The Phase Rule and Its Applications Part 12

[Ill.u.s.tration: FIG. 34.]

The vapour pressure of the different systems of sodium sulphate and water can best be studied with the help of the diagram in Fig. 34.[216] The curve ABCD represents the vapour-pressure curve of the saturated solution of anhydrous sodium sulphate. GC is the pressure curve of decahydrate + anhydrous salt, which, as we have seen, cuts the curve ABCD at the transition temperature, 32.6. Since at this point the solution is saturated with respect to both the anhydrous salt and the decahydrate, the vapour-pressure curve of the saturated solution of the latter must also pa.s.s through the point C.[217] As at temperatures below this point the solubility of the decahydrate is less than that of the anhydrous salt, the vapour pressure of the solution will, in accordance with Babo's law (p. 126), be higher than that of the solution of the anhydrous salt; which was also found experimentally to be the case (curve HC).

{141}

In connection with the vapour pressure of the saturated solutions of the anhydrous salt and the decahydrate, attention must be drawn to a conspicuous deviation from what was found to hold in the case of one-component systems in which a vapour phase was present (p. 31). There, it was seen that the vapour pressure of the more stable system was always _lower_ than that of the less stable; in the present case, however, we find that this is no longer so. We have already learned that at temperatures below 32.5 the system decahydrate--solution--vapour is more stable than the system anhydrous salt--solution--vapour; but the vapour pressure of the latter system is, as has just been stated, lower than that of the former.

At temperatures above the transition point the vapour pressure of the saturated solution of the decahydrate will be lower than that of the saturated solution of the anhydrous salt.

This behaviour depends on the fact that the less stable form is the more soluble, and that the diminution of the vapour pressure increases with the amount of salt dissolved.

With regard to sodium sulphate heptahydrate the same considerations will hold as in the case of the decahydrate. Since at 24 the four phases heptahydrate, anhydrous salt, solution, vapour can coexist, the vapour-pressure curves of the systems hydrate--anhydrous salt--vapour (curve EB) and hydrate--solution--vapour (curve FB) must cut the pressure curve of the saturated solution of the anhydrous salt at the above temperature, as represented in Fig. 34 by the point B. This const.i.tutes, therefore, a second quadruple point, which is, however, metastable.

From the diagram it is also evident that the dissociation pressure of the heptahydrate is higher than that of the decahydrate, although it contains less water of crystallization. The system heptahydrate--anhydrous salt--vapour must be metastable with respect to the system decahydrate--anhydrous salt--vapour, and will pa.s.s into the latter.[218]

Whether or not there is a temperature at which the vapour-pressure curves of the two systems intersect, and below which the heptahydrate becomes the more stable form, is not known.

{142}

In the case of sodium sulphate there is only one stable hydrate. Other salts are known which exhibit a similar behaviour; and we shall therefore expect that the solubility relations.h.i.+ps will be represented by a diagram similar to that for sodium sulphate. A considerable number of such cases have, indeed, been found,[219] and in some cases there is more than one metastable hydrate. This is found, for example, in the case of nickel iodate,[220] the solubility curves for which are given in Fig. 35. As can be seen from the figure, suspended transformation occurs, the solubility curves having in some cases been followed to a considerable distance beyond the transition point. One of the most brilliant examples, however, of suspended transformation in the case of salt hydrates, and the sluggish transition from the less stable to the more stable form, is found in the case of the hydrates of calcium chromate.[221]

[Ill.u.s.tration: FIG. 35.]

In the preceding cases, the dissociation-pressure curve of the hydrated salt cuts the vapour-pressure curve of the saturated {143} solution of the anhydrous salt. It can, however, happen that the dissociation-pressure curve of one hydrate cuts the solubility curve, not of the anhydrous salt, but of a lower hydrate; in this case there will be more than one stable hydrate, each having a stable solubility curve; and these curves will intersect at the temperature of the transition point. Various examples of this behaviour are known, and we choose for ill.u.s.tration the solubility relations.h.i.+ps of barium acetate and its hydrates[222] (Fig. 36).

[Ill.u.s.tration: FIG. 36.]

At temperatures above 0, barium acetate can form two stable hydrates, a trihydrate and a monohydrate. The solubility of the trihydrate increases very rapidly with rise of temperature, and has been determined up to 26.1.

