double salt at the transition point. As is evident, this decomposition will
occur when the solution which is saturated at the temperature of the
transition point, with respect to the two single salts (point C), does not
contain these salts in the same ratio in which they are present in the
double salt. If point C lay on the dotted line bisecting the right angle,
then the pure saturated solution of the double salt would not be
supersaturated with respect to either of the single salts, and the double
salt would, therefore, not be decomposed by water. As has already been
mentioned, this behaviour is found in the case of optically active
isomerides, the solubilities of which are identical.
At the transition point, therefore, the isothermal curve also consists of
two branches; but the point of intersection of the two branches now
represents a solution which is saturated not {276} only with respect to the
single salts, but also for the double salt in presence of the single salts.
We have just seen that by a change of temperature the two solubility
curves, that for the two single salts and that for the double salt, were
made to approach one another (_cf._ Figs. 104 and 105). In the previous
chapter, however, we found that on passing the transition point to the
region of stability for the double salt, the solution which is saturated
for a mixture of the two constituent salts, is supersaturated for the
double salt. In this case, therefore, point C must lie above the solubility
curve of the pure double salt (Fig. 106), and a solution of the composition
C, if brought in contact with double salt, will deposit the latter. If the
single salts were also present, then as the double salt separated out, the
single salts would pass into solution, because so long as the two single
salts are present, the composition of the solution must remain unaltered.
If one of the single salts disappear before the other, there will be left
double salt plus A or double salt plus B, according to which was in excess;
and the composition of the solution will be either that represented by D
(saturated for double salt plus A), or that of the point F (saturated for
double salt plus B).
[Illustration: FIG. 106.]
In connection with the isothermal represented in Fig. 106, it should be
noted that at this particular temperature a solution saturated with respect
to the pure double salt is no longer supersaturated for one of the single
salts (point D); so that at the temperature of this isothermal the double
salt is not decomposed by water. At this temperature, further, the boundary
curve consists of three branches AD, DF, and FB, which give the composition
of the solutions in equilibrium with pure A, double salt, and pure B
respectively; while the points D and F represent solutions saturated for
double salt plus A and double salt plus B.
On continuing to alter the temperature in the same direction {277} as
before, the relative shifting of the solubility curves becomes more marked,
as shown in Fig. 107. At the temperature of this isothermal, the solution
saturated for the double salt now lies in a region of distinct unsaturation
with respect to the single salts; and the double salt can now exist as
solid phase in contact with solutions containing both relatively more of A
(curve ED), and relatively more of B (curve DF), than is contained in the
double salt itself.
[Illustration: FIG. 107.]
Transition Interval.--From what has been said, and from an examination of
the isothermal diagrams, Figs. 104-107, it will be seen that by a variation
of the temperature we can pass from a condition where the double salt is
quite incapable of existing in contact with solution (supersaturation being
excluded), to a condition where the existence of the double salt in
presence of solution becomes possible; only in the presence, however, of
one of the single salts (_transition point_, Fig. 105). A further change of
temperature leads to a condition where the stable existence of the pure
double salt in contact with solution just becomes possible (Fig. 106); and
from this point onwards, pure saturated solutions of the double salt can be
obtained (Fig. 107). _At any temperature, therefore, between that
represented by Fig. 105, and that represented by Fig. 106, the double salt
undergoes partial decomposition, with deposition of one of the constituent
salts._ The temperature range between the transition point and the
temperature at which a stable saturated solution of the pure double salt
just begins to be possible, is known as the _transition interval_ (p. 270).
As the figures show, the transition interval is limited on the one side by
the transition temperature, and on the other by the temperature at which
the solution saturated for double salt and the less soluble of the single
salts, contains the component salts in the same ratio as they are present
in the double salt. The greater the difference in the solubility of the
single salts, the larger will be the transition interval. {278}
Isothermal Evaporation.--The isothermal solubility curves are of great
importance for obtaining an insight into the behaviour of a solution when
subjected to isothermal evaporation. To simplify the discussion of the
relationships found here, we shall still suppose that the double salt
contains the single salts in equimolecular proportions; and we shall, in
the first instance, suppose that the unsaturated solution with which we
commence, also contains the single salts in the same ratio. The composition
of the solution must, therefore, be represented by some point lying on the
line OD, the bisectrix of the right angle.
From what has been said, it is evident that when the formation of a double
salt can occur, three temperature intervals can be distinguished, viz. the
single-salt interval, the transition interval, and the double-salt
interval.[359] When the temperature lies in the first interval, evaporation
leads first of all to the crystallization of one of the single salts, and
then to the separation of both the single salts together. In the second
temperature interval, evaporation again leads, in the first place, to the
deposition of one of the single salts, and afterwards to the
crystallization of the double salt. In the third temperature interval, only
the double salt crystallizes out. This will become clearer from what
follows.
[Illustration: FIG. 108.]
[Illustration: FIG. 109.]
If an unsaturated solution of the two single salts in equimolecular
proportion (_e.g._ point _x_, Fig. 108) is evaporated at a temperature at
which the formation of double salt is impossible, the component A, the
solubility curve of which is {279} cut by the line OD, will first separate
out; the solution will thereby become richer in B. On continued
evaporation, more A will be deposited, and the composition of the solution
will change until it attains the composition represented by the point C,
when both A and B will be deposited, and the composition of the solution
will remain unchanged. The result of evaporation will therefore be a
mixture of the two components.
If the formation of double salt is possible, but if the temperature lies
within the transition interval, the relations will be represented by a
diagram like Fig. 109. Isothermal evaporation of the solution X will lead
to the deposition of the component A, and the composition of the solution
will alter in the direction DE; at the latter point the double salt will be
formed, and the composition of the solution will remain unchanged so long
as the two solid phases are present. As can be seen from the diagram,
however, the solution in E contains less of component A than is contained
in the double salt. Deposition of the double salt at E, therefore, would
lead to a relative decrease in the concentration of A in the solution, and
to counterbalance this, _the salt which separated out at the commencement
must redissolve_.
Since the salts were originally present in equimolecular proportions, the
final result of evaporation will be the pure double salt. If when the
solution has reached the point E the salt A which had separated out is
removed, double salt only will be left as solid phase. At a given
temperature, however, a single solid phase can exist in equilibrium with
solutions of different composition. If, therefore, isothermal evaporation
is continued after the removal of the salt A, double salt will be
deposited, and the composition of the solution will change in the direction
EF. At the point F the salt B will separate out, and on evaporation both
double salt and the salt B will be deposited. In the former case (when the
salt A disappears on evaporation) we are dealing with an _incongruently
saturated solution_; but in the latter case, where both solid phases
continue to be deposited, the solution is said to be _congruently
saturated_.[360]
A "congruently saturated solution" is one from which the {280} solid phases
are continuously deposited during isothermal evaporation to dryness,
whereas in the case of "incongruently saturated solutions," at least one of
the solid phases disappears during the process of evaporation.
[Illustration: FIG. 110.]
Lastly, if the temperature lies outside the transition interval, isothermal
evaporation of an unsaturated solution of the composition X (Fig. 110) will
lead to the deposition of pure double salt from beginning to end. If a
solution of the composition Y is evaporated, the component A will first be
deposited and the composition of the solution will alter in the direction
of E, at which point double salt will separate out. Since the solution at
this point contains relatively more of A than is present in the double
salt, both the double salt and the single salt A will be deposited on
continued evaporation, in order that the composition of the solution shall
remain unchanged. In the case of solution Z, first component B and
afterwards the double salt will be deposited. The result will, therefore,
be a mixture of double salt and the salt B (congruently saturated
solutions),
It may be stated here that the same relationships as have been explained
above for double salts are also found in the resolution of racemic
compounds by means of optically active substances (third method of
Pasteur). In this case the single salts are doubly active substances
(_e.g._ strychnine-_d_-tartrate and strychnine-_l_-tartrate), and the
double salt is a partially racemic compound.[361]
Crystallization of Double Salt from Solutions containing Excess of One
Component.--One more case of isothermal crystallization may be discussed.
It is well known that a double salt which is decomposed by pure water can
nevertheless be obtained pure by crystallization from a solution containing
excess of one of the single salts (_e.g._ in the case of carnallite). Since
the double salt is partially decomposed by water, the temperature of the
experiment must be within the transition {281} interval, and the relations
will, therefore, be represented by a diagram like Fig. 109. If, now,
instead of starting with an unsaturated solution containing the single
salts in equimolecular proportions, we commence with one in which excess of
one of the salts is present, as represented by the point Y, isothermal
evaporation will cause the composition to alter in the direction YD', the
relative amounts of the single salts remaining the same throughout. When
the composition of the solution reaches the point D', pure double salt will
be deposited. The separation of double salt will, however, cause a relative
decrease in the concentration of the salt A, and the composition of the
solution will, therefore, alter in the direction D'F. If the evaporation is
discontinued before the solution has attained the composition F, only
double salt will have separated out. Even within the transition interval,
therefore, pure double salt can be obtained by crystallization, provided
the original solution has a composition represented by a point lying
between the two lines OE and OF. Since, as already shown, the composition
of the solution alters on evaporation in the direction EF, it will be best
to employ a solution having a composition near to the line OE.
Formation of Mixed Crystals.--If the two single salts A and B do not
crystallize out pure from solution, but form an unbroken series of mixed
crystals, it is evident that an invariant system cannot be produced. The
solubility curve will therefore be continuous from A to B; the liquid
solutions of varying composition being in equilibrium with solid solutions
also of varying composition. If, however, the series of mixed crystals is
not continuous, there will be a break in the solubility curve at which two
solid solutions of different composition will be in equilibrium with liquid
solution. This, of course, will constitute an invariant system, and the
point will correspond to the point C in Fig. 108. A full discussion of
these systems would, however, lead us too far, and the above indication of
the behaviour must suffice.[362]
{282}
Application to the Characterization of Racemates.--The form of the
isothermal solubility curves is also of great value for determining whether
an inactive substance is a racemic compound or a conglomerate of equal
proportions of the optical antipodes.[363]
As has already been pointed out, the formation of racemic compounds from
the two enantiomorphous isomerides, is analogous to the formation of double
salts. The isothermal solubility curves, also, have a similar form. In the
case of the latter, indeed, the relationships are simplified by the fact
that the two enantiomorphous forms have identical solubility, and the
solubility curves are therefore symmetrical to the line bisecting the angle
of the co-ordinates. Further, with the exception of the partially racemic
compounds to be mentioned later, there is no transition interval.
In Fig. 111, are given diagrammatically two isothermal solubility curves
for optically active substances. From what has been said in the immediately
preceding pages, the figure ought really to explain itself. The upper
isothermal _acb_ represents the solubility relations when the formation of
a racemic compound is excluded, as, _e.g._ in the case of rubidium _d_- and
_l_-tartrates above the transition point (p. 265). The solution at the
point _c_ is, of course, inactive, and _is unaffected by addition of either
the _d_- or _l_- form_. The lower isothermal, on the other hand, would be
obtained at a temperature at which the racemic compound could be formed.
The curve _a'e_ is the solubility curve for the _l_- form; _b'f_, that for
the _d_- form; and _edf_, that for the racemic compound in presence of
solutions of varying concentration. The point _d_ corresponds to saturation
for the pure racemic compound.
[Illustration: FIG. 111.]
From these curves now, it will be evident that it will be possible, in any
given case, to decide whether or not an inactive body is a mixture or a
racemic compound. For this purpose, {283} two solubility determinations are
made, first with the inactive material alone (in excess), and then with the
inactive material plus excess of one of the optically active forms. If we
are dealing with a mixture, the two solutions thus obtained will be
identical; both will have the composition corresponding to the point _c_,
and will be inactive. If, however, the inactive material is a racemic
compound, then two different solutions will be obtained; namely, an
inactive solution corresponding to the point _d_ (Fig. 111), and an
_active_ solution corresponding either to _e_ or to _f_, according to which
enantiomorphous form was added.
_Partially racemic compounds._[364] In this case we are no longer dealing
with enantiomorphous forms, and the solubility of the two oppositely active
isomerides is no longer the same. The symmetry of the solubility curves
therefore disappears, and a figure is obtained which is identical in its
general form with that found in the case of ordinary double salts (Fig.
112). In this case there is a transition interval.
[Illustration: FIG. 112.]
The curves _acb_ belong to a temperature at which the partially racemic
compound cannot be formed; _a'dfb'_, to the temperature at which the
compound just begins to be stable in contact with water, and _a"ed'f'b"_
belongs to a temperature at which the partially racemic compound is quite
stable in contact with water. Suppose now solubility determinations, made
in the first case with the original material alone, and then with the
original body plus each of the two compounds, formed from the
enantiomorphous substances separately, then if the original body was a
mixture, identical solutions will be obtained in all three cases (point
_c_); if it was a partially racemic compound, three different solutions
(_e_, _d'_, and _f'_) will be obtained if the temperature was outside the
transition interval, and two solutions, _d_ and _f_, if the temperature
belonged to the transition interval.
