As the temperature of the saturated solution falls, silver nitrate is deposited, and on lowering the temperature sufficiently a point will at last be reached at which ice also begins to separate out. Since there are now four phases co-existing, viz. silver nitrate, ice, solution, vapour, the system is invariant, and the point is a _quadruple point_. This quadruple point, therefore, forms the lower limit of the solubility curve of silver nitrate. Below this point the solution becomes metastable.

Ice as Solid Phase.--Ice melts or is in equilibrium with water at a temperature of 0. The melting point, will, however, be lowered by the solution of silver nitrate in the water; and the greater the concentration of the salt in the solution the greater will be the depression of the temperature of equilibrium. On continuing the addition of silver nitrate, a point will at length be reached at which the salt is no longer dissolved, but remains in the solid form along with the ice. We again obtain, therefore, the invariant system ice--salt--solution--vapour. The temperature at which this invariant system can exist has been found by Middelberg[193] to be -7.3, the solution at this point containing 47.1 per cent. of silver nitrate.

The same general behaviour will be found in the case of all other systems of two components belonging to this cla.s.s; that is, in the case of systems from which the components crystallise out in the pure state, and in which the fused components are miscible in all proportions. In all such cases, therefore, the solubility curves (curves of equilibrium) can be represented diagrammatically as in Fig. 29. In this figure OA represents the solubility curve of the salt, and OB the freezing {117} point curve of ice. O is the quadruple point at which the invariant system exists, and may be regarded as the point of intersection of the solubility curve with the freezing-point curve. Since this point is fixed, the condition of the system as regards temperature, vapour pressure, and concentration of the components (or composition of the solution), is perfectly definite. From the way, also, in which the condition is attained, it is evident that the quadruple point is the lowest temperature that can be obtained with mixtures of the two components in presence of vapour. It is known as the _cryohydric point_, or, generally, the _eutectic point_.[194]

[Ill.u.s.tration: FIG. 29.]

Cryohydrates.[195]--On cooling a solution of common salt in water to a temperature of -3, Guthrie observed that the hydrate NaCl,2H_{2}O separated out. This salt continued to be deposited until at a temperature of -22 opaque crystals made their appearance, and the liquid pa.s.sed into the solid state without change of temperature. A similar behaviour was found by Guthrie in the case of a large number of other salts, a temperature below that of the melting point of ice being reached at which on continued withdrawal of heat, the solution solidified at a constant temperature. When the system had attained this minimum temperature, it was found that the composition of the solid and the liquid phases was the same, and remained unchanged throughout the period of solidification. This is shown by the following figures, which give the composition of different samples of the solid phase deposited from the solution at constant temperature.[196]

{118}

--------------------------------- No.

Temperature of

NaCl.

solidification.

Per cent.

----

-----------------

---------- 1

-21 to -22

23.72 2

-22

23.66 3

-22

23.73 4

-23

23.82 5

-23

23.34 6

-23

23.35 --------------------------------- Mean 23.6 ---------------------------------

Conversely, a mixture of ice and salt containing 23.6 per cent. of sodium chloride will melt at a definite and constant temperature, and exhibit, therefore, a behaviour supposed to be characteristic of a pure chemical compound. This, then, combined with the fact that the solid which was deposited was crystalline, and that the same constant temperature was attained, no matter with what proportions of water and salt one started, led Guthrie to the belief that the solids which thus separated at constant temperature were definite chemical compounds, to which he gave the general name _cryohydrate_. A large number of such cryohydrates were prepared and a.n.a.lysed by Guthrie, and a few of these are given in the following table, together with the temperature of the cryohydric point:[197]--

CRYOHYDRATES.

------------------------------------------------------------------ Salt.

Cryohydric point.

Percentage of anhydrous

salt in the cryohydrate.

------------------------------------------------------------------ Sodium bromide

-24

41.33 Sodium chloride

-22

23.60 Pota.s.sium iodide

-22

52.07 Sodium nitrate

-17.5

40.80 Ammonium sulphate

-17

41.70 Ammonium chloride

-15

19.27 Sodium iodide

-15

59.45 Pota.s.sium bromide

-13

32.15 Pota.s.sium chloride

-11.4

20.03 Magnesium sulphate

-5

21.86 Pota.s.sium nitrate

-2.6

11.20 Sodium sulphate

-0.7

4.55 ------------------------------------------------------------------

{119}

The chemical individuality of these cryohydrates was, however, called in question by Pfaundler,[198] and disproved by Offer,[199] who showed that in spite of the constancy of the melting point, the cryohydrates had the properties, not of definite chemical compounds, but of mixtures; the arguments given being that the heat of solution and the specific volume are the same for the cryohydrate as for a mixture of ice and salt of the same composition; and it was further shown that the cryohydrate had not a definite crystalline form, but separated out as an opaque ma.s.s containing the two components in close juxtaposition. The heterogeneous nature of cryohydrates can also be shown by a microscopical examination.

