The Phase Rule and Its Applications Part 9

With regard to the _partial pressure_ of the components, the behaviour is more uniform. The partial pressure of one component is in all cases lowered by the addition of the other component, the diminution being approximately proportional to the amount added. If two liquid phases are present, the partial pressure of the components, as well as the total pressure, is constant, and is the same for both phases. That is to say, in the case of the two liquids, saturated solution of water in ether, and of ether in water, the partial pressure of the ether in the vapour in contact with the one solution is the same as that in the vapour over the other solution.[177]

Complete Miscibility.--Although the phenomena of complete miscibility are here treated under a separate heading, it must not be thought that there is any essential difference between those cases where the liquids exhibit limited miscibility and those in which only one h.o.m.ogeneous solution is formed. As has been already pointed out, the solubility relations alter with the temperature; and liquids which at one temperature can dissolve in one another only to a limited extent, are found at some other temperature to possess the property of complete miscibility. Conversely, we may expect that liquids which at one temperature, say at the ordinary temperature, are miscible in all proportions, will be found at some other temperature to be only partially miscible. Thus, for example, it was found by Guthrie that ethyl alcohol and carbon disulphide, which are miscible in all proportions at the ordinary temperature, possess only limited miscibility at temperatures below -14.4.[178] Nevertheless, it is doubtful if the critical solution temperature is in all cases experimentally realizable.

Pressure-Concentration Diagram.--Since, in the cases of complete miscibility of two liquid components, there are never more than two phases present, the system must always be bivariant; and two of the variables pressure, temperature or concentration of the components, must be arbitrarily chosen {105} before the system becomes defined. For this reason the Phase Rule affords only a slight guidance in the study of such equilibria; and we shall therefore not enter in detail into the behaviour of these h.o.m.ogeneous mixtures. All that the Phase Rule can tell us in connection with these solutions, is that at constant temperature the vapour pressure of the solution varies with the composition of the liquid phase; and if the composition of the liquid phase remains unchanged, the pressure also must remain unchanged. This constancy of composition is exhibited not only by pure liquids, but also by liquid solutions in all cases where the vapour pressure of the solution reaches a maximum or minimum value. This is the case, for example, with mixtures of constant boiling point.[179]

{106}

CHAPTER VII

SOLUTIONS OF SOLIDS IN LIQUIDS, ONLY ONE OF THE COMPONENTS BEING VOLATILE

General.--When a solid is brought into contact with a liquid in which it can dissolve, a certain amount of it pa.s.ses into solution; and the process continues until the concentration reaches a definite value independent of the amount of solid present. A condition of equilibrium is established between the solid and the solution; the solution becomes _saturated_. Since the number of components is two, and the number of phases three, viz.

solid, liquid solution, vapour, the system is univariant. If, therefore, one of the factors, pressure, temperature, or concentration of the components (in the solution[180]), is arbitrarily fixed, the state of the system becomes perfectly defined. Thus, at any given temperature, the vapour pressure of the system and the concentration of the components have a definite value. If the temperature is altered, the vapour pressure and also, in general, the concentration will undergo change. Likewise, if the pressure varies, while the system is isolated so that no heat can pa.s.s between it and its surroundings, the concentration and the temperature must also undergo variation until they attain values corresponding to the particular pressure.

That the temperature has an influence, sometimes a very considerable influence, on the amount of substance pa.s.sing into solution, is sufficiently well known; the effect of pressure, although less apparent, is no less certain. If at any given temperature the volume of the vapour phase is diminished, {107} vapour will condense to liquid, in order that the pressure may remain constant, and so much of the solid will pa.s.s into solution that the concentration may remain unchanged; for, so long as the three phases are present, the state of the system cannot alter. If, however, one of the phases, _e.g._ the vapour phase, disappears, the system becomes bivariant; at any given temperature, therefore, there may be different values of concentration and pressure.

The direction in which change of concentration will occur with change of pressure can be predicted by means of the theorem of Le Chatelier, if it is known whether solution is accompanied by increase or diminution of the total volume. If diminution of the total volume of the system occurs on solution, increase of pressure will increase the solubility; in the reverse case, increase of pressure will diminish the solubility.