At temperatures above 24.7, however, the trihydrate is metastable with respect to the monohydrate; for at this temperature the solubility curve of the latter hydrate cuts that of the former. This is, therefore, the transition temperature for the trihydrate and monohydrate. The solubility curve of the monohydrate succeeds that of the trihydrate, and exhibits a conspicuous point of minimum solubility at about 30. Below 24.7 the {144} monohydrate is the less stable hydrate, but its solubility has been determined to a temperature of 22. At 41 the solubility curve of the monohydrate intersects that of the anhydrous salt, and this is therefore the transition temperature for the monohydrate and anhydrous salt. Above this temperature the anhydrous salt is the stable solid phase. Its solubility curve also pa.s.ses through a minimum.

The diagram of solubilities of barium acetate not only ill.u.s.trates the way in which the solubility curves of the different stable hydrates of a salt succeed one another, but it has also an interest and importance from another point of view. In Fig. 36 there is also shown a faintly drawn curve which is continuous throughout its whole course. This curve represents the solubility of barium acetate as determined by Krasnicki.[223] Since, however, three different solid phases can exist under the conditions of experiment, it is evident, from what has already been stated (p. 111), that the different equilibria between barium acetate and water could not be represented by one _continuous_ curve.

Another point which these experiments ill.u.s.trate and which it is of the highest importance to bear in mind is, that in making determinations of the solubility of salts which are capable of forming hydrates, it is not only necessary to determine the composition of the solution, but _it is of equal importance to determine the composition of the solid phase in contact with it_. In view of the fact, also, that the solution equilibrium is in many cases established with comparative slowness, it is necessary to confirm the point of equilibrium, either by approaching it from higher as well as from lower temperatures, or by actually determining the rate with which the condition of equilibrium is attained. This can be accomplished by actual weighing of the dissolved salt or by determinations of the density of the solution, as well as by other methods.

{145}

2. _The Compounds formed have a Definite Melting Point._

In the cases which have just been considered we saw that the salt hydrates on being heated did not undergo complete fusion, but that a solid was deposited consisting of a lower hydrate or of the anhydrous salt. It has, however, been long known that certain crystalline salt hydrates (_e.g._ sodium thiosulphate, Na_{2}S_{2}O_{3},5H_{2}O, sodium acetate, NaC_{2}H_{3}O_{2},3H_{2}O) melt completely in their water of crystallization, and yield a liquid of the _same composition_ as the crystalline salt. In the case of sodium thiosulphate pentahydrate the temperature of liquefaction is 56; in the case of sodium acetate trihydrate, 58. These two salts, therefore, have a definite melting point.

For the purpose of studying the behaviour of such salt hydrates, we shall choose not the cases which have just been mentioned, but two others which have been more fully studied, viz. the hydrates of calcium chloride and of ferric chloride.

Solubility Curve of Calcium Chloride Hexahydrate.[224]--Although calcium chloride forms several hydrates, each of which possesses its own solubility, it is nevertheless the solubility curve of the hexahydrate which will chiefly interest us at present, and we shall therefore first discuss that curve by itself.

[Ill.u.s.tration: FIG. 37.]

The solubility of this salt has been determined from the cryohydric point, which lies at about -55, up to the melting point of the salt.[225] The solubility increases with rise of temperature, as is shown by the figures in the following table, and by the (diagrammatic) curve AB in Fig. 37. In the table, the numbers under the heading "solubility" denote the number of grams of CaCl_{2} dissolved in 100 grams {146} of water; those under the heading "composition," the number of gram-molecules of water in the solution to one gram-molecule of CaCl_{2}.

SOLUBILITY OF CALCIUM CHLORIDE HEXAHYDRATE.

----------------------------------------- Temperature. Solubility. Composition.

----------------------------------------- -55 42.5 14.5 -25 50.0 12.3 -10 55.0 11.2 0 59.5 10.37 10 65.0 9.49 20 74.5 8.28 25 82.0 7.52 28.5 90.5 6.81 29.5 95.5 6.46 30.2 102.7 6.00 29.6 109.0 5.70 29.2 112.8 5.41 -----------------------------------------

So far as the first portion of the curve is concerned, it resembles the most general type of solubility curve. In the present case the solubility is so great and increases so rapidly with rise of temperature, that a point is reached at which the water of crystallization of the salt is sufficient for its complete solution. This temperature is 30.2; and since the composition of the solution is the same as that of the solid salt, viz. 1 mol. of CaCl_{2} to 6 mols. of water, this temperature must be the melting point of the hexahydrate. At this point the hydrate will fuse or the solution will solidify without change of temperature and without change of composition. Such a melting point is called a _congruent_ melting point.

