to make its appearance at the temperature of the quadruple point, it will
not necessarily do so; and it is therefore possible to follow the
solubility curve of sodium sulphate decahydrate to a higher temperature.
Since, however, the solubility of the decahydrate at temperatures above the
quadruple point is greater than that of the anhydrous salt, the solution
which is _saturated_ with respect to the former will be _supersaturated_
with respect to the latter. On bringing a small quantity of the anhydrous
salt in contact with the solution, therefore, anhydrous salt will be
deposited; and all the hydrated salt present will ultimately undergo
conversion into the anhydrous salt, through the medium of the solution. In
this case, as in all cases, the solid phase, which is the most stable at
the temperature of the experiment, has at that temperature the least
solubility.
Similarly, the solubility curve of anhydrous sodium sulphate has been
followed to temperatures below 32.5deg. Below this temperature, however,
the solubility of this salt is greater than that of the decahydrate, and
the saturated solution of the anhydrous salt will therefore be
supersaturated for the decahydrate, and will deposit this salt if a
"nucleus" is added to the solution. From this we see that at temperatures
above 32.5deg the anhydrous salt is the stable form, while the decahydrate
is unstable (or metastable); at temperatures below 32.5deg the decahydrate
is stable. This temperature, therefore, is the _transition temperature_ for
decahydrate and anhydrous salt.
From Fig. 33 we see further that the solubility curve of the anhydrous salt
(which at all temperatures below 32.5deg is metastable) is cut by the
solubility curve of the heptahydrate; and this point of intersection (at a
temperature of 24.2deg) must be the _transition point_ for heptahydrate and
anhydrous salt. Since at all temperatures the solubility of the
heptahydrate is greater than that of the decahydrate, the former hydrate
must be metastable with respect to the latter; so that throughout its whole
course the solubility curve of the heptahydrate {138} represents only
metastable equilibria. Sodium sulphate, therefore, forms only one stable
hydrate, the decahydrate.
The solubility relations of sodium sulphate illustrate very clearly the
importance of the solid phase for the definition of saturation and
supersaturation. Since the solubility curve of the anhydrous salt has been
followed backwards to a temperature of about 18deg, it is readily seen,
from Fig. 33, that at a temperature of, say, 20deg three different
_saturated_ solutions of sodium sulphate are possible, according as the
anhydrous salt, the heptahydrate or the decahydrate, is present as the
solid phase. Two of these solutions, however, would be metastable and
_supersaturated with respect to the decahydrate_.
Further, the behaviour of sodium sulphate and water furnishes a very good
example of the fact that a "break" in the solubility curve occurs when, and
only when, the solid phase undergoes change. So long as the decahydrate,
for example, remained unaltered in contact with the solution, the
solubility curve was continuous; but when the anhydrous salt appeared in
the solid phase, a distinct change in the direction of the solubility curve
was observed.
Dehydration by Means of Anhydrous Sodium Sulphate.--The change in the
relative stability of sodium sulphate decahydrate and anhydrous salt in
presence of water at a temperature of 32.5deg explains why the latter salt
cannot be employed for dehydration purposes at temperatures above the
transition point. The dehydrating action of the anhydrous salt depends on
the formation of the decahydrate; but since at temperatures above 33deg the
latter is unstable, and cannot be formed in presence of the anhydrous salt,
this salt cannot, of course, effect a dehydration above that temperature.
Pressure-Temperature Diagram.--The consideration of the
pressure-temperature relations of the two components, sodium sulphate and
water, must include not only the vapour pressure of the saturated
solutions, but also that of the crystalline hydrates. The vapour pressures
of salt hydrates have already been treated in a general manner (Chap. V.),
so that it is only necessary here to point out the connection between the
two classes of systems. {139}
In most cases the vapour pressure of a salt hydrate, _i.e._ the vapour
pressure of the system hydrate--anhydrous salt (or lower hydrate)--vapour,
is at all temperatures lower than that of the system anhydrous salt (or
lower hydrate)--solution--vapour. This, however, is not a necessity; and
cases are known where the vapour pressure of the former system is, under
certain circumstances, equal to or higher than that of the latter. An
example of this is found in sodium sulphate decahydrate.
On heating Na_{2}SO_{4},10H_{2}O, a point is reached at which the
dissociation pressure into anhydrous salt and water vapour becomes equal to
the vapour pressure of the saturated solution of the anhydrous salt, as is
apparent from the following measurements;[212] the differences in pressure
being expressed in millimetres of a particular oil.
Temperature: 29.0deg 30.83deg 31.79deg 32.09deg 32.35deg 32.6deg
Difference of
pressure: 23.8 10.8 5.6 3.6 1.6 0
At 32.6deg, therefore, the vapour pressures of the two systems
Na_{2}SO_{4},10H_{2}O--Na_{2}SO_{4}--vapour
Na_{2}SO_{4}--solution--vapour
are equal; at this temperature the four phases, Na_{2}SO_{4},10H_{2}O;
Na_{2}SO_{4}; solution; vapour, can coexist. From this it is evident that
when sodium sulphate decahydrate is heated to 32.6deg, the two new phases
anhydrous salt and solution will be formed (suspended transformation being
supposed excluded), and the hydrate will appear to undergo _partial
fusion_; and during the process of "melting" the vapour pressure and
temperature will remain constant.[213] This is, however, not a true but a
so-called _incongruent_ melting point; for the composition of the liquid
phase is not the same as that of the solid. As has already been pointed out
(p. 137), we are dealing here with the _transition point_ of the
decahydrate and anhydrous salt, _i.e._ with the reaction
Na_{2}SO_{4},10H_{2}O <--> Na_{2}SO_{4} + 10H_{2}O.
Since at the point of partial fusion of the decahydrate four {140} phases
can coexist, the point is a quadruple point in a two-component system, and
the system at this point is therefore invariant. The temperature of this
point is therefore perfectly definite, and on this account the proposal has
been made to adopt this as a fixed point in thermometry.[214] The
temperature is, of course, practically the same as that at which the two
solubility curves intersect (p. 112). If, however, the vapour phase
disappears, the system becomes univariant, and the equilibrium temperature
undergoes change with change of pressure. The transition curve has been
determined by Tammann,[215] and shown to pass through a point of maximum
temperature.
[Illustration: FIG. 34.]
The vapour pressure of the different systems of sodium sulphate and water
can best be studied with the help of the diagram in Fig. 34.[216] The curve
ABCD represents the vapour-pressure curve of the saturated solution of
anhydrous sodium sulphate. GC is the pressure curve of decahydrate +
anhydrous salt, which, as we have seen, cuts the curve ABCD at the
transition temperature, 32.6deg. Since at this point the solution is
saturated with respect to both the anhydrous salt and the decahydrate, the
vapour-pressure curve of the saturated solution of the latter must also
pass through the point C.[217] As at temperatures below this point the
solubility of the decahydrate is less than that of the anhydrous salt, the
vapour pressure of the solution will, in accordance with Babo's law
(p. 126), be higher than that of the solution of the anhydrous salt; which
was also found experimentally to be the case (curve HC).
{141}
In connection with the vapour pressure of the saturated solutions of the
anhydrous salt and the decahydrate, attention must be drawn to a
conspicuous deviation from what was found to hold in the case of
one-component systems in which a vapour phase was present (p. 31). There,
it was seen that the vapour pressure of the more stable system was always
_lower_ than that of the less stable; in the present case, however, we find
that this is no longer so. We have already learned that at temperatures
below 32.5deg the system decahydrate--solution--vapour is more stable than
the system anhydrous salt--solution--vapour; but the vapour pressure of the
latter system is, as has just been stated, lower than that of the former.
At temperatures above the transition point the vapour pressure of the
saturated solution of the decahydrate will be lower than that of the
saturated solution of the anhydrous salt.
This behaviour depends on the fact that the less stable form is the more
soluble, and that the diminution of the vapour pressure increases with the
amount of salt dissolved.
With regard to sodium sulphate heptahydrate the same considerations will
hold as in the case of the decahydrate. Since at 24deg the four phases
heptahydrate, anhydrous salt, solution, vapour can coexist, the
vapour-pressure curves of the systems hydrate--anhydrous salt--vapour
(curve EB) and hydrate--solution--vapour (curve FB) must cut the pressure
curve of the saturated solution of the anhydrous salt at the above
temperature, as represented in Fig. 34 by the point B. This constitutes,
therefore, a second quadruple point, which is, however, metastable.
From the diagram it is also evident that the dissociation pressure of the
heptahydrate is higher than that of the decahydrate, although it contains
less water of crystallization. The system heptahydrate--anhydrous
salt--vapour must be metastable with respect to the system
decahydrate--anhydrous salt--vapour, and will pass into the latter.[218]
Whether or not there is a temperature at which the vapour-pressure curves
of the two systems intersect, and below which the heptahydrate becomes the
more stable form, is not known.
{142}
In the case of sodium sulphate there is only one stable hydrate. Other
salts are known which exhibit a similar behaviour; and we shall therefore
expect that the solubility relationships will be represented by a diagram
similar to that for sodium sulphate. A considerable number of such cases
have, indeed, been found,[219] and in some cases there is more than one
metastable hydrate. This is found, for example, in the case of nickel
iodate,[220] the solubility curves for which are given in Fig. 35. As can
be seen from the figure, suspended transformation occurs, the solubility
curves having in some cases been followed to a considerable distance beyond
the transition point. One of the most brilliant examples, however, of
suspended transformation in the case of salt hydrates, and the sluggish
transition from the less stable to the more stable form, is found in the
case of the hydrates of calcium chromate.[221]
[Illustration: FIG. 35.]
In the preceding cases, the dissociation-pressure curve of the hydrated
salt cuts the vapour-pressure curve of the saturated {143} solution of the
anhydrous salt. It can, however, happen that the dissociation-pressure
curve of one hydrate cuts the solubility curve, not of the anhydrous salt,
but of a lower hydrate; in this case there will be more than one stable
hydrate, each having a stable solubility curve; and these curves will
intersect at the temperature of the transition point. Various examples of
this behaviour are known, and we choose for illustration the solubility
relationships of barium acetate and its hydrates[222] (Fig. 36).
[Illustration: FIG. 36.]
At temperatures above 0deg, barium acetate can form two stable hydrates, a
trihydrate and a monohydrate. The solubility of the trihydrate increases
very rapidly with rise of temperature, and has been determined up to
26.1deg. At temperatures above 24.7deg, however, the trihydrate is
metastable with respect to the monohydrate; for at this temperature the
solubility curve of the latter hydrate cuts that of the former. This is,
therefore, the transition temperature for the trihydrate and monohydrate.
The solubility curve of the monohydrate succeeds that of the trihydrate,
and exhibits a conspicuous point of minimum solubility at about 30deg.
Below 24.7deg the {144} monohydrate is the less stable hydrate, but its
solubility has been determined to a temperature of 22deg. At 41deg the
solubility curve of the monohydrate intersects that of the anhydrous salt,
and this is therefore the transition temperature for the monohydrate and
anhydrous salt. Above this temperature the anhydrous salt is the stable
solid phase. Its solubility curve also passes through a minimum.
The diagram of solubilities of barium acetate not only illustrates the way
in which the solubility curves of the different stable hydrates of a salt
succeed one another, but it has also an interest and importance from
another point of view. In Fig. 36 there is also shown a faintly drawn curve
which is continuous throughout its whole course. This curve represents the
solubility of barium acetate as determined by Krasnicki.[223] Since,
however, three different solid phases can exist under the conditions of
experiment, it is evident, from what has already been stated (p. 111), that
the different equilibria between barium acetate and water could not be
represented by one _continuous_ curve.
Another point which these experiments illustrate and which it is of the
highest importance to bear in mind is, that in making determinations of the
solubility of salts which are capable of forming hydrates, it is not only
necessary to determine the composition of the solution, but _it is of equal
importance to determine the composition of the solid phase in contact with
it_. In view of the fact, also, that the solution equilibrium is in many
cases established with comparative slowness, it is necessary to confirm the
point of equilibrium, either by approaching it from higher as well as from
lower temperatures, or by actually determining the rate with which the
condition of equilibrium is attained. This can be accomplished by actual
weighing of the dissolved salt or by determinations of the density of the
solution, as well as by other methods.
