The Phase Rule and Its Applications Part 11

EAO Ice--salt.

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Deliquescence.--As is evident from Fig. 32, salt can exist in contact with water vapour at pressures under those represented by OAMF. If, however, the pressure of the vapour is increased until it reaches a value lying on this curve at temperatures above the cryohydric point, solution will be formed; for the curve AMF represents the equilibria between salt--solution--vapour.

From this, therefore, it is clear that if the pressure of the aqueous vapour in the atmosphere is greater than that of the saturated solution of a salt, that salt will, on being placed in the air, form a solution; it will _deliquesce_.

Separation of Salt on Evaporation.--With the help of Fig. 32 it is possible to state in a general manner whether or not salt will be deposited when a solution is evaporated under a constant pressure.[208]

The curve AMF (Fig. 32) is the vapour-pressure curve of the saturated solutions of the salt, _i.e._ it represents, as we have seen, the maximum vapour pressure at which salt can exist in contact with solution and vapour. The dotted line _aa_ represents atmospheric pressure. If, now, an unsaturated solution, the composition of which is represented by the point _x_, is heated in an open vessel, the temperature will rise, and the vapour pressure of the solution will increase. The system will, therefore, pa.s.s along a line represented diagrammatically by _xx'_. At the point _x'_ the vapour pressure of the system becomes equal to 1 atm.; and as the vessel is open to the air, the pressure cannot further rise; the solution boils. If the heating is continued, water pa.s.ses off, the concentration increases, and the boiling point rises. The system will therefore pa.s.s along the line _x'm_, until at the point _m_ solid salt separates out (provided supersaturation is excluded). The system is now univariant, and continued heating will no longer cause an alteration of the concentration; as water pa.s.ses off, solid salt will be deposited, and the solution will evaporate to dryness.

If, however, the atmospheric pressure is represented not by _aa_ but by _bb_, then, as Fig. 32 shows, the maximum vapour {131} pressure of the system salt--solution--vapour never reaches the pressure of 1 atm. Further, since the curve _bb_ lies in the area of the bivariant system solution--vapour there can at no point be a separation of the solid form; for the system solid--solution--vapour can exist only along the curve AMF.

On evaporating the solution of a salt in an open vessel, therefore, salt can be deposited only if at some temperature the pressure of the saturated solution is equal to the atmospheric pressure. This is found to be the case with most salts. In the case of aqueous solutions of sodium and pota.s.sium hydroxide, however, the vapour pressure of the saturated solution never reaches the value of 1 atm., and on evaporating these solutions, therefore, in an open vessel, there is no separation of the solid. Only a h.o.m.ogeneous fused ma.s.s is obtained. If, however, the evaporation be carried out under a pressure which is lower than the maximum pressure of the saturated solution, separation of the solid substance will be possible.

General Summary.--The systems which have been discussed in the present chapter contained water as one of their components, and an anhydrous salt as the other. It will, however, be clear that the relations.h.i.+ps which were found in the case of these will be found also in other cases where it is a question of the equilibria between two components, which crystallize out in the pure state, and only one of which possesses a measurable vapour pressure. A similar behaviour will, for example, be found in the case of many pairs of organic substances; and in all cases the equilibria will be represented by a diagram of the general appearance of Fig. 29 or Fig. 30.

That is to say: Starting from the fusion point of component I., the system will pa.s.s, by progressive addition of component II., to regions of lower temperature, until at last the cryohydric or eutectic point is reached. On further addition of component II., the system will pa.s.s to regions of higher temperature, the solid phase now being component II. If the fused components are miscible with one another in all proportions a continuous curve will be obtained leading up to the point of fusion of component II.

Slight changes of direction, it is true, due to changes in the crystalline form, may be found along this curve, {132} but throughout its whole course there will be but one liquid phase. If, on the other hand, the fused components are not miscible in all proportions, then the second curve will exhibit a marked discontinuity, and two liquid phases will make their appearance.

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CHAPTER VIII

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

B.--HYDRATED SALT AND WATER.

In the preceding chapter we discussed the behaviour of systems formed of two components, only one of which was volatile, in those cases where the two components separated from solution in the pure state. In the present chapter we shall consider those systems in which combination between the components can occur with the formation of definite compounds; such as are found in the case of crystalline salt hydrates. Since a not inconsiderable amount of study has been devoted to the systems formed by hydrated salts and water, systems which are of great chemical interest and importance, the behaviour of these will first call for discussion in some detail, and it will be found later that the relations.h.i.+ps which exist in such systems appear also in a large number of other two-component systems.

The systems belonging to this group may be divided into two cla.s.ses according as the compounds formed possess a definite melting point, _i.e._ form a liquid phase of the same composition, or do not do so. We shall consider the latter first.