{284}
_Representation in Space._
Space Model for Carnallite.--Interesting and important as the isothermal
solubility curves are, they are insufficient for the purpose of obtaining a
clear insight into the complete behaviour of the systems of two salts and
water. A short description will, therefore, be given here of the
representation in space of the solubility relations of potassium and
magnesium chlorides, and of the double salt which they form,
carnallite.[365]
[Illustration: FIG. 113.]
Fig. 113 is a diagrammatic sketch of the model for carnallite looked at
sideways from above. Along the X-axis is measured the concentration of
magnesium chloride in the {285} solution; along the Y-axis, the
concentration of potassium chloride; while along the T-axis is measured the
temperature. The three axes are at right angles to one another. The
XT-plane, therefore, contains the solubility curve of magnesium chloride;
the YT-plane, the solubility curve of potassium chloride, and in the space
between the two planes, there are represented the composition of solutions
containing both magnesium and potassium chlorides. Any _surface_ between
the two planes will represent the various solutions in equilibrium with
only one solid phase, and will therefore indicate the area or field of
existence of bivariant ternary systems. A _line_ or _curve_ formed by the
intersection of two surfaces will represent solutions in equilibrium with
two solid phases (viz. those belonging to the intersecting surfaces), and
will show the conditions for the existence of univariant systems. Lastly,
_points_ formed by the intersection of three surfaces will represent
invariant systems, in which a solution can exist in equilibrium with three
solid phases (viz. those belonging to the three surfaces).
We shall first consider the solubility relations of the single salts. The
complete equilibrium curve for magnesium chloride and water is represented
in Fig. 113 by the series of curves ABF_{1} G_{1} H_{1} J_{1} L_{1} N_{1}.
AB is the freezing-point curve of ice in contact with solutions containing
magnesium chloride, and B is the cryohydric point at which the solid phases
ice and MgCl_{2},12H_{2}O can co-exist with solution. BFG is the solubility
curve of magnesium chloride dodecahydrate. This curve shows a point of
maximum temperature at F_{1}, and a retroflex portion F_{1}G_{1}. The curve
is therefore of the form exhibited by calcium chloride hexahydrate, or the
hydrates of ferric chloride (Chapter VIII.). G_{1} is a transition point at
which the solid phase changes from dodecahydrate to octahydrate, the
solubility of which is represented by the curve G_{1}H_{1}. At H_{1} the
octahydrate gives place to the hexahydrate, which is the solid phase in
equilibrium with the solutions represented by the curve H_{1}J_{1}. J_{1}
and L_{1} are also transition points at which the solid phase undergoes
change, in the former case from hexahydrate to tetrahydrate; and in the
latter case, {286} from tetrahydrate to dihydrate. The complete curve of
equilibrium for magnesium chloride and water is, therefore, somewhat
complicated, and is a good example of the solubility curves obtained with
salts capable of forming several hydrates.
The solubility curve of potassium chloride is of the simplest form,
consisting only of the two branches AC, the freezing-point curve of ice,
and CO, the solubility curve of the salt. C is the cryohydric point. This
point and the two curves lie in the YT-plane.
On passing to the ternary systems, the composition of the solutions must be
represented by points or curves situated _between_ the two planes. We shall
now turn to the consideration of these. BD and CD are ternary eutectic
curves (p. 284). They give the composition of solutions in equilibrium with
ice and magnesium chloride dodecahydrate (BD), and with ice and potassium
chloride (CD). D is a _ternary cryohydric point_. If the temperature is
raised and the ice allowed to disappear, we shall pass to the solubility
curve for MgCl_{2},12H_{2}O + KCl (curve DE). At E carnallite is formed and
the potassium chloride disappears; EFG is then the solubility curve for
MgCl_{2},12H_{2}O + carnallite (KMgCl_{3},6H_{2}O). This curve also shows a
point of maximum temperature (F) and a retroflex portion. GH and HJ
represent the solubility curves of carnallite + MgCl_{2},8H_{2}O and
carnallite + MgCl_{2},6H_{2}O, G and H being transition points. JK is the
solubility curve for carnallite + MgCl_{2},4H_{2}O. At the point K we have
the _highest temperature at which carnallite can exist with magnesium
chloride in contact with solution_. Above this temperature decomposition
takes place and potassium chloride separates out.
If at the point E, at which the two single salts and the double salt are
present, excess of potassium chloride is added, the magnesium chloride will
all disappear owing to the formation of carnallite, and there will be left
carnallite and potassium chloride. The solubility curve for a mixture of
these two salts is represented by EMK; a simple curve exhibiting, however,
a temperature maximum at M. This maximum point corresponds with the fact
that dry carnallite melts at this temperature with separation of potassium
chloride. _At all temperatures {287} above this point, the formation of
double salt is impossible_. The retroflex portion of the curve represents
solutions in equilibrium with carnallite and potassium chloride, but in
which the ratio MgCl_{2} : KCl is greater than in the double salt.
Throughout its whole course, _the curve EMK represents solutions in which
the ratio of MgCl_{2} : KCl is greater than in the double salt_. As this is
a point of some importance, it will be well, perhaps, to make it clearer by
giving one of the isothermal curves, _e.g._ the curve for 10deg, which is
represented diagrammatically in Fig. 114. E and F here represent solutions
saturated for carnallite plus magnesium chloride hydrate, and for
carnallite plus potassium chloride. As is evident, the point F lies above
the line representing equimolecular proportions of the salts (OD).
[Illustration: FIG. 114.]
Summary and Numerical Data.--We may now sum up the different systems which
can be formed, and give the numerical data from which the model is
constructed.[366]
I. _Bivariant Systems._
--------------------------------------
Solid phase. | Area of existence.
--------------------------------------
Ice | ABDC
KCl | CDEMKLNO
Carnallite | EFGHJKM
MgCl_{2},12H_{2}O | BF_{1}G_{1}GFED
MgCl_{2},8H_{2}O | G_{1}H_{1}HG
MgCl_{2},6H_{2}O | H_{1}I_{1}IH
MgCl_{2},4H_{2}O | I_{1}L_{1}LKI
MgCl_{2},2H_{2}O | L_{1}N_{1}NL
--------------------------------------
II. _Univariant Systems._--The different univariant systems have already
been described. The course of the curves will be sufficiently indicated if
the temperature and composition of the solutions for the different
invariant systems are given.
{288}
III.--_Invariant Systems--Binary and Ternary._
-------------------------------------------------------------------------
| | | Composition of solution.
Point. | Solid Phases. | Temper- | Gram-molecules of salt
| | ature. | per 1000 gram-mol. water.
-------------------------------------------------------------------------
A | Ice | 0deg | --
| | |
B | Ice; MgCl_{2},12H_{2}O | -33.6deg | 49.2 MgCl_{2}
| | |
C | Ice; KCl | -11.1deg | 59.4 KCl
| | |
D |{ Ice; MgCl_{2},12H_{2}O; }| -34.3deg | 43 MgCl_{2}; 3 KCl
|{ KCl }| |
| | |
E |{ MgCl_{2},12H_{2}O; KCl; }| -21deg | 66.1 MgCl_{2}; 4.9 KCl
|{ carnallite }| |
| | |
F_{1} | MgCl_{2},12H_{2}O | -16.4deg | 83.33 MgCl_{2}
| | |
F |{ MgCl_{2},12H_{2}O; }| -16.6deg |{ Almost same as F_{1};
|{ carnallite }| |{ contains small amount
| | |{ of KCl
| | |
G_{1} |{ MgCl_{2},12H_{2}O; }| -16.8deg | 87.5 MgCl_{2}
|{ MgCl_{2},8H_{2}O }| |
| | |
G |{ MgCl_{2},12H_{2}O; }| -16.9deg |{ Almost same as G_{1},
|{ MgCl_{2},8H_{2}O; }| |{ but contains small
|{ carnallite }| |{ quantity of KCl
| | |
H_{1} |{ MgCl_{2},8H_{2}O; }| -3.4deg | 99 MgCl_{2}
|{ MgCl_{2},6H_{2}O }| |
| | |
H |{ MgCl_{2},8H_{2}O; }|ca.-3.4deg|{ Almost same as H_{1},
|{ MgCl_{2},6H_{2}O; }| |{ but contains small
|{ carnallite }| |{ amount of KCl
| | |
J_{1} |{ MgCl_{2},6H_{2}O; }| 116.67deg| 161.8 MgCl_{2}
|{ MgCl_{2},4H_{2}O }| |
| | |
J |{ MgCl_{2},6H_{2}O; }| 115.7deg | 162 MgCl_{2}; 4 KCl
|{ MgCl_{2},4H_{2}O; }| |
|{ carnallite }| |
| | |
K |{ MgCl_{2},4H_{2}O; KCl; }| 152.5deg | 200 MgCl_{2}; 24 KCl
|{ carnallite }| |
| | |
L_{1} |{ MgCl_{2},4H_{2}O; }| 181deg | 238.1 MgCl_{2}
|{ MgCl_{2},2H_{2}O }| |
| | |
L |{ MgCl_{2},4H_{2}O; }| 176deg | 240 MgCl_{2}; 41 KCl
|{ MgCl_{2},2H_{2}O; KCl }| |
| | |
M | Carnallite; KCl | 167.5deg | 166.7 MgCl_{2}; 41.7 KCl
| | |
[N_{1} | MgCl_{2},2H_{2}O | 186deg | ca. 241 MgCl_{2}]
| | |
N | MgCl_{2},2H_{2}O; KCl | 186deg | 240 MgCl_{2}; 63 KCl
| | |
[O | KCl | 186deg | 195.6 KCl]
-------------------------------------------------------------------------
With the help of the data in the preceding table and of the solid model it
will be possible to state in any given case what will be the behaviour of a
system composed of magnesium chloride, potassium chloride and water. One or
two different cases will be very briefly described; and the reader should
have no difficulty in working out the behaviour under other conditions with
the help of the model and the numerical data just given. {289}
In the first place it may be again noted that at a temperature above
167.5deg (point M) carnallite cannot exist. If, therefore, a solution of
magnesium and potassium chlorides is evaporated at a temperature above this
point, the result will be a mixture of potassium chloride and either
magnesium chloride tetrahydrate or magnesium chloride dihydrate, according
as the temperature is below or above 176deg. The isothermal curve here
consists of only two branches.
Further, reference has already been made to the fact that all points of the
carnallite area correspond to solutions in equilibrium with carnallite, but
in which the ratio of MgCl_{2} to KCl is greater than in the double salt. A
solution which is saturated with respect to double salt alone will be
supersaturated with respect to potassium chloride. At all temperatures,
therefore, carnallite is decomposed by water with separation of potassium
chloride; hence all solutions obtained by adding excess of carnallite to
water will lie on the curve EM. _A pure saturated solution of carnallite
cannot be obtained._
If an unsaturated solution of the two salts in equimolecular amounts is
evaporated, potassium chloride will first be deposited, because the plane
bisecting the right angle formed by the X and Y axes cuts the area for that
salt. Deposition of potassium chloride will lead to a relative increase in
the concentration of magnesium chloride in the solution; and on continued
evaporation a point (on the curve EM) will be reached at which carnallite
will separate out. So long as the two solid phases are present, the
composition of the solution must remain unchanged. Since the separation of
carnallite causes a decrease in the relative concentration of the potassium
chloride in the solution, the portion of this salt which was deposited at
the commencement must _redissolve_, and carnallite will be left on
evaporating to dryness. (_Incongruently saturated solution._)
Although carnallite is decomposed by pure water, it will be possible to
crystallize it from a solution having a composition represented by any
point in the carnallite area. Since during the separation of the double
salt the relative amount of magnesium chloride increases, it is most
advantageous to {290} commence with a solution the composition of which is
represented by a point lying just above the curve EM (cf. p. 281).
From the above description of the behaviour of carnallite in solution, the
processes usually employed for obtaining potassium chloride will be readily
intelligible.[367]
Ferric Chloride--Hydrogen Chloride--Water.--In the case of another system
of three components which we shall now describe, the relationships are
considerably more complicated than in those already discussed. They deserve
discussion, however, on account of the fact that they exhibit a number of
new phenomena.
In the system formed by the three components, ferric chloride, hydrogen
chloride, and water, not only can various compounds of ferric chloride and
water (p. 152), and of hydrogen chloride and water be formed, each of which
possesses a definite melting point, but various ternary compounds are also
known. Thus we have the following solid phases:--
2FeCl_{3},12H_{2}O HCl,3H_{2}O 2FeCl_{3},2HCl,12H_{2}O
2FeCl_{3},7H_{2}O HCl,2H_{2}O 2FeCl_{3},2HCl,8H_{2}O
2FeCl_{3},5H_{2}O HCl,H_{2}O 2FeCl_{3},2HCl,4H_{2}O
2FeCl_{3},4H_{2}O
FeCl_{3}
From this it will be readily understood that the complete study of the
conditions of temperature and concentration under which solutions can
exist, either with one solid phase or with two or three solid phases, are
exceedingly complicated; and, as a matter of fact, only a few of the
possible equilibria have been investigated. We shall attempt here only a
brief description of the most important of these.[368]
If we again employ rectangular co-ordinates for the graphic {291}
representation of the results, we have the two planes XOT and YOT (Fig.