{145}
2. _The Compounds formed have a Definite Melting Point._
In the cases which have just been considered we saw that the salt hydrates
on being heated did not undergo complete fusion, but that a solid was
deposited consisting of a lower hydrate or of the anhydrous salt. It has,
however, been long known that certain crystalline salt hydrates (_e.g._
sodium thiosulphate, Na_{2}S_{2}O_{3},5H_{2}O, sodium acetate,
NaC_{2}H_{3}O_{2},3H_{2}O) melt completely in their water of
crystallization, and yield a liquid of the _same composition_ as the
crystalline salt. In the case of sodium thiosulphate pentahydrate the
temperature of liquefaction is 56deg; in the case of sodium acetate
trihydrate, 58deg. These two salts, therefore, have a definite melting
point. For the purpose of studying the behaviour of such salt hydrates, we
shall choose not the cases which have just been mentioned, but two others
which have been more fully studied, viz. the hydrates of calcium chloride
and of ferric chloride.
Solubility Curve of Calcium Chloride Hexahydrate.[224]--Although calcium
chloride forms several hydrates, each of which possesses its own
solubility, it is nevertheless the solubility curve of the hexahydrate
which will chiefly interest us at present, and we shall therefore first
discuss that curve by itself.
[Illustration: FIG. 37.]
The solubility of this salt has been determined from the cryohydric point,
which lies at about -55deg, up to the melting point of the salt.[225] The
solubility increases with rise of temperature, as is shown by the figures
in the following table, and by the (diagrammatic) curve AB in Fig. 37. In
the table, the numbers under the heading "solubility" denote the number of
grams of CaCl_{2} dissolved in 100 grams {146} of water; those under the
heading "composition," the number of gram-molecules of water in the
solution to one gram-molecule of CaCl_{2}.
SOLUBILITY OF CALCIUM CHLORIDE HEXAHYDRATE.
-----------------------------------------
Temperature. | Solubility. | Composition.
-----------------------------------------
-55deg | 42.5 | 14.5
-25deg | 50.0 | 12.3
-10deg | 55.0 | 11.2
0deg | 59.5 | 10.37
10deg | 65.0 | 9.49
20deg | 74.5 | 8.28
25deg | 82.0 | 7.52
28.5deg | 90.5 | 6.81
29.5deg | 95.5 | 6.46
30.2deg | 102.7 | 6.00
29.6deg | 109.0 | 5.70
29.2deg | 112.8 | 5.41
-----------------------------------------
So far as the first portion of the curve is concerned, it resembles the
most general type of solubility curve. In the present case the solubility
is so great and increases so rapidly with rise of temperature, that a point
is reached at which the water of crystallization of the salt is sufficient
for its complete solution. This temperature is 30.2deg; and since the
composition of the solution is the same as that of the solid salt, viz. 1
mol. of CaCl_{2} to 6 mols. of water, this temperature must be the melting
point of the hexahydrate. At this point the hydrate will fuse or the
solution will solidify without change of temperature and without change of
composition. Such a melting point is called a _congruent_ melting point.
But the solubility curve of calcium chloride hexahydrate differs markedly
from the other solubility curves hitherto considered in that it possesses a
_retroflex portion_, represented in the figure by BC. As is evident from
the figure, therefore, calcium chloride hexahydrate exhibits the peculiar
and, as it was at first thought, impossible behaviour that it can be in
equilibrium at one and the same temperature with two different solutions,
one of which contains more, the other less, water than the solid hydrate;
for it must be remembered that {147} throughout the whole course of the
curve ABC the solid phase present in equilibrium with the solution is the
hexahydrate.
Such a behaviour, however, on the part of calcium chloride hexahydrate will
appear less strange if one reflects that the melting point of the hydrate
will, like the melting point of other substances, be lowered by the
addition of a second substance. If, therefore, water is added to the
hydrate at its melting point, the temperature at which the solid hydrate
will be in equilibrium with the liquid phase (solution) will be lowered; or
if, on the other hand, anhydrous calcium chloride is added to the hydrate
at its melting point (or what is the same thing, if water is removed from
the solution), the temperature at which the hydrate will be in equilibrium
with the liquid will also be lowered; _i.e._ the hydrate will melt at a
lower temperature. In the former case we have the hydrate in equilibrium
with a solution containing more water, in the latter case with a solution
containing less water than is contained in the hydrate itself.
It has already been stated (p. 109) that the solubility curve (in general,
the equilibrium curve) is continuous so long as the solid phase remains
unchanged; and we shall therefore expect that the curve ABC will be
continuous. Formerly, however, it was considered by some that the curve was
not continuous, but that the melting point is the point of intersection of
two curves, a solubility curve and a fusion curve. Although the earlier
solubility determinations were insufficient to decide this point
conclusively, more recent investigation has proved beyond doubt that the
curve is continuous and exhibits no break.[226]
{148}
Although in taking up the discussion of the equilibria between calcium
chloride and water, it was desired especially to call attention to the form
of the solubility curve in the case of salt hydrates possessing a definite
melting point, nevertheless, for the sake of completeness, brief mention
may be made of the other systems which these two components can form.
[Illustration: FIG. 38.]
Besides the hexahydrate, the solubility curve of which has already been
described, calcium chloride can also crystallize in two different forms,
each of which contains four molecules {149} of water of crystallization;
these are distinguished as [alpha]-tetrahydrate, and [beta]-tetrahydrate.
Two other hydrates are also known, viz. a dihydrate and a monohydrate. The
solubility curves of these different hydrates are given in Fig. 38.
On following the solubility curve of the hexahydrate from the ordinary
temperature upwards, it is seen that at a temperature of 29.8deg
represented by the point H, it cuts the solubility curve of the
[alpha]-tetrahydrate. This point is therefore a quadruple point at which
the four phases hexahydrate, [alpha]-tetrahydrate, solution, and vapour can
coexist. It is also the transition point for these two hydrates. Since, at
temperatures above 29.8deg, the [alpha]-tetrahydrate is the stable form, it
is evident from the data given before (p. 146), as also from Fig. 38, that
the portion of the solubility curve of the hexahydrate lying above this
temperature represents _metastable_ equilibria. The realization of the
metastable melting point of the hexahydrate is, therefore, due to suspended
transformation. At the transition point, 29.8deg, the solubility of the
hexahydrate and [alpha]-tetrahydrate is 100.6 parts of CaCl_{2} in 100
parts of water.
The retroflex portion of the solubility curve of the hexahydrate extends to
only 1deg below the melting point of the hydrate. At 29.2deg crystals of a
new hydrate, [beta]-tetrahydrate, separate out, and the solution, which now
contains 112.8 parts of CaCl_{2} to 100 parts of water, is saturated with
respect to the two hydrates. Throughout its whole extent the solubility
curve EDF of the [beta]-tetrahydrate represents metastable equilibria. The
upper limit of the solubility curve of [beta]-tetrahydrate is reached at
38.4deg (F), the point of intersection with the curve for the dihydrate.
Above 29.8deg the stable hydrate is the [alpha]-tetrahydrate; and its
solubility curve extends to 45.3deg (K), at which temperature it cuts the
solubility curve of the dihydrate. The curve of the latter hydrate extends
to 175.5deg (L), and is then succeeded by the curve for the monohydrate.
The solubility curve of the anhydrous salt does not begin until a
temperature of about 260deg. The whole diagram, therefore, shows a
succession of stable hydrates, a metastable hydrate, a metastable melting
point and retroflex solubility curve. {150}
Pressure-Temperature Diagram.--The complete study of the equilibria between
the two components calcium chloride and water would require the discussion
of the vapour pressure of the different systems, and its variation with the
temperature. For our present purpose, however, such a discussion would not
be of great value, and will therefore be omitted here; in general, the same
relationships would be found as in the case of sodium sulphate (p. 138),
except that the rounded portion of the solubility curve of the hexahydrate
would be represented by a similar rounded portion in the pressure
curve.[227] As in the case of sodium sulphate, the transition points of the
different hydrates would be indicated by breaks in the curve of pressures.
Finally, mention may again be made of the difference of the pressure of
dissociation of the hexahydrate according as it becomes dehydrated to the
[alpha]- or the [beta]-tetrahydrate (p. 88).
The Indifferent Point.--We have already seen that at 30.2deg calcium
chloride hexahydrate melts congruently, and that, provided the pressure is
maintained constant, addition or withdrawal of heat will cause the complete
liquefaction or solidification, without the temperature of the system
undergoing change. This behaviour, therefore, is similar to, but is not
quite the same as the fusion of a simple substance such as ice; and the
difference is due to the fact that in the case of the hexahydrate the
emission of vapour by the liquid phase causes an alteration in the
composition of the latter, owing to the non-volatility of the calcium
chloride; whereas in the case of ice this is, of course, not so.
Consider, however, for the present that the vapour phase is absent, and
that we are dealing with the two-phase system solid--solution. Then, since
there are two components, the system is bivariant. For any given value of
the pressure, therefore, we should expect that the system could exist at
different temperatures; which, indeed, is the case. It has, however,
already been noted that when the composition of the liquid phase becomes
the same as that of the solid, the system then behaves as a _univariant_
system; for, at a given pressure, the system solid--solution can exist only
at _one_ temperature, change of temperature producing complete
transformation in {151} one or other direction. _The variability of the
system has therefore been diminished._
This behaviour will perhaps be more clearly understood when one reflects
that since the composition of the two phases is the same, the system may be
regarded as being formed of _one component_, just as the system NH_{4}Cl
<--> NH_{3} + HCl was regarded as being composed of one component when the
vapour had the same total composition as the solid (p. 13). One component
in two phases, however, constitutes a univariant system, and we can
therefore see that calcium chloride hexahydrate in contact with solution of
the same composition will constitute a univariant system. The temperature
of equilibrium will, however, vary with the pressure;[228] if the latter is
constant, the temperature will also be constant.
A point such as has just been referred to, which represents the special
behaviour of a system of two (or more) components, in which the composition
of two phases becomes identical, is known as an _indifferent point_,[229]
and it has been shown[230] that at a given pressure the temperature in the
indifferent point is the _maximum_ or _minimum_ temperature possible at the
particular pressure[231] (cf. critical solution temperature). At such a
point a system loses one degree of freedom, or behaves like a system of the
next lower order.
The Hydrates of Ferric Chloride.--A better illustration of the formation of
compounds possessing a definite melting point, and of the existence of
retroflex solubility curves, is afforded by the hydrates of ferric
chloride, which not only possess definite points of fusion, but these
melting points are stable. A very brief description of the relations met
with will suffice.[232]
{152}
Ferric chloride can form no less than four stable hydrates, viz.
Fe_{2}Cl_{6},12H_{2}O, Fe_{2}Cl_{6},7H_{2}O, Fe_{2}Cl_{6},5H_{2}O, and
Fe_{2}Cl_{6},4H_{2}O, and each of these hydrates possesses a definite,
stable melting point. On analogy with the behaviour of calcium chloride,
therefore, we shall expect that the solubility curves of these different
hydrates will exhibit a series of _temperature maxima_; the points of
maximum temperature representing systems in which the composition of the
solid and liquid phases is the same. A graphical representation of the
solubility relations is given in Fig. 39, and the composition of the
different saturated solutions which can be formed is given in the following
tables, the composition being expressed in molecules of Fe_{2}Cl_{6} to 100
molecules of water. The figures printed in thick type refer to transition
and melting points.
[Illustration: FIG. 39.]
{153}
COMPOSITION OF THE SATURATED SOLUTIONS OF FERRIC CHLORIDE AND ITS
HYDRATES.
(_The name placed at the head of each table is the solid phase._)
ICE.
---------------------------
Temperature. | Composition.
---------------------------
+/--55deg | +/-2.75
-40deg | 2.37
-27.5deg | 1.90
-20.5deg | 1.64
-10deg | 1.00
0deg | 0
---------------------------
Fe_{2}Cl_{6},12H_{2}O.
---------------------------
Temperature. | Composition.
---------------------------
-55deg | +/-2.75
-41deg | 2.81
-27deg | 2.98
0deg | 4.13
10deg | 4.54
20deg | 5.10
30deg | 5.93
35deg | 6.78
36.5deg | 7.93
37deg | 8.33
36deg | 9.29
33deg | 10.45
30deg | 11.20
27.4deg | 12.15
20deg | 12.83
10deg | 13.20
8deg | 13.70
---------------------------
Fe_{2}Cl_{6},7H_{2}O.
---------------------------
Temperature. | Composition.
---------------------------
20deg | 11.35
27.4deg | 12.15
32deg | 13.55
32.5deg | 14.29
30deg | 15.12
25deg | 15.54
---------------------------
Fe_{2}Cl_{6},5H_{2}O.
---------------------------
Temperature. | Composition.
---------------------------
20deg | 11.35
12deg | 12.87
20deg | 13.95
27deg | 14.85
30deg | 15.12
35deg | 15.64
50deg | 17.50
55deg | 19.15
56deg | 20.00
55deg | 20.32
---------------------------
Fe_{2}Cl_{6},4H_{2}O
---------------------------
Temperature. | Composition.