This conclusion has also been verified by experiment, as is shown by the following figures.[181]

--------------------------------------------------------------- Change of Solubility (at 18) (grams salt volume by in 1 gram of solution).

dissolving 1 gm. --------------------------- Salt. of salt in the saturated Pressure Pressure solution. = 1 atm. = 500 atm.

------------------+----------------+----------+---------------- Sodium chloride -0.07 0.264 0.270 Ammonium chloride +0.10 0.272 0.258 Alum -0.067 0.115 0.142 (_p_ = 400 atm.) -------------------------------------------------------------

As can be seen, a large increase of the pressure brings about a no more than appreciable alteration of the solubility; a result which is due, as in the case of the alteration of the fusion point with the pressure, to the small change in volume accompanying solution or increase of pressure. For all practical purposes, therefore, the solubility as determined under atmospheric pressure may be taken as equal to the true {108} solubility, that is, the solubility when the system is under the pressure of its own vapour.

The Saturated Solution.--From what has been said above, it will be seen that the condition of saturation of a solution can be defined only with respect to a certain solid phase; if no solid is present, the system is undefined, for it then consists of only two phases, and is therefore bivariant. Under such circ.u.mstances not only can there be at one given temperature solutions of different concentration, all containing less of one of the components than when that component is present in the solid form, but there can also exist solutions containing more of that component than corresponds to the equilibrium when the solid is present. In the former case the solutions are _unsaturated_, in the latter case they are _supersaturated with respect to a certain solid phase_; in themselves, the solutions are stable, and are neither unsaturated nor supersaturated.

Further, if the solid substance can exist in different allotropic modifications, the particular form of the substance which is in equilibrium with the solution must be known, in order that the statement of the solubility may be definite; for each form has its own solubility, and, as we shall see presently, the less stable form has the greater solubility (cf. p. 47). In all determinations of the solubility, therefore, not only must the concentration of the components in the solution be determined, but equal importance should be attached to the characterisation of the solid phase present.

In this connection, also, one other point may be emphasised. For the production of the equilibrium between a solid and a liquid, time is necessary, and this time not only varies with the state of division of the solid and the efficiency of the stirring, but is also dependent on the nature of the substance.[182] Considerable care must therefore be taken that sufficient time is allowed for equilibrium to be established. Such care is more especially needful when changes may occur in the solid phase, and neglect of it has greatly diminished the value of many of the older determinations of solubility.

Form of the Solubility Curve.--The solubility curve--that {109} is, the curve representing the change of concentration of the components in the solution with the temperature--differs markedly from the curve of vapour pressure (p. 63), in that it possesses no general form, but may vary in the most diverse manner. Not only may the curve have an almost straight and horizontal course, or slope or curve upwards at varying angles; but it may even slope downwards, corresponding to a decrease in the solubility with rise of temperature; may exhibit maxima or minima of solubility, or may, as in the case of some hydrated salts, pa.s.s through a point of maximum temperature. In the latter case the salt may possess two values of solubility at the same temperature. We shall consider these cases in the following chapter.

[Ill.u.s.tration: FIG. 26.]

The great variety of form shown by solubility curves is at once apparent from Fig. 26, in which the solubility curves of various substances (not, however, drawn to scale) are reproduced.[183]

Varied as is the form of the solubility curve, its _direction_, nevertheless, can be predicted by means of the theorem of van't Hoff and Le Chatelier; for in accordance with that theorem (p. 57) increase of solubility with the temperature must occur in those cases where the process of solution is accompanied by an _absorption_ of heat; and a decrease in the solubility with rise of temperature will be found in cases where solution occurs with _evolution_ of heat. Where there is no heat effect accompanying solution, {110} change of temperature will be without influence on the solubility; and if the sign of the heat of solution changes, the direction of the solubility curve must also change, _i.e._ must show a maximum or minimum point. This has in all cases been verified by experiment.[184]

In applying the theorem of Le Chatelier to the course of the solubility curve, it should be noted that by heat of solution there is meant, not the heat effect produced on dissolving the salt in a large amount of solvent (which is the usual signification of the expression), but the heat which is absorbed or evolved when the salt is dissolved in the almost saturated solution (the so-called last heat of solution). Not only does the heat effect in the two cases have a different value, but it may even have a different sign. A striking example of this is afforded by cupric chloride, as the following figures show:[185]--

