The Phase Rule and Its Applications Part 23

Vapour Pressure. Quintuple Point.--In the case of Glauber's salt, we saw that at a certain temperature the vapour pressure curve of the hydrated salt cut that of the saturated solution of anhydrous sodium sulphate. That point, it will be remembered, was a quadruple point at which the four phases sodium sulphate decahydrate, anhydrous sodium sulphate, solution, and vapour, could co-exist; and was also the point of intersection of the curves for four univariant systems. In the case of the formation of double salts, similar relations.h.i.+ps are met with; and also certain differences, due to the fact that we are now dealing with systems of three components.

Two cases will be chosen here for brief description, one in which formation, the other in which decomposition of the double salt occurs with rise of temperature.

On heating a mixture of sodium sulphate decahydrate and magnesium sulphate heptahydrate, it is found that at 22 partial liquefaction occurs with formation of astracanite. At this temperature, therefore, there can coexist the five phases--

Na_{2}SO_{4},10H_{2}O; MgSO_{4},7H_{2}O; Na_{2}Mg(SO_{4})_{2},4H_{2}O; solution; vapour.

This const.i.tutes, therefore, a _quintuple point_; and since there are three components present in five phases, the system is invariant. This point, also, will be the point of intersection of curves for five univariant systems, which, in this case, must each be composed of four phases. These systems are--

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I. Na_{2}SO_{4},10H_{2}O; MgSO_{4},7H_{2}O; Na_{2}Mg(SO_{4})_{2},4H_{2}O; vapour.

II. Na_{2}SO_{4},10H_{2}O; MgSO_{4},7H_{2}O; solution; vapour.

III. MgSO_{4},7H_{2}O; Na_{2}Mg(SO_{4})_{2},4H_{2}O; solution; vapour.

IV. Na_{2}SO_{4},10H_{2}O; Na_{2}Mg(SO_{4})_{2},4H_{2}O; solution; vapour.

V. Na_{2}SO_{4},10H_{2}O; MgSO_{4},7H_{2}O; Na_{2}Mg(SO_{4})_{2},4H_{2}O; solution.

[Ill.u.s.tration: FIG. 98.]

On representing the vapour pressures of these different systems graphically, a diagram is obtained such as is shown in Fig. 98,[342] the curves being numbered in accordance with the above list. When the system I.

is heated, the vapour pressure increases until at the quintuple point the liquid phase (solution) is formed, and it will then depend on the relative amounts of the different phases whether on further heating there is formed system III., IV., or V. If either of the first two is produced, we shall obtain the vapour pressure of the solutions saturated with respect to both double salt and one of the single salts; while if the vapour phase disappears, there will be obtained the pressure of the condensed systems formed of double salt, two single salts and solution. This curve, therefore, indicates the _change of the transition point with pressure_; and since in the ordinary determinations of the transition point in open vessels, we are in reality dealing with condensed systems under the pressure of 1 atm., it will be evident that the transition point does not accurately coincide with the quintuple point (at which the system is under the pressure of its own vapour). As in the case of other condensed systems, however, pressure has only a slight influence on the temperature of the transition point. Whether or not pressure raises or lowers the transition point will depend on whether transformation is accompanied by an increase or {263} diminution of volume (theorem of Le Chatelier, p. 58). In the case of the formation of astracanite, expansion occurs, and the transition point will therefore be raised by increase of pressure. Although measurements have not been made in the case of this system, the existence of such a curve has been experimentally verified in the case of copper and calcium acetates and water (v. _infra_).[343]

[Ill.u.s.tration: FIG. 99.]

The vapour pressure diagram in the case of copper calcium acetate and water (Fig. 99), is almost the reverse of that already discussed. In this case, the double salt decomposes on heating, and the decomposition is accompanied by a contraction. Curve I. is the vapour pressure curve for double salt, two single salts (p. 260), and vapour; curves II. and III. give the vapour pressures of solutions saturated with respect to double salt and one of the single salts; curve IV. is the curve of pressures for the solutions saturated with respect to the two single salts; while curve V. again represents the change of the transition point with pressure. On examining this diagram, it is seen that whereas {264} astracanite could exist both above and below the quintuple point, copper calcium acetate can exist only _below_ the quintuple point. This behaviour is found only in those cases in which the double salt is decomposed by rise of temperature, and where the decomposition is accompanied by a diminution of volume.[344]