1. _The Compounds formed do not have a Definite Melting Point._

Concentration-Temperature Diagram.--In the case of salts which can form crystalline hydrates, the temperature-concentration diagram, representing the equilibria of the {134} different possible systems, must necessarily be somewhat more complicated than where no such combination of the components occurs. For, as has already been pointed out, each substance has its own solubility curve; and there will therefore be as many solubility curves as there are solid phases possible, _the curve for each particular solid phase being continuous so long as it remains unchanged in contact with the solution_. As an example of the relations.h.i.+ps met with in such cases, we shall first of all consider the systems formed of sodium sulphate and water.

[Ill.u.s.tration: FIG. 33.]

Sodium Sulphate and Water.--At the ordinary temperatures, sodium sulphate crystallises from water with ten molecules of water of crystallisation, forming Glauber's salt. On determining the solubility of this salt in water, it is found that the solubility increases as the temperature rises, the values of the solubility, represented graphically by the curve AC (Fig.

33), being given in the following table.[209] The numbers denote grams of sodium sulphate, calculated as anhydrous salt, dissolved by 100 grams of water.

SOLUBILITY OF Na_{2}SO_{4},10H_{2}O.

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

-------------------------- 0 5.02 10 9.00 15 13.20 18 16.80 20 19.40 25 28.00 30 40.00 33 50.76 34 55.00 --------------------------

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On continuing the investigation at higher temperatures, it was found that the solubility no longer increased, but _decreased with rise of temperature_. At the same time, it was observed that the solid phase was now different from that in contact with the solution at temperatures below 33; for whereas in the latter case the solid phase was sodium sulphate decahydrate, at temperatures above 33 the solid phase was the anhydrous salt. The course of the solubility curve of anhydrous sodium sulphate is shown by BD, and the values of the solubility are given in the following table:--[210]

SOLUBILITY OF ANHYDROUS SODIUM SULPHATE.

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

-------------------------- 18 53.25 20 52.76 25 51.53 30 50.37 33 49.71 34 49.53 36 49.27 40.15 48.78 50.40 46.82 --------------------------

As is evident from the figure, the solubility curve which is obtained when anhydrous sodium sulphate is present as the solid phase, cuts the curve representing the solubility of the decahydrate, at a temperature of about 33.

If a solution of sodium sulphate which has been saturated at a temperature of about 34 be cooled down to a temperature below 17, while care is taken that the solution is protected against access of particles of Glauber's salt, crystals of a second hydrate of sodium sulphate, having the composition Na_{2}SO_{4},7H_{2}O, separate out. On determining the composition of the solutions in equilibrium with this hydrate at different temperatures, the following values were obtained, these values being represented by the curve FE (Fig. 33):--

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SOLUBILITY OF Na_{2}SO_{4},7H_{2}O.

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

-------------------------- 0 19.62 10 30.49 15 37.43 18 41.63 20 44.73 25 52.94 26 54.97 --------------------------

Since, as has already been stated, each solid substance has its own solubility curve, there are three separate curves to be considered in the case of sodium sulphate and water. Where two curves cut, the solution must be saturated with respect to two solid phases; at the point B, therefore, the point of intersection of the solubility curve of anhydrous sodium sulphate with that of the decahydrate, the solution must be saturated with respect to these two solid substances. But a system of two components existing in four phases, anhydrous salt--hydrated salt--solution--vapour, is invariant; and this invariability will remain even if only three phases are present, provided that one of the factors, pressure, temperature, or concentration of components retains a constant value. This is the case when solubilities are determined in open vessels; the pressure is then equal to atmospheric pressure. Under these circ.u.mstances, then, the system, anhydrous sodium sulphate--decahydrate--solution, will possess no degree of freedom, and can exist, therefore, only at one definite temperature and when the solution has a certain definite composition. The temperature of this point is 32.482 on a mercury thermometer, or 32.379 on the hydrogen thermometer.[211]

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Suspended Transformation.--Although it is possible for the anhydrous salt to make its appearance at the temperature of the quadruple point, it will not necessarily do so; and it is therefore possible to follow the solubility curve of sodium sulphate decahydrate to a higher temperature.

Since, however, the solubility of the decahydrate at temperatures above the quadruple point is greater than that of the anhydrous salt, the solution which is _saturated_ with respect to the former will be _supersaturated_ with respect to the latter. On bringing a small quant.i.ty of the anhydrous salt in contact with the solution, therefore, anhydrous salt will be deposited; and all the hydrated salt present will ultimately undergo conversion into the anhydrous salt, through the medium of the solution. In this case, as in all cases, the solid phase, which is the most stable at the temperature of the experiment, has at that temperature the least solubility.

Similarly, the solubility curve of anhydrous sodium sulphate has been followed to temperatures below 32.5. Below this temperature, however, the solubility of this salt is greater than that of the decahydrate, and the saturated solution of the anhydrous salt will therefore be supersaturated for the decahydrate, and will deposit this salt if a "nucleus" is added to the solution. From this we see that at temperatures above 32.5 the anhydrous salt is the stable form, while the decahydrate is unstable (or metastable); at temperatures below 32.5 the decahydrate is stable. This temperature, therefore, is the _transition temperature_ for decahydrate and anhydrous salt.

