temperature. | Solubility.
--------------------------
0deg | 19.62
10deg | 30.49
15deg | 37.43
18deg | 41.63
20deg | 44.73
25deg | 52.94
26deg | 54.97
--------------------------
Since, as has already been stated, each solid substance has its own
solubility curve, there are three separate curves to be considered in the
case of sodium sulphate and water. Where two curves cut, the solution must
be saturated with respect to two solid phases; at the point B, therefore,
the point of intersection of the solubility curve of anhydrous sodium
sulphate with that of the decahydrate, the solution must be saturated with
respect to these two solid substances. But a system of two components
existing in four phases, anhydrous salt--hydrated salt--solution--vapour,
is invariant; and this invariability will remain even if only three phases
are present, provided that one of the factors, pressure, temperature, or
concentration of components retains a constant value. This is the case when
solubilities are determined in open vessels; the pressure is then equal to
atmospheric pressure. Under these circumstances, then, the system,
anhydrous sodium sulphate--decahydrate--solution, will possess no degree of
freedom, and can exist, therefore, only at one definite temperature and
when the solution has a certain definite composition. The temperature of
this point is 32.482deg on a mercury thermometer, or 32.379deg on the
hydrogen thermometer.[211]
{137}