---------------------------
20deg | 11.35
50deg | 19.96
55deg | 20.32
60deg | 20.70
69deg | 21.53
72.5deg | 23.35
73.5deg | 25.00
72.5deg | 26.15
70deg | 27.90
66deg | 29.20
---------------------------
Fe_{2}Cl_{6} (ANHYDROUS).
---------------------------
Temperature. | Composition.
---------------------------
20deg | 11.35
66deg | 29.20
70deg | 29.42
75deg | 28.92
80deg | 29.20
100deg | 29.75
---------------------------
The lowest portion of the curve, AB, represents the equilibria between ice
and solutions containing ferric chloride. It represents, in other words,
the lowering of the fusion point of ice by addition of ferric chloride. At
the point B (-55deg), the cryohydric point (p. 117) is reached, at which
the solution is in equilibrium with ice and ferric chloride dodecahydrate.
As {154} has already been shown, such a point represents an invariant
system; and the liquid phase will, therefore, solidify to a mixture of ice
and hydrate without change of temperature. If heat is added, ice will melt
and the system will pass to the curve BCDN, which is the solubility curve
of the dodecahydrate. At C (37deg), the point of maximum temperature, the
hydrate melts completely. The retroflex portion of this curve can be
followed backwards to a temperature of 8deg, but below 27.4deg (D), the
solutions are supersaturated with respect to the heptahydrate; point D is
the eutectic point for dodecahydrate and heptahydrate. The curve DEF is the
solubility curve of the heptahydrate, E being the melting point, 32.5deg.
On further increasing the quantity of ferric chloride, the temperature of
equilibrium is lowered until at F (30deg) another eutectic point is
reached, at which the heptahydrate and pentahydrate can co-exist with
solution. Then follow the solubility curves for the pentahydrate, the
tetrahydrate, and the anhydrous salt; G (56deg) is the melting point of the
former hydrate, J (73.5deg) the melting point of the latter. H and K, the
points at which the curves intersect, represent eutectic points; the
temperature of the former is 55deg, that of the latter 66deg. The dotted
portions of the curves represent metastable equilibria.
As is seen from the diagram, a remarkable series of solubility curves is
obtained, each passing through a point of maximum temperature, the whole
series of curves forming an undulating "festoon." To the right of the
series of curves the diagram represents unsaturated solutions; to the left,
supersaturated.
If an unsaturated solution, the composition of which is represented by a
point in the field to the right of the solubility curves, is cooled down,
the result obtained will differ according as the composition of the
solution is the same as that of a cryohydric point, or of a melting point,
or has an intermediate value. Thus, if a solution represented by _x__{1} is
cooled down, the composition will remain unchanged as indicated by the
horizontal dotted line, until the point D is reached. At this point,
dodecahydrate and heptahydrate will separate out, and the liquid will
ultimately solidify completely to a mixture or "conglomerate" of these two
hydrates; the temperature of {155} the system remaining constant until
complete solidification has taken place. If, on the other hand, a solution
of the composition _x__{3} is cooled down, ferric chloride dodecahydrate
will be formed when the temperature has fallen to that represented by C,
and the solution will completely solidify, without alteration of
temperature, with formation of this hydrate. In both these cases,
therefore, a point is reached at which complete solidification occurs
without change of temperature.
Somewhat different, however, is the result when the solution has an
intermediate composition, as represented by _x__{2} or _x__{4}. In the
former case the dodecahydrate will first of all separate out, but on
further withdrawal of heat the temperature will fall, the solution will
become relatively richer in ferric chloride, owing to separation of the
hydrate, and ultimately the eutectic point D will be reached, at which
complete solidification will occur. Similarly with the second solution.
Ferric chloride dodecahydrate will first be formed, and the temperature
will gradually fall, the composition of the solution following the curve CB
until the cryohydric point B is reached, when the whole will solidify to a
conglomerate of ice and dodecahydrate.
Suspended Transformation.--Not only can the upper branch of the solubility
curve of the dodecahydrate be followed backwards to a temperature of 8deg,
or about 19deg below the temperature of transition to the heptahydrate; but
suspended transformation has also been observed in the case of the
heptahydrate and the pentahydrate. To such an extent is this the case that
the solubility curve of the latter hydrate has been followed downwards to
its point of intersection with the curve for the dodecahydrate. This point
of intersection, represented in Fig. 39 by M, lies at a temperature of
about 15deg; and at this temperature, therefore, it is possible for the two
solid phases dodecahydrate and pentahydrate to coexist, so that M is a
eutectic point for the dodecahydrate and the pentahydrate. It is, however,
a metastable eutectic point, for it lies in the region of supersaturation
with respect to the heptahydrate; and it can be realized only because of
the fact that the latter hydrate is not readily formed.
Evaporation of Solutions at Constant Temperature.--On {156} evaporating
dilute solutions of ferric chloride at constant temperature, a remarkable
series of changes is observed, which, however, will be understood with the
help of Fig. 40. Suppose an unsaturated solution, the composition of which
is represented by the point _x__{1}, is evaporated at a temperature of
about 17deg - 18deg. As water passes off, the composition of the solution
will follow the dotted line of constant temperature, until at the point
where it cuts the curve BC the solid hydrate Fe_{2}Cl_{6},12H_{2}O
separates out. As water continues to be removed, the hydrate must be
deposited (in order that the solution shall remain saturated), until
finally the solution dries up to the hydrate. As dehydration proceeds, the
heptahydrate can be formed, and the dodecahydrate will finally pass into
the heptahydrate; and this, in turn, into the pentahydrate.
[Illustration: FIG. 40.]
But the heptahydrate is not always formed by the dehydration of the
dodecahydrate, and the behaviour on evaporation is therefore somewhat
perplexing at first sight. After the solution has dried to the
dodecahydrate, as explained above, further removal of water causes
liquefaction, and the system is now represented by the point of
intersection at _a_; at this point the solid hydrate is in equilibrium with
a solution containing relatively more ferric chloride. If, therefore,
evaporation is continued, the solid hydrate must _pass into solution_ in
order that the composition of the latter may remain unchanged, so that
ultimately a liquid will again be obtained. A very slight further
dehydration will bring the solution into the state represented by _b_, at
which the pentahydrate is formed, and the solution will at last disappear
and leave this hydrate alone.
Without the information to be obtained from the curves in Figs. 39 and 40,
the phenomena which would be observed on carrying out the evaporation at a
temperature of about 31 - 32deg {157} would be still more bewildering. The
composition of the different solutions formed will be represented by the
perpendicular line _x__{2}12345. Evaporation will first cause the
separation of the dodecahydrate, and then total disappearance of the liquid
phase. Then liquefaction will occur, and the system will now be represented
by the point 2, in which condition it will remain until the solid hydrate
has disappeared. Following this there will be deposition of the
heptahydrate (point 3), with subsequent disappearance of the liquid phase.
Further dehydration will again cause liquefaction, when the concentration
of the solution will be represented by the point 4; the heptahydrate will
ultimately disappear, and then will ensue the deposition of the
pentahydrate, and complete solidification will result. On evaporating a
solution, therefore, of the composition _x__{2}, the following series of
phenomena will be observed: solidification to dodecahydrate; liquefaction;
solidification to heptahydrate; liquefaction; solidification to
pentahydrate.[233]
Although ferric chloride and water form the largest and best-studied series
of hydrates possessing definite melting points, examples of similar
hydrates are not few in number; and more careful investigation is
constantly adding to the list.[234] In all these cases the solubility curve
will show a point of maximum temperature, at which the hydrate melts, and
will end, above and below, in a cryohydric point. Conversely, if such a
curve is found in a system of two components, we can argue that a definite
compound of the components possessing a definite melting point is formed.
Inevaporable Solutions.--If a saturated solution in contact with two
hydrates, or with a hydrate and anhydrous salt is heated, the temperature
and composition of the solution will, of course, remain unchanged so long
as the two solid phases are present, for such a system is invariant. In
addition to this, however, the _quantity_ of the solution will also remain
unchanged, the water which evaporates being supplied by the higher hydrate.
The same phenomenon is also observed in the case of cryohydric points when
ice is a solid phase; so long as the latter is present, evaporation will be
accompanied {158} by fusion of the ice, and the quantity of solution will
remain constant. Such solutions are called _inevaporable_.[235]
[Illustration: FIG. 41.]
Illustration.--In order to illustrate the application of the principles of
the Phase Rule to the study of systems formed by a volatile and a
non-volatile component, a brief description may be given of the behaviour
of sulphur dioxide and potassium iodide, which has formed the subject of a
recent investigation. After it had been found[236] that liquid sulphur
dioxide has the property of dissolving potassium iodide, and that the
solutions thus obtained present certain peculiarities of behaviour, the
question arose as to whether or not compounds are formed between the
sulphur dioxide and the potassium iodide, and if so, what these compounds
are. To find an answer to this question, Walden and Centnerszwer[237] made
a complete investigation of the solubility curves (equilibrium curves) of
these two components, the investigation extending from the freezing point
to the critical point of sulphur dioxide. For convenience of reference, the
results which they obtained are represented diagrammatically in Fig. 41.
The freezing point (A) of pure sulphur dioxide was found to be -72.7deg.
Addition of potassium iodide lowered the freezing point, but the maximum
depression obtained was very small, and was reached when the concentration
of the potassium iodide in the solution was only 0.336 mols. per cent.
Beyond this point, an increase in the concentration of the iodide was
accompanied by an elevation of the freezing point, the change of the
freezing point with the concentration being represented by the curve BC.
The solid {159} which separated from the solutions represented by BC was a
bright _yellow_ crystalline substance. At the point C (-23.4deg) a
temperature-maximum was reached; and as the concentration of the potassium
iodide was continuously increased, the temperature of equilibrium first
fell and then slowly rose, until at +0.26deg (E) a second
temperature-maximum was registered. On passing the point D, the solid which
was deposited from the solution was a _red_ crystalline substance. On
withdrawing sulphur dioxide from the system, the solution became turbid,
and the temperature remained constant. The investigation was not pursued
farther at this point, the attention being then directed to the equilibria
at higher temperatures.
When a solution of potassium iodide in liquid sulphur dioxide containing
1.49 per cent. of potassium iodide was heated, solid (potassium iodide) was
deposited at a temperature of 96.4deg. Solutions containing more than about
3 per cent. of the iodide separated, on being heated, into two layers, and
the temperature at which the liquid became heterogeneous fell as the
concentration was increased; a temperature-minimum being obtained with
solutions containing 12 per cent. of potassium iodide. On the other hand,
solutions containing 30.9 per cent. of the iodide, on being heated,
deposited potassium iodide; while a solution containing 24.5 per cent. of
the salt first separated into two layers at 89.3deg, and then, on cooling,
solid was deposited and one of the liquid layers disappeared.
Such are, in brief, the results of experiment; their interpretation in the
light of the Phase Rule is the following:--
The curve AB is the freezing-point curve of solid sulphur dioxide in
contact with solutions of potassium iodide. BCD is the solubility curve of
the yellow crystalline solid which is deposited from the solutions. C, the
temperature-maximum, is the melting point of this _yellow_ solid, and the
composition of the latter must be the same as that of the solution at this
point (p. 145), which was found to be that represented by the formula
KI,14SO_{2}. B is therefore the eutectic point, at which solid sulphur
dioxide and the compound KI,14SO_{2} can exist together in equilibrium with
solution and vapour. The curve DE is the solubility curve of the _red_
crystalline solid, and the {160} point E, at which the composition of
solution and solid is the same, is the melting point of the solid. The
composition of this substance was found to be KI,4SO_{2}.[238] D is,
therefore, the eutectic point at which the compounds KI,14SO_{2} and
KI,4SO_{2} can coexist in equilibrium with solution and vapour. The curve
DE does not exhibit a retroflex portion; on the contrary, on attempting to
obtain more concentrated solutions in equilibrium with the compound
KI,4SO_{2}, a new solid phase (probably potassium iodide) was formed. Since
at this point there are four phases in equilibrium, viz. the compound
KI,4SO_{2}, potassium iodide, solution, and vapour, the system is
invariant. E is, therefore, the _transition point_ for KI,4SO_{2} and KI.
Passing to higher temperatures, FG is the solubility curve of potassium
iodide in sulphur dioxide; at G two liquid phases are formed, and the
system therefore becomes invariant (cf. p. 121). The curve GHK is the
solubility curve for two partially miscible liquids; and since complete
miscibility occurs on _lowering_ the temperature, the curve is similar to
that obtained with triethylamine and water (p. 101). K is also an invariant
point at which potassium iodide is in equilibrium with two liquid phases
and vapour.
