The Phase Rule and Its Applications Part 21

By the continued addition of acetic acid, the composition of the successive conjugate solutions in equilibrium with one another becomes, as the table shows, more nearly the same, and a point is at length reached at which the two solutions become identical. This will therefore be a _critical point_ (p. 98). Increased addition of acetic acid beyond this point will lead to a single h.o.m.ogeneous solution.

These relationships are represented graphically by the curve _a_K_b_, Fig.

84. The points on the branch _a_K represent the composition of the solutions relatively rich in chloroform (heavier layer), those on the curve _b_K the composition of solutions relatively rich in water (lighter layer); and the points on these two branches representing conjugate solutions are joined together by "tie-lines." Thus, the points _a'b'_ represent conjugate solutions, and the line _a'b'_ is a tie-line.

[Ill.u.s.tration: FIG. 84.]

Since, now, acetic acid when added to a heterogeneous mixture of chloroform and water does not enter in equal amounts into the two layers, but in amounts depending on its coefficient of distribution between chloroform and water,[321] the {243} tie-lines will not be parallel to AB, but will be inclined at an angle. As the solutions become more nearly the same, the tie-lines diminish in length, and at last, when the conjugate solutions become identical, shrink to a point. For the reason that the tie-lines are, in general, not parallel to the side of the triangle, the critical point at which the tie-line vanishes will not be at the summit of the curve, but somewhere below this, as represented by the point K.

The curve _a_K_b_, further, forms the boundary between the heterogeneous and h.o.m.ogeneous systems. A mixture of chloroform, water, and acetic acid represented by any point outside the curve _a_K_b_, will form only one h.o.m.ogeneous phase; while any mixture represented by a point within the curve, will separate into two layers having the composition represented by the ends of the tie-line pa.s.sing through that point. Thus, a mixture of the total composition _x_, will separate into two layers having the composition _a'_ and _b'_ respectively.

Since three components existing in three phases (two liquid and a vapour phase) const.i.tute a bivariant system, the final result, _i.e._ the composition of the two layers and the total vapour pressure, will not depend merely on the temperature, as in the case of two-component systems (p. 102), but also on the composition of the mixture with which we start.

At constant temperature, however, all mixtures, the composition of which is represented by a point on one and the same tie-line, will separate into the same two liquid phases, although the relative _amounts_ of the two phases will vary. If we omit the vapour phase, the condition of the system will depend on the pressure as well as on the temperature and composition of the initial mixture. By keeping the pressure constant, _e.g._ at atmospheric pressure (by working with open vessels), the system again becomes bivariant. We see, therefore, that the position of the curve _a_K_b_, or, in other words, the composition of the different conjugate ternary solutions, will vary with the temperature, and only with the temperature, if we a.s.sume either constancy of pressure or the presence of the vapour phase. Since at the critical point the condition is imposed that the two liquid phases become identical, one degree of freedom is thereby {244} lost, and therefore only one degree of freedom remains. The critical point, therefore, depends on the temperature, and only on the temperature; always on the a.s.sumption, of course, that the pressure is constant, or that a vapour phase is present. Fig. 84, therefore, represents an isothermal (p. 239).

It is of importance to note that the composition of the different ternary solutions obtained by the addition of acetic acid to a heterogeneous mixture of chloroform and water, will depend not only on the amount of acetic acid added, but also on the relative amounts of chloroform and water at the commencement. Suppose, for example, that we start with chloroform and water in the proportions represented by the point _c'_ (Fig. 84). On mixing these, two liquid layers having the composition _a_ and _b_ respectively will be formed. Since by the addition of acetic acid the relative amounts of these two substances in the system as a whole cannot undergo alteration, the total composition of the different ternary systems which will be obtained must be represented by a point on the line C_c'_ (p. 238). Thus, for example, by the addition of acetic acid a system may be obtained, the total composition of which is represented by the point _c"_.

Such a system, however, will separate into two conjugate ternary solutions, the composition of which will be represented by the ends of the tie-line pa.s.sing through the point _c"_. So long as the total composition of the system lies below the point S, _i.e._ the point of intersection of the line C_c'_ with the boundary curve, two liquid layers will be formed; while all systems having a total composition represented by a point on the line C_c'_, above S, will form only one h.o.m.ogeneous solution.

From the figure, also, it is evident that as the amount of acetic acid is increased, the relative amounts of the two liquid layers formed differ more and more until at S a limiting position is reached, when the amount of the one liquid layer dwindles to nought, and only one solution remains.