115): the concentration of ferric chloride being measured along the X-axis,
the concentration of hydrogen chloride along the Y-axis, and the
temperature along the T-axis. The curve ABCDEFGHJK is, therefore, the
solubility curve of ferric chloride in water (p. 152), and the curve
A'B'C'D'E'F' the solubility curve of hydrogen chloride and its hydrates. B'
and D' are the melting points of the hydrates HCl,3H_{2}O and HCl,2H_{2}O.
In the space between these two planes are represented those systems in
which all three components are present. As already stated, only a few of
the possible ternary systems have been investigated, and these are
represented in Fig. 116. The figure shows the model resting on the
XOT-plane, so that the lower edge represents the solubility curve of ferric
chloride, the concentration increasing from right to left. The
concentration of hydrogen chloride is measured upwards, and the temperature
forwards. The further end of the model represents the isothermal surface
for -30deg. The surface of the model on the left does not correspond with
the plane YOT in Fig. 115, but with a parallel plane which cuts the
concentration axis for ferric chloride at a point representing 65
gm.-molecules FeCl_{3} in 100 gm.-molecules of water. The upper surface
corresponds with a plane parallel to the axis XOT, at a distance
corresponding with the concentration of 50 gm.-molecules HCl in 100
gm.-molecules of water.
[Illustration: FIG. 115.]
Ternary Systems.--We pass over the binary system FeCl_{3}--H_{2}O, which
has already been discussed (p. 152), and the similar system HCl--H_{2}O
(see Fig. 115), and turn to the discussion of some of the ternary systems
represented by {292} points on the surface of the model between the planes
XOT and YOT. As in the case of carnallite, a plane represents the
conditions of concentration of solution and temperature under which a
ternary solution can be in equilibrium with a _single_ solid phase
(bivariant systems), a line represents the conditions for the coexistence
of a solution with two solid phases (univariant systems), and a point the
conditions for equilibrium with three solid phases (invariant systems).
[Illustration: FIG. 116.]
In the case of a binary system, in which 2FeCl_{3},12H_{2}O is in
equilibrium with a solution of the same composition, addition of hydrogen
chloride must evidently lower the temperature at which equilibrium can
exist; and the same holds, of course, {293} for all other binary solutions
in equilibrium with this solid phase. In this way we obtain the surface I.,
which represents the temperatures and concentrations of solutions in which
2FeCl_{3},12H_{2}O can be in equilibrium with a ternary solution containing
ferric chloride, hydrogen chloride, and water. This surface is analogous to
the curved surface K_{1}K_{2}_k__{4}_k__{3} in Fig. 97 (p. 256). Similarly,
the surfaces II., III., IV., and V. represent the conditions for
equilibrium between the solid phases 2FeCl_{3},7H_{2}O; 2FeCl_{3},5H_{2}O;
2FeCl_{3},4H_{2}O; FeCl_{3} and ternary solutions respectively. The lines
CL, EM, GN, and IO on the model represent univariant systems in which a
ternary solution is in equilibrium with two solid phases, viz. with those
represented by the adjoining fields. These lines correspond with the
ternary eutectic curves _k__{3}K_{1} and _k__{4}K_{2} in Fig. 97. Besides
the surfaces already mentioned, there are still three others, VI., VII.,
and VIII., which also represent the conditions for equilibrium between one
solid phase and a ternary solution; but in these cases, the solid phase is
not a binary compound or an anhydrous salt, but a ternary compound
containing all three components. The solid phases which are in equilibrium
with the ternary solutions represented by the surfaces VI., VII., and
VIII., are 2FeCl_{3},2HCl,4H_{2}O; 2FeCl_{3},2HCl,8H_{2}O; and
2FeCl_{3},2HCl,12H_{2}O respectively.
The model for FeCl_{3}--HCl--H_{2}O exhibits certain other peculiarities
not found in the case of MgCl_{2}--KCl--H_{2}O. On examining the model more
closely, it is found that the field of the ternary compound
2FeCl_{3},2HCl,8H_{2}O (VII.) resembles the surface of a sugar cone, and
has a projecting point, the end of which corresponds with a higher
temperature than does any other point of the surface. At the point of
maximum temperature the composition of the liquid phase is the same as that
of the solid. This point, therefore, represents the melting point of the
double salt of the above composition.
The curves representing univariant systems are of two kinds. In the one
case, the two solid phases present are both binary compounds; or one is a
binary compound and the other is one of the components. In the other case,
either one or both solid phases are ternary compounds. Curves belonging
{294} to the former class (so-called _border curves_) start from binary
eutectic points, and their course is always towards lower temperatures,
_e.g._ CL, EM, GN, IO. Curves belonging to the latter class (so-called
_medial curves_) would, in a triangular diagram, lie entirely within the
triangle. Such curves are YV, WV, VL, LM, MV, NS, ST, SO, OZ. These curves
do not always run from higher to lower temperatures, but may even exhibit a
point of maximum temperature. Such maxima are found, for example, at U
(Fig. 116), and also on the curves ST and LV.
Finally, whereas all the other ternary univariant curves run in valleys
between the adjoining surfaces, we find at the point X a similar appearance
to that found in the case of carnallite, as the univariant curve here rises
above the surrounding surface. The point X, therefore, does not correspond
with a eutectic point, but with a transition point. At this point the
ternary compound 2FeCl_{3},2HCl,12H_{2}O melts with separation of
2FeCl_{3},12H_{2}O, just as carnallite melts at 168deg with separation of
potassium chloride.
The Isothermal Curves.--A deeper insight into the behaviour of the system
FeCl_{3}--HCl--H_{2}O is obtained from a study of the isothermal curves,
the complete series of which, so far as they have been studied, is given in
Fig. 117.[369] In this figure the lightly drawn curves represent isothermal
solubility curves, the particular temperature being printed beside the
curve.[370] The dark lines give the composition of the univariant systems
at different temperatures. The point of intersection of a dark with a light
curve gives the composition of the univariant solution at the temperature
represented by the light curve; and the point of intersection of two dark
lines gives the composition of the invariant solution in equilibrium with
three solid phases. The dotted lines represent metastable systems, and the
points P, Q, and R represent solutions of {295} the composition of the
ternary salts, 2FeCl_{3},2HCl,4H_{2}O; 2FeCl_{3},2HCl,8H_{2}O; and
2FeCl_{3},2HCl,12H_{2}O.
[Illustration: FIG. 117.]
The farther end of the model (Fig. 116) corresponds, as already mentioned,
to the temperature -30deg, so that the outline evidently represents the
isothermal curve for that temperature. Fig. 117 does not show this.
We can, however, follow the isothermal for -20deg, which is the extreme
curve on the right in Fig. 117. Point A represents the solubility
of 2FeCl_{3},12H_{2}O in water. If hydrogen chloride is added, the
concentration of ferric chloride in the solution first decreases
and then increases, until at point 34 the ternary double salt
2FeCl_{3},2HCl,12H_{2}O is formed. If the addition of hydrogen chloride is
continued, the ferric chloride disappears ultimately, and only the ternary
double salt remains. This salt can coexist with solutions of the
composition represented by the curve which passes through the points 173,
174, 175. At the last-mentioned point, the ternary salt with 8H_{2}O is
formed. The composition of the solutions with which this salt is in
equilibrium at -20deg is represented by the curve which passes through a
point of maximal concentration with respect to HCl, and cuts the curve SN
at the point 112, at which the solution is in equilibrium with the two
solid phases 2FeCl_{3},4H_{2}O and 2FeCl_{3},2HCl,8H_{2}O. The succeeding
portion of the isotherm represents the solubility curve at -20deg of
2FeCl_{3},4H_{2}O, which cuts the dark line OS at point 113, at which the
solution is in equilibrium with the two solid phases 2FeCl_{3},4H_{2}O and
2FeCl_{3},2HCl,4H_{2}O. Thereafter comes the solubility curve of the latter
compound.
The other isothermal curves can be followed in a similar manner. If the
temperature is raised, the region of existence of the ternary double salts
becomes smaller and smaller, and at temperatures above 30deg the ternary
salts with 12H_{2}O and 8H_{2}O are no longer capable of existing. If the
temperature is raised above 46deg, only the binary compounds of ferric
chloride and water and the anhydrous salt can exist as solid phases.
The isothermal curve for 0deg represents the solubility curve for
2FeCl_{3},12H_{2}O; 2FeCl_{3},7H_{2}O; 2FeCl_{3},5H_{2}O; and
2FeCl_{3},4H_{2}O. {296}
Finally, in the case of the system FeCl_{3}--HCl--H_{2}O, we find
_closed_ isothermal curves. Since, as already stated, the salt
2FeCl_{3},2HCl,8H_{2}O has a definite melting point, the temperature
of which is therefore higher than that at which this compound is in
equilibrium with solutions of other composition, it follows that the line
of intersection of an isothermal plane corresponding with a temperature
immediately below the melting point of the salt with the cone-shaped
surface of its region of existence, will form a closed curve. This is shown
by the isotherm for -4.5deg, which surrounds the point Q, the melting point
of the ternary salt.
The following table gives some of the numerical data from which the curves
and the model have been constructed:--
-------------------------------------------------------------------------
| | | Composition of the sol-
| | | ution in gm.-mols. salt
Point. | Solid phases. | Temper- | to 100 gm.-mols. water.
| | ature. |------------------------
| | | HCl | FeCl_{3}
-------------------------------------------------------------------------
A | 2FeCl_{3},12H_{2}O | -20deg | -- | 6.56
| | | |
C |{ 2FeCl_{3},12H_{2}O; }| 27.4deg | -- | 24.30
|{ 2FeCl_{3},7H_{2}O }| | |
| | | |
E |{ 2FeCl_{3},7H_{2}O; }| 30deg | -- | 30.24
|{ 2FeCl_{3},5H_{2}O }| | |
| | | |
G |{ 2FeCl_{3},5H_{2}O; }| 55deg | -- | 40.64
|{ 2FeCl_{3},4H_{2}O }| | |
| | | |
J | 2FeCl_{3},4H_{2}O; FeCl_{3} | 66deg | -- | 58.40
| | | |
|{ 2FeCl_{3},12H_{2}O; }| | |
L |{ 2FeCl_{3},7H_{2}O; }| -7.5deg | 19.22 | 23.72
|{ 2FeCl_{3},2HCl,8H_{2}O }| | |
| | | |
|{ 2FeCl_{3},7H_{2}O; }| | |
M |{ 2FeCl_{3},5H_{2}O; }| -7.3deg | 23.08 | 28.55
|{ 2FeCl_{3},2HCl,8H_{2}O }| | |
| | | |
|{ 2FeCl_{3},5H_{2}O; }| | |
N |{ 2FeCl_{3},4H_{2}O; }| -16deg | 28.40 | 31.89
|{ 2FeCl_{3},2HCl,8H_{2}O }| | |
| | | |
|{ 2FeCl_{3},4H_{2}O; }| | |
S |{ 2FeCl_{3},2HCl,8H_{2}O; }| -27.5deg | 32.33 | 34.21
|{ 2FeCl_{3},2HCl,4H_{2}O }| | |
| | | |
|{ 2FeCl_{3},4H_{2}O; }| | |
O |{ FeCl_{3}; }| 29deg | 33.71 | 49.84
|{ 2FeCl_{3},2HCl,4H_{2}O }| | |
| | | |
U |{ 2FeCl_{3},7H_{2}O; }| -4.5deg | 20.66 | 25.74
|{ 2FeCl_{3},2HCl,8H_{2}O }| | |
| | | |
|{ 2FeCl_{3},12H_{2}O; }| | |
V |{ 2FeCl_{3},2HCl,12H_{2}O; }| -13deg | 22.40 | 18.00
|{ 2FeCl_{3},2HCl,8H_{2}O }| | |
| | | |
X |{ 2FeCl_{3},12H_{2}O; }| -12.5deg | 22.14 | 16.69
|{ 2FeCl_{3},2HCl,12H_{2}O }| | |
| | | |
Q | 2FeCl_{3},2HCl,8H_{2}O | -3deg (melting point)
-------------------------------------------------------------------------
Basic Salts.--Another class of systems in the study of {297} which the
Phase Rule has performed exceptional service, is that of the basic salts.
In many cases it is impossible, by the ordinary methods of analysis, to
decide whether one is dealing with a definite chemical individual or with a
mixture. The question whether a solid phase is a chemical individual can,
however, be answered, in most cases, with the help of the principles which
we have already learnt. Let us consider, for example, the formation of
basic salts from bismuth nitrate, and water. In this case we can choose as
components Bi_{2}O_{3}, N_{2}O_{5}, and H_{2}O; since all the systems
consist of these in varying amounts. If we are dealing with a condition of
equilibrium at constant temperature between liquid and solid phases, three
cases can be distinguished,[371] viz.--
1. The solutions in different experiments have the same composition, but
the composition of the precipitate alters. In this case there must be two
solid phases.
2. The solutions in different experiments can have varying composition,
while the composition of the precipitate remains unchanged. In this case
only one solid phase exists, a definite compound.