At the cryohydric point, therefore, we are not dealing with a single solid phase, but with two solid phases, ice and salt; the cryohydric point, therefore, as already stated, is a quadruple point and represents an invariant system.

Although on cooling a solution to the cryohydric point, separation of ice may occur, it will not necessarily take place; the system may become metastable. Similarly, separation of salt may not take place immediately the cryohydric point is reached. It will, therefore, be possible to follow the curves BO and AO beyond the quadruple point,[200] which is thereby clearly seen to be the point of intersection of the solubility curve of the salt and the freezing-point curve of ice. At this point, also, the curves of the univariant systems ice--salt--vapour and ice--salt--solution intersect.

Changes at the Quadruple Point.--Since the invariant system ice--salt--solution--vapour can exist only at a definite temperature, addition or withdrawal of heat must cause the disappearance of one of the phases, whereby the system will become univariant. So long as all four phases are present the temperature, pressure, and concentration of the components in the solution must remain constant. When, therefore, heat is added to or withdrawn from the system, mutually compensatory changes will take place within the system whereby the {120} condition of the latter is preserved. These changes can in all cases be foreseen with the help of the theorem of van't Hoff and Le Chatelier; and, after what was said in Chap.

IV., need only be briefly referred to here. In the first place, addition of heat will cause ice to melt, and the concentration of the solution will be thereby altered; salt must therefore dissolve until the original concentration is reached, and the heat of fusion of ice will be counteracted by the heat of solution of the salt. Changes of volume of the solid and liquid phases must also be taken into account; an alteration in the volume of these phases being compensated by condensation or evaporation. All four phases will therefore be involved in the change, and the final state of the system will be dependent on the amounts of the different phases present; the ultimate result of addition or withdrawal of heat or of change of pressure at the quadruple point will be one of the four univariant systems: ice--solution--vapour; salt--solution--vapour; ice--salt--vapour; ice--salt--solution. If the vapour phase disappear, there will be left the univariant system ice--salt--solution, and the temperature at which this system can exist will alter with the pressure.

Since in this case the influence of pressure is comparatively slight, the temperature of the quadruple point will differ only slightly from that of the cryohydric point as determined under atmospheric pressure.

Freezing Mixtures.--Not only will the composition of a univariant system undergo change when the temperature is varied, but, conversely, if the _composition_ of the system is caused to change, corresponding changes of temperature must ensue. Thus, if ice is added to the univariant system salt--solution--vapour, the ice must melt and the temperature fall; and if sufficient ice is added, the temperature of the cryohydric point must be at length reached, for it is only at this temperature that the four phases ice--salt--solution--vapour can coexist. Or, on the other hand, if salt is added to the system ice--solution--vapour, the concentration of the solution will increase, ice must melt, and the temperature must thereby fall; and this process also will go on until the cryohydric point is reached. In both cases ice melts and there is a change in the {121} composition of the solution; in the former case, salt will be deposited[201] because the solubility diminishes as the temperature falls; in the latter, salt will pa.s.s into solution. This process may be accompanied either by an evolution or, more generally, by absorption of heat; in the former case the effect of the addition of ice will be partially counteracted; in the latter case it will be augmented.

These principles are made use of in the preparation of _freezing mixtures_.

The lowest temperature which can be reached by means of these (under atmospheric pressure) is the cryohydric point. This temperature-minimum is, however, not always attained in the preparation of a freezing mixture, and that for various reasons. The chief of these are radiation and the heat absorbed in cooling the solution produced. The lower the temperature falls, the more rapid does the radiation become; and the rate at which the temperature sinks decreases as the amount of solution increases. Both these factors counteract the effect of the latent heat of fusion and the heat of solution, so that a point is reached (which may lie considerably above the cryohydric point) at which the two opposing influences balance. The absorption of heat by the solution can be diminished by allowing the solution to drain off as fast as it is produced; and the effect of radiation can be partially annulled by increasing the rate of cooling. This can be done by the more intimate mixing of the components. Since, under atmospheric pressure, the temperature of the cryohydric point is constant, the cryohydrates are very valuable for the production of baths of constant low temperature.