As already mentioned, the decomposition of copper calcium acetate into the single salts and saturated solution is accompanied by a contraction, and it was therefore to be expected that increase of pressure would _lower_ the transition point. This expectation of theory was confirmed by experiment, for van't Hoff and Spring found that although the transition point under atmospheric pressure is about 75, decomposition of the double salt took place even at the ordinary temperature when the pressure was increased to 6000 atm.[345]

Solubility Curves at the Transition Point.--At the transition point, as has already been shown, the double salt and the two const.i.tuent salts can exist in equilibrium with the same solution. The transition point, therefore, must be the point of intersection of two solubility curves; the solubility curve of the double salt and the solubility curve of the mixtures of the two const.i.tuent salts. It should be noted here that we are not dealing with the solubility curves of the single salts separately, for since the systems are composed of three components, a single solid phase can, at a given temperature, be in equilibrium with solutions of different composition, and two solid phases in contact with solution (and vapour) are therefore necessary to give an univariant system. The same applies, of course, to the solubility of the double salt; for a double salt also const.i.tutes a single phase, and can therefore exist in equilibrium with solutions of varying composition. If, however, we make the restriction (which we do for the present) that the double salt is not decomposed by water, then the solution will contain the const.i.tuent salts in the same relative proportions as they are contained in the double salt, and the system may therefore be regarded as one of _two_ components, viz. double salt and water. In this case one solid phase is sufficient, with solution and {265} vapour, to give an univariant system; and at a given temperature, therefore, the solubility will have a perfectly definite value.

Since in almost all cases the solubility is determined in open vessels, we shall in the following discussion consider that the vapour phase is absent, and that the system is under a constant pressure, that of the atmosphere.

With this restriction, therefore, four phases will const.i.tute an invariant system, three phases an univariant, and two phases a bivariant system.

It has already been learned that in the case of sodium sulphate and water, the solubility curve of the salt undergoes a sudden change in direction at the transition point, and that this is accompanied by a change in the solid phase in equilibrium with the solution. The same behaviour is also found in the case of double salts. To ill.u.s.trate this, we shall briefly discuss the solubility relations of a few double salts, beginning with one of the simplest cases, that of the formation of rubidium racemate from rubidium _d_- and _l_-tartrates. The solubilities are represented diagrammatically in Fig. 100, the numerical data being contained in the following table, in which the solubility is expressed as the number of gram-molecules Rb_{2}C_{4}H_{4}O_{6} in 100 gm.-molecules of water.[346]

--------------------------------------------------------------- Temperature. Solubility of tartrate Solubility of racemate.

mixture. --------------------------------------------------------------- 25 13.03 10.91 35 -- 12.63 40.4 -- 13.48 40.7 13.46 -- 54 13.83 -- ---------------------------------------------------------------

In Fig. 100 the curve AB represents the solubility of the racemate, while A'BC represents the solubility of the mixed tartrates. Below the transition point, therefore, the solubility of the racemate is less than that of the mixed tartrates. The solution, saturated with respect to the latter, will be supersaturated with respect to the racemate; and if a nucleus of this is present, racemate will be deposited, and the mixed tartrates, if present in equimolecular amounts, will ultimately {266} entirely disappear, and only racemate will be left as solid phase. The solution will then have the composition represented by a point on the curve AB. Conversely, above the transition point, the saturated solution of the racemate would be supersaturated with respect to the two tartrates, and transformation into the latter would ensue. If, therefore, a solution of equimolecular proportions of rubidium _d_- and _l_-tartrates is allowed to evaporate at a temperature above 40, a mixture of the two tartrates will be deposited; while at temperatures below 40 the racemate will separate out.

[Ill.u.s.tration: FIG. 100.]

Similar relations.h.i.+ps are met with in the case of sodium ammonium _d_- and _l_-tartrate and sodium ammonium racemate; but in this case the racemate is the stable form in contact with solution above the transition point (27).[347] Below the transition point, therefore, the solubility curve of the mixed tartrates will lie below the solubility curve of the racemate.

