The Phase Rule and Its Applications Part 22

[Ill.u.s.tration: FIG. 93.]

The third chief case which can occur is that no two of the components are completely miscible with one another. In this case, therefore, we shall obtain three paraboloid boundary curves, as shown in Fig. 93. If, now, we imagine these three curves to expand in towards the centre of the triangle, as might happen, for example, by lowering the temperature, a point will {252} be reached at which the curves partly overlap, and we shall get the appearance shown in Fig. 94.

The points _a_, _b_, and _c_ represent the points where the three curves cut, and the triangle _abc_ is a region where the curves overlap. From this diagram we can see that any mixture having a composition represented by a point in one of the clear s.p.a.ces at the corners of the larger triangle, will form a h.o.m.ogeneous solution; if the composition corresponds to any point lying in one of the quadrilateral regions _x__{1}, _x__{2} or _x__{3}, two ternary solutions will be formed; while, if the composition is represented by any point in the inner triangle, separation into three layers will occur.

[Ill.u.s.tration: FIG. 94.]

Since in the clear regions at the corners of the triangle we have three components in two phases, liquid and vapour, the systems have three degrees of freedom. At constant temperature, therefore, the condition of the system is not defined until the concentrations of two of the components are fixed.

A system belonging to one of the quadrilateral s.p.a.ces has, as we have seen, two degrees of freedom; besides the temperature, one concentration must be fixed. Lastly, a system the composition of which falls within the inner triangle _abc_, will form three layers, and will therefore possess only one degree of freedom. If the temperature is fixed, the composition of the three layers is also determined, viz. that of the points _a_, _b_, and _c_ respectively; and a change in the composition of the original mixture can lead only to a difference in the relative amounts of the three layers, not to a difference in their composition.

An example of a system which can form three liquid phases is found in water, ether, and succinic nitrile.[330]

{253}

CHAPTER XV

PRESENCE OF SOLID PHASES

A. The Ternary Eutectic Point.--In pa.s.sing to the consideration of those ternary systems in which one or more solid phases can exist together with one liquid phase, we shall first discuss not the solubility curves, as in the case of two-component systems, but the simpler relations.h.i.+ps met with at the freezing point. That is, we shall first of all examine the freezing point curves of ternary systems.

[Ill.u.s.tration: FIG. 95.]

Since it is necessary to take into account not only the changing composition of the liquid phase, but also the variation of the temperature, we shall employ the right prism for the graphic representation of the systems, as shown in Fig. 95. A, B, and C in this figure, therefore, denote the melting points of the pure components. If we start with the component A at its melting point, and add B, which is capable of dissolving in liquid A, the freezing point of A will be lowered; and, similarly, the freezing point of B by addition of A. In this way we get the freezing point curve A_k__{1}B for the binary system; _k__{1}; being an eutectic point. This curve will of course lie in the plane formed by one face of the prism. In a similar manner we obtain the freezing point curves A_k__{2}C and B_k__{3}C.

These curves give the composition of the binary liquid phases in equilibrium {254} with one of the pure components, or at the eutectic points, with a mixture of two solid components. If, now, to the system represented say by the point _k__{1}, a small quant.i.ty of the third component, C, is added, the temperature at which the two solid phases A and B can exist in equilibrium with the liquid phase is lowered; and this depression of the eutectic point is all the greater the larger the addition of C. In this way we obtain the curve _k__{1}K, which slopes inwards and downwards, and indicates the varying composition of the ternary liquid phase with which a mixture of solid A and B are in equilibrium. Similarly, the curves _k__{2}K and _k__{3}K are the corresponding eutectic curves for A and C, and B and C in equilibrium with ternary solutions. At the point K, the three solid components are in equilibrium with the liquid phase; and this point, therefore, represents _the lowest temperature attainable with the three components given_. Each of the ternary eutectic curves, as they may be called, is produced by the intersection of two surfaces, while at the ternary eutectic point, three surfaces, viz. A_k__{1}K_k__{2}, B_k__{1}K_k__{3}, and C_k__{1}K_k__{3} intersect. Any point on one of these surfaces represents a ternary solution in equilibrium with only one component in the solid state; the lines or curves of intersection of these represent equilibria with two solid phases, while at the point K, the ternary eutectic point, there are three solid phases in equilibrium with a liquid and a vapour phase. The surfaces just mentioned represent bivariant systems. One component in the solid state can exist in equilibrium with a ternary liquid phase under varying conditions of temperature and concentration of the components in the solution; and before the state of the system is defined, these two variables, temperature and composition of the liquid phase, must be fixed. On the other hand, the curves formed by the intersection of these planes represent univariant systems; at a given temperature two solid phases can exist in equilibrium with a ternary solution, only when the latter has a definite composition. Lastly, the ternary eutectic point, K, represents an invariant system; three solid phases can exist in equilibrium with a ternary solution, only when the latter has one fixed composition and when the temperature has a definite value. This eutectic point, therefore, {255} has a perfectly definite position, depending only on the nature of the three components.