2. _Partial Miscibility of the Fused Components._

On pa.s.sing to the study of the second cla.s.s of systems of two components belonging to this group, namely, those in which the fused components are not miscible in all proportions, we find that the relationships are not quite so simple as {122} in the case of silver nitrate and water. In the latter case, only one liquid phase was possible; in the cases now to be studied, two liquid phases can be formed, and there is a marked discontinuity in the solubility curve on pa.s.sing from the cryohydric point to the melting point of the second (non-volatile) component.

Paratoluidine dissolves in water, and the solubility increases as the temperature rises.[202] At 44.2, however, paratoluidine in contact with water melts, and two liquid phases are formed, viz. a solution of water in fused paratoluidine and a solution of fused paratoluidine in water. We have, therefore, the phenomenon of _melting under the solvent_. This melting point will, of course, be lower than the melting point of the pure substance, because the solid is now in contact with a solution, and, as we have already seen, addition of a foreign substance lowers the melting point. Such cases of melting under the solvent are by no means rare, and a review of the relationships met with may, therefore, be undertaken here. As an example, there may be chosen the equilibrium between succinic nitrile, C_{2}H_{4}(CN)_{2} and water, which has been fully studied by Schreinemakers.[203]

[Ill.u.s.tration: FIG. 30.]

If to the system ice--water at 0 succinic nitrile is added, the temperature will fall; and continued addition of the nitrile will lead at last to the cryohydric point _b_ (Fig. 30), at which solid nitrile, ice, solution, and vapour can coexist. The temperature of the cryohydric point is -1.2, and the composition of the solution is 1.29 mol. of nitrile in 100 mol. of solution. From _a_ to _b_ the solid phase in contact with the solution is ice. {123} If the temperature be now raised so as to cause the disappearance of the ice, and the addition of nitrile be continued, the concentration of the nitrile in the solution will increase as represented by the curve _bc_. At the point _c_ (18.5), when the concentration of the nitrile in the solution has increased to 2.5 molecules per cent., the nitrile melts and two liquid phases are formed; the concentration of the nitrile in these two phases is given by the points _c_ and _c'_. As there are now four phases present, viz. solid nitrile, solution of fused nitrile in water, solution of water in fused nitrile, and vapour, the system is _invariant_. Since at this point the concentration, temperature, and pressure are completely defined, addition or withdrawal of heat can only cause a change in the relative amounts of the phases, _but no variation of the concentrations_ of the respective phases. As a matter of fact, continued addition of nitrile and addition of heat will cause an increase in the amount of the liquid phase containing excess of nitrile (_i.e._ the solution of water in fused nitrile), whereas the other liquid phase, the solution of fused nitrile in water, will gradually disappear. When it has completely disappeared, the system will be represented by the point _c'_, where the molecular concentration of nitrile is now 75 per cent., and again becomes univariant, the three phases being solid nitrile, liquid phase containing excess of nitrile, and vapour; and as the amount of the water is diminished the temperature of equilibrium rises, until at 54 the melting point of the pure nitrile is reached.

Return now to the point c. At this point there exists the invariant system solid nitrile, two liquid phases, vapour. If heat be added, the solid nitrile will disappear, and there will be left the univariant system, consisting of two liquid phases and vapour.[204] Such a system will exhibit relationships similar to those already studied in the previous chapter. As the temperature rises, the mutual solubility of the two fused components becomes greater, until at _d_ (55.5) the critical solution temperature is reached, and the fused components become miscible in all proportions.

At all temperatures and concentrations lying to the right {124} of the curve _abcdc'e_ there can be only one liquid phase; in the field _cdc'_ there are two liquid phases.