But the solubility curve of calcium chloride hexahydrate differs markedly from the other solubility curves. .h.i.therto considered in that it possesses a _retroflex portion_, represented in the figure by BC. As is evident from the figure, therefore, calcium chloride hexahydrate exhibits the peculiar and, as it was at first thought, impossible behaviour that it can be in equilibrium at one and the same temperature with two different solutions, one of which contains more, the other less, water than the solid hydrate; for it must be remembered that {147} throughout the whole course of the curve ABC the solid phase present in equilibrium with the solution is the hexahydrate.

Such a behaviour, however, on the part of calcium chloride hexahydrate will appear less strange if one reflects that the melting point of the hydrate will, like the melting point of other substances, be lowered by the addition of a second substance. If, therefore, water is added to the hydrate at its melting point, the temperature at which the solid hydrate will be in equilibrium with the liquid phase (solution) will be lowered; or if, on the other hand, anhydrous calcium chloride is added to the hydrate at its melting point (or what is the same thing, if water is removed from the solution), the temperature at which the hydrate will be in equilibrium with the liquid will also be lowered; _i.e._ the hydrate will melt at a lower temperature. In the former case we have the hydrate in equilibrium with a solution containing more water, in the latter case with a solution containing less water than is contained in the hydrate itself.

It has already been stated (p. 109) that the solubility curve (in general, the equilibrium curve) is continuous so long as the solid phase remains unchanged; and we shall therefore expect that the curve ABC will be continuous. Formerly, however, it was considered by some that the curve was not continuous, but that the melting point is the point of intersection of two curves, a solubility curve and a fusion curve. Although the earlier solubility determinations were insufficient to decide this point conclusively, more recent investigation has proved beyond doubt that the curve is continuous and exhibits no break.[226]

{148}

Although in taking up the discussion of the equilibria between calcium chloride and water, it was desired especially to call attention to the form of the solubility curve in the case of salt hydrates possessing a definite melting point, nevertheless, for the sake of completeness, brief mention may be made of the other systems which these two components can form.

[Ill.u.s.tration: FIG. 38.]

Besides the hexahydrate, the solubility curve of which has already been described, calcium chloride can also crystallize in two different forms, each of which contains four molecules {149} of water of crystallization; these are distinguished as [alpha]-tetrahydrate, and [beta]-tetrahydrate.

Two other hydrates are also known, viz. a dihydrate and a monohydrate. The solubility curves of these different hydrates are given in Fig. 38.

On following the solubility curve of the hexahydrate from the ordinary temperature upwards, it is seen that at a temperature of 29.8 represented by the point H, it cuts the solubility curve of the [alpha]-tetrahydrate.

This point is therefore a quadruple point at which the four phases hexahydrate, [alpha]-tetrahydrate, solution, and vapour can coexist. It is also the transition point for these two hydrates. Since, at temperatures above 29.8, the [alpha]-tetrahydrate is the stable form, it is evident from the data given before (p. 146), as also from Fig. 38, that the portion of the solubility curve of the hexahydrate lying above this temperature represents _metastable_ equilibria. The realization of the metastable melting point of the hexahydrate is, therefore, due to suspended transformation. At the transition point, 29.8, the solubility of the hexahydrate and [alpha]-tetrahydrate is 100.6 parts of CaCl_{2} in 100 parts of water.

The retroflex portion of the solubility curve of the hexahydrate extends to only 1 below the melting point of the hydrate. At 29.2 crystals of a new hydrate, [beta]-tetrahydrate, separate out, and the solution, which now contains 112.8 parts of CaCl_{2} to 100 parts of water, is saturated with respect to the two hydrates. Throughout its whole extent the solubility curve EDF of the [beta]-tetrahydrate represents metastable equilibria. The upper limit of the solubility curve of [beta]-tetrahydrate is reached at 38.4 (F), the point of intersection with the curve for the dihydrate.