Instead of employing the prism, the change in the composition of the ternary solutions can also be indicated by means of the _projections_ of the curves _k__{1}K, _k__{2}K, and _k__{3}K on the base of the prism, the particular temperature being written beside the different eutectic points and curves. This is shown in Fig. 96.

[Ill.u.s.tration: FIG. 96.]

The numbers which are given in this diagram refer to the eutectic points for the system bis.m.u.th--lead--tin, the data for which are as follows:--[331]

-------------------------------------------------------------------- Melting point of Percentage composition of Temperature of binary pure metal. binary eutectic mixture. eutectic point.

-------------------------------------------------------------------- Bi Pb Sn Bis.m.u.th, 268 55 45 -- Bi--Pb, 127 Lead, 325 58 -- 42 Bi--Sn, 133 Tin, 232 -- 37 63 Pb--Sn, 182 --------------------------------------------------------------------

-------------------------------------------------- Percentage composition of Temperature of ternary ternary eutectic mixture. eutectic point.

-------------------------------------------------- Bi Pb Sn 52 32 16 96 --------------------------------------------------

Formation of Compounds.--In the case just discussed, the components crystallized out from solution in the pure state. If, however, combination can take place between two of the components, the relations.h.i.+ps will be somewhat different; the curves which are obtained in such a case being represented in Fig. 97. From the figure, we see that the two components B {256} and C form a compound, and the freezing point curve of the binary system has therefore the form shown in Fig. 64 (p. 209). Further, there are two _ternary_ eutectic points, K_{1} and K_{2}, the solid phases present being A, B, and compound, and A, C, and compound respectively.

[Ill.u.s.tration: FIG. 97.]

The particular point, now, to which it is desired to draw attention is this. Suppose the ternary eutectic curves projected on a plane parallel to the face of the prism containing B and C, _i.e._ suppose the concentrations of the two components B and C, between which interaction can occur, expressed in terms of a constant amount of the third component A,[332]

curves will then be obtained which are in every respect a.n.a.logous to the freezing point curves of binary systems. Thus, suppose the eutectic curves _k__{1}K and _k__{2}K in Fig. 95 projected on the face BC of the prism, then evidently a curve will be obtained consisting of two branches meeting in an eutectic point. On the other hand, the projection of the ternary eutectic curves in Fig. 97 on the face BC of the prism, will give a curve consisting of three portions, as shown by the outline _k__{1}K_{1}K_{2}_k__{2} in Fig. 97.

Various examples of this have been studied, and the following table contains some of the data for the system ethylene bromide (A), picric acid (B), and [beta]-naphthol (C), obtained by Bruni.[333]

{257}

------------------------------------------------------------------------- Temperature Solid phases present.

------------------------------------------------------------------------- Point _k__{1} 9.41 Ethylene bromide, picric acid.

Curve _k__{1}K_{1} -- " "

Point K_{1} 9.32 Ethylene bromide, picric acid, and [beta]-naphthol picrate.

Curve K_{1}D'K_{2} -- Ethylene bromide, [beta]-naphthol picrate.

Point D' 9.75 " " " "

Point K_{2} 8.89 " " [beta]-naphthol, and picrate.

Curve K_{2}_k__{2} -- " " [beta]-naphthol.

Point _k__{2} 9.04 " " "

From what has been said, it will be apparent that if the ternary eutectic curve of a three-component system (in which one of the components is present in constant amount) is determined, it will be possible to state, from the form of curve obtained, whether or not the two components present in varying amount crystallize out pure or combine with one another to form a compound. It may be left to the reader to work out the curves for the other possible systems; but it will be apparent, that the projections of the ternary eutectic curves in the manner given will yield a series of curves alike in all points to the binary curves given in Figs. 63-65, pp. 208-210.

Since, from the method of investigation, the temperatures of the eutectic curves will depend on the melting point of the third component (A), it is possible, by employing substances with widely differing melting points, to investigate the interaction of the two components (_e.g._ two optical antipodes) B and C over a range of temperature; and thus determine the range of stability of the compound, if one is formed. Since, in some cases, two substances which at one temperature form mixed crystals combine at another temperature to form a definite compound, the relations.h.i.+ps which have just been described can be employed, and indeed, have been employed, to determine the temperature at which this change occurs.[334] By means of this method, Adriani found that below 103 _i_-camphoroxime exists as a racemic compound, while above {258} that temperature it occurs as a racemic mixed crystal[335] (_cf._ p. 219).