From the figure it will be easy to see what will be the result of bringing together succinic nitrile and water at different temperatures and in different amounts. Since _b_ is the lowest temperature at which liquid can exist in stable equilibrium with solid, ice and succinic nitrile can be mixed in any proportions at temperatures below _b_ without undergoing change. Between _b_ and _c_ succinic nitrile will be dissolved until the concentration reaches the value on the curve _bc_, corresponding to the given temperature. On adding the nitrile to water at temperatures between _c_ and _d_, it will dissolve until a concentration lying on the curve _cd_ is attained; at this point two liquid phases will be formed, and further addition of nitrile will cause the one liquid phase (that containing excess of nitrile) to increase, while the other liquid phase will decrease, until it finally disappears and there is only one liquid phase left, that containing excess of nitrile. This can dissolve further quant.i.ties of the nitrile, and the concentration will increase until the curve _c'e_ is reached, when the concentration will remain unchanged, and addition of solid will merely increase the amount of the solid phase.

If a solution represented by any point in the field lying below the curve _bcd_ is heated to a temperature above _d_, the critical solution temperature, then the concentration of the nitrile can be increased to any desired amount without at any time two liquid phases making their appearance; the system can then be cooled down to a temperature represented by any point between the curves _dc'e_. In this way it is possible to pa.s.s continuously from a solution containing excess of one component to solutions containing excess of the other, as represented by the dotted line _x.x.xx_ (_v._ p. 100). At no point is there formation of two liquid phases.

Supersaturation.--Just as suspended transformation is rarely met with in the pa.s.sage from the solid to the liquid state, so also it is found in the case of the melting of substances under the solvent that suspended fusion does not occur; but that when the temperature of the invariant point is reached at which, therefore, the formation of two liquid layers is possible, {125} these two liquid layers, as a matter of fact, make their appearance. Suspended transformation can, however, take place from the side of the liquid phase, just as water or other liquid can be cooled below the normal freezing point without solidification occurring. The question, therefore, arises as to the relative solubilities of the solid and the supercooled liquid at the same temperature.

[Ill.u.s.tration: FIG. 31.]

The answer to this question can at once be given from what we have already learned (p. 113), if we recollect that at temperatures below the point of fusion under the solvent, the solid form, at temperatures above that point, the liquid form, is the more stable; at this temperature, therefore, the relative stability of the solid and liquid forms changes. Since, as we have already seen, the less stable form has the greater solubility, it follows that the supercooled liquid, being the less stable form, must have the greater solubility. This was first proved experimentally by Alexejeff[205]

in the case of benzoic acid and water, the solubility curves for which are given in Fig. 31. As can be seen from the figure, the prolongation of the curve for liquid--liquid, which represents the solubility of the supercooled liquid benzoic acid, lies above that for the solubility of the {126} solid benzoic acid in water; the solution saturated with respect to the supercooled liquid is therefore supersaturated with respect to the solid form. A similar behaviour has been found in the case of other substances.[206]

Pressure-Temperature Diagram.--Having considered the changes which occur in the concentration of the components in a solution with the temperature, we may conclude the discussion of the equilibrium between a salt and water by studying the variation of the vapour pressure.

Since in systems of two components the two phases, solution and vapour, const.i.tute a bivariant system, the vapour pressure is undefined, and may have different values at the same temperature, depending on the concentration. In order that there may be for each temperature a definite corresponding pressure of the vapour, a third phase must be present. This condition is satisfied by the system solid--liquid (solution)--vapour; that is, by the saturated solution (p. 108). In the case of a saturated solution, therefore, the pressure of the vapour at any given temperature is constant.

Vapour Pressure of Solid--Solution--Vapour.--It has long been known that the addition of a non-volatile solid to a liquid in which it is soluble lowers the vapour pressure of the solvent; and the diminution of the pressure is approximately proportional to the amount of substance dissolved (Law of Babo). The vapour-pressure curve, therefore, of a solution of a salt in water must lie below that for pure water. Further, in the case of a pure liquid, the vaporization curve is a function only of the temperature (p. 63), whereas, in the case of a solution, the pressure varies both with the temperature and the _concentration_. These two factors, however, act in opposite directions; for although the vapour pressure in all cases increases as the temperature rises, increase of concentration, as we have seen, lowers the vapour pressure. Again, since the concentration itself varies with the temperature, two cases have to be considered, viz. where the concentration increases with rise of {127} temperature, and where the concentration diminishes with rise of temperature.