3. The composition both of the solution and of the precipitate varies. In
this case the solid phase is a solid solution or a mixed crystal.
In order, therefore, to decide what is the nature of a precipitate produced
by the hydrolysis of a normal salt, it is only necessary to ascertain
whether and how the composition of the precipitate alters with alteration
in the composition of the solution. If the composition of the solution is
represented by abscissae, and the composition of the precipitate by
ordinates, the form of the curves obtained would enable us to answer our
question; for vertical lines would indicate the presence of two solid
phases (1st case), horizontal lines the presence of only one solid phase
(2nd case), and slanting lines the presence of mixed crystals (3rd case).
This method of representation cannot, however, be carried out in most
cases. It is, however, {298} generally possible to find one pair or several
pairs of components, the _relative amounts_ of which in the solution or in
the precipitate undergo change when, and only when, the composition of the
solution or of the precipitate changes. Thus, in the case of bismuth,
nitrate, and water, we can represent the ratio of Bi_{2}O_{3} : N_{2}O_{5}
in the precipitate as ordinates, and N_{2}O_{5} : H_{2}O in the solution as
abscissae. A horizontal line then indicates a single solid phase, and a
vertical line two solid phases. An example of this is given in Fig.
118.[372]
[Illustration: FIG. 118.]
Bi_{2}O_{3}--N_{2}O_{5}--H_{2}O.--Although various systems have been
studied in which there is formation of basic salts,[373] we shall content
ourselves here with the description of some of the conditions for the
formation of basic salts of bismuth nitrate, and for their equilibrium in
contact with solutions.[374]
Three normal salts of bismuth oxide and nitric acid are known, viz.
Bi_{2}O_{3},3N_{2}O_{5},10H_{2}O(S_{10});
Bi_{2}O_{3},3N_{2}O_{5},4H_{2}O(S_{4}); and
Bi_{2}O_{3},3N_{2}O_{5},3H_{2}O(S_{3}). Besides these normal salts, there
are the following basic salts:--
{299}
Bi_{2}O_{3},N_{2}O_{5},2H_{2}O (represented by B_{1-1-2})
Bi_{2}O_{3},N_{2}O_{5},H_{2}O ( " " B_{1-1-1})
6Bi_{2}O_{3},5N_{2}O_{5},9H_{2}O ( " " B_{6-5-9})
2Bi_{2}O_{3},N_{2}O_{5},H_{2}O ( " " B_{2-1-1})
Probably some others also exist. The problem now is to find the conditions
under which these different normal and basic salts can be in equilibrium
with solutions of varying concentration of the three components. Having
determined the equilibrium conditions for the different salts, it is then
possible to construct a model similar to that for MgCl_{2}--KCl--H_{2}O or
for FeCl_{3}--HCl--H_{2}O, from which it will be possible to determine the
limits of stability of the different salts, and to predict what will occur
when we bring the salts in contact with solutions of nitric acid of
different concentrations and at different temperatures.
For our present purpose it is sufficient to pick out only some of the
equilibria which have been studied, and which are represented in the model
(Fig. 119). In this case use has been made of the triangular method of
representation, so that the surface of the model lies within the prism.
[Illustration: FIG. 119.]
This model shows the three surfaces, A, B, and C, which represent the
conditions for the stable existence of the salts B_{1-1-1}, S_{10}, and
S_{3} in contact with solution at different {300} temperatures. The front
surface of the model represents the temperature 9deg, and the farther end
the temperature 75.5deg. The dotted curve represents the isotherm for
20deg. The prominences between the surfaces represent, of course, solutions
which are saturated in respect of two solid phases. Thus, for example,
_pabc_ represents solutions in equilibrium with B_{1-1-1} and S_{10}; and
the ridge _qdc_, solutions in equilibrium with S_{10} and S_{3}. The point
_b_, which lies at 75.5deg, is the point of maximum temperature for S_{10}.
If the temperature is raised above this point, S_{10} decomposes into the
basic salt B_{1-1-1} and solution. This point is therefore analogous to the
point M in the carnallite model, at which this salt decomposes into
potassium chloride and solution (p. 284); or to the point at which the salt
2FeCl_{3},2HCl,12H_{2}O decomposes into 2FeCl_{3},12H_{2}O and solution
(p. 294). The curve _pab_ has been followed to the temperature of 72deg
(point _c_). The end of the model is incomplete, but it is probable that in
the neighbourhood of the point _c_ there exists a quintuple point at which
the basic salt B_{1-2-2} appears. In the neighbourhood of _e_ also there
probably exists another quintuple point at which S_{4} is formed. These
systems have, however, not been studied.
The following tables give some of the numerical data:--
ISOTHERM FOR 20deg.
----------------------------------------------------------------------
| Composition of the solution. Gram-mols.
| in 1000 gm.-mols. of water.
Solid phase. |----------------------------------------
| Bi_{2}O_{3} | N_{2}O_{5}
-----------------------------|-----------------|----------------------
B_{1-1-1} | 10.50 | 38.65
-- | 27.20 | 83.84
B_{1-1-1}; S_{10} | 30.15 | 97.97
S_{10} | 29.70 | 96.57
-- | 19.65 | 98.76
-- | 10.51 | 162.58
-- | 33.51 | 355.87
S_{10}; S_{3} | 51.00 | 403.0
S_{3} | 14.35 | 492.0
-- | 7.45 | 592.9
----------------------------------------------------------------------
SYSTEMS IN EQUILIBRIUM WITH B_{1-1-1} AND S_{10} (CURVE _pabc_).
------------------------------------------------------------
| Composition of the solution. Gram-mols.
| in 1000 gm.-mols. of water.
Temperature. |----------------------------------------
| Bi_{2}O_{3} | N_{2}O_{5}
-------------------|---------------|------------------------
9deg | 26.7 | 88.2
20deg (point _a_) | 30.15 | 97.97
30deg | 33.6 | 112.3
50deg | 41.8 | 148.4
65deg | 57.21 | 190.8
75.5deg (point _b_)| 87.9 | 288.4
72deg (point _c_) | 96.0 | 327.0
------------------------------------------------------------
SYSTEMS IN EQUILIBRIUM WITH S_{10} AND S_{3} (CURVE _qde_).
--------------------------------------------------------
| Composition of the solution. Gram-mols.
| in 1000 gm.-mols. of water.
Temperature. |-----------------------------------------
| Bi_{2}O_{3} | N_{2}O_{5}
--------------|---------------|-------------------------
11.5deg | 44.5 | 396
20deg | 51.0 | 405.4
50deg | 66.5 | 444.2
65deg | 80.0 | 454.4
--------------------------------------------------------
Basic Mercury Salts.--The Phase Rule has also been applied by A. J.
Cox[375] in an investigation of the basic salts of mercury, the result of
which has been to show that, of the salts mentioned in text-books, quite a
number are incorrectly stated to be chemical compounds or chemical
individuals (p. 92). The investigation, which was carried out essentially
in the manner described above, included the salts mentioned in the
following table; and of the basic salts said to be derived from them, only
those mentioned really exist. In the following table, the numbers in the
second column give the minimum values of the concentration of the acid,
expressed in equivalent normality, necessary for the existence of the {301}
corresponding salts in contact with solution at the temperature given in
the third column:--
-------------------------------------------------------------
Salt. | Normality of | Temperature.
| acid. |
-------------------------------------------------------------
HgCrO_{4} | 1.41 | 50deg
3HgO.CrO_{3} | 2.6 x 10^{-4} | 50deg
| |
Hg(NO_{3})_{2}.H_{2}O | 18.72 | 25deg
3HgO.N_{2}O_{5} | 0.159 | 25deg
| |
HgSO_{4} | 6.87 | 25deg
3HgO.SO_{3} | 1.3 x 10^{-3} | 25deg
| |
HgF_{2} | 1.14 | 25deg
| |
HgNO_{3}.H_{2}O | 2.95 | 25deg
5Hg_{2}O.3N_{2}O_{5}.2H_{2}O | ca. 0.293 | 25deg
2Hg_{2}O.N_{2}O_{5}(?) | 0.110 | 25deg
3Hg_{2}O.N_{2}O_{5}.2H_{2}O(?) | 1.7 x 10^{-3} | 25deg
| |
Hg_{2}SO_{4} | 4.2 x 10^{-3} | 25deg
2Hg_{2}O.SO_{3}.H_{2}O | 5.6 x 10^{-4} | 25deg
-------------------------------------------------------------
Mercuric fluoride does not form any basic salt.
Since two succeeding members of a series can coexist only in contact with a
solution of definite concentration, we can prepare acid solutions of
definite concentration by bringing an excess of two such salts in contact
with water.
Indirect Determination of the Composition of the Solid Phase.--It has
already been shown (p. 228) how the composition of the solid phase in a
system of two components can be determined without analysis, and we shall
now describe how this can be done in a system of three components.[376]
We shall assume that we are dealing with the aqueous solution of two salts
which can give rise to a double salt, in which case we can represent the
solubility relations in a system of rectangular co-ordinates. In this case
we should obtain, as before (Fig. 120), the isotherm _adcb_, if we express
the {302} composition of the solution in gram-molecules of A or of B to 100
gram-molecules of water.
[Illustration: FIG. 120.]
Let us suppose, now, that the double salt is in equilibrium with the
solution at a definite temperature, and that the composition of the
solution is represented by the point e. The greater part of the solution is
now separated from the solid phase, and the latter, _together with the
adhering mother liquor_, is analyzed. The composition (expressed, as
before, in gram-molecules of A and B to 100 gram molecules of water) will
be represented by a point (_e.g._ _f_) on the line _e_S, where S represents
the composition of the double salt. That this is so will be evident when
one considers that the composition of the whole mass must lie between the
composition of the solution and that of the double salt, no matter what the
relative amounts of the solid phase and the mother liquor.
If, in a similar manner, we analyze a solution of a different composition
in equilibrium with the same double salt (not necessarily at the same
temperature as before), and also the mixture of solid phase and solution,
we shall obtain two other points, as, for example, _g_ and _h_, and the
line joining these must likewise pass through S. The method of finding the
{303} composition of an unknown double salt consists, therefore, in
finding, in the manner just described, the position of two lines such as
_ef_ and _gh_. The point of intersection of these lines then gives the
composition of the double salt.
If the double salt is anhydrous, the point S lies at infinity, and the
lines _ef_ and _gh_ are parallel to each other.
The same result is arrived at by means of the triangular method of
representation.[377] If we start with the three components in known
amounts, and represent the initial composition of the whole by a point in
the triangle, and then ascertain the final composition of the solution in
equilibrium with the solid phase at a definite temperature, the line
joining the points representing the initial and end concentration passes
through the point representing the composition of the solid phase. If two
determinations are made with solutions having different initial and final
concentrations in equilibrium with the same solid phase, then the point of
intersection of the two lines so obtained gives the composition of the
solid phase.
* * * * *
{304}
CHAPTER XVII
ABSENCE OF A LIQUID PHASE
In the preceding chapters dealing with equilibria in three-component
systems, our attention was directed only to those cases in which liquid
solutions formed one or more phases. Mention must, however, be made of
certain systems which contain no liquid phase, and in which only solids and
gases are in equilibrium. Since, in all cases, there can be but one gas
phase, four solid phases will be necessary in order to form an invariant
system. When only three solid phases are present, the system is univariant;
and when only two solid phases coexist with gas, it is bivariant. If,
however, we make the restriction that the gas pressure is constant, we
diminish the variability by one.
On account of their great industrial importance, we shall describe briefly
some of the systems belonging to this class.
Iron, Carbon Monoxide, Carbon Dioxide.--Some of the most important systems
of three components in which equilibrium exists between solid and gas
phases are those formed by the three components--iron, carbon monoxide, and
carbon dioxide--and they are of importance especially for the study of the
processes occurring in the blast furnace.
If carbon monoxide is passed over reduced iron powder at a temperature of
about 600deg, the iron is oxidized and the carbon monoxide reduced with
separation of carbon in accordance with the equation
Fe + CO = FeO + C
This reaction is succeeded by the two reactions
FeO + CO = Fe + CO_{2}
CO_{2} + C = 2CO
{305}
[Illustration: FIG. 121.]
The former of these reactions is not complete, but leads to a definite
equilibrium. The result of the different reactions is therefore an
equilibrium between the three solid phases, carbon, iron, and ferrous
oxide, and the gas phase consisting of carbon monoxide and dioxide. We have
here four phases; and if the total pressure is maintained constant,
equilibrium can occur only at a definite temperature.
Since, under certain conditions, we can also have the reaction
Fe_{3}O_{4} + CO = 3FeO + CO_{2}
{306} a second series of equilibria can be obtained of a character similar
to the former. These various equilibria have been investigated by Baur and
Glaessner,[378] and the following is a short account of the results of
their work.
Mixtures of the solid phases in equilibrium with carbon monoxide and
dioxide were heated in a porcelain tube at a definite temperature until
equilibrium was produced, and the gas was then pumped off and analyzed. The
results which were obtained are given in the following tables, and
represented graphically in Fig. 121.
SOLID PHASES: Fe_{3}O_{4}; FeO.