B. Equilibria at Higher Temperatures. Formation of Double Salts.--After having studied the relations.h.i.+ps which are found in the neighbourhood of the freezing points of the components, we now pa.s.s to the discussion of the equilibria which are met with at higher temperatures. In this connection we shall confine the discussion entirely to the systems formed of two salts and water, dealing more particularly with those cases in which the water is present in relatively large amount and acts as solvent. Further, in studying these systems, one restriction must be made, viz. that the single salts are salts either of the same base or of the same acid; or are, in other words, capable of yielding a common ion in solution. Such a restriction is necessary, because otherwise the system would be one not of three but of four components.[336]

Transition Point.--As is very well known, there exist a number of hydrated salts which, on being heated, undergo apparent partial fusion; and in Chapter V. the behaviour of such hydrates was more fully studied in the light of the Phase Rule. Glauber's salt, or sodium sulphate decahydrate, for example, on being heated to a temperature of about 32.5, partially liquefies, owing to the fact that the water of crystallization is split off and anhydrous sodium sulphate formed, as shown by the equation--

Na_{2}SO_{4},10H_{2}O = Na_{2}SO_{4} + 10H_{2}O

The temperature of 32.5, it was learned, const.i.tuted a _transition point_ for the decahydrate and anhydrous salt plus water; decomposition of the hydrated salt occurring above this temperature, combination of the anhydrous salt and water below it.

a.n.a.logous phenomena are met with in systems const.i.tuted of two salts and water in which the formation of double salts can take place. Thus, for example, if _d_-sodium pota.s.sium {259} tartrate is heated to above 55, apparent partial fusion occurs, and the two single salts, _d_-sodium tartrate and _d_-pota.s.sium tartrate, are deposited, the change which occurs being represented by the equation--

4NaKC_{4}O_{6}H_{4},4H_{2}O = 2Na_{2}C_{4}O_{6}H_{4},2H_{2}O + 2K_{2}C_{4}O_{6}H_{4},H_{2}O + 11H_{2}O

On the other hand, if sodium and pota.s.sium tartrates are mixed with water in the proportions shown on the right side of the equation, the system will remain partially liquid so long as the temperature is maintained above 55 (in a closed vessel to prevent loss of water), but on allowing the temperature to fall below this point, complete solidification will ensue, owing to the formation of the hydrated double salt. Below 55, therefore, the hydrated double salt is the stable system, while above this temperature the two single salts plus saturated solution are stable.[337]

A similar behaviour is found in the case of the double salt copper dipota.s.sium chloride (CuCl_{2},2KCl,2H_{2}O or CuK_{2}Cl_{4},2H_{2}O).[338]

When this salt is heated to 92, partial liquefaction occurs, and the original blue plate-shaped crystals give place to brown crystalline needles and white cubes; while on allowing the temperature to fall, re-formation of the blue double salt ensues. The temperature 92 is, therefore, a transition point at which the reversible reaction--

CuK_{2}Cl_{4},2H_{2}O <--> CuKCl_{3} + KCl + 2H_{2}O

takes place.

The decomposition of sodium pota.s.sium tartrate, or of copper dipota.s.sium chloride, differs in so far from that of Glauber's salt that _two_ new solid phases are formed; and in the case of copper dipota.s.sium chloride, one of the decomposition products is itself a double salt.

In the two examples of double salt decomposition which have just been mentioned, sufficient water was yielded to cause a partial liquefaction; but other cases are known where this is not so. Thus, when copper calcium acetate is heated to a {260} temperature of 75, although decomposition of the double salt into the two single salts occurs as represented by the equation[339]--

CuCa(C_{2}H_{3}O_{2})_{4},8H_{2}O = Cu(C_{2}H_{3}O_{2})_{2},H_{2}O + Ca(C_{2}H_{3}O_{2})_{2},H_{2}O + 6H_{2}O

the amount of water split off is insufficient to give the appearance of partial fusion, and, therefore, only a change in the crystals is observed.

The preceding examples, in which decomposition of the double salt was effected by a rise of temperature, were chosen for first consideration as being more a.n.a.logous to the case of Glauber's salt; but not a few examples are known where the reverse change takes place, formation of the double salt occurring _above_ the transition point, and decomposition into the const.i.tuent salts below it. Instances of this behaviour are found in the case of the formation of astracanite from sodium and magnesium sulphates, and of sodium ammonium racemate from the two sodium ammonium tartrates, to which reference will be made later. Between these various systems, however, there is no essential difference; and whether decomposition or formation of the double salt occurs at temperatures above the transition point, will of course depend on the heat of change at that point. For, in accordance with van't Hoff's law of movable equilibrium (p. 58), that change will take place at the higher temperature which is accompanied by an absorption of heat. If, therefore, the formation of the double salt from the single salts is accompanied by an absorption of heat, the double salt will be formed from the single salts on raising the temperature; but if the reverse is the case, then the double salt on being heated will decompose into the const.i.tuent salts.[340]

In those cases, now, which have so far been studied, the change at the transition point is accompanied by a taking up or a splitting off of water; and _in such cases the general rule can be given, that if the water of crystallization of the two const.i.tuent {261} salts together is greater than that of the double salt, the latter will be produced from the former on raising the temperature_ (_e.g._ astracanite from sodium and magnesium sulphates); _but if the double salt contains more water of crystallization than the two single salts, increase of temperature will effect the decomposition of the double salt_. When we seek for the connection between this rule and the law of van't Hoff, it is found in the fact that the heat effect involved in the hydration or dehydration of the salts is much greater than that of the other changes which occur, and determines, therefore, the sign of the total heat effect.[341]