The same reasoning can be carried through for different initial amounts of chloroform and water, but it would be fruitless to discuss all the different systems which can be obtained. The reason for the preceding discussion was to show that {245} although the addition of acetic acid to a mixture of chloroform and water will, in all cases, lead ultimately to a limiting system, beyond which h.o.m.ogeneity occurs, that point is not necessarily the critical point. On the contrary, in order that addition of acetic acid shall lead to the critical mixture, it is necessary to start with a binary mixture of chloroform and water in the proportions represented by the point _c'_. In this case, addition of acetic acid will give rise to a series of conjugate ternary solutions, the composition of which will gradually approach to one another, and at last become identical.

From the foregoing it will be evident that the amount of acetic acid required to produce a h.o.m.ogenous solution, will depend on the relative amounts of chloroform and water from which we start, and can be ascertained by joining the corner C with the point on the line AB representing the total composition of the initial binary system. The point where this line intersects the boundary curve _a_K_b_ will indicate the minimum amount of acetic acid which, under these particular conditions, is necessary to give one h.o.m.ogeneous solution.

Retrograde Solubility.--As a consequence of the fact that acetic acid distributes itself unequally between chloroform and water, and the critical point K, therefore, does not lie at the summit of the curve, it is possible to start with a h.o.m.ogeneous solution in which the percentage amount of acetic acid is greater than at the critical point, and to pa.s.s from this first to a heterogenous and then again to a h.o.m.ogenous system merely by altering the relative amounts of chloroform and water. This phenomenon, to which the term _retrograde solubility_ is applied, will be observed not only in the case of chloroform, water, and acetic acid, but in all other systems in which the critical point lies below the highest point of the boundary curve for heterogeneous systems. This will be seen from the diagram, Fig. 85. Starting with the h.o.m.ogeneous system represented by _x_, in which, therefore, the concentration of C is greater than in the critical mixture (K), if the relative amounts of A and B are altered in the direction _xx'_, while the amount of C is maintained constant, the system will become heterogeneous when the composition reaches the point _y_, and will remain {246} heterogeneous with changing composition until the point _y'_ is pa.s.sed, when it will again become h.o.m.ogeneous. If the relative concentration of C is increased above that represented by the line SS, this phenomenon will, of course, no longer be observed.

[Ill.u.s.tration: FIG. 85.]

Relationships similar to those described for chloroform, water, and acetic acid are also found in the case of a number of other trios, _e.g._ ether, water, and alcohol; chloroform, water, and alcohol.[322] They have also been observed in the case of a considerable number of molten metals.[323]

Thus, molten lead and silver, as well as molten zinc and silver, mix in all proportions; but molten lead and zinc are only partially miscible with one another. When melted together, therefore, the last two metals will separate into two liquid layers, one rich in lead, the other rich in zinc. If silver is now added, and the temperature maintained above the freezing point of the mixture, the silver pa.s.ses for the most part, in accordance with the law of distribution, into the upper layer, which is rich in zinc; silver being more soluble in molten zinc than in molten lead. This is clearly shown by the following figures:--[324]

{247}

-------------------------------------------------- Heavier alloy. Lighter alloy.

-------------------------------------------------- Percentage amount of Percentage amount of Silver. Lead. Zinc. Silver. Lead. Zinc.

-------------------------------------------------- 1.25 96.69 2.06 38.91 3.12 57.97 1.71 96.43 1.86 45.01 3.37 51.62 5.55 93.16 1.29 54.93 4.21 40.86 --------------------------------------------------

The numbers in the same horizontal row give the composition of the conjugate alloys, and it is evident that the upper layer consists almost entirely of silver and zinc. On allowing the mixture to cool slightly, the upper layer solidifies first, and can be separated from the still molten lead layer. It is on this behaviour of silver towards a mixture of molten lead and zinc that the Parkes's method for the desilverization of lead depends.[325] If aluminium is also added, a still larger proportion of silver pa.s.ses into the lighter layer, and the desilverization of the lead is more complete.[326]

[Ill.u.s.tration: FIG. 86.]

[Ill.u.s.tration: FIG. 87.]

The Influence of Temperature.--As has already been said, a ternary system existing in three phases possesses two degrees of freedom; and the state of the system is therefore dependent not only on the relative concentration of the components, but also on the temperature. As the temperature changes, therefore, the boundary curve of the heterogeneous system will also alter; and in order to represent this alteration we shall make use of the right prism, in which the temperature is measured upwards. In this way the boundary curve pa.s.ses into a boundary surface (called a dineric surface), as shown in Fig. 86. In this figure the curve _akb_ is the isothermal for the ternary system; the curve _a_K_b_ shows the change in the _binary_ system AB with the temperature, with {248} a critical point at K. This curve has the same meaning as those given in Chapter VI. The curve _k_K is a critical curve joining together the critical points of the different isothermals. In such a case as is shown in Fig. 86, there does not exist any real critical temperature for the ternary system, for as the temperature is raised, the amount of C in the "critical" solution becomes less and less, and at K only two components, A and B, are present. In the case, however, represented in Fig. 87, a real ternary critical point is found. In this figure _ak'b_ is an isothermal, _ak"_ is the curve for the binary system, and K is the ternary critical point. All points outside the helmet-shaped boundary surface represent h.o.m.ogeneous ternary solutions, while all points within the surface belong to heterogeneous systems. Above the temperature of the point K, the three components are miscible in all proportions. An example of a ternary system yielding such a boundary surface is that consisting of phenol, water, and acetone.[327] In this case the critical temperature K is 92, and the composition at this ternary critical point is--

Water 59 per cent.