The complete investigation of the equilibria between sulphur dioxide and
potassium iodide, therefore, shows that these two components form the
compounds KI,14SO_{2} and KI,4SO_{2}; and that when solutions having a
concentration between those represented by the points G and K are heated,
separation into two layers occurs. The temperatures and concentrations of
the different characteristic points are as follows:--
-------------------------------------------------------------
| | Composition of
Point. | Temperature. | the solution
| | per cent. KI.
-------------------------------------------------------------
A (m.p. of SO_{2}) | -72.7deg | --
B (eutectic point) | -- | 0.86
C (m.p. of KI,14SO_{2}) | -23.4deg | 17.63
E (m.p. of KI,4SO_{2}) | +0.26deg| 39.33
G (KI + two liquid phases) |(about) 88deg | 24.0
H (critical solution point) | 77.3deg | 12
K (KI + two liquid phases) |(about) 88deg | 2.7
-------------------------------------------------------------
* * * * *
{161}
CHAPTER IX
EQUILIBRIA BETWEEN TWO VOLATILE COMPONENTS
General.--In the two preceding chapters certain restrictions were imposed
on the discussion of the equilibria between two components; but in the
present chapter the restriction that only one of the components is volatile
will be allowed to fall, and the general behaviour of two volatile[239]
components, each of which is capable of forming a liquid solution with the
other, will be studied. As we shall see, however, the removal of the
previous restriction produces no alteration in the general aspect of the
equilibrium curves for concentration and temperature, but changes to some
extent the appearance of the pressure-temperature diagram. The latter would
become still more complicated if account were taken not only of the total
pressure but also of the partial pressures of the two components in the
vapour phase; this complication, however, will not be introduced in the
present discussion.[240] In this chapter we shall consider the systems
formed by the two components iodine and chlorine, and sulphur dioxide and
water.
Iodine and Chlorine.--The different systems furnished by iodine and
chlorine, rendered classical by the studies of Stortenbeker,[241] form a
very complete example of equilibria in a two-component system. We shall
first of all consider the {162} relations between concentration and
temperature, with the help of the accompanying diagram, Fig. 42.
[Illustration: FIG. 42.]
Concentration-Temperature Diagram.--In this diagram the temperatures are
taken as the abscissae, and the composition of the solution, expressed in
atoms of chlorine to one atom of iodine,[242] is represented by the
ordinates. In the diagram, A represents the melting point of pure iodine,
114deg. If chlorine is added to the system, a solution of chlorine in
liquid iodine is obtained, and the temperature at which solid iodine is in
equilibrium with the liquid solution will be all the lower the greater the
concentration of the chlorine. We therefore obtain the curve ABF, which
represents the composition of the solution {163} with which solid iodine is
in equilibrium at different temperatures. This curve can be followed down
to 0deg, but at temperatures below 7.9deg (B) it represents metastable
equilibria. At B iodine monochloride can be formed, and if present the
system becomes invariant; B is therefore a quadruple point at which the
four phases, iodine, iodine monochloride, solution, and vapour, can
coexist. Continued withdrawal of heat at this point will therefore lead to
the complete solidification of the solution to a mixture or conglomerate of
iodine and iodine monochloride, while the temperature remains constant
during the process. B is the eutectic point for iodine and iodine
monochloride.
Just as we found in the case of aqueous salt solutions that at temperatures
above the cryohydric or eutectic point, two different solutions could
exist, one in equilibrium with ice, the other in equilibrium with the salt
(or salt hydrate), so in the case of iodine and chlorine there can be two
solutions above the eutectic point B, one containing a lower proportion of
chlorine in equilibrium with iodine, the other containing a higher
proportion of chlorine in equilibrium with iodine monochloride. The
composition of the latter solution is represented by the curve BCD. As the
concentration of chlorine is increased, the temperature at which there is
equilibrium between iodine monochloride and solution rises until a point is
reached at which the composition of the solution is the same as that of the
solid. At this point (C), iodine monochloride melts. Addition of one of the
components will lower the temperature of fusion, and a continuous
curve,[243] exhibiting a retroflex portion as in the case of
CaCl_{2},6H_{2}O, will be obtained. At temperatures below its melting
point, therefore, iodine monochloride can be in equilibrium with two
different solutions.
The upper portion of this curve, CD, can be followed downwards to a
temperature of 22.7deg. At this temperature iodine trichloride can separate
out, and a second quadruple {164} point (D) is obtained. This is the
eutectic point for iodine monochloride and iodine trichloride.
By addition of heat and increase in the amount of chlorine, the iodine
monochloride disappears, and the system passes along the curve DE, which
represents the composition of the solutions in equilibrium with solid
iodine trichloride. The concentration of chlorine in the solution increases
as the temperature is raised, until at the point E, where the solution has
the same composition as the solid, the maximum temperature is reached; the
iodine trichloride melts. On increasing still further the concentration of
chlorine in the solution, the temperature of equilibrium falls, and a
continuous curve, similar to that for the monochloride, is obtained. The
upper branch of this curve has been followed down to a temperature of
30deg, the solution at this point containing 99.6 per cent. of
chlorine.[244] The very rounded form of the curve is due to the trichloride
being largely dissociated in the liquid state.
One curve still remains to be considered. As has already been mentioned,
iodine monochloride can exist in two crystalline forms, only one of which,
however, is stable at temperatures below the melting point; the two forms
are _monotropic_ (p. 44). The stable form which melts at 27.2deg, is called
the [alpha]-form, while the less stable variety, melting at 13.9deg, is
known as the [beta]-form. If, now, the presence of [alpha]-ICl is excluded,
it is possible to obtain the [beta]-form, and to study the conditions of
equilibrium between it and solutions of iodine and chlorine, from the
eutectic point F to the melting point G. As the [beta]-ICl becomes less
stable in presence of excess of chlorine, it has not been possible to study
the retroflex portion of the curve represented by the dotted continuation
of FG.
The following table gives some of the numerical data from which Fig. 42 was
constructed.[245]
{165}
IODINE AND CHLORINE.
I. _Invariant systems._
-------------------------------------------------------------------------
| | Phases present.
Temper-| Pressure.+--------------------+-----------------+--------------
ature. | | Solid. | Liquid. | Vapour.
--------+----------+--------------------+-----------------+--------------
7.9deg | 11 mm. | I_{2},[alpha]-ICl | I[wavy]Cl_{0.66}| I + Cl_{0.92}
0.9deg | -- | I_{2},[beta]-ICl | I[wavy]Cl_{0.72}| --
22.7deg | 42 mm. | [alpha]-ICl,ICl_{3}| I[wavy]Cl_{1.19}| I + Cl_{1.75}
[-102deg| <1 atm. | ICl_{3},Cl_{2} | I[wavy]Cl_{m} | I + Cl_{n}]
--------+----------+--------------------+-----------------+--------------
II. _Melting points._
A. Iodine,[246] 114.15deg (pressure 89.8 mm.).
C. [alpha]-Iodine monochloride, 27.2deg (pressure 37 mm.).
E. Iodine trichloride, 101deg (pressure 16 atm.).
G. [beta]-Iodine monochloride, 13.9deg.
Since the vapour pressure at the melting point of iodine trichloride
amounts to 16 atm., the experiments must of course be carried out
in closed vessels. At 63.7deg the vapour pressure of the system
trichloride--solution--vapour is equal to 1 atm.
Pressure-Temperature Diagram.--In this diagram there are represented the
values of the vapour pressure of the saturated solutions of chlorine and
iodine. To give a complete picture of the relations between pressure,
temperature, and concentration, a solid model would be required, with three
axes at right angles to one another along which could be measured the
values of pressure, temperature, and concentration of the components in the
solution. Instead of this, however, there may be employed the accompanying
projection figure[247] (Fig. 43), the lower portion of which shows the
projection of the equilibrium curve on the surface containing the
concentration and temperature axes, while the upper portion is the
projection on the plane containing the pressure and temperature axes. The
lower portion is therefore a concentration-temperature diagram; {166} the
upper portion, a pressure-temperature diagram. The corresponding points of
the two diagrams are joined by dotted lines.
[Illustration: FIG. 43.]
Corresponding to the point C, the melting point of pure iodine, there is
the point C_{1}, which represents the vapour pressure of iodine at its
melting point. At this point three curves cut: 1, the sublimation curve of
iodine; 2, the vaporization curve of fused iodine; 3, C_{1}B_{1}, the
vapour-pressure curve of the saturated solutions in equilibrium with solid
iodine. Starting, therefore, with the system solid iodine--liquid iodine,
addition of chlorine will cause the temperature of equilibrium to fall
continuously, while the vapour pressure will first increase, pass through a
maximum and then fall continuously {167} until the eutectic point, B
(B_{1}), is reached.[248] At this point the system is invariant, and the
pressure will therefore remain constant until all the iodine has
disappeared. As the concentration of the chlorine increases in the manner
represented by the curve B_f_H, the pressure of the vapour also increases
as represented by the curve B_{1}_f__{1}H_{1}. At H_{1}, the eutectic point
for iodine monochloride and iodine trichloride, the pressure again remains
constant until all the monochloride has disappeared. As the concentration
of the solution passes along the curve HF, the pressure of the vapour
increases as represented by the curve H_{1}F_{1}; F_{1} represents the
pressure of the vapour at the melting point of iodine trichloride. If the
concentration of the chlorine in the solution is continuously increased
from this point, the vapour pressure first increases and then decreases,
until the eutectic point for iodine trichloride and solid chlorine is
reached (D_{1}). Curves Cl_{2} solid and Cl_{2} liquid represent the
sublimation and vaporization curves of chlorine, the melting point of
chlorine being -102deg.
Although complete measurements of the vapour pressure of the different
systems of pure iodine to pure chlorine have not been made, the
experimental data are nevertheless sufficient to allow of the general form
of the curves being indicated with certainty.
Bivariant Systems.--To these, only a brief reference need be made. Since
there are two components, two phases will form a bivariant system. The
fields in which these systems can exist are shown in Fig. 43 and Fig. 44,
which is a more diagrammatic representation of a portion of Fig. 43.
I. Iodine--vapour.
II. Solution--vapour.
III. Iodine trichloride--vapour.
IV. Iodine monochloride--vapour.
[Illustration: FIG. 44.]
The conditions for the existence of these systems will probably be best
understood from Fig. 44. Since the curve B'A' {168} represents the
pressures under which the system iodine--solution--vapour can exist,
increase of volume (diminution of pressure) will cause the volatilization
of the solution, and the system iodine--vapour will remain. If, therefore,
we start with a system represented by _a_, diminution of pressure at
constant temperature will lead to the condition represented by _x_. On the
other hand, increase of pressure at _a_ will lead to the condensation of a
portion of the vapour phase. Since, now, the concentration of chlorine in
the vapour is greater than in the solution, condensation of vapour would
increase the concentration of chlorine in the solution; a certain amount of
iodine must therefore pass into solution in order that the composition of
the latter shall remain unchanged.[249] If, therefore, the volume of vapour
be sufficiently great, continued diminution of volume will ultimately lead
to the disappearance of all the iodine, and there will remain only solution
and vapour (field II.). As the diminution of volume is continued, the
vapour pressure and the concentration of the chlorine in the solution will
increase, until when the pressure has reached the value _b_, iodine
monochloride can separate out. The system, therefore, again becomes
univariant, and at constant temperature the pressure and composition of the
phases must remain unchanged. Diminution of volume will therefore not
effect an increase of pressure, but a condensation of the vapour; and since
this is richer in chlorine than the {169} solution, solid iodine
monochloride must separate out in order that the concentration of the
solution remain unchanged.[250] As the result, therefore, we obtain the
bivariant system iodine monochloride--vapour.
A detailed discussion of the effect of a continued increase of pressure
will not be necessary. From what has already been said and with the help of
Fig. 44, it will readily be understood that this will lead successively to
the univariant system (_c_), iodine monochloride--solution--vapour; the
bivariant system solution--vapour (field II.); the univariant system (_d_),
iodine trichloride--solution--vapour; and the bivariant system _x'_, iodine
trichloride--vapour. If the temperature of the experiment is above the
melting point of the monochloride, then the systems in which this compound
occurs will not be formed.
Sulphur Dioxide and Water.--In the case just studied we have seen that the
components can combine to form definite compounds possessing stable melting
points. The curves of equilibrium, therefore, resemble in their general
aspect those of calcium chloride and water, or of ferric chloride and
water. In the case of sulphur dioxide and water, however, the melting point
of the compound formed cannot be realized, because transition to another
system occurs; retroflex concentration-temperature curves are therefore not
found here, but the curves exhibit breaks or sudden changes in direction at
the transition points, as in the case of the systems formed by sodium
sulphate and water. The case of sulphur dioxide and water is also of
interest from the fact that two liquid phases can be formed.