Above 29.8 the stable hydrate is the [alpha]-tetrahydrate; and its solubility curve extends to 45.3 (K), at which temperature it cuts the solubility curve of the dihydrate. The curve of the latter hydrate extends to 175.5 (L), and is then succeeded by the curve for the monohydrate. The solubility curve of the anhydrous salt does not begin until a temperature of about 260. The whole diagram, therefore, shows a succession of stable hydrates, a metastable hydrate, a metastable melting point and retroflex solubility curve. {150}

Pressure-Temperature Diagram.--The complete study of the equilibria between the two components calcium chloride and water would require the discussion of the vapour pressure of the different systems, and its variation with the temperature. For our present purpose, however, such a discussion would not be of great value, and will therefore be omitted here; in general, the same relations.h.i.+ps would be found as in the case of sodium sulphate (p. 138), except that the rounded portion of the solubility curve of the hexahydrate would be represented by a similar rounded portion in the pressure curve.[227] As in the case of sodium sulphate, the transition points of the different hydrates would be indicated by breaks in the curve of pressures.

Finally, mention may again be made of the difference of the pressure of dissociation of the hexahydrate according as it becomes dehydrated to the [alpha]- or the [beta]-tetrahydrate (p. 88).

The Indifferent Point.--We have already seen that at 30.2 calcium chloride hexahydrate melts congruently, and that, provided the pressure is maintained constant, addition or withdrawal of heat will cause the complete liquefaction or solidification, without the temperature of the system undergoing change. This behaviour, therefore, is similar to, but is not quite the same as the fusion of a simple substance such as ice; and the difference is due to the fact that in the case of the hexahydrate the emission of vapour by the liquid phase causes an alteration in the composition of the latter, owing to the non-volatility of the calcium chloride; whereas in the case of ice this is, of course, not so.

Consider, however, for the present that the vapour phase is absent, and that we are dealing with the two-phase system solid--solution. Then, since there are two components, the system is bivariant. For any given value of the pressure, therefore, we should expect that the system could exist at different temperatures; which, indeed, is the case. It has, however, already been noted that when the composition of the liquid phase becomes the same as that of the solid, the system then behaves as a _univariant_ system; for, at a given pressure, the system solid--solution can exist only at _one_ temperature, change of temperature producing complete transformation in {151} one or other direction. _The variability of the system has therefore been diminished._

This behaviour will perhaps be more clearly understood when one reflects that since the composition of the two phases is the same, the system may be regarded as being formed of _one component_, just as the system NH_{4}Cl <--> NH_{3} + HCl was regarded as being composed of one component when the vapour had the same total composition as the solid (p. 13). One component in two phases, however, const.i.tutes a univariant system, and we can therefore see that calcium chloride hexahydrate in contact with solution of the same composition will const.i.tute a univariant system. The temperature of equilibrium will, however, vary with the pressure;[228] if the latter is constant, the temperature will also be constant.

A point such as has just been referred to, which represents the special behaviour of a system of two (or more) components, in which the composition of two phases becomes identical, is known as an _indifferent point_,[229]

and it has been shown[230] that at a given pressure the temperature in the indifferent point is the _maximum_ or _minimum_ temperature possible at the particular pressure[231] (cf. critical solution temperature). At such a point a system loses one degree of freedom, or behaves like a system of the next lower order.

The Hydrates of Ferric Chloride.--A better ill.u.s.tration of the formation of compounds possessing a definite melting point, and of the existence of retroflex solubility curves, is afforded by the hydrates of ferric chloride, which not only possess definite points of fusion, but these melting points are stable. A very brief description of the relations met with will suffice.[232]

{152}

Ferric chloride can form no less than four stable hydrates, viz.

Fe_{2}Cl_{6},12H_{2}O, Fe_{2}Cl_{6},7H_{2}O, Fe_{2}Cl_{6},5H_{2}O, and Fe_{2}Cl_{6},4H_{2}O, and each of these hydrates possesses a definite, stable melting point. On a.n.a.logy with the behaviour of calcium chloride, therefore, we shall expect that the solubility curves of these different hydrates will exhibit a series of _temperature maxima_; the points of maximum temperature representing systems in which the composition of the solid and liquid phases is the same. A graphical representation of the solubility relations is given in Fig. 39, and the composition of the different saturated solutions which can be formed is given in the following tables, the composition being expressed in molecules of Fe_{2}Cl_{6} to 100 molecules of water. The figures printed in thick type refer to transition and melting points.

[Ill.u.s.tration: FIG. 39.]

{153}

COMPOSITION OF THE SATURATED SOLUTIONS OF FERRIC CHLORIDE AND ITS HYDRATES.