----------------------------------------------------------- Number of gram-molecules of CuCl_{2}, 2H_{2}O dissolved in 198 Heat effect.

gram-molecules of water. -----------------------------------+----------------------- 1 +37 K 2.02 +66 "

4.15 +105 "

7.07 +117 "

9.95 +117 "

11 +91 "

18.8 -10 "

19.6 -31 "

24.75 -198 "

In the above table the positive sign indicates evolution of heat, the negative sign, absorption of heat; and the values of the heat effect are expressed in centuple calories. Judging from the heat effect produced on dissolving cupric chloride in a large bulk of water, we should predict that the solubility of that salt would diminish with rise of temperature; as a matter of fact, it increases. This is in accordance with the fact that {111} the last heat of solution is _negative_ (as expressed above), _i.e._ solution of the salt in the almost saturated solution is accompanied by absorption of heat. We are led to expect this from the fact that the heat of solution changes sign from positive to negative as the concentration increases; experiment also showed it to be the case.

Despite its many forms, it should be particularly noted that the solubility curve of any substance is _continuous_, so long as the solid phase, or solid substance in contact with the solution, remains unchanged. If any "break" or discontinuous change in the direction of the curve occurs, it is a sign that the _solid phase has undergone alteration_. Conversely, if it is known that a change takes place in the solid phase, a break in the solubility curve can be predicted. We shall presently meet with examples of this.[186]

A.--ANHYDROUS SALT AND WATER.

The Solubility Curve.--In studying the equilibria in those systems of two components in which the liquid phase is a solution or phase of varying composition, we shall in the present chapter limit the discussion to those cases where no compounds are formed, but where the components crystallise out in the pure state. Since some of the best-known examples of such systems are yielded by the solutions of anhydrous salts in water, we shall first of all briefly consider some of the results which have been obtained with them.

For the most part the solubility curves have been studied only at temperatures lying between 0 and 100, the solid phase in contact with the solution being the anhydrous salt. For the representation of these equilibria, the concentration-temperature {112} diagram is employed, the concentration being expressed as the number of grams of the salt dissolved in 100 grams of water, or as the number of gram-molecules of salt in 100 gram-molecules of water. The curves thus obtained exhibit the different forms to which reference has already been made. So long as the salt remains unchanged the curve will be continuous, but if the salt alters its form, then the solubility curve will show a break.

[Ill.u.s.tration: FIG. 27.]

Now, we have already seen in Chapter III. that certain substances are capable of existing in various crystalline forms, and these forms are so related to one another that at a given temperature the relative stability of each pair of polymorphic forms undergoes change. Since each crystalline variety of a substance must have its own solubility, there must be a break in the solubility curve at the temperature of transition of the two enantiotropic forms. At this point the two solubility curves must cut, for since the two forms are in equilibrium with respect to their vapour, they must also be in equilibrium with respect to their solutions. From the table on p. 63 it is seen that pota.s.sium nitrate, ammonium nitrate, silver nitrate, thallium nitrate, thallium picrate, are capable of existing in two or more different enantiotropic crystalline forms, the range of stability of these forms being limited by definite temperatures (transition temperature). Since the transition point is not altered by a solvent (provided the latter is not absorbed by the solid phase), we should find on studying the solubility of these substances in water that the solubility curve would exhibit a change in direction at the temperature of transition.

As a matter of fact this has been verified, more especially in the case of ammonium nitrate[187] {113} and thallium picrate.[188] The following table contains the values of the solubility of ammonium nitrate obtained by Muller and Kaufmann, the solubility being expressed in gram-molecules NH_{4}NO_{3} in 100 gram-molecules of water. In Fig. 27 these results are represented graphically. The equilibrium point was approached both from the side of unsaturation and of supersaturation, and the condition of equilibrium was controlled by determinations of the density of the solution.

SOLUBILITY OF AMMONIUM NITRATE.