-----------------------------------------------------------------
| | Duration of | | Percentage of
No. | Tube filled | the experiment | Temperature. |
| with | in hours. | | CO_{2} | CO
-----------------------------------------------------------------
1 | CO | 14 | 600deg | 59.3 | 40.7
2 | CO | 15 | 590deg | 54.7 | 45.3
3 | CO_{2} | 16 | 590deg | 64.6 | 35.4
4 | CO | 24 | 590deg | 58.4 | 41.6
5 | CO | 22 | 730deg | 67.7 | 32.3
6 | CO_{2} | 22 | 730deg | 86.1 | 31.9
7 | CO | 22 | 750deg | 68.4 | 31.6
8 | CO_{2} | 22 | 610deg | 64.9 | 35.1
9 | CO | 23 | 420deg | 56.0 | 44.0
10 | CO | 47 | 350deg | 65.6 | 34.4
11 | CO_{2} | 46 | 350deg | 72.8 | 27.2
12 | CO | 53 | 350deg | 64.0 | 36.0
13 | CO | 18 | 570deg | 53.4 | 46.6
14 | CO | 19 | 680deg | 60.5 | 39.5
15 | CO_{2} | 24 | 540deg | 55.5 | 44.5
16 | CO | 21 | 630deg | 57.5 | 42.5
17 | CO_{2} | 17 | 690deg | 65.5 | 34.5
18 | CO_{2} | 17 | 670deg | 67.0 | 33.0
19 | CO_{2} | 24 | 410deg | 58.5 | 41.5
20 | CO | 24 | 490deg | 51.7 | 48.8
21 | CO_{2} | 23 | 590deg | 54.4 | 45.6
22 | CO_{2} | 4 | 950deg | 77.0 | 23.0
23 | CO_{2} | 15 | 850deg | 73.4 | 26.6
24 | CO | 8 | 800deg | 71.2 | 28.8
25 | CO_{2} | 24 | 540deg | 56.7 | 43.3
-----------------------------------------------------------------
{307}
SOLID PHASES: FeO; Fe.
------+-------------+-------------+--------------+---------------
| | Duration of | | Percentage of
No. | Tube filled | experiment | Temperature. |
| with | in hours. | | CO_{2} | CO
------+-------------+-------------+--------------+--------+------
I. | CO | 15 | 800deg | 35.2 | 64.8
II. | CO | 18 | 530deg | 29.1 | 70.9
III. | CO | 13 | 880deg | 30.2 | 69.6
IV. | CO_{2} | 24 | 870deg | 32.3 | 67.7
V. | CO | 18 | 760deg | 36.9 | 63.1
VI. | CO_{2} | 16 | 820deg | 34.7 | 65.3
VII. | CO_{2} | 18 | 730deg | 41.1 | 58.9
VIII. | CO | 18 | 630deg | 34.9 | 65.1
IX. | CO_{2} | 17 | 630deg | 61.6 | 58.4
X. | CO | 18 | 540deg | 25.0 | 75.0
XI. | CO_{2} | 25 | 540deg | 36.5 | 63.5
------+-------------+-------------+--------------+--------+------
As is evident from the above tables and from the curves in Fig. 121, the
curve of equilibrium in the case of the reaction
Fe_{3}O_{4} + CO = 3FeO + CO_{2}
exhibits a maximum for the ratio CO : CO_{2}, at 490deg, while, for the
reaction
FeO + CO = Fe + CO_{2}
this ratio has a minimum value at 680deg. From these curves can be derived
the conditions under which the different solid phases can exist in contact
with gas. Thus, for example, at a temperature of 690deg, FeO and
Fe_{3}O_{4} can coexist with a mixture of 65.5 per cent. of CO_{2} and 34.5
per cent. of CO. If the partial pressure of CO_{2} is increased, there
occurs the reaction
3FeO + CO_{2} = Fe_{3}O_{4} + CO
and if carbon dioxide is added in sufficient amount, the ferrous oxide
finally disappears completely. If, on the other hand, the partial pressure
of CO is increased, there occurs the reaction
Fe_{3}O_{4} + CO = 3FeO + CO_{2}
and all the ferric oxide can be made to disappear. We see, therefore, that
Fe_{3}O_{4} can only exist at temperatures and in {308} contact with
mixtures of carbon monoxide and dioxide, represented by the area which lies
below the under curve in Fig. 121. Similarly, the region of existence of
FeO is that represented by the area between the two curves; while metallic
iron can exist under the conditions of temperature and composition of gas
phase represented by the area above the upper curve in Fig. 121. If,
therefore, ferric oxide or metallic iron is heated for a sufficiently long
time at temperatures above 700deg (to the right of the dotted line; _vide
infra_), complete transformation to ferrous oxide finally occurs.
In another series of equilibria which can be obtained, carbon is one of the
solid phases. In Fig. 121 the equilibria between carbon, carbon monoxide,
and carbon dioxide under pressures of one and of a quarter atmosphere, are
represented by dotted lines.[379]
If we consider only the dotted line on the right, representing the
equilibria under atmospheric pressure, we see that the points in which the
dotted line cuts the other two curves must represent systems in which
carbon monoxide and carbon dioxide are in equilibrium with FeO +
Fe_{3}O_{4} + C, on the one hand, and with Fe + FeO + C on the other. These
systems can only exist at one definite temperature, if we make the
restriction that the pressure is maintained constant (atmospheric
pressure). Starting, therefore, with the equilibrium FeO + Fe_{3}O_{4} + CO
+ CO_{2} at a temperature of about 670deg, and then add carbon to the
system, the reaction
C + CO_{2} = 2CO
will occur, because the concentration of CO_{2} is greater than what
corresponds with the system FeO + Fe_{3}O_{4} + C in equilibrium with
carbon monoxide and dioxide. In consequence of this reaction, the
equilibrium between FeO + Fe_{3}O_{4} and the gas phase is disturbed, and
the change in the composition of the gas phase is opposed by the reaction
Fe_{3}O_{4} + CO = 3FeO + CO_{2}, which continues until either all the
carbon {309} or all the ferric oxide is used up. If the ferric oxide first
disappears, the equilibrium corresponds with a point on the dotted line in
the middle area of Fig. 121, which represents equilibria between FeO + C as
solid phases, and a mixture of carbon monoxide and dioxide as gas phase. If
the temperature is higher than 685deg, at which temperature the curve for
C--CO--CO_{2} cuts that for Fe--FeO--CO--CO_{2}; then, when all the ferric
oxide has disappeared, the concentration of CO_{2} is still too great for
the coexistence of FeO and C. Consequently, there occurs the reaction C +
CO_{2} = 2CO, and the composition of the gas phase alters until a point on
the upper curve is reached. A further increase in the concentration of CO
is opposed by the reaction FeO + CO = Fe + CO_{2}, and the pressure remains
constant until all the ferrous oxide is reduced and only iron and carbon
remain in equilibrium with gas. If the quantities of the substances have
been rightly chosen, we ultimately reach a point on the dotted curve in the
upper part of Fig. 121.
Fig. 121 shows us, also, what are the conditions under which the reduction
of ferric to ferrous oxide by carbon can occur. Let us suppose, for
example, that we start with a mixture of carbon monoxide and dioxide at
about 600deg (the lowest point on the dotted line), and maintain the total
pressure constant and equal to one atmosphere. If the temperature is
increased, the concentration of the carbon dioxide will diminish, owing to
the reaction C + CO_{2} = 2CO, but the ferric oxide will undergo no change
until the temperature reaches 647deg, the point of intersection of the
dotted curve with the curve for FeO and Fe_{3}O_{4}. At this point further
increase in the concentration of carbon monoxide is opposed by the
reduction of ferric oxide in accordance with the equation Fe_{3}O_{4} + CO
= 3FeO + CO_{2}. The pressure, therefore, remains constant until all the
ferric oxide has disappeared. If the temperature is still further raised,
we again obtain a univariant system, FeO + C, in equilibrium with gas
(univariant because the total pressure is constant); and if the temperature
is raised the composition of the gas must undergo change. This is effected
by the reaction C + CO_{2} = 2CO. When the {310} temperature rises to
685deg, at which the dotted curve cuts the curve for Fe--FeO, further
change is prevented by the reaction FeO + CO = Fe + CO_{2}. When all the
ferrous oxide is used up, we obtain the system Fe + C in equilibrium with
gas. If the temperature is now raised, the composition of the gas undergoes
change, as shown by the dotted line. The two temperatures, 647deg and
685deg, give, evidently, the limits within which ferric or ferrous oxide
can be reduced directly by carbon.
It is further evident that at any temperature to the right of the dotted
line, carbon is unstable in presence of iron or its oxides; while at
temperatures lower than those represented by the dotted line, it is stable.
In the blast furnace, therefore, separation of carbon can occur only at
lower temperatures, and the carbon must disappear on raising the
temperature.
Finally, it may be remarked that the equilibrium curves show that ferrous
oxide is most easily reduced at 680deg, since the concentration of the
carbon monoxide required at this temperature is a minimum. On the other
hand, ferric oxide is reduced with greatest difficulty at 490deg, since at
this temperature the requisite concentration of carbon monoxide is a
maximum.
Other equilibria between solid and gas phases are: Equilibrium between
iron, ferric oxide, water vapour, and hydrogen,[380] and the equilibria
between carbon, carbon monoxide, carbon dioxide, water vapour, and
hydrogen,[381] which is of importance for the manufacture of water gas.
* * * * *
{311}
CHAPTER XVIII
SYSTEMS OF FOUR COMPONENTS
In the systems which have so far been studied, we have met with cases where
two or three components could enter into combination; but in no case did we
find double decomposition occurring. The reason of this is that in the
systems previously studied, in which double decomposition might have been
possible, namely in those systems in which two salts acted as components,
the restriction was imposed that either the basic or the acid constituent
of these salts must be the same; a restriction imposed, indeed, for the
very purpose of excluding double decomposition. Now, however, we shall
allow this restriction to fall, thereby extending the range of study.
Hitherto, in connection with four-component systems, the attention has been
directed solely to the study of aqueous solutions of salts, and more
especially of the salts which occur in sea-water, _i.e._ chiefly, the
sulphates and chlorides of magnesium, potassium, and sodium. The importance
of these investigations will be recognized when one recollects that by the
evaporation of sea-water there have been formed the enormous salt-beds at
Stassfurt, which constitute at present the chief source of the sulphates
and chlorides of magnesium and potassium. The investigations, therefore,
are not only of great geological interest as tending to elucidate the
conditions under which these salt-beds have been formed, but are of no less
importance for the industrial working of the deposits.
It is, however, not the intention to enter here into any detailed
description of the different systems which have so far been studied, and of
the sometimes very complex relationships {312} met with, but merely to
refer briefly to some points of more general import in connection with
these systems.[382]
Reciprocal Salt-Pairs. Choice of Components.--When two salts undergo double
decomposition, the interaction can be expressed by an equation such as
NH_{4}Cl + NaNO_{3} = NaCl + NH_{4}NO_{3}
Since one pair of salts--NaCl + NH_{4}NO_{3}--is formed from the other
pair--NH_{4}Cl + NaNO_{3}--by double decomposition, the two pairs of salts
are known as _reciprocal salt-pairs_.[383] It is with systems in which the
component salts form reciprocal salt-pairs that we have to deal here.
It must be noted, however, that the four salts formed by two reciprocal
salt-pairs do not constitute a system of four, but only of _three_
components. This will be understood if it is recalled that only so many
constituents are taken as components as are necessary to _express_ the
composition of all the phases present (p. 12). It will be seen, now, that
the composition of each of the four salts which can be present together can
be expressed in terms of three of them. Thus, for example, in the case of
NH_{4}Cl, NaNO_{3}, NH_{4}NO_{3}, NaCl, we can express the composition of
NH_{4}Cl by NH_{4}NO_{3} + NaCl - NaNO_{3}; or of NaNO_{3} by NH_{4}NO_{3}
+ NaCl - NH_{4}Cl. In all these cases it will be seen that negative
quantities of one of the components must be employed; but that we have seen
to be quite permissible (p. 12). The number of components is, therefore,
three; but any three of the four salts can be chosen.
Since, then, two reciprocal salt-pairs constitute only three {313}
components or independently variable constituents, another component is
necessary in order to obtain a four-component system. As such, we shall
choose water.
Transition Point.--In the case of the formation of double salts from two
single salts, we saw that there was a point--the _quintuple point_--at
which five phases could coexist. This point we also saw to be a transition
point, on one side of which the double salt, on the other side the two
single salts in contact with solution, were found to be the stable system.
A similar behaviour is found in the case of reciprocal salt-pairs. The
four-component system, two reciprocal salt-pairs and water, can give rise
to an invariant system in which the six phases, four salts, solution,
vapour, can coexist; the temperature at which this is possible constitutes
a _sextuple point_. Now, this sextuple point is also a transition point, on
the one side of which the one salt-pair, on the other side the reciprocal
salt-pair, is stable in contact with solution.