Acetone 12 "

Phenol 29 "

[Ill.u.s.tration: FIG. 88.]

The difference between the two cla.s.ses of systems just mentioned, is seen very clearly by a glance at the Figs. 88 and 89, which show the projection of the isothermals on the base of the prism. In Fig. 88, the projections yield paraboloid curves, the two branches of which are cut by one side of the triangle; and the critical point is represented by a point on {249} this side. In the second case (Fig. 89), however, the projections of the isothermals form ellipsoidal curves surrounding the supreme critical point, which now lies _inside the triangle_. At lower temperatures, these isothermal boundary curves are cut by a side of the triangle; at the critical temperature, _k"_, of the binary system AB, the boundary curve _touches_ the side AB, while at still higher temperatures the boundary curve comes to lie entirely within the triangle. At any given temperature, therefore, between the critical point of the binary system (_k"_), and the supreme critical point of the ternary system (K), each pair of the three components are miscible with one another in all proportions; for the region of heterogeneous systems is now bounded by a closed curve lying entirely within the triangle. Outside this curve only h.o.m.ogeneous systems are found.

Binary mixtures, therefore, represented by any point on one of the sides of the triangle must be h.o.m.ogeneous, for they all lie outside the boundary curve for heterogeneous states.

[Ill.u.s.tration: FIG. 89.]

2. _The three components can form two pairs of partially miscible liquids._

In the case of the three components water, alcohol, and succinic nitrile, water and alcohol are miscible in all proportions, but not so water and succinic nitrile, or alcohol and succinic nitrile.

[Ill.u.s.tration: FIG. 90.]

[Ill.u.s.tration: FIG. 91.]

As we have already seen (p. 122), water and succinic nitrile can form two liquid layers between the temperatures 18.5 and 55.5; while alcohol and nitrile can form two liquid layers between 13 and 31. If, then, between these two temperature limits, alcohol is added to a heterogeneous mixture of water and nitrile, or water is added to a mixture of alcohol and nitrile, two heterogeneous ternary systems will be formed, {250} and two boundary curves will be obtained in the triangular diagram, as shown in Fig. 90.[328] On changing the temperature, the boundary curves will also undergo alteration, in a manner similar to that just discussed. As the temperature falls, the two curves will spread out more and more into the centre of the triangle, and might at last meet one another; while at still lower temperatures we may imagine the curves still further expanding so that the two heterogeneous regions flow into one another and form a _band_ on the triangular diagram (Fig. 91). This, certainly, has not been realized in the case of the three components mentioned, because at a temperature higher than that at which the two heterogeneous regions could fuse together, solid separates out.

[Ill.u.s.tration: FIG. 92.]

The gradual expansion of a paraboloid into a band-like area of heterogeneous ternary systems, has, however, been observed in the case of water, phenol, and aniline.[329] In Fig. 92 are shown three isothermals, viz. those for 148, 95, and 50. At 148, water and aniline form two layers having the composition--

Water, 83.5 per cent. } { water, 20 per cent.

} and { Aniline, 16.5 " } { aniline, 80 "

{251}

and the critical point _k'_ has the composition--

Water, 65; phenol, 13.2; aniline, 21.8 per cent.

At 95, the composition of the two binary solutions is--

Water, 93 per cent. } { water 8 per cent.

} and { Aniline, 7 " } { aniline, 92 "

while the point _k"_ has the composition

Water, 69.9; phenol, 26.6; aniline, 3.5 per cent.

At 50, the region of heterogeneous states now forms a band, and the two layers formed by water and aniline have the composition--

Water, 96.5 per cent. } { water, 5.5 per cent.

} and { Aniline, 3.5 " } { aniline, 94.5 "

while the two layers formed by water and phenol have the composition--

Water, 89 per cent.} { water, 38 per cent.

} and { Phenol, 11 " } { phenol, 62 "

All mixtures of water, phenol, and aniline, therefore, the composition of which is represented by any point within the band _abcd_, will form two ternary solutions; while if the composition is represented by a point outside the band, only one h.o.m.ogeneous solution will be produced.

3. _The three components form three pairs of partially miscible liquids._