Below the transition point, therefore, sodium ammonium racemate will break up in contact with solution into a mixture of sodium ammonium _d_- and _l_-tartrates. At a higher temperature, 35, sodium ammonium racemate undergoes decomposition into sodium racemate and ammonium racemate.[348]

The behaviour of sodium ammonium racemate is of interest from the fact that it was the first racemic substance to be resolved into its optically active forms by a process of crystallization. On neutralizing a solution of racemic tartaric acid, half with soda and half with ammonia, and allowing the solution to evaporate, Pasteur[349] obtained a mixture of sodium ammonium {267} _d_- and _l_-tartrates. Since Pasteur was unaware of the existence of a transition point, the success of his experiment was due to the happy chance that he allowed the solution to evaporate at a temperature below 27; for had he employed a temperature above this, separation of the racemate into the two enantiomorphous forms would not have occurred. For this reason the attempt of Staedel to perform the same resolution met only with failure.[350]

Decomposition of the Double Salt by Water.--In the two cases just described, the solubility relations.h.i.+ps at the transition point are of a simpler character than in the case of most double salts. If, at a temperature above the transition point, a mixture of rubidium _d_- and _l_-tartrates in equimolecular proportions is brought in contact with water a solution will be obtained, which is saturated with respect to both enantiomorphous forms; and since the solubility of the two optical antipodes is identical, and the effect of one on the solubility of the other also the same, the solution will contain equimolecular amounts of the _d_- and _l_-salt. If, now, the solution is cooled down in contact with the solid salts to just below the transition point, it becomes supersaturated with respect to the racemate, and this will be deposited. The solution thereby becomes unsaturated with respect to the mixture of the active salts, and these must therefore pa.s.s into solution. As the latter are equally soluble, equal amounts of each will dissolve, and a further quant.i.ty of the racemate will be deposited. These processes of solution and deposition will continue until the single tartrates have completely disappeared, and only racemate is left as solid phase. As a consequence of the identical solubility of the two tartrates, therefore, no excess of either form will be left on pa.s.sing through the transition point. From this it will be evident that the racemate can exist as single solid phase in contact with its saturated solution at the transition point; or, in other words, the racemate is not decomposed by water at the transition point. The same behaviour will evidently be exhibited by sodium ammonium racemate at 27, for the two enantiomorphous sodium ammonium tartrates have also identical solubility.

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Very different, however, is the behaviour of, say, astracanite, or of the majority of double salts; for the solubility of the const.i.tuent salts is now no longer the same. If, for example, excess of a mixture of sodium sulphate and magnesium sulphate, in equimolecular proportions, is brought in contact with water below the transition point (22), more magnesium sulphate than sodium sulphate will dissolve, the solubility of these two salts in a common solution being given by the following figures, which express number of molecules of the salt in 100 molecules of water.[351]

COMPOSITION OF SOLUTIONS SATURATED WITH RESPECT TO Na_{2}SO_{4},10H_{2}O AND MgSO_{4},7H_{2}O.

---------------------------------------- Temperature. Na_{2}SO_{4}. MgSO_{4}.

---------------------------------------- 18.5 2.16 4.57 24.5 3.43 4.68 ----------------------------------------

At the transition point, then, it is evident that the solution contains more magnesium sulphate than sodium sulphate: and this must still be the case when astracanite, which contains sodium sulphate and magnesium sulphate in equimolecular proportions, separates out. If, therefore, the temperature is raised slightly above the transition point, magnesium sulphate and sodium sulphate will pa.s.s into solution, the former, however, in larger quant.i.ties than the latter, and astracanite will be deposited; and this will go on until all the magnesium sulphate has disappeared, and a mixture of astracanite and sodium sulphate decahydrate is left as solid phases. Since there are now three phases present, the system is univariant (by reason of the restriction previously made that the vapour phase is absent), and at a given temperature the solution will have a definite composition; as given in the following table:--

COMPOSITION OF SOLUTIONS SATURATED WITH RESPECT TO Na_{2}Mg(SO_{4})_{2},4H_{2}O AND Na_{2}SO_{4},10H_{2}O.

---------------------------------------- Temperature. Na_{2}SO_{4}. MgSO_{4}.