The sextuple point is the point of intersection of the curves of six
univariant systems, viz. four solubility curves with three solid phases
each, a vapour-pressure curve for the system: two reciprocal
salt-pairs--vapour; and a transition curve for the condensed system: two
reciprocal salt-pairs--solution. If we omit the vapour phase and work under
atmospheric pressure (in open vessels), we find that the transition point
is the point of intersection of four solubility curves.
Just as in the case of three-component systems we saw that the presence of
one of the single salts along with the double salt was necessary in order
to give a univariant system, so in the four-component systems the presence
of a third salt is necessary as solid phase along with one of the
salt-pairs. In the case of the reciprocal salt-pairs mentioned above, the
transition point would be the point of intersection of the solubility
curves of the systems with the following groups of salts as solid phases:
Below the transition point: NH_{4}Cl + NaNO_{3} + NaCl; NH_{4}Cl + NaNO_{3}
+ NH_{4}NO_{3}; above the transition point: NaCl + NH_{4}NO_{3} + NaNO_{3};
NaCl + NH_{4}NO_{3} + NH_{4}Cl. From this we see that the two salts
NH_{4}Cl and NaNO_{3} would be able to exist together with solution below
the transition point, but not above it. This transition point has not been
determined. {314}
Formation of Double Salts.--In all cases of four-component systems so far
studied, the transition points have not been points at which one salt-pair
passed into its reciprocal, but at which a double salt was formed. Thus, at
4.4deg Glauber's salt and potassium chloride form glaserite and sodium
chloride, according to the equation
2Na_{2}SO_{4},10H_{2}O + 3KCl = K_{3}Na(SO_{4})_{2} + 3NaCl + 20H_{2}O
Above the transition point, therefore, there would be K_{3}Na(SO_{4})_{2},
NaCl and KCl; and it may be considered that at a higher temperature the
double salt would interact with the potassium chloride according to the
equation
K_{3}Na(SO_{4})_{2} + KCl = 2K_{2}SO_{4} + NaCl
thus giving the reciprocal of the original salt-pair. This point has,
however, not been experimentally realized.[384]
Transition Interval.--A double salt, we learned (p. 277), when brought in
contact with water at the transition point undergoes partial decomposition
with separation of one of the constituent salts; and only after a certain
range of temperature (transition interval) has been passed, can a pure
saturated solution be obtained. A similar behaviour is also found in the
case of reciprocal salt-pairs. If one of the salt-pairs is brought in
contact with water at the transition point, interaction will occur and one
of the salts of the reciprocal salt-pair will be deposited; and this will
be the case throughout a certain range of temperature, after which it will
be possible to prepare a solution saturated only for the one salt-pair. In
the case of ammonium chloride and sodium nitrate the lower limit of the
transition interval is 5.5deg, so that above this temperature and up to
that of the transition point (unknown), ammonium chloride and sodium
nitrate in contact with water would give rise to a third salt by double
decomposition, in this case to sodium chloride.[385]
{315}
Graphic Representation.--For the graphic representation of systems of four
components, four axes may be chosen intersecting at a point like the edges
of a regular octahedron (Fig. 122).[386] Along these different axes the
equivalent molecular amounts of the different salts are measured.
[Illustration: FIG. 122.]
[Illustration: FIG. 123.]
To represent a given system consisting of _x_B, _y_C, and _z_D in a given
amount of water (where B, C, and D represent equivalent molecular amounts
of the salts), measure off on OB and OC lengths equal to _x_ and _y_
respectively. The point of intersection _a_ (Fig. 122) represents a
solution containing _x_B and _y_C (_ab_ = _x_; _ac_ = _y_). From _a_ a line
_a_P is drawn parallel to OD and equal to _z_. P then represents the
solution of the above composition.
It is usual, however, not to employ the three-dimensional figure, but its
horizontal and vertical projections. Fig. 122, if projected on the base of
the octahedron, would yield a diagram such as is shown in Fig. 123. The
projection of the edges of the octahedron form two axes at right angles and
give rise to four quadrants similar to those employed for the
representation of ternary solutions (p. 273). Here, the point _a_
represents a ternary solution saturated with respect to B and C; and _a_P,
quaternary solutions in equilibrium with the same two salts as solid
phases. Such a diagram represents the conditions of equilibrium only for
one definite temperature, and corresponds, therefore, to the isothermal
diagrams for ternary systems (p. 273). In such a diagram, since the
temperature and {316} pressure are constant (vessels open to the air), a
surface will represent a solution in equilibrium with only one solid phase;
a line, a solution with two solid phases, and a point, one in equilibrium
with three solid phases.
[Illustration: FIG. 124.]
Example.--As an example of the complete isothermal diagram, there may be
given one representing the equilibria in the system composed of water and
the reciprocal salt-pair sodium sulphate--potassium chloride for the
temperature 0deg (Fig. 124).[387] The amounts of the different salts are
measured along the four axes, and the composition of the solution is {317}
expressed in equivalent gram-molecules per 1000 gram-molecules of
water.[388]
The outline of this figure represents four ternary solutions in which the
component salts have a common acid or basic constituent; viz. sodium
chloride--sodium sulphate, sodium sulphate--potassium sulphate, potassium
sulphate--potassium chloride, potassium chloride--sodium chloride. These
four sets of curves are therefore similar to those discussed in the
previous chapter. In the case of sodium and potassium sulphate, a double
salt, _glaserite_ [K_{3}Na(SO_{4})_{2}] is formed. Whether glaserite is
really a definite compound or not is still a matter of doubt, since
isomorphic mixtures of Na_{2}SO_{4} and K_{2}SO_{4} have been obtained.
According to van't Hoff and Barscholl,[389] glaserite is an isomorphous
mixture; but Gossner[390] considers it to be a definite compound having the
formula K_{3}Na(SO_{4})_{2}. Points VIII. and IX. represent solutions
saturated with respect to glaserite and sodium sulphate, and glaserite and
potassium sulphate respectively.
The lines which pass inwards from these boundary curves represent solutions
containing three salts, but in contact with only two solid phases; and the
points where three lines meet, or where three fields meet, represent
solutions in equilibrium with three solid phases; with the phases, namely,
belonging to the three concurrent fields.
If it is desired to represent a solution containing the salts say in the
proportions, 51Na_{2}Cl_{2}, 9.5K_{2}Cl_{2}, 3.5K_{2}SO_{4}, the difficulty
is met with that two of the salts, sodium chloride and potassium sulphate,
lie on opposite axes. To overcome this difficulty the difference 51 - 3.5 =
47.5 is taken and measured off along the sodium chloride axis; and the
solution is therefore represented by the point 47.5Na_{2}Cl_{2},
9.5K_{2}Cl_{2}. In order, therefore, to find the amount of potassium
sulphate present {318} from such a diagram, it is necessary to know the
total number of salt molecules in the solution. When this is known, it is
only necessary to subtract from it the sum of the molecules of sodium and
potassium chloride, and the result is equal to twice the number of
potassium sulphate molecules. Thus, in the above example, the total number
of salt molecules is 64. The number of molecules of sodium and potassium
chloride is 57; 64 - 57 = 7, and therefore the number of potassium sulphate
molecules is 3.5.
Another method of representation employed is to indicate the amounts of
only two of the salts in a plane diagram, and to measure off the total
number of molecules along a vertical axis. In this way a solid model is
obtained.
The numerical data from which Fig. 124 was constructed are contained in the
following table, which gives the composition of the different solutions at
0deg:--[391]
----------------------------------------
| |
| |
Point. | Solid phases. |
| |
----------------------------------------
I. | NaCl |
| |
II. | KCl |
| |
III. | Na_{2}SO_{4},10H_{2}O |
| |
IV. | K_{2}SO_{4} |
| |
V. | NaCl; KCl |
| |
VI. | NaCl; Na_{2}SO_{4},10H_{2}O |
| |
VII. | KCl; K_{2}SO_{4} |
| |
VIII. |{ Glaserite; }|
|{ Na_{2}SO_{4},10H_{2}O }|
| |
IX. | Glaserite; K_{2}SO_{4} |
| |
X. |{ Na_{2}SO_{4},10H_{2}O; KCl; }|
|{ NaCl }|
| |
XI. |{ Na_{2}SO_{4},10H_{2}O; KCl; }|
|{ glaserite }|
| |
XII. | K_{2}SO_{4}; KCl; glaserite |
----------------------------------------
[Transcriber's note: table continued below...]
-------------------------------------------------------------------------
Composition of solution in gram-mols. | Total
per 1000 gram-mols. water. | number
-------------------------------------------------------------| of salt
Na_{2}Cl_{2}. | K_{2}Cl_{2}. | Na_{2}SO_{4}. | K_{2}SO_{4}. | molecules.
-------------------------------------------------------------------------
55 | -- | -- | -- | 55
| | | |
-- | 34.5 | -- | -- | 34.5
| | | |
-- | -- | 6 | -- | 6
| | | |
-- | -- | -- | 9 | 9
| | | |
46.5 | 12.5 | -- | -- | 59
| | | |
47.5 | -- | 8 | -- | 55.5
| | | |
-- | 34.5 | -- | 1 | 35.5
| | | |
-- | -- | 10 | 10 | 20
| | | |
| | | |
-- | -- | 7.5 | 10 | 17.5
| | | |
51 | 9.5 | -- | 3.5 | 64
| | | |
| | | |
40.5 | 13 | -- | 3.5 | 57
| | | |
| | | |
18 | 23 | -- | 3 | 44
-------------------------------------------------------------------------
From the aspect of these diagrams the conditions under which the salts can
coexist can be read at a glance. Thus, {319} for example, Fig. 124 shows
that at 0deg Glauber's salt and potassium chloride can exist together with
solution; namely, in contact with solutions having the composition X--XI.
This temperature must therefore be below the transition point of this
salt-pair (p. 314). On raising the temperature to 4.4deg, it is found that
the curve VIII.--XI. moves so that the point XI. coincides with point X. At
this point, therefore, there will be _four_ concurrent fields, viz.
Glauber's salt, potassium chloride, glaserite, and sodium chloride. But
these four salts can coexist with solution only at the transition point; so
that 4.4deg is the transition temperature of the salt-pair: Glauber's
salt--potassium chloride. At higher temperatures the line VIII.--XI. moves
still further to the left, so that the field for Glauber's salt becomes
entirely separated from the field for potassium chloride. This shows that
at temperatures above the transition point the salt-pair Glauber's
salt--potassium chloride cannot coexist in presence of solution.
[Illustration: FIG. 125.]
If it is only desired to indicate the mutual relationships of the different
components and the conditions for their coexistence (_paragenesis_), a
simpler diagram than Fig. 124 can be employed. Thus if the boundary curves
of Fig. 124 are so drawn that they cut one another at right angles, a
figure such as Fig. 125 is obtained, the Roman numerals here corresponding
with those in Fig. 124.
Ammonia-Soda Process.--One of the most important applications of the Phase
Rule to systems of four components with reciprocal salt-pairs has recently
been made by Fedotieff[392] in his investigations of the conditions for the
formation of sodium carbonate by the so-called ammonia-soda (Solvay) {320}
process.[393] This process consists, as is well known, in passing carbon
dioxide through a solution of common salt saturated with ammonia.
Whatever differences of detail there may be in the process as carried out
in different manufactories, the reaction which forms the basis of the
process is that represented by the equation
NaCl + NH_{4}HCO_{3} = NaHCO_{3} + NH_{4}Cl
We are dealing here, therefore, with reciprocal salt-pairs, the behaviour
of which has just been discussed in the preceding pages. The present case
is, however, simpler than that of the salt-pair Na_{2}SO_{4}.10H_{2}O +
KCl, inasmuch as under the conditions of experiment neither hydrates nor
double salts are formed. Since the study of the reaction is rendered more
difficult on account of the fact that ammonium bicarbonate in solution,
when under atmospheric pressure, undergoes decomposition at temperatures
above 15deg, this temperature was the one chosen for the detailed
investigation of the conditions of equilibrium. Since, further, it has been
shown by Bodlaender[394] that the bicarbonates possess a definite
solubility only when the pressure of carbon dioxide in the solution has a
definite value, the measurements were carried out in solutions saturated
with this gas. This, however, does not constitute another component,
because we have made the restriction that the sum of the partial pressures
of carbon dioxide and water vapour is equal to 1 atmosphere. The
concentration of the carbon dioxide is, therefore, not independently
variable (p. 10).
[Illustration: FIG. 126.]
In order to obtain the data necessary for a discussion of the conditions of
soda formation by the ammonia-soda process, solubility determinations with
the four salts, NaCl, NH_{4}Cl, NH_{4}HCO_{3}, and NaHCO_{3} were made,
first with the single salts and then {321} with the salts in pairs. The
results obtained are represented graphically in Fig. 126, which is an
isothermal diagram similar to that given by Fig. 124. The points I., II.,
III., IV., represent the composition of solutions in equilibrium with two
solid salts. We have, however, seen (p. 314) that the transition point,
when the experiment is carried out under constant pressure (atmospheric
pressure), is the point of intersection of four solubility curves, each of
which represents the composition of solutions in equilibrium with three
salts, viz. one of the reciprocal salt-pairs along with a third salt.