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

--------------+-------------+--------------+---------------- 12.2 34.50 32.7 57.90 20.2 43.30 34.0 58.89 25.05 48.19 35.0 59.80 28.0 51.86 36.0 61.00 30.0 54.40 37.5 62.90 30.2 54.61 38.0 63.60 31.9 57.20 39.0 65.09 32.1 57.60 40.0 66.80 ------------------------------------------------------------

From the graphic representation of the solubility given in Fig. 27, there is seen to be a distinct change in the direction of the curve at a temperature of 32; and this break in the curve corresponds to the transition of the [beta]-rhombic into the [alpha]-rhombic form of ammonium nitrate (p. 63).

Suspended Transformation and Supersaturation.--As has already been learned, the transformation of the one crystalline form into the other does not necessarily take place immediately the transition point has been pa.s.sed; and it has therefore been found possible in a number of cases to follow the solubility curve of a given crystalline form beyond the point at which it ceases to be the most stable modification. Now, it will be readily seen from Fig. 27 that if the two solubility curves be prolonged beyond the point of intersection, the solubility of the less stable form is greater than that of the more stable. A solution, therefore, which is saturated with respect to the less stable form, _i.e._ which is in equilibrium with that form, is _supersaturated with respect to the more stable modification_. If, {114} therefore, a small quant.i.ty of the more stable form is introduced into the solution, the latter must deposit such an amount of the more stable form that the concentration of the solution corresponds to the solubility of the stable form at the particular temperature. Since, however, the solution is now _unsaturated_ with respect to the less stable variety, the latter, if present, must pa.s.s into solution; and the two processes, deposition of the stable and solution of the metastable form, must go on until the latter form has entirely disappeared and a saturated solution of the stable form is obtained. There will thus be a conversion, through the medium of the solvent, of the less stable into the more stable modification. This behaviour is of practical importance in the determination of transition points (_v._ Appendix).

From the above discussion it will be seen how important is the statement of the solid phase for the definition of saturation and supersaturation.[189]

Solubility Curve at Higher Temperatures.--On pa.s.sing to the consideration of the solubility curves at higher temperatures, two chief cases must be distinguished.

(1) The two components in the fused state can mix in all proportions.

(2) The two components in the fused state cannot mix in all proportions.

1. _Complete Miscibility of the Fused Components._

[Ill.u.s.tration: FIG. 28.]

The best example of this which has been studied, so far as anhydrous salts and water are concerned, is that of silver nitrate and water. The solubility of this salt at temperatures {115} above 100 has been studied chiefly by Etard[190] and by Tilden and Shenstone.[191] The values obtained by Etard are given in the following table, and represented graphically in Fig. 28.

SOLUBILITY OF SILVER NITRATE.

--------------------------------------------------- Temperature. Parts of dry salt in 100 parts of solution.

--------------------+------------------------------ -7 46.2 -1 52.1 +5 56.3 10 61.2 20 67.8 40.5 76.8 73 84.0 135 92.8 182 96.9 ---------------------------------------------------

In this figure the composition of the solution is expressed in parts of silver nitrate in 100 parts by weight of the solution, so that 100 per cent. represents pure silver nitrate. As can be seen, the solubility increases with the temperature. At a temperature of about 160 there should be a break in the curve due to change of crystalline form (p. 63). Such a change in the direction of the solubility curve, however, does not in any way alter the essential nature of the relationships discussed here, and may for the present be left out of account. On following the solubility curve of silver nitrate to higher temperatures, therefore, the concentration of silver nitrate in the solution gradually increases, until at last, at a temperature of 208,[192] the melting point of pure silver nitrate is reached, and the concentration of the water has become zero. The curve throughout its whole extent represents the equilibrium between silver nitrate, solution, and vapour. Conversely, starting with pure silver nitrate in contact with the fused salt, addition of water will lower the melting point, _i.e._ will lower the temperature at which the solid salt can exist in contact with the liquid; {116} and the depression will be all the greater the larger the amount of water added. As the concentration of the water in the liquid phase is increased, therefore, the system will pa.s.s back along the curve from higher to lower temperatures, and from greater to smaller concentrations of silver nitrate in the liquid phase. The curve in Fig. 28 may, therefore, be regarded either as the solubility curve of silver nitrate in water, or as the freezing point curve for silver nitrate in contact with a solution consisting of that salt and water.