The relations which are found here will be best understood with the help of Fig. 32.[207] In this figure, OB represents the sublimation curve of ice, and BC the vaporization curve of water; the curve for the solution must lie below this, and must cut the sublimation curve of ice at some temperature below the melting point. The point of intersection A is the cryohydric point. If the solubility increases with rise of temperature, the increase of the vapour pressure due to the latter will be partially annulled. Since at first the effect of increase of temperature more than counteracts the depressing action of increase of concentration, the vapour pressure will increase on raising the temperature above the cryohydric point. If the elevation of temperature is continued, however, to the melting point of the salt, the effect of increasing concentration makes itself more and more felt, so that the vapour-pressure curve of the solution falls more and more below that of the pure liquid, and the pressure will ultimately become equal to that of the pure salt; that is to say, practically equal to zero.

The curve will therefore be of the general form AMF shown in Fig. 32. If the solubility should diminish with rise of temperature, the two factors, temperature and concentration, will act in the same direction, and the vapour-pressure curve will rise relatively more rapid than that of the pure liquid; since, however, the pure salt is ultimately obtained, the vapour-pressure curve must in this case also finally approach the value zero.

[Ill.u.s.tration: FIG. 32.]

Other Univariant Systems.--Besides the univariant system {128} salt--solution--vapour already considered, three others are possible, viz.

ice--solution--vapour, ice--salt--solution, and ice--salt--vapour.

The fusion point of a substance is lowered, as we have seen, by the addition of a foreign substance, and the depression is all the greater the larger the quant.i.ty of substance added. The vapour pressure of the water, also, is lowered by the solution in it of other substances, so that the vapour pressure of the system ice--solution--vapour must decrease as the temperature falls from the fusion point of ice to the cryohydric point.

This curve is represented by BA (Fig. 32), and is coincident with the sublimation curve of ice.

This, at first sight, strange fact will be readily understood when we consider that since ice and solution are together in equilibrium with the same vapour, they must have the same vapour pressure. For suppose at any given temperature equilibrium to have been established in the system ice--solution--vapour, removal of the ice will not alter this equilibrium.

Suppose, now, the ice and the solution placed under a bell-jar so that they have a common vapour, but are not themselves in contact; then, if they do not have the same vapour pressure, distillation must take place and the solution will become more dilute or more concentrated. Since, at the completion of this process, the ice and solution are now in equilibrium when they are not in contact, they must also be in equilibrium when they are in contact (p. 32). But if distillation has taken place the concentration of the solution must have altered, so that the ice will now be in equilibrium with a solution of a different concentration from before.

But according to the Phase Rule ice cannot at one and the same temperature be in equilibrium with two solutions of different concentration, for the system ice--solution--vapour is univariant, and at any given temperature, therefore, not only the pressure but also the _concentration of the components in the solution must be constant_. Distillation could not, therefore, take place from the ice to the solution or _vice versa_; that is to say, the solution and the ice must have the same vapour pressure--the sublimation pressure of ice. The reason of the coincidence is the non-volatility of the salt: had {129} the salt a measurable vapour pressure itself, the sublimation curve of ice and the curve for ice--solution--vapour would no longer fall together.

The curve AO represents the pressures of the system ice--salt--vapour. This curve will also be coincident with the sublimation curve of ice, on account of the non-volatility of the salt.

The equilibria of the fourth univariant system ice--salt--solution are represented by AE. Since this is a condensed system, the effect of a small change of temperature will be to cause a large change of pressure, as in the case of the fusion point of a pure substance. The direction of this curve will depend on whether there is an increase or diminution of volume on solidification; but the effect in any given case can be predicted with the help of the theorem of Le Chatelier.

Since the cryohydric point is a quadruple point in a two-component system, it represents an invariant system. The condition of the system is, therefore, completely defined; the four phases, ice, salt, solution, vapour, can co-exist only when the temperature, pressure, and concentration of the solution have constant and definite values. Addition or withdrawal of heat, therefore, can cause no alteration of the condition of the system except a variation of the relative amounts of the phases. Addition of heat at constant volume will ultimately lead to the system salt--solution--vapour or the system ice--solution--vapour, according as ice or salt disappears first. This is readily apparent from the diagram (Fig. 32), for the systems ice--salt--solution and ice--salt--vapour can exist only at temperatures below the cryohydric point (provided the curve for ice--salt--solution slopes towards the pressure axis).

Bivariant Systems.--Besides the univariant systems already discussed, various bivariant systems are possible, the conditions for the existence of which are represented by the different areas of Fig. 32. They are as follows:--

_Area._ _System._

OAMF Salt--vapour.

CBAMF Solution--vapour; salt--solution.

EABD Salt--solution; ice--solution.