The phases which occur are--Solid: ice, sulphur dioxide hydrate,
SO_{2},7H_{2}O. Liquid: two solutions, the one containing excess of sulphur
dioxide, the other excess of water, and represented by the symbols SO_{2}
[wavy] _x_H_{2}O (solution I.), and H_{2}O [wavy] _y_SO_{2} (solution II.).
Vapour: a mixture of sulphur dioxide and water vapour in varying
proportions. Since there are two components, sulphur dioxide and water, the
number of {170} possible systems is considerable. Only the following,
however, have been studied:--
I. _Invariant Systems: Four co-existing phases._
(_a_) Ice, hydrate, solution, vapour.
(_b_) Hydrate, solution I., solution II., vapour.
II. _Univariant Systems: Three co-existing phases._
(_a_) Hydrate, solution I., vapour.
(_b_) Hydrate, solution II., vapour.
(_c_) Solution I., solution II., vapour.
(_d_) Hydrate, solution I., solution II.
(_e_) Hydrate, ice, vapour.
(_f_) Ice, solution II., vapour.
(_g_) Ice, hydrate, solution II.
III. _Bivariant Systems: Two co-existing phases._
(_a_) Hydrate, solution I.
(_b_) Hydrate, solution II.
(_c_) Hydrate, vapour.
(_d_) Hydrate, ice.
(_e_) Solution I., solution II.
(_f_) Solution I., vapour.
(_g_) Solution I., ice.
(_h_) Solution II., vapour.
(_i_) Solution II., ice.
(_j_) Ice, vapour.
[Illustration: FIG. 45.]
Pressure-Temperature Diagram.[251]--If sulphur dioxide is passed into water
at 0deg, a solution will be formed and the temperature at which ice can
exist in equilibrium with this solution will fall more and more as the
concentration of the sulphur dioxide increases. At -2.6deg, however, a
cryohydric point is reached at which solid hydrate separates out,
and the system becomes invariant. The curve AB (Fig. 45) therefore
represents the pressure of the system ice--solution II.--vapour, and B
represents the temperature and pressure at which the invariant system
ice--hydrate--solution II.--vapour can exist. At this point the temperature
is -2.6deg, and the pressure 21.1 cm. If heat is withdrawn from this
system, the solution will ultimately {171} solidify to a mixture of
ice and hydrate, and there will be obtained the univariant system
ice--hydrate--vapour. The vapour pressure of this system has been
determined down to a temperature of -9.5deg, at which temperature the
pressure amounts to 15 cm. The pressures for this system are represented by
the curve BC. If at the point B the volume is diminished, the pressure must
remain constant, but the relative amounts of the different phases will
undergo change. If suitable quantities of these are present, diminution of
volume will ultimately lead to the total condensation of the vapour phase,
and there will remain the univariant system ice--hydrate--solution. The
temperature of equilibrium of this system will alter with the pressure,
but, as in the case of the melting point of a simple substance, great
differences of pressure will cause only comparatively small changes in the
temperature of equilibrium. The change of the cryohydric point with the
pressure is represented by the line BE; the actual values have not been
determined, but the curve must slope towards the pressure axis because
fusion is accompanied by diminution of volume, as in the case of pure ice.
{172}
A fourth univariant system can be formed at B. This is the system
hydrate--solution II.--vapour. The conditions for the existence of
this system are represented by the curve BF, which may therefore be
regarded as the vapour-pressure curve of the saturated solution of
sulphur dioxide heptahydrate in water. Unlike the curve for iodine
trichloride--solution--vapour, this curve cannot be followed to the melting
point of the hydrate. Before this point is reached, a second liquid phase
appears, and an invariant system consisting of hydrate--solution
I.--solution II.--vapour is formed. We have here, therefore, the phenomenon
of melting under the solution as in the case of succinic nitrile and water
(p. 122). This point is represented in the diagram by F; the temperature at
this point is 12.1deg, and the pressure 177.3 cm. The range of stable
existence of the hydrate is therefore from -2.6deg to 12.1deg;
nevertheless, the curve FB has been followed down to a temperature of
-6deg, at which point ice formed spontaneously.
So long as the four phases hydrate, two liquid phases, and vapour are
present, the condition of the system is perfectly defined. By altering the
conditions, however, one of the phases can be made to disappear, and a
univariant system will then be obtained. Thus, if the vapour phase is made
to disappear, the univariant system solution I.--solution II.--hydrate,
will be left, and the temperature at which this system is in equilibrium
will vary with the pressure. This is represented by the curve FI; under a
pressure of 225 atm. the temperature of equilibrium is 17.1deg. Increase of
pressure, therefore, raises the temperature at which the three phases can
coexist.
Again, addition of heat to the invariant system at F will cause the
disappearance of the solid phase, and there will be formed the univariant
system solution I.--solution II.--vapour. In the case of this system the
vapour pressure increases as the temperature rises, as represented by the
curve FG. Such a system is analogous to the case of ether and water, or
other two partially miscible liquids (p. 103). As the temperature changes,
the composition of the two liquid phases will undergo change; but this
system has not been studied fully.
The fourth curve, which ends at the quadruple point F, is {173} that
representing the vapour pressure of the system hydrate--solution I.--vapour
(FH). This curve has been followed to a temperature of 0deg, the pressure
at this point being 113 cm. The metastable prolongation of GF has also been
determined. Although, theoretically, this curve must lie below FH, it was
found that the difference in the pressure for the two curves was within the
error of experiment.
Bivariant Systems.--The different bivariant systems, consisting of two
phases, which can exist within the range of temperature and pressure
included in Fig. 45, were given on p. 170. The conditions under which these
systems can exist are represented by the areas in the diagram, and the
fields of the different bivariant systems are indicated by letters,
corresponding to the letters on p. 170. Just as in the case of
one-component systems (p. 29), we found that the field lying between any
two curves gave the conditions of existence of that phase which was common
to the two curves, so also in the case of two-component systems, a
bivariant two-phase system occurs in the field enclosed[252] by the two
curves to which the two phases are common. As can be seen, the same
bivariant system can occur in more than one field.
As is evident from Fig. 45, three different bivariant systems are capable
of existing in the area HFI; which of these will be obtained will depend on
the relative masses of the different phases in the univariant or invariant
system. Thus, starting with a system represented by a point on the curve
HF, diminution of volume at constant temperature will cause the
condensation of a portion of the vapour, which is rich in sulphur dioxide;
since this would increase the concentration of sulphur dioxide in the
solution, it must be counteracted by the passage of a portion of the
hydrate (which is relatively poor in sulphur dioxide) into the solution.
If, therefore, the amount of hydrate present is relatively very small, the
final result of the compression will be the production of the system _f_,
solution I.--vapour. On the other hand, if the vapour is present in
relatively small amount, it will be the first phase to disappear, {174} and
the bivariant system _a_, hydrate--solution I., will be obtained. Finally,
if we start with the invariant system at F, compression will cause the
condensation of vapour, while the composition of the two solutions will
remain unchanged. When all the vapour has disappeared, the univariant
system hydrate--solution I.--solution II. will be left. If, now, the
pressure is still further increased, while the temperature is kept below
12deg, more and more hydrate must be formed at the expense of the two
liquid phases (because 12deg is the lower limit for the coexistence of the
two liquid phases), and if the amount of the solution I. (containing excess
of sulphur dioxide) is relatively small, it will disappear before solution
II., and there will be obtained the bivariant system hydrate--solution II.
(bivariant system _b_).
In a similar manner, account can be taken of the formation of the other
bivariant systems.
A behaviour similar to that of sulphur dioxide and water is shown by
chlorine and water and by bromine and water, although these have not been
so fully studied.[253] In the case of hydrogen bromide and water, and of
hydrogen chloride and water, a hydrate, viz. HBr,2H_{2}O and HCl,2H_{2}O,
is formed which possesses a definite melting point, as in the case of
iodine trichloride. In these cases, therefore, a retroflex curve is
obtained. Further, just as in the case of the chlorides of iodine the upper
branch of the retroflex curve ended in a eutectic point, so also in the
case of the hydrate HBr,2H_{2}O the upper branch of the curve ends in a
eutectic point at which the system dihydrate--monohydrate--solution--vapour
can exist. Before the melting point of the monohydrate is reached, two
liquid phases are formed, as in the case of sulphur dioxide and water.
* * * * *
{175}
CHAPTER X
SOLID SOLUTIONS. MIXED CRYSTALS
General.--With the conception of gaseous and liquid solutions, every one is
familiar. Gases can mix in all proportions to form homogeneous solutions.
Gases can dissolve in or be "absorbed" by liquids; and solids, also, when
brought in contact with liquids, "pass into solution" and yield a
homogeneous liquid phase. On the other hand, the conception of a _solid
solution_ is one which in many cases is found more difficult to appreciate;
and the existence and behaviour of solid solutions, in spite of their not
uncommon occurrence and importance, are in general comparatively little
known.
The reason of this is to be found, to some extent, no doubt, in the fact
that the term "solid solution" was introduced at a comparatively recent
date,[254] but it is probably also due in some measure to a somewhat hazy
comprehension of the definition of the term "solution" itself. As has
already been said (p. 92), a solution is a homogeneous phase, the
composition of which can vary continuously within certain limits; the
definition involves, therefore, no condition as to the physical state of
the substances. Accordingly, solid solutions are homogeneous solid phases,
the composition of which can undergo continuous variation within certain
limits. Just as we saw that the range of variation of composition is more
limited in the case of liquids than in the case of gases, so also we find
that the limits of miscibility are in general still more restricted in the
case of solids. Examples of complete miscibility are, however, not unknown
even in the case of solid substances.
Solid solutions have long been known, although, of course, {176} they were
not defined as such. Thus, the phenomena of "occlusion" of gases by metals
and other substances (occlusion of hydrogen by palladium; occlusion of
hydrogen by iron) are due to the formation of solid solutions. The same is
probably also true of the phenomena of "adsorption," as in the removal of
organic colouring matter by charcoal, although, in this case, surface
tension no doubt plays a considerable part.[255]
As examples of the solution of gases in solids there may be cited (in
addition to the phenomena of occlusion already mentioned), the hydrated
silicates and the zeolites. During dehydration these crystalline substances
remain clear and transparent, and the pressure of the water vapour which
they emit varies with the degree of hydration or the concentration of water
in the mineral.[256] As examples of the solution of solids in solids we
have the cementation of iron by charcoal, the formation of glass, and the
crystallization together of isomorphous substances.
Although we have here spoken of the glasses as "solid solutions," it should
be mentioned that the term "solid" is used in its popular sense. Strictly
speaking, the glasses are to be regarded as supercooled liquids (see also
p. 53, footnote).
In discussing the equilibria in systems containing a solid solution, it is
of essential importance to remember that a solid solution constitutes only
_one_ phase, a phase of varying composition, as in the case of liquid
solutions.
Solution of Gases in Solids.--Comparatively little work has been done in
this connection, the investigations being limited chiefly to the phenomena
of occlusion or adsorption of gases by charcoal.[257] We shall, therefore,
indicate only briefly {177} and in a general manner, the behaviour which
the Phase Rule enables us to foresee.[258]
In dealing with the systems formed by the two phases gas--solid, three
chief cases call for mention:--
I. _The gas is not absorbed by the solid, but when the pressure reaches a
certain value, combination of the two components can result._
[Illustration: Fig. 46.]
The graphic representation of such a system is shown in Fig. 46, the
ordinates being the pressures of the gas, and the abscissae the
concentrations of the gaseous component in the solid phase. Since there is
no formation of a solid solution, the concentration of gas in the solid
phase remains zero until the pressure has increased to the point A. At this
point combination can take place. There will now be three phases present,
viz. solid component, compound, and vapour. The system is therefore
univariant, and if the temperature is maintained constant, the vapour
pressure will be constant, irrespective of the amount of compound formed,
_i.e._ irrespective of the relative amounts of gas and solid. This is
indicated by the line AB. When the solid component has entirely
disappeared, the system ceases to be univariant, and if no absorption
occurs, the pressure will increase again, as shown by BC. If a second
compound can be formed, then a second _pc_-line will be obtained, similar
to the preceding. To this group belong the salt hydrates (Chap. VII.).
II. _The gas may be absorbed and may also form a compound._
If absorption of gas occurs with formation of a solid solution, then, as
the system consists of two phases, solution--vapour, it is bivariant. At
constant temperature, therefore, the pressure will still vary with the
concentration of the gaseous component in the solid phase. This is
represented by the curve AB in Fig. 47. When, however, the pressure has
reached a certain value, combination can take place; and since there are
now three phases present, the system is {178} univariant, and at constant
temperature the pressure is constant, as shown by the line BC.