Since, now, it was found that the stable salt-pair at temperatures between
0deg and 30deg is sodium bicarbonate and ammonium chloride, determinations
were made of the composition of solutions in equilibrium with NaHCO_{3} +
NH_{4}Cl + NH_{4}HCO_{3} and with NaHCO_{3} + NH_{4}Cl + NaCl as solid
phases. Under the {322} conditions of experiment (temperature = 15deg)
sodium chloride and ammonium bicarbonate cannot coexist in contact with
solution. These determinations gave the data necessary for the construction
of the complete isothermal diagram (Fig. 127). The most important of these
data are given in the following table (temperature, 15deg):--
-------------------------------------------------------------------------
| | Composition of the solution in gram-molecules
| | to 1000 gram-molecules
Point. | Solid phases. | of water.
| |----------------------------------------------
| | NaHCO_{3} | NaCl | NH_{4}HCO_{3} | NH_{4}Cl
-------------------------------------------------------------------------
-- | NaHCO_{3} | 1.08 | -- | -- | --
-- | NaCl | -- | 6.12 | -- | --
-- | NH_{4}HCO_{3} | -- | -- | 2.36 | --
-- | NH_{4}Cl | -- | -- | -- | 6.64
I. | NaHCO_{3}; NaCl | 0.12 | 6.06 | -- | --
II. | NaCl; NH_{4}Cl | -- | 4.55 | -- | 3.72
III. | NH_{4}Cl; | -- | -- | 0.81 | 6.40
| NH_{4}HCO_{3} | | | |
IV. | NaHCO_{3}; | 0.71 | -- | 2.16 | --
| NH_{4}HCO_{3} | | | |
P_{1} | NaHCO_{3}; | 0.93 | 0.51 | -- | 6.28
| NH_{4}HCO_{3}; | | | |
| NH_{4}Cl | | | |
P_{2} | NaHCO_{3}; | 0.18 | 4.44 | -- | 3.73
| NaCl; NH_{4}Cl | | | |
-------------------------------------------------------------------------
With reference to the solution represented by the point P_{1}, it may be
remarked that it is an incongruently saturated solution (p. 279). If sodium
chloride is added to this solution, the composition of the latter undergoes
change; and if a sufficient amount of the salt is added, the solution P_{2}
is obtained.
Turning now to the practical application of the data so obtained, consider
first what is the influence of concentration on the yield of soda. Since
the reaction consists essentially in a double decomposition between sodium
chloride and ammonium bicarbonate, then, after the deposition of the sodium
bicarbonate, we obtain a solution containing sodium chloride, ammonium
chloride, and sodium bicarbonate. In order to ascertain to what extent the
sodium chloride has been converted into solid sodium bicarbonate, it is
necessary to examine the composition of the solution which is obtained
{323} with definite amounts of sodium chloride and ammonium bicarbonate.
[Illustration: FIG. 127.]
Consider, in the first place, the solutions represented by the curve
P_{2}P_{1}. With the help of this curve we can state the conditions under
which a solution, saturated for ammonium chloride, is obtained, after
deposition of sodium bicarbonate. In the following table the composition of
the solutions is given which are obtained with different initial amounts of
sodium chloride and ammonium bicarbonate. The last two columns give the
percentage amount of the sodium used, which is deposited as solid sodium
bicarbonate (U_{Na}); and likewise the percentage amount of ammonium
bicarbonate which is usefully converted into sodium bicarbonate, that is to
say, the amount of the radical HCO_{3} deposited (U_{NH_{4}}):-- {324}
------+---------------------+
|Initial composition |
|of the solutions: |
|grams of salt to 1000|
Point.|grams of water. |
+------+--------------+
| NaCl | NH_{4}HCO_{3}|
------+------+--------------+
P_{2} | 479 | 295 |
-- | 448 | 360 |
-- | 417 | 431 |
P_{1} | 397 | 496 |
------+------+--------------+
[Transcriber's note: table continued below...]
+----------------------------------+---------+----------
| | |
|Composition of solutions obtained:| |
|gram-equivalents per 1000 grams |U_{Na} |U_{NH_{4}}
|of water. |per cent.|per cent.
+----------+------+------+---------+ |
| HCO_{3} | Cl | Na | NH_{4} | |
+----------+------+------+---------+---------+----------
| 0.18 | 8.17 | 4.62 | 3.73 | 43.4 | 95.1
| 0.31 | 7.65 | 3.39 | 4.56 | 55.7 | 93.4
| 0.51 | 7.13 | 2.19 | 5.45 | 69.2 | 90.5
| 0.92 | 6.79 | 1.44 | 6.28 | 78.8 | 85.1
+----------+------+------+---------+---------+----------
This table shows that the greater the excess of sodium chloride, the
greater is the percentage utilization of ammonia (Point P_{2}); and the
more the amount of sodium chloride decreases, the greater is the percentage
amount of sodium chloride converted into bicarbonate. In the latter case,
however, the percentage utilization of the ammonium bicarbonate decreases;
that is to say, less sodium bicarbonate is deposited, or more of it remains
in solution.
Consider, in the same manner, the relations for solutions represented by
the curve P_{2}IV, which gives the composition of solutions saturated with
respect to sodium bicarbonate and ammonium bicarbonate. In this case we
obtain the following results:--
------+---------------------+
|Initial composition |
|of the solutions: |
|grams of salt to 1000|
Point.|grams of water. |
+------+--------------+
| NaCl | NH_{4}HCO_{3}|
------+------+--------------+
P_{1} | 397 | 496 |
-- | 351 | 446 |
-- | 316 | 412 |
-- | 294 | 389 |
-- | 234 | 327 |
------+------+--------------+
[Transcriber's note: table continued below...]
+----------------------------------+------+----------
| | |
|Composition of solutions obtained:| |
|in gram-equivalents per 1000 grams|U_{Na}|U_{NH_{4}}
|of water. | |
+----------+------+------+---------+ |
| HCO_{3} | Cl | Na | NH_{4} | |
+----------+------+------+---------+------+----------
| 0.92 | 6.79 | 1.44 | 6.28 | 78.8 | 85.1
| 0.99 | 6.00 | 1.34 | 5.65 | 77.7 | 82.5
| 1.07 | 5.41 | 1.27 | 5.21 | 76.4 | 79.5
| 1.12 | 5.03 | 1.23 | 4.92 | 75.5 | 75.1
| 1.30 | 4.00 | 1.16 | 4.14 | 71.0 | 68.6
+----------+------+------+---------+------+----------
As is evident from this table, diminution in the relative amount of sodium
chloride exercises only a slight influence {325} on the utilization of this
salt, but is accompanied by a rapid diminution of the effective
transformation of the ammonium bicarbonate. So far as the efficient
conversion of the sodium is concerned, we see that it reaches its maximum
at the point P_{1}, and that it decreases both with increase and with
decrease of the relative amount of sodium chloride employed; and faster,
indeed, in the former than in the latter case. On the other hand, the
effective transformation of the ammonium bicarbonate reaches its maximum at
the point P_{2}, and diminishes with increase in the relative amount of
ammonium bicarbonate employed. Since sodium chloride is, in comparison with
ammonia--even when this is regenerated--a cheap material, it is evidently
more advantageous to work with solutions which are relatively rich in
sodium chloride (solutions represented by the curve P_{1}P_{2}). This fact
has also been established empirically.
When, as is the case in industrial practice, we are dealing with solutions
which are saturated not for two salts but only for sodium bicarbonate, it
is evident that we have then to do with solutions the composition of which
is represented by points in the area P_{1}P_{2}I,IV. Since in the
commercial manufacture, the aim must be to obtain as complete a utilization
of the materials as possible, the solutions employed industrially must lie
in the neighbourhood of the curves P_{2}P_{1}IV, as is indicated by the
shaded portion in Fig. 127. The best results, from the manufacturer's
standpoint, will be obtained, as already stated, when the composition of
the solutions approaches that given by a point on the curve P_{2}P_{1}.
Considered from the chemical standpoint, the results of the experiments
lead to the conclusion that the Solvay process, _i.e._ passage of carbon
dioxide through a solution of sodium chloride saturated with ammonia, is
not so good as the newer method of Schloesing, which consists in bringing
together sodium chloride and ammonium bicarbonate with water.[395]
{326}
Preparation of Barium Nitrite.--Mention may also be made here of the
preparation of barium nitrite by double decomposition of barium chloride
and sodium nitrite.[396]
The reaction with which we are dealing here is represented by the equation
BaCl_{2} + 2NaNO_{2} = 2NaCl + Ba(NO_{2})_{2}
It was found that at the ordinary temperature NaCl and Ba(NO_{2})_{2} form
the stable salt-pair. If, therefore, barium chloride and sodium nitrite are
brought together with an amount of water insufficient for complete
solution, transformation to the stable salt-pair occurs, and sodium
chloride and barium nitrite are deposited. When, however, a stable
salt-pair is in its transition interval (p. 315), a third salt--in this
case barium chloride--will be deposited, as we have already learned. On
bringing barium chloride and sodium nitrite together with water, therefore,
three solid phases are obtained, viz. BaCl_{2}, NaCl, Ba(NO_{2})_{2}. These
three phases, together with solution and vapour, constitute a univariant
system, so that at each temperature the composition of the solution must be
constant.
Witt and Ludwig found that the presence of solid barium chloride can be
prevented by adding an excess of sodium nitrite, as can be readily foreseen
from what has been said. Since the solution in presence of the three solid
phases must have a definite composition at a definite temperature, the
addition of sodium nitrite to the solution must have, as its consequence,
the solution of an equivalent amount of barium chloride, and the deposition
of an equivalent amount of sodium chloride and barium nitrite. By
sufficient addition of sodium nitrite, the complete disappearance of the
solid barium chloride can be effected, and there will remain only the
stable salt-pair sodium chloride and barium nitrite. As was pointed out by
Meyerhoffer, however, the disappearance of the barium chloride is effected,
not by a change in the {327} composition of the solution, but by the
necessity for the composition of the solution remaining constant.
[Illustration: FIG. 128.]
Barium Carbonate and Potassium Sulphate.--As has been found by
Meyerhoffer,[397] these two salts form the stable pair, not only at the
ordinary temperature, but also at the melting point. For the ordinary
temperatures this was proved in the following manner: A solution with the
solid phases K_{2}SO_{4} and K_{2}CO_{3}.2H_{2}O in excess can only coexist
in contact either with BaCO_{3} or with BaSO_{4}, since, evidently, in one
of the two groups the stable system must be present. Two solutions were
prepared, each with excess of K_{2}SO_{4} + K_{2}CO_{3}.2H_{2}O, {328} and
to one was added BaCO_{3} and to the other BaSO_{4}. After stirring for a
few days, the barium sulphate was completely transformed to BaCO_{3},
whereas the barium carbonate remained unchanged. Consequently, BaCO_{3} +
K_{2}SO_{4} + K_{2}CO_{3}.2H_{2}O is stable, and, therefore, so also is
BaCO_{3} + K_{2}SO_{4}. That BaCO_{3} + K_{2}SO_{4} is the stable pair also
at the melting point was proved by a special analytical method which allows
of the detection of K_{2}CO_{3} in a mixture of the four solid salts. This
analysis showed that a mixture of BaCO_{3} + K_{2}SO_{4}, after being fused
and allowed to solidify, contains only small amounts of K_{2}CO_{3}; and
this is due entirely to the fact that BaCO_{3} + K_{2}SO_{4} on fusion
deposits a little BaSO_{4}, thereby giving rise at the same time to the
separation of an equivalent amount of K_{2}CO_{3}.
The different solubilities are shown in Fig. 128. In this diagram the
solubility of the two barium salts has been neglected. A is the solubility
of K_{2}CO_{3}.2H_{2}O; addition of BaCO_{3} does not alter this. B is the
solubility of K_{2}CO_{3}.2H_{2}O + K_{2}SO_{4} + BaCO_{3}. A and B almost
coincide, since the potassium sulphate is very slightly soluble in the
concentrated solution of potassium carbonate. D gives the concentration of
the solution in equilibrium with K_{2}SO_{4} + BaSO_{4}. The most
interesting point is C. This solution is obtained by adding a small
quantity of water to BaCO_{3} + K_{2}SO_{4}, whereupon, being in the
transition interval, BaSO_{4} separates out and an equivalent amount of
K_{2}CO_{3} goes into solution. C is the end point of the curve CO, which
is called the Guldberg-Waage curve, because these investigators determined
several points on it.
In their experiments, Guldberg and Waage found the ratio K_{2}CO_{3} :
K_{2}SO_{4} in solution to be constant and equal to 4. This result is,
however, not exact, for the curve CO is not a straight line, as it should
be if the above ratio were constant; but it is concave to the abscissa
axis, and more so at lower than at higher temperatures.
The following table refers to the temperature of 25deg. The Roman numbers
in the first column refer to the points in Fig. 128. The numbers in the
column [Sigma]_k__{2} give the amount, {329} in gram-molecules, of
K_{2}CO_{3} + K_{2}SO_{4} contained in 1000 gram-molecules of water:--
SOLUBILITY DETERMINATIONS AT 25deg.