---------------------------------------- 22 2.95 4.70 24.5 3.45 3.62 ----------------------------------------

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From the above figures, therefore, it will be seen that at a temperature just above the transition point a solution in contact with the two solid phases, astracanite and Glauber's salt, contains a relatively smaller amount of sodium sulphate than a pure solution of astracanite would; for in this case there would be equal molecular amounts of Na_{2}SO_{4} and MgSO_{4}. A solution which is saturated with respect to astracanite alone, will contain more sodium sulphate than the solution saturated with respect to astracanite plus Glauber's salt, and the latter will therefore be deposited. From this, therefore, it is clear that if astracanite is brought in contact with water at about the transition point, it will undergo decomposition with separation of Glauber's salt (supersaturation being excluded).

[Ill.u.s.tration: FIG. 101.]

This will perhaps be made clearer by considering Fig. 101. In this diagram the ordinates represent the ratio of sodium sulphate to magnesium sulphate in the solutions, and the abscissae represent the temperatures. The line AB represents solutions saturated with respect to a mixture of the single salts (p. 268); BC refers to solutions in equilibrium with astracanite and magnesium sulphate; while BX represents the composition of solutions in contact with the solid phases astracanite and Glauber's salt. The values of the solubility are contained in the following table, and in that on p. 268, and are, as before, expressed in gm.-molecules of salt in 100 gm.-molecules of water.[352]

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------------------------------------------------------------------------- Astracanite Astracanite Temperature. + sodium sulphate. + magnesium sulphate.

---------------------------- ------------------------------ Na_{2}SO_{4}. MgSO_{4}. Na_{2}SO_{4}. MgSO_{4}.

------------------------------------------------------------------------- 18.5 -- -- 3.41 4.27 22 2.95 4.70 2.85 4.63 24.5 3.45 3.62 2.68 4.76 30 4.58 2.91 2.30 5.31 35 4.30 2.76 1.73 5.88 -------------------------------------------------------------------------

At the transition point the ratio of sodium sulphate to magnesium sulphate is approximately 1 : 1.6. In the case of solutions saturated with respect to both astracanite and Glauber's salt, the relative amount of sodium sulphate increases as the temperature rises, while in the solutions saturated for astracanite and magnesium sulphate, the ratio of sodium sulphate to magnesium sulphate decreases.

If, now, we consider only the temperatures above the transition point, we see from the figure that solutions represented by points above the line BX contain relatively more sodium sulphate than solutions in contact with astracanite and Glauber's salt; and solutions lying below the line BC contain relatively more magnesium sulphate than solutions saturated with this salt and astracanite. These solutions will therefore not be stable, but will deposit in the one case, astracanite and Glauber's salt, and in the other case, astracanite and magnesium sulphate, until a point on BX or BC is reached. All solutions, however, lying to the right of CBX, will be _unsaturated_ with respect to these two pairs of salts, and only the solutions represented by the line XY (and which contain equimolecular amounts of sodium and magnesium sulphates) will be saturated with respect to the pure double salt.

Transition Interval.--Fig. 101 will also render intelligible a point of great importance in connection with astracanite, and of double salts generally. At temperatures between those represented by the points B and X, the double salt when brought in contact with water will be decomposed with separation of sodium sulphate. Above the temperature of the point {271} X, however, the solution of the pure double salt is stable, because it can still take up a little of either of the components. At temperatures, then, above that at which the solution in contact with the double salt and the less soluble single salt, contains the single salts in the ratio in which they are present in the double salt, solution of the latter will take place without decomposition. _The range of temperature between that at which double salt can begin to be formed (the transition point) and that at which it ceases to be decomposed by water is called the transition interval._[353] If the two single salts have identical solubility at the transition point, the transition interval diminishes to nought.

In those cases where the double salt is the stable form below the transition point, the transition interval will extend downwards to a lower temperature. Fig. 101 will then have the reverse form.

Summary.--With regard to double salts we have learned that their formation from and their decomposition into the single salts, is connected with a definite temperature, the _transition temperature_. At this transition temperature two vapour pressure curves cut, viz. a curve of dehydration of a mixture of the single salts and the solubility curve of the double salt; or the dehydration curve of the double salt and the solubility curve of the mixed single salts. The solubility curves, also, of these two systems intersect at the transition point, but although the formation of the double salt commences at the transition point, complete stability in contact with water may not be attained till some temperature above (or below) that point. _Only when the temperature is beyond the transition interval, will a double salt dissolve in water without decomposition (_e.g._ the alums)._

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CHAPTER XVI