III. _Absorption of gas occurs, but at a certain concentration the solid
solution can separate into two immiscible solid solutions._
We have seen, in Chapter VI., that two liquids can form two immiscible
solutions, and the same has also been found true of solid solutions, as we
shall presently learn more fully. If, now, two immiscible solutions are
formed, then the system will become univariant, and at constant temperature
the _pc_-curve will be a straight line, as in the case of the formation of
a compound (cf. p. 86). The behaviour of this system will, therefore, also
be represented diagrammatically by Fig. 47.
[Illustration: FIG. 47.]
_Palladium and Hydrogen._--The phenomenon of the absorption of hydrogen by
palladium, to which Graham gave the name "occlusion," is one that has
claimed the attention of several investigators. Although Graham was not of
opinion that a compound is formed, but rather that the gas undergoes very
great condensation, acts as a quasi-metal (to which he gave the name
hydrogenium), and forms a homogeneous alloy with the palladium, later
investigations, especially those of Troost and Hautefeuille,[259] pointed
to the formation of a definite chemical compound, having the formula
Pd_{2}H. This conclusion has, however, not been confirmed by subsequent
investigation.[260]
Roozeboom and Hoitsema[261] sought to arrive at a final decision as to the
nature of the phenomenon by an investigation of the equilibrium between
hydrogen and palladium on the basis of the Phase Rule classification given
above. If a compound is formed, diminution of volume would cause no
increase of pressure, but only an increase in the amount of the compound.
As this is the only case of gas absorption which has been {179} accurately
studied from this point of view, a brief account of the results obtained
will be given here, although these are not so clear and free from ambiguity
as one would desire.
The scientists just mentioned investigated the variation of the pressure of
hydrogen with the amount absorbed by the metal at different temperatures,
and a few of their results, typical of all, are represented graphically in
Fig. 48; the curves indicating the variation of the gas pressure with the
concentration of the hydrogen in the palladium at the temperatures 120deg,
170deg, and 200deg. As can be seen, the curve consists of three parts, an
ascending portion which passes gradually and continuously into an almost
horizontal but slightly ascending middle part, which in turn passes without
break into a second rapidly ascending curve. This, as Fig. 48 indicates, is
the general form of the curve; but the length of the middle portion varies
with the temperature, being shorter at higher than at lower temperatures.
[Illustration: FIG. 48.]
What is the interpretation to be put on these curves? With regard to the
two end portions, these represent bivariant, two-phase systems, consisting
of a solid solution and gas. They correspond, therefore, to curve AB in
Fig. 47. If the middle portion were horizontal, it would indicate either
the formation of a compound or of two immiscible solid solutions. If a
compound Pd_{2}H were formed, then the middle portion would at all
temperatures end at the same value of the concentration, viz. that
corresponding to 0.5 atoms of hydrogen to 1 atom of palladium. As the
figure shows, however, this is not the case; the higher the temperature,
the lower is the concentration at which the middle passes into the terminal
portion of the curve. {180} Such a behaviour would, however, agree with the
assumption of the formation of two solid solutions, the "miscibility" of
which increases with the temperature, as in the case of the liquid
solutions of phenol and water (p. 97). Nevertheless, although the
assumption of the formation of two solid solutions is more satisfactory
than that of the formation of a compound, it does not entirely explain the
facts. If two solid solutions are formed, the pressure curve should be
horizontal, but this is not the case; and the deviation from the horizontal
does not appear to be due to impurities either in the gas or in the metal,
but is apparently a peculiarity of the system. Further, the gradual instead
of abrupt passage of the three portions of the curve into one another
remains unexplained. Hoitsema has expressed the opinion that the occlusion
of hydrogen by palladium is a process of continuous absorption, the
peculiar form of the curve--the flat middle portion--being possibly due to
a condensation of the gas, even at temperatures far above the critical
temperature of liquid hydrogen.
While, therefore, the occlusion of hydrogen by palladium still presents
some unexplained phenomena, the behaviour found by Hoitsema would appear to
disprove conclusively the formation of a definite chemical compound.[262]
SOLUTION OF SOLIDS IN SOLIDS. MIXED CRYSTALS.
The introduction by van't Hoff of the term "solid solution" resulted from
the discovery of a number of deviations from the Raoult-van't Hoff law for
the depression of the freezing point by dissolved substances. In all cases,
the depression was too small; in some instances, indeed, the freezing point
may be raised. To explain these irregularities, van't Hoff assumed that the
dissolved substance crystallized out along with the solid solvent; and he
showed how this would account for the {181} deviations from the law of the
depression of the freezing point, which had been developed on the
assumption that only the pure solvent crystallized out from the
solution.[263]
The "mixed crystals" which were thus obtained, and which van't Hoff called
dilute solid solutions, showed great resemblance in their behaviour to
ordinary liquid solutions, and obeyed the laws applicable to these. These
laws, however, can no longer be applied in the case of the concentrated
solid solutions formed by the crystallization together of isomorphous
substances, and known as isomorphous mixtures. Indeed, it has been
contended[264] that these isomorphous mixtures should not be considered as
solid solutions at all, although no sharp line of demarcation can be drawn
between the two classes. The differences, however, in the behaviour of the
two groups are of a quantitative rather than a qualitative nature; and
since we are concerned at present only with the qualitative behaviour, we
shall make no distinction between the crystalline solid solutions and the
isomorphous mixtures, but shall study the behaviour of the two classes
under the head of "mixed crystals."
Mixed crystals can be formed either by sublimation[265] or from a liquid
phase; and in the latter case the mixed crystals can be deposited either
from solution in a common solvent or from a mixture of the fused
components. In this method of formation, which alone will be discussed in
the present chapter, we are dealing with the fusion curves of two
substances, where, however, the liquid solution is in equilibrium not with
one of the pure components, but with a solid solution or mixed crystal. The
simple scheme (Fig. 29, p. 117) which was obtained in the case of two
components which crystallize out in the pure state, is no longer sufficient
in the case of the formation of mixed crystals. With the help of the Phase
Rule, however, the different possible systems can be classified; and
examples of the different cases predicted by the Phase Rule have also been
obtained by experiment.
{182}
We shall now consider briefly the formation of mixed crystals by
isomorphous substances; the consideration of the formation of mixed
crystals of isodimorphous substances will, on account of the complexity of
the relationships, not be undertaken here.[266]
_Formation of Mixed Crystals of Isomorphous Substances._
For the purpose of representing the relationships found here we shall
employ a temperature-concentration diagram,[267] in which the ordinates
represent the temperature and the abscissae the concentration of the
components. Since there are two solutions, the liquid and the solid, and
since the concentration of the components in these two phases is not, in
general, the same, two curves will be required for each system, one
relating to the liquid phase, the other relating to the solid. The
temperature at which solid begins to be deposited from the liquid solution
will be called the _freezing point_ of the mixture, and the temperature at
which the solid solution just begins to liquefy will be called the _melting
point_ of the solid solution. The temperature-concentration curve for the
liquid phase will therefore be the freezing-point curve; that for the solid
solution, the melting-point curve. The latter will be represented by a
dotted line.[268]
{183}
I.--THE TWO COMPONENTS CAN FORM AN UNBROKEN SERIES OF MIXED CRYSTALS.
Since, as has already been pointed out (p. 176), a mixed crystal (solid
solution) constitutes only one phase, it is evident that if the two
components are miscible with one another in all proportions in the solid
state, there can never be more than one solid phase present, viz. the solid
solution or mixed crystal. If the components are completely miscible in the
solid state, they will also be completely miscible in the liquid state, and
there can therefore be only one liquid phase. The system can at no point
become invariant, because there can never be more than three phases
present. When, therefore, the two components form a continuous series of
mixed crystals, the equilibrium curve must also be continuous. Of these
systems three types are found.
[Illustration: FIG. 49.]
(_a_) _The freezing points of all mixtures lie between the freezing points
of the pure components_ (Curve I., Fig. 49).
Examples.--This type of curve is represented by the mixed crystals of
naphthalene and [beta]-naphthol.[269] The addition of [beta]-naphthol to
naphthalene raises the freezing point of the latter, and the rise is
directly proportional to the amount of naphthol added. The freezing point
curve is therefore a straight line joining the melting points of the two
components. This behaviour, however, is rather exceptional, the
freezing-point curve lying generally above, sometimes also below, the
straight line joining the melting points of the pure components. Thus the
freezing-point curve of mixtures of [alpha]-monochlorocinnamic aldehyde and
[alpha]-monobromocinnamic aldehyde[270] lies above the {184} straight line
joining the melting points of the pure components (31.22deg and 69.56deg),
as is evident from the following table:--
----------------------------------------------------------------------
Molecules of bromo- | |
cinnamic aldehyde in | Freezing point. | Deviation from straight
100 mols. of mixture. | | line.
----------------------------------------------------------------------
0.00 | 31.22deg | --
10.48 | 37.28deg | 2.04deg
21.91 | 43.12deg | 3.50deg
30.07 | 46.80deg | 4.05deg
45.04 | 52.94deg | 4.45deg
62.16 | 58.82deg | 3.77deg
82.98 | 65.07deg | 2.03deg
93.50 | 67.91deg | 0.84deg
100.00 | 69.56deg | --
----------------------------------------------------------------------
Melting-point Curve.--This curve, like the freezing-point curve, must also
be continuous, and the melting points of the different solid solutions will
lie between the melting points of the pure components. This is represented
by the dotted line in Fig. 49, I. The relative position of the two curves,
which can be deduced with the help of thermodynamics and also by
experimental determination, is found in all cases to be in accordance with
the following rule: At any given temperature, _the concentration of that
component by the addition of which the freezing point is depressed, is
greater in the liquid than in the solid phase_; or, conversely, _the
concentration of that component by the addition of which the freezing point
is raised, is greater in the solid than in the liquid phase_. An
illustration of this rule is afforded by the two substances chloro- and
bromo-cinnamic aldehyde already mentioned. As can be seen from the above
table, the addition of chlorocinnamic aldehyde lowers the melting point of
the bromo-compound. In accordance with the rule, therefore, the
concentration of the chloro-compound in the liquid phase must be greater
than in the solid phase; and this was found experimentally. At a
temperature of 49.44deg, the liquid contained 58.52 per cent., the solid
only 52.57 per cent. of the chlorocinnamic aldehyde.
From this it will also be clear that on cooling a fused mixture of two
substances capable of forming mixed crystals, {185} the temperature of
solidification will not remain constant during the separation of the solid;
nor, on the other hand, will the temperature of liquefaction of the solid
solution be constant. Thus, for example, if a liquid solution of two
components, A and B, having the composition represented by the point _x_
(Fig. 50), is allowed to cool, the system will pass along the line _xx'_.
At the temperature of the point _a_, mixed crystals will be deposited, the
composition of which will be that represented by b. As the temperature
continues to fall, more and more solid will be deposited; and since the
solid phase is relatively rich in the component B, the liquid will become
relatively poorer in this. The composition of the liquid solution will
therefore pass along the curve _ad_, the composition of the solid solution
at the same time passing along the curve _bc_; at the point _c_ the liquid
will solidify completely.[271]
[Illustration: FIG. 50.]
Conversely, if mixed crystals of the composition and at the temperature
_x'_ are heated, liquefaction will begin at the temperature _c_, yielding a
liquid of the composition d. On continuing to add heat, the temperature of
the mass will rise, more of the solid will melt, and the composition of the
two phases will change as represented by the curves _da_ and _cb_. When the
temperature has risen to _a_, complete liquefaction will have occurred. The
process of solidification or of liquefaction is therefore extended over a
temperature interval _ac_.
Even when the freezing-point curve is a straight line joining {186} the
melting points of the pure components, the melting-point curve will not
necessarily coincide with the freezing-point curve, although it may
approach very near to it; complete coincidence can take place only when the
melting points of the two components are identical. An example of this will
be given later (Chap. XII.).
(_b_) _The freezing-point curve passes through a maximum_ (Curve II., Fig.
49).
[Illustration: FIG. 51.]
This curve exhibits the greatest degree of contrast to the freezing-point
curve which is obtained when the pure components crystallize out. For,
since the curve passes through a maximum, it is evident that the freezing
point of each of the components must be _raised_ by the addition of the
other component.
Example.--Very few cases belonging to this type are known. The best example
is found in the freezing-point curve of mixtures of _d_- and
_l_-carvoxime[272] (C_{10}H_{14}N.OH). The freezing points and melting
points of the different mixtures of _d_- and _l_-carvoxime are given in the
following table, and represented graphically in Fig. 51:--
---------------+----------------+-----------------+-----------------
Per cent. of | Per cent. of | Freezing point. | Melting point.