-----+-------------------------------------+-----------------------+
| | 100 gms. of the |
| | solution contain, |
No. | Solid phases. | in grams, |
| | | |
| |K_{2}CO_{3}|K_{2}SO_{4}|
-----+-------------------------------------+-----------+-----------+
I. | K_{2}CO_{3}.2H_{2}O + BaCO_{3} | 53.2 | -- |
| | | |
II. |{ K_{2}CO_{3}.2H_{2}O + K_{2}SO_{4} }| 53.0 | 0.023 |
|{ + BaCO_{3} }| | |
| | | |
III.}| K_{2}SO_{4} + BaCO_{3} | { 28.5 | 0.886 |
IV. }| | { 22.1 | 1.72 |
| | | |
V. | BaCO_{3} + K_{2}SO_{4} + BaSO_{4} | 17.81 | 2.485 |
| | | |
VI. }| K_{2}SO_{4} + BaSO_{4} | { 12.6 | 3.92 |
VII.}| | { 5.85 | 6.76 |
| | | |
VIII.| K_{2}SO_{4} | -- | 10.76 |
| | | |
IX. }| BaCO_{3} + BaSO_{4} | { 7.35 | 0.602 |
X. }| | { 2.85 | 0.173 |
-----+-------------------------------------+-----------+-----------+
[Transcriber's note: table continued below...]
-----+-----------------------+-----------------+-----------
| 1000 moles | |
| of water contain, | | K_{2}CO_{3}
No. | in moles, |[Sigma]_k__{2} | -----------
| | | | K_{2}SO_{4}
|K_{2}CO_{3}|K_{2}SO_{4}| |
-----+-----------+-----------+-----------------+-----------
I. | 147.9 | -- | -- | --
| | | |
II. | 147.8 | 0.051 | -- | --
| | | |
| | | |
III.}| 52.58 | 1.296 | -- | --
IV. }| 37.79 | 2.333 | -- | --
| | | |
V. | 29.11 | 3.220 | 32.32 | 9.03
| | | |
VI. }| 19.66 | 4.853 | -- | --
VII.}| 8.724 | 7.995 | -- | --
| | | |
VIII.| -- | 12.47 | -- | --
| | | |
IX. }| 10.43 | 0.676 | 11.11 | 15.0
X. }| 3.828 | 0.184 | 4.0 | 21.0
-----+-----------+-----------+-----------------+-----------
The Guldberg-Waage curve at 100deg was also determined, and it was found
that the ratio K_{2}CO_{3}: K_{2}SO_{4} is also not constant, although the
variations are not so great as at 25deg.
GULDBERG-WAAGE CURVE AT 100deg.
----------------------+-----------------------+-----------------+-------
|100 moles of water | | K2CO3
Solid phases. |contain, in moles, | [Sigma]_k__{2} | -----
| | | | K2SO4
|K_{2}CO_{3}|K_{2}SO_{4}| |
----------------------+-----------+-----------+-----------------+-------
BaCO_{3} + K_{2}SO_{4}| 23.9 | 12.65 | 35.65 | 1.82
+ BaSO_{4} | | | |
BaCO_{3} + BaSO_{4} | 6.28 | 2.02 | 8.3 | 3.1
" " | 3.17 | 0.851 | 4.025 | 3.7
----------------------+-----------+-----------+-----------------+-------
* * * * *
{330}
APPENDIX
EXPERIMENTAL DETERMINATION OF THE TRANSITION POINT
For the purpose of determining the transition temperature, a number of
methods have been employed, and the most important of these will be briefly
described here. In any given case it is sometimes possible to employ more
than one method, but all are not equally suitable, and the values of the
transition point obtained by the different methods are not always
identical. Indeed, a difference of several degrees in the value found may
quite well occur.[398] In each case, therefore, some care must be taken to
select the method most suitable for the purpose.
I. The Dilatometric Method.--Since, in the majority of cases,
transformation at the transition point is accompanied by an appreciable
change of volume, it is only necessary to ascertain the temperature at
which this change of volume occurs, in order to determine the transition
point. For this purpose the _dilatometer_ is employed, an apparatus which
consists of a bulb with capillary tube attached, and which constitutes a
sort of large thermometer (Fig. 129). Some of the substance to be examined
is passed into the bulb A through the tube B, which is then sealed off. The
rest of the bulb and a small portion of the capillary tube is then filled
with some liquid, which, of course, must be without chemical action on the
substance under investigation. A liquid, however, may be employed which
dissolves the substance, for, as we have seen (p. 70), the transformation
at the transition point is, as a rule, accelerated by the presence of a
solvent. On the other hand, the liquid must not dissolve in the substance
under examination, for the temperature of transformation would be thereby
altered.
{331}
In using the dilatometer, two methods of procedure may be followed.
According to the first method, the dilatometer containing the form stable
at lower temperatures is placed in a thermostat, maintained at a constant
temperature, until it has taken the temperature of the bath. The height of
the meniscus is then read on a millimetre scale attached to the capillary.
The temperature of the thermostat is then raised degree by degree, and the
height of the meniscus at each point ascertained. If, now, no change takes
place in the solid, the expansion will be practically uniform, or the rise
in the level of the meniscus per degree of temperature will be practically
the same at the different temperatures, as represented diagrammatically by
the line AB in Fig. 130. On passing through the transition point, however,
there will be a more or less sudden increase in the rise of the meniscus
per degree (line BC) if the specific volume of the form stable at higher
temperatures is greater than that of the original modification; thereafter,
the expansion will again be uniform (line CD). Similarly, on cooling,
contraction will at first be uniform and then at the transition point there
will be a relatively large diminution of volume.
[Illustration: FIG. 129.]
[Illustration: FIG. 130.]
If, now, transformation occurred immediately the transition point was
reached, the sudden expansion and contraction would take place at the same
temperature. It is, however, generally found that there is a lag, and that
with rising temperature the relatively large expansion does not take place
until a temperature somewhat higher than the transition point; and with
falling temperature the contraction occurs at a temperature somewhat below
the transition point. This is represented in Fig. 130 by the lines BC and
EF. The amount of lag will vary from case to case, and will {332} also
depend on the length of time during which the dilatometer is maintained at
constant temperature.
As an example, there may be given the results obtained in the determination
of the transition point at which sodium sulphate and magnesium sulphate
form astracanite (p. 268).[399] The dilatometer was charged with a mixture
of the two sulphates.
--------------------------------------------------------
Temperature. | Level of oil in capillary. | Rise per 1deg.
--------------------------------------------------------
15.6deg | 134 |
16.6deg | 141 | 7
17.6deg | 148 | 7
18.6deg | 154 | 6
19.6deg | 161 | 7
20.6deg | 168 | 7
21.6deg | 241 | 73
22.6deg | 243 | 2
23.6deg | 251 | 8
24.6deg | 259 | 8
--------------------------------------------------------
The transition point, therefore, lies about 21.6deg (p. 268).
The second method of manipulation depends on the fact that, while above or
below the transition point transformation of one form into the other can
take place, at the transition point the two forms undergo no change. The
bulb of the dilatometer is, therefore, charged with a mixture of the stable
and metastable forms and a suitable liquid, and is then immersed in a bath
at constant temperature. After the temperature of the bath has been
acquired, readings of the height of the meniscus are made from time to time
to ascertain whether expansion or contraction occurs. If expansion is
found, the temperature of the thermostat is altered until a temperature is
obtained at which a gradual contraction takes place. The transition point
must then lie between these two temperatures; and by repeating the
determinations it will be possible to reduce the difference between the
temperatures at which expansion and contraction take place to, say, 1deg,
and to fix the temperature of the transition point, therefore, to within
half a degree. By this method the transition point, for example, of sulphur
was found to be 95.6deg under a pressure of 4 atm.[400] The following are
the figures obtained by Reicher, who used a mixture {333} of 1 part of
carbon disulphide (solvent for sulphur) and 5 parts of turpentine as the
measuring liquid.
TEMPERATURE 95.1deg.
-----------------------------------
Time in minutes. | Level of liquid.
-----------------------------------
5 | 343.5
30 | 340.5
55 | 335.75
65 | 333
-----------------------------------
TEMPERATURE 96.1deg.
-----------------------------------
Time in minutes. | Level of liquid.
-----------------------------------
5 | 342.75
30 | 354.75
55 | 360.5
60 | 361.5
-----------------------------------
TEMPERATURE 95.6deg.
-----------------------------------
Time in minutes. | Level of liquid.
-----------------------------------
5 | 368.75
100 | 368
110 | 368.75
-----------------------------------
At a temperature of 95.1deg there is a contraction, _i.e._ monoclinic
sulphur passes into the rhombic, the specific volume of the former being
greater than that of the latter. At 96.1deg, however, there is expansion,
showing that at this temperature rhombic sulphur passes into monoclinic;
while at 95.6deg there is neither expansion nor contraction. This is,
therefore, the transition temperature; and since the dilatometer was sealed
up to prevent evaporation of the liquid, the pressure within it was 4 atm.
II. Measurement of the Vapour Pressure.--In the preceding pages it has been
seen repeatedly that the vapour pressures of the two systems undergoing
reciprocal transformation become identical at the transition point (more
strictly, at the triple or {334} multiple point), and the latter can
therefore be determined by ascertaining the temperature at which this
identity of vapour pressure is established. The apparatus usually employed
for this purpose is the Bremer-Frowein tensimeter (p. 91).
Although this method has not as yet been applied to systems of one
component, it has been used to a considerable extent in the case of systems
containing water or other volatile component. An example of this has
already been given in Glauber's salt (p. 139).
III. Solubility Measurements.--The temperature of the transition point can
also be fixed by means of solubility measurements, for at that point the
solubility of the two systems becomes identical. Reference has already been
made to several cases in which this method was employed, _e.g._ ammonium
nitrate (p. 112), Glauber's salt (p. 134), astracanite and sodium and
magnesium sulphates (p. 268).
The determinations of the solubility can be carried out in various ways.
One of the simplest methods, which also gives sufficiently accurate results
when the temperature is not high or when the solvent is not very volatile,
can be carried out in the following manner. The solid substance is finely
powdered (in order to accelerate the process of solution), and placed in
sufficient quantity along with the solvent in a tube carefully closed by a
glass stopper; the latter is protected by a rubber cap, such as a rubber
finger-stall. The tube is then rotated in a thermostat, the temperature of
which does not vary more than one or two tenths of a degree, until
saturation is produced. The solution is withdrawn by means of a pipette to
which a small glass tube, filled with cotton wool to act as a filter, is
attached. The solution is then run into a weighing bottle, and weighed;
after which the amount of solid in solution is determined in a suitable
manner.
For more accurate determinations of the solubility, especially when the
solvent is appreciably volatile at the temperature of experiment, other
methods are preferable. In Fig. 131 is shown the apparatus employed by H.
Goldschmidt,[401] and used to a considerable extent in the laboratory of
van't Hoff. This consists essentially of three parts: _a_, a tube in which
the solvent and salt are placed; this is closed at the foot by an
india-rubber stopper. Through this stopper there passes the bent tube _cb_,
which connects the tube _a_ with the weighing-tube d. At _c_ there is a
plug of cotton wool. Tube _e_ is open to the air. The wider portion of the
tube _cb_, which passes through the rubber stopper in _a_, can be closed by
a plug {335} attached to a glass rod _ff_, which passes up through a hollow
Witt stirrer, _g_. After being fitted together, the whole apparatus is
immersed in the thermostat. After the solution has become saturated, the
stopper of the bent tube is raised by means of the rod _ff_ and a
suction-pump attached to the end of e. The solution is thereby drawn into
the weighing-tube _d_, the undissolved salt being retained by the plug at
c. The apparatus is then removed from the thermostat, tube _d_ detached and
immediately closed by a ground stopper. It is then carefully dried and
weighed.
[Illustration: FIG. 131.]
Another form of solubility vessel, due to Meyerhoffer and Saunders, is
shown in Fig. 132.[402] This consists of a single tube, and the stirring is
effected by means of a glass screw.
[Illustration: FIG. 132.]
The progress of the solution towards saturation can be very well tested by
determining the density of the solution from time to {336} time. This is
most conveniently carried out by means of the pipette shown in Fig.
133.[403] With this pipette the solution can not only be removed for
weighing, but the volume can be determined at the same time. It consists of
the wide tube _a_, to which the graduated capillary _b_, furnished with a
cap _c_, is attached. To the lower end of the pipette the tube _e_, with
plug of cotton wool, can be fixed. After the pipette has been filled by
sucking at the end of _b_, the stop-cock _d_ is closed and the cap _c_
placed on the capillary. The apparatus can then be weighed, and the volume
of the solution be ascertained by means of the graduations.
As has already been insisted, particular care must be paid to the
characterization of the solid in contact with the solution.
[Illustration: FIG. 133.]
IV. Thermometric Method.--If a substance is heated, its temperature will
gradually rise until the melting point is reached, and the temperature will
then remain constant until all the solid has passed into liquid. Similarly,
if a substance which can undergo transformation is heated, the temperature
will rise until the transition point is reached, and will then remain
constant until complete transformation has taken place.