From Fig. 33 we see further that the solubility curve of the anhydrous salt (which at all temperatures below 32.5 is metastable) is cut by the solubility curve of the heptahydrate; and this point of intersection (at a temperature of 24.2) must be the _transition point_ for heptahydrate and anhydrous salt. Since at all temperatures the solubility of the heptahydrate is greater than that of the decahydrate, the former hydrate must be metastable with respect to the latter; so that throughout its whole course the solubility curve of the heptahydrate {138} represents only metastable equilibria. Sodium sulphate, therefore, forms only one stable hydrate, the decahydrate.

The solubility relations of sodium sulphate ill.u.s.trate very clearly the importance of the solid phase for the definition of saturation and supersaturation. Since the solubility curve of the anhydrous salt has been followed backwards to a temperature of about 18, it is readily seen, from Fig. 33, that at a temperature of, say, 20 three different _saturated_ solutions of sodium sulphate are possible, according as the anhydrous salt, the heptahydrate or the decahydrate, is present as the solid phase. Two of these solutions, however, would be metastable and _supersaturated with respect to the decahydrate_.

Further, the behaviour of sodium sulphate and water furnishes a very good example of the fact that a "break" in the solubility curve occurs when, and only when, the solid phase undergoes change. So long as the decahydrate, for example, remained unaltered in contact with the solution, the solubility curve was continuous; but when the anhydrous salt appeared in the solid phase, a distinct change in the direction of the solubility curve was observed.

Dehydration by Means of Anhydrous Sodium Sulphate.--The change in the relative stability of sodium sulphate decahydrate and anhydrous salt in presence of water at a temperature of 32.5 explains why the latter salt cannot be employed for dehydration purposes at temperatures above the transition point. The dehydrating action of the anhydrous salt depends on the formation of the decahydrate; but since at temperatures above 33 the latter is unstable, and cannot be formed in presence of the anhydrous salt, this salt cannot, of course, effect a dehydration above that temperature.

Pressure-Temperature Diagram.--The consideration of the pressure-temperature relations of the two components, sodium sulphate and water, must include not only the vapour pressure of the saturated solutions, but also that of the crystalline hydrates. The vapour pressures of salt hydrates have already been treated in a general manner (Chap. V.), so that it is only necessary here to point out the connection between the two cla.s.ses of systems. {139}

In most cases the vapour pressure of a salt hydrate, _i.e._ the vapour pressure of the system hydrate--anhydrous salt (or lower hydrate)--vapour, is at all temperatures lower than that of the system anhydrous salt (or lower hydrate)--solution--vapour. This, however, is not a necessity; and cases are known where the vapour pressure of the former system is, under certain circ.u.mstances, equal to or higher than that of the latter. An example of this is found in sodium sulphate decahydrate.

On heating Na_{2}SO_{4},10H_{2}O, a point is reached at which the dissociation pressure into anhydrous salt and water vapour becomes equal to the vapour pressure of the saturated solution of the anhydrous salt, as is apparent from the following measurements;[212] the differences in pressure being expressed in millimetres of a particular oil.

Temperature: 29.0 30.83 31.79 32.09 32.35 32.6 Difference of pressure: 23.8 10.8 5.6 3.6 1.6 0

At 32.6, therefore, the vapour pressures of the two systems

Na_{2}SO_{4},10H_{2}O--Na_{2}SO_{4}--vapour Na_{2}SO_{4}--solution--vapour

are equal; at this temperature the four phases, Na_{2}SO_{4},10H_{2}O; Na_{2}SO_{4}; solution; vapour, can coexist. From this it is evident that when sodium sulphate decahydrate is heated to 32.6, the two new phases anhydrous salt and solution will be formed (suspended transformation being supposed excluded), and the hydrate will appear to undergo _partial fusion_; and during the process of "melting" the vapour pressure and temperature will remain constant.[213] This is, however, not a true but a so-called _incongruent_ melting point; for the composition of the liquid phase is not the same as that of the solid. As has already been pointed out (p. 137), we are dealing here with the _transition point_ of the decahydrate and anhydrous salt, _i.e._ with the reaction Na_{2}SO_{4},10H_{2}O <--> Na_{2}SO_{4} + 10H_{2}O.

Since at the point of partial fusion of the decahydrate four {140} phases can coexist, the point is a quadruple point in a two-component system, and the system at this point is therefore invariant. The temperature of this point is therefore perfectly definite, and on this account the proposal has been made to adopt this as a fixed point in thermometry.[214] The temperature is, of course, practically the same as that at which the two solubility curves intersect (p. 112). If, however, the vapour phase disappears, the system becomes univariant, and the equilibrium temperature undergoes change with change of pressure. The transition curve has been determined by Tammann,[215] and shown to pa.s.s through a point of maximum temperature.