_d_-carvoxime. | _l_-carvoxime. | |
---------------+----------------+-----------------+-----------------
100 | 0 | 72.0deg | 72.0deg
99 | 1 | 72.4deg | --
98 | 2 | 73.0deg | --
95 | 5 | 75.4deg | 73.0deg
90 | 10 | 79.0deg | 75.0deg
80 | 20 | 84.6deg | 80.0deg
70 | 30 | 88.2deg | 85.0deg
60 | 40 | 90.4deg | --
50 | 50 | 91.4deg | 91.4deg
25 | 75 | 86.4deg | 82.0deg
8 | 92 | 77.4deg | --
1 | 99 | 72.4deg | --
0 | 100 | 72.0deg | 72.0deg
---------------+----------------+-----------------+-----------------
{187}
In this figure, the melting-point curve, _i.e._ the
temperature-concentration curve for the mixed crystals, is represented by
the lower curve. Since the addition of the laevo-form to the dextro-form
raises the melting point of the latter, the concentration of the laevo-form
(on the right-hand branch of the curve) must, in accordance with the rule
given, be greater in the solid phase than in the liquid. Similarly, since
addition of the dextro-form raises the melting point of the laevo-form, the
solid phase (on the left-hand branch of the curve) must be richer in
dextro- than in laevo-carvoxime. At the maximum point, the melting-point
and freezing-point curves touch; at this point, therefore, the composition
of the solid and liquid phases must be identical. It is evident, therefore,
that at the maximum point the liquid will solidify, or the solid will
liquefy completely without change of temperature; and, accordingly, mixed
crystals of the composition represented by the maximum point will exhibit a
definite melting point, and will in this respect behave like a simple
substance.
(_c_) _The freezing-point curve passes through a minimum_ (Curve III., Fig.
49).
In this case, as in the case of those systems where the pure components are
deposited, a minimum freezing point is obtained. In the latter case,
however, there are two freezing-point curves which intersect at a eutectic
point; in the case where mixed crystals are formed there is only one
continuous curve. On one side of the minimum point the liquid phase
contains relatively more, on the other side relatively less, of the one
component than does the solid phase; while at the minimum point the
composition of the two phases is the same. At this point, therefore,
complete solidification or complete liquefaction will occur without change
of temperature, and the mixed crystals will accordingly exhibit a definite
melting point.
[Illustration: FIG. 52.]
{188}
Example.--As an example of this there may be taken the mixed crystals of
mercuric bromide and iodide.[273] Mercuric bromide melts at 236.5deg, and
mercuric iodide at 255.4deg. The mixed crystal of definite constant melting
point (minimum point) contains 59 mols. per cent. of mercuric bromide, the
melting point being 216.1deg.
The numerical data are contained in the following table, and represented
graphically in Fig. 52:--
-----------------------------------------------------
Mols. per cent. of | |
HgBr_{2}. | Freezing point. | Melting point.
-----------------------------------------------------
100 | 236.5deg | 236deg
90 | 228.8deg | 226deg
80 | 222.2deg | 219deg
70 | 217.8deg | 217deg
65 | 216.6deg | 216deg
60 | 216.1deg | 215.5deg
55 | 216.3deg | 216deg
50 | 217.3deg | 216deg
40 | 221.1deg | 218deg
30 | 227.8deg | 223deg
20 | 236.2deg | 231deg
10 | 245.5deg | 242deg
0 | 255.4deg | 254deg
-----------------------------------------------------
[Illustration: FIG. 53.]
Fractional Crystallization of Mixed Crystals.--With the help of the
diagrams already given it will be possible to predict what will be the
result of the fractional crystallization of a fused mixture of two
substances which can form mixed crystals. Suppose, for example, a fused
mixture of the composition _x_ (Fig. 53) is cooled down; then, as we have
already seen, when the temperature has fallen to _a_, mixed crystals of
composition, _b_, are deposited. If the temperature is allowed to fall
{189} to _x'_, and the solid then separated from the liquid, the mixed
crystals so obtained will have the composition represented by e. If, now,
the mixed crystals _e_ are completely fused and the fused mass allowed to
cool, separation of solid will occur when the temperature has fallen to the
point _f_. The mixed crystals which are deposited have now the composition
represented by _g_, i.e. _they are richer in B than the original mixed
crystals_. By repeating this process, the composition of the successive
crops of mixed crystals which are obtained approximates more and more to
that of the pure component B, while, on the other hand, the composition of
the liquid phase produced tends to that of pure A. By a systematic and
methodical repetition of the process of fractional crystallization,
therefore, a _practically_ complete separation of the components can be
effected; a perfect separation is theoretically impossible.
From this it will be readily understood that in the case of substances the
freezing point of which passes through a maximum, fractional
crystallization will ultimately lead to mixed crystals having the
composition of the maximum point, while the liquid phase will more and more
assume the composition of either pure A or pure B, according as the initial
composition was on the A side or the B side of the maximum point. In those
cases, however, where the curves exhibit a minimum, the solid phase which
separates out will ultimately be one of the pure components, while a liquid
phase will finally be obtained which has the composition of the minimum
point.
II.--THE TWO COMPONENTS DO NOT FORM A CONTINUOUS SERIES OF MIXED CRYSTALS.
This case corresponds to that of the partial miscibility of liquids. The
solid component A can "dissolve" the component B until the concentration of
the latter in the mixed crystal has reached a certain value. Addition of a
further amount of B will not alter the composition of the mixed crystal,
but there will be formed a second solid phase consisting {190} of a
solution of A in B. At this point the four phases, mixed crystals
containing excess of A, mixed crystals containing excess of B, liquid
solution, vapour, can coexist; this will therefore be an invariant point.
The temperature-concentration curves will therefore no longer be
continuous, but will exhibit a break or discontinuity at the point at which
the invariant system is formed.
(_a_) _The freezing-point curve exhibits a transition point_ (Curve I.,
Fig. 54).
As is evident from the figure, addition of B raises the melting point of A,
and, in accordance with the rule previously given, the concentration of B
in the mixed crystals will be greater than in the solution. This is
represented in the figure by the dotted curve AD. On the other hand,
addition of A lowers the melting point of B, and the two curves BC and BE
are obtained for the liquid and solid phases respectively. At the
temperature of the line CDE the liquid solution of the composition
represented by C is in equilibrium with the two different mixed crystals
represented by D and E. At this temperature, therefore, the _tc_-curve for
the solid phase exhibits a discontinuity; and, since the solid phase
undergoes change at this point, the freezing-point curve must show a break
(p. 111).
[Illustration: FIG. 54.]
Example.--Curves of the form given in Fig. 54 I. have been found
experimentally in the case of silver nitrate and sodium nitrate.[274] The
following table contains the numerical data, which are also represented
graphically in Fig. 55:--
{191}
-----------------------------------------------------
Molecules NaNO_{3} | Freezing point. | Melting point.
per cent. | |
-----------------------------------------------------
0 | 208.6deg | 208.6deg
8 | 211.4deg | 210deg
15.06 | 215deg | 212deg
19.46 | 217.2deg | 214.8deg
21.9 | 222deg | 215deg
26 | 228.4deg | 216.5deg
29.7 | 234.8deg | 217.5deg
36.2 | 244.4deg | 217.5deg
47.3 | 259.4deg | 237.6deg
58.9 | 272deg | 257deg
72 | 284deg | 274deg
100 | 308deg | 308deg
-----------------------------------------------------
The temperature of the transition point is 217.5deg; at this point the
liquid contains 19.5, and the two conjugate solid solutions 26 and 38
molecules of sodium nitrate per cent. respectively.
[Illustration: FIG. 55.]
[Illustration: FIG. 56.]
(_b_) _The freezing-point curve exhibits a eutectic point_ (Curve II., Fig.
54). {192}
In this case the freezing point of each of the components is lowered by the
addition of the other, until at last a point is reached at which the liquid
solution solidifies to a mixture or conglomerate of two mixed crystals.
Examples.--Curves belonging to this class have been obtained in the case of
potassium and thallium nitrates[275] and of naphthalene and monochloracetic
acid.[276] The data for the latter are given in the following table and
represented in Fig. 56:--
-------------------------------------------------------------------------
| Liquid solution. | Solid solution.
------------------------------------------------------------
Temperature. | | | |
| Per cent. | Per cent. | Per cent. | Per cent.
| naphthalene. | acid. | naphthalene. | acid.
-------------------------------------------------------------------------
62deg | -- | 100 | -- | 100
60deg | 4.0 | 96.0 | 1.7 | 98.3
55deg | 21.0 | 79.0 | 2.1 | 97.9
53.5deg | 29.4 | 70.0 | -- | --
55deg | 31.3 | 68.7 | 59.6 | 40.4
60deg | 42.4 | 57.6 | 80.3 | 19.7
65deg | 53.3 | 46.7 | 89.2 | 10.8
70deg | 69.7 | 2.3 | 95.4 | 4.6
75deg | 84.4 | 15.6 | 96.6 | 3.4
79.9deg | 100 | -- | 100 | --
-------------------------------------------------------------------------
At the eutectic point the liquid solution is in equilibrium with two
different mixed crystals the composition of which is represented by D and E
respectively. If, therefore, a fused mixture containing the two components
A and B in the proportions represented by C is cooled down, it will, when
the temperature has reached the point C, solidify completely to a
_conglomerate_ of mixed crystals, D and E.
[Illustration: FIG. 57.]
[Illustration: FIG. 58.]
Changes in Mixed Crystals with the Temperature.--In the case of the
different types of systems represented in Fig. 49, a homogeneous liquid
solution of the two components will exist at temperatures above the
freezing-point curve, a homogeneous mixed crystal at temperatures below the
melting-point curve, while at any point between the freezing-point and
melting-point {193} curves the mixture will separate into a solid phase and
a liquid phase. In the case, however, of the two types shown in Fig. 54 the
relationships are somewhat more complicated. As before, the area above the
freezing-point curve gives the conditions under which homogeneous liquid
solutions can exist; but below the melting-point curve two different mixed
crystals can coexist. This will be best understood from Figs. 57 and 58. D
and E represent, as we have seen, the composition of two mixed crystals
which are in equilibrium with the liquid solution at the temperature of the
point C. These two mixed crystals represent, in the one case, a saturated
solution of B in A (point D), and the other a saturated solution of A in B
(point E). Just as we saw that the mutual solubility of two liquids varied
with the temperature, so also in the case of two solids; as the temperature
alters, the solubility of the two solid components in one another will
change. This alteration is indicated diagrammatically in Figs. 57 and 58 by
the dotted curve similar to the solubility curves for two mutually soluble
liquids (p. 101).
Suppose, now, that a mixed crystal of the composition _x_ is cooled down,
it will remain unchanged until, when the temperature has fallen to _t'_,
the homogeneous mixed crystal breaks up into a conglomerate of two mixed
crystals the composition of {194} which is represented by _x'_ and _x"_
respectively. From this, then, it can be seen that in the case of
substances which form two solid solutions, the mixed crystals which are
desposited from the liquid fused mass need not remain unchanged in the
solid state, but may at some lower temperature lose their homogeneity. This
fact is of considerable importance for the formation of alloys.[277]
A good example of this will soon be met with in the case of the iron and
carbon alloys. The alloys of copper and tin also furnish examples of the
great changes which may take place in the alloy between the temperature at
which it separates out from the fused mass and the ordinary temperature.
Thus, for example, one of the alloys of copper and tin which separates out
from the liquid as a solid solution breaks up, on cooling, into the
compound Cu_{3}Sn and liquid:[278] a striking example of a solid substance
partially liquefying on being cooled.
* * * * *
{195}
CHAPTER XI
EQUILIBRIUM BETWEEN DYNAMIC ISOMERIDES
It has long been known that certain substances, _e.g._ acetoacetic ester,
are capable when in solution or in the fused state, of reacting as if they
possessed two different constitutions; and in order to explain this
behaviour the view was advanced (by Laar) that in such cases a hydrogen
atom oscillated between two positions in the molecule, being at one time
attached to oxygen, at another time to carbon, as represented by the
formula--
CH_{3}.C--CH.CO_{2}C_{2}H_{5}
. ^
. |
O<-H
When the hydrogen is in one position, the substance will act as an
hydroxy-compound; with hydrogen in the other position, as a ketone.
Substances possessing this double function are called _tautomeric_.
Doubt, however, arose as to the validity of the above explanation, and this
doubt was confirmed by the isolation of the two isomerides in the solid
state, and also by the fact that the velocity of change of the one
isomeride into the other could in some cases be quantitatively measured.
These and other observations then led to the view, in harmony with the laws
of chemical dynamics, that tautomeric substances in the dissolved or fused
state represent a _mixture_ of two isomeric forms, and that equilibrium is
established not by _intra_- but by _inter_-molecular change, as expressed
by the equation--
CH_{3}.CO.CH_{2}.CO_{2}C_{2}H_{5} <--> CH_{3}.C(OH):CH.CO_{2}C_{2}H_{5}
{196} In the solid state, the one or other of the isomerides represents the
stable form; but in the liquid state (solution or fusion) the stable
condition is an equilibrium between the two forms.
A similar behaviour is also found in the case of other isomeric substances
where the isomerism is due to difference of structure, _i.e._ structure
isomerism (_e.g._ in the case of the oximes
C_{6}H_{5}.C.H C_{6}H_{5}.C.H
|| and || ),
N.OH HO.N
or to difference in configuration, _i.e._ stereoisomerism (_e.g._ optically
active substances), or to polymerism (_e.g._ acetaldehyde and paraldehyde).
In all such cases, although the different solid forms correspond to a
single definite constitution, in the liquid state a condition of
equilibrium between the two modifications is established. As a general name
for these different classes of substances, the term "dynamic isomerides"
has been introduced; and the different kinds of isomerism are classed
together under the title "dynamic isomerism."[279]
By reason of the importance of these phenomena in the study more especially
of Organic Chemistry, a brief account of the equilibrium relations
exhibited by systems composed of dynamic isomerides may be given here.[280]
In studying the fusion and solidification of those substances which exhibit
the relationships of dynamic isomerism, the phenomena observed will vary
somewhat according as the reversible transformation of the one form into
the other takes place with measurable velocity at temperatures in the
neighbourhood of the melting points, or only at some higher temperature. If
the transformation is very rapid, the system will behave like a
one-component system, but if the isomeric change is comparatively slow, the
behaviour will be that of a two-component system.
Temperature-Concentration Diagram.--The relationships which are met with
here will be most readily understood with {197} the help of Fig. 59.
Suppose, in the first instance, that isomeric transformation does not take
place at the temperature of the melting point, then the freezing point
curve will have the simple form ACB; the formation of compounds being for
the present excluded. This is the simplest type of curve, and gives the
composition of the solutions in equilibrium with the one modification
([alpha] modification) at different temperatures (curve AC); and of the
solutions in equilibrium with the other modification ([beta] modification)
at different temperatures (curve BC). C is the eutectic point at which the
two solid isomerides can exist side by side in contact with the solution.
[Illustration: FIG. 59.]
Now, suppose that isomeric transformation takes place with measurable
velocity. If the pure [alpha]-modification is heated to a temperature _t'_
above its melting point, and the liquid maintained at that temperature
until equilibrium has been established, a certain amount of the [beta]-form
will be present in the liquid, the composition of which will be represented
by the point _x'_. The same condition of equilibrium will also be reached
by starting with pure [beta]. Similarly, if the temperature of the liquid
is maintained at the temperature _t"_, equilibrium will be reached, we
shall suppose, when the solution has the composition _x"_. The curve DE,
therefore, which passes through all the different values of _x_
corresponding to different values of _t_, will represent the change of
equilibrium with the temperature. It will slope to the right (as in the
figure) if the transformation of [alpha] into [beta] is accompanied by
absorption of heat; to the left if the transformation is accompanied by
evolution of heat, in accordance with van't Hoff's Law of movable
equilibrium. If transformation occurs without heat effect, the equilibrium
will be independent of the {198} temperature, and the equilibrium curve DE
will therefore be perpendicular and parallel to the temperature axis.
We must now find the meaning of the point D. Suppose the pure [alpha]- or
pure [beta]-form heated to the temperature _t'_, and the temperature
maintained constant until the liquid has the composition _x'_ corresponding
to the equilibrium at that temperature. If the temperature is now allowed
to fall sufficiently slowly so that the condition of equilibrium is
continually readjusted as the temperature changes, the composition of the
solution will gradually alter as represented by the curve _x'_D. Since D is
on the freezing point curve of pure [alpha], this form will be deposited on
cooling; and since D is also on the equilibrium curve of the liquid, D is
the only point at which solid can exist in stable equilibrium with the
liquid phase. (The vapour phase may be omitted from consideration, as we
shall suppose the experiments carried out in open vessels.) All systems
consisting of the two hylotropic[281] isomeric substances [alpha] and
[beta] will, therefore, ultimately freeze at the point D, which is called
the "natural" freezing point[282] of the system; provided, of course, that
sufficient time is allowed for equilibrium to be established. From this it
is apparent that _the stable modification at temperatures in the
neighbourhood of the melting point is that which is in equilibrium with the
liquid phase at the natural freezing point_.
From what has been said, it will be easy to predict what will be the
behaviour of the system under different conditions. If pure [alpha] is
heated, a temperature will be reached at which it will melt, but this
melting point will be sharp only if the velocity of isomeric transformation
is comparatively slow; _i.e._ slow in comparison with the determination of
the melting point. If the substance be maintained in the fused condition
for some time, a certain amount of the [beta] modification will be formed,
and on lowering the temperature the pure [alpha] form will be deposited,
not at the temperature of the melting point, but at some lower temperature
depending on the concentration of the [beta] modification in the liquid
phase. If isomeric transformation {199} takes place slowly in comparison
with the rate at which deposition of the solid occurs, the liquid will
become increasingly rich in the [beta] modification, and the freezing point
will, therefore, sink continuously. At the eutectic point, however, the
[beta] modification will also be deposited, and the temperature will remain
constant until all has become solid. If, on the other hand, the velocity of
transformation is sufficiently rapid, then as quickly as the [alpha]
modification is deposited, the equilibrium between the two isomeric forms
in the liquid phase will continuously readjust itself, and the end-point of
solidification will be the natural freezing point.
Similarly, starting with the pure [beta] modification, the freezing point
after fusion will gradually fall owing to the formation of the [alpha]
modification; and the composition of the liquid phase will pass along the
curve BC. If, now, the rate of cooling is not too great, or if the velocity
of isomeric transformation is sufficiently rapid, complete solidification
will not occur at the eutectic point; for at this temperature solid and
liquid are not in stable equilibrium with one another. On the contrary, a
further quantity of the [beta] modification will undergo isomeric change,
the liquid phase will become richer in the [alpha] form, and the freezing
point will _rise_; the solid phase in contact with the liquid being now the
[alpha] modification. The freezing point will continue to rise until the
point D is reached, at which complete solidification will take place
without further change of temperature.
The diagram also allows us to predict what will be the result of rapidly
cooling a fused mixture of the two isomerides. Suppose that either the
[alpha] or the [beta] modification has been maintained in the fused state
at the temperature _t'_ sufficiently long for equilibrium to be
established. The composition of the liquid phase will be represented by
_x'_. If the liquid is now _rapidly_ cooled, the composition will remain
unchanged as represented by the dotted line _x'_G. At the temperature of
the point G solid [alpha] modification will be deposited. If the cooling is
not carried below the point G, so as to cause complete solidification, the
freezing point will be found to rise with time, owing to the conversion of
some of the [beta] form into the [alpha] form {200} in the liquid phase;
and this will continue until the composition of the liquid has reached the
point D. From what has just been said, it can also be seen that if the
freezing point curves can be obtained by actual determination of the
freezing points of different synthetic mixtures of the two isomerides, it
will be possible to determine the condition of equilibrium in the fused
state at any given temperature without having recourse to analysis. All
that is necessary is to rapidly cool the fused mass, after equilibrium has
been established, and find the freezing point at which solid is deposited;
that is, find the point at which the line of constant temperature cuts the
freezing point curve. The composition corresponding to this temperature
gives the composition of the equilibrium mixture at the given temperature.
It will be evident, from what has gone before, that the degree of
completeness with which the different curves can be realised will depend on
the velocity with which isomeric change takes place, and on the rapidity
with which the determinations of the freezing point can be carried out. As
the two extremes we have, on the one hand, practically instantaneous
transformation, and on the other, practically infinite slowness of
transformation. In the former case, only one melting and freezing point
will be found, viz. the natural freezing point; in the latter case, the two
isomerides will behave as two perfectly independent components, and the
equilibrium curve DE will not be realised.
The diagram which is obtained when isomeric transformation does not occur
within measurable time at the temperature of the melting point is somewhat
different from that already given in Fig. 59. In this case, the two
freezing point curves AC and BC (Fig. 60) can be readily realized, as no
isomeric change occurs in the liquid phase. Suppose, however, that at a
higher temperature, _t'_, reversible isomeric transformation can take
place, the composition of the liquid phase will alter until at the point
_x'_ a condition of equilibrium is reached; and the composition of the
liquid at higher temperatures will be represented by the curve _x'_F. Below
the temperature _t'_ the position of the equilibrium curve is hypothetical;
but as the temperature {201} falls the velocity of transformation
diminishes, and at last becomes _practically_ zero. The equilibrium curve
can therefore be regarded as dividing into two branches _x'_G and _x'_H. At
temperatures between G and _t'_ the [alpha] modification can undergo
isomeric change leading to a point on the curve G_x'_; and the [beta]
modification can undergo change leading to a point on the curve H_x'_. The
same condition of equilibrium is therefore not reached from each side, and
we are therefore dealing not with true but with false equilibrium (p. 5).
Below the temperatures G and H, isomeric transformation does not occur in
measurable time. We shall not, however, enter into a detailed discussion of
the equilibria in such systems, more especially as they are not systems in
true equilibrium, and as the temperature at which true equilibrium can be
established with appreciable velocity alters under the influence of
catalytic agents.[283] Examples of such systems will no doubt be found in
the case of optically active substances, where both isomerides are
apparently quite stable at the melting point. In the case of such
substances, also, the action of catalytic agents in producing isomeric
transformation (racemisation) is well known.
[Illustration: FIG. 60.]
Transformation of the Unstable into the Stable Form.--As has already been
stated, the stable modification in the neighbourhood of the melting point
is that one which is in equilibrium with the liquid phase at the natural
freezing point. In the case of polymorphic substances, we have seen (p. 39)
that that form which is stable in the neighbourhood of the melting point
melts at the higher temperature. That was a {202} consequence of the fact
that the two polymorphic forms on melting gave identical liquid phases. In
the present case, however, the above rule does not apply, for the simple
reason that the liquid phase obtained by the fusion of the one modification
is not identical with that obtained by the fusion of the other. In the case
of isomeric substances, therefore, the form of lower melting point _may_ be
the more stable; and where this behaviour is found it is a sign that the
two forms are isomeric (or polymeric) and not polymorphic.[284] An example
of this is found in the case of the isomeric benzaldoximes (p. 203).
Since in Fig. 59 the [alpha] modification has been represented as the
stable form, the transformation of the [beta] into the [alpha] form will be
possible at all temperatures down to the transition point. At temperatures
below the eutectic point, transformation will occur without formation of a
liquid phase; but at temperatures above the eutectic point liquefaction can
take place. This will be more readily understood by drawing a line of
constant temperature, HK, at some point between C and B. Then if the [beta]
modification is maintained for a sufficiently long time at that
temperature, a certain amount of the [alpha] modification will be formed;
and when the composition of the mixture has reached the point H, fusion
will occur. If the temperature is maintained constant, isomeric
transformation will continue to take place in the liquid phase until the
equilibrium point for that temperature is reached. If this temperature is
higher than the natural melting point, the mixture will remain liquid all
the time; but if it is below the natural melting point, then the [alpha]
modification will be deposited when the system reaches the condition
represented by the point on the curve AC corresponding to the particular
temperature. As isomeric transformation continues, the freezing point of
the system will rise until it reaches the natural freezing point D.
Similarly, if the [alpha] modification is maintained at a temperature above
that of the point D, liquefaction will ultimately occur, and the system
will again reach the final state represented by D.[285]
{203}
Examples.--_Benzaldoximes._ The relationships which have just been
discussed from the theoretical point of view will be rendered clearer by a
brief description of cases which have been experimentally investigated. The
first we shall consider is that of the two isomeric benzaldoximes:[286]--
C_{6}H_{5}.C.H C_{6}H_{5}.C.H
|| ||
HO.N N.OH
Benzantialdoxime Benzsynaldoxime
([alpha]-modification). ([beta]-modification).
Fig. 61 gives a graphic representation of the results obtained.
The melting point of the [alpha] modification is 34-35deg; the melting
point of the unstable [beta]-modification being 130deg. The freezing curves
AC and BC were obtained by determining the freezing points of different
mixtures of known composition, and the numbers so obtained are given in the
following table.
{204}
----------------------------------------------------
Grams of the [alpha] modification |
in 100 gm. of mixture. | Freezing point.
----------------------------------+-----------------
26.2 | 101deg
49.2 | 79deg
73.7 | 46deg
91.7 | 26.2deg
95.0 | 28.6deg
96.0 | 30.0deg
----------------------------------------------------
[Illustration: FIG. 61.]