The Phase Rule and Its Applications

ids; and solids, also, when brought in contact with liquids, "pass into solution" and yield a homogeneous liquid phase. On the other hand, the conception of a solid solution is one which in many

is a homogeneous phase, the composition of which can vary continuously within certain limits; the definition involves, therefore, no condition as to the physical state of the substances. Accordingly, solid solutions are homogeneous solid phases, the composition of which can undergo continuous variation within certain limits.

nces (occlusion of hydrogen by palladium; occlusion of hydrogen by iron) are due to the formation of solid solutions. The same is probably also true of the phen

these crystalline substances remain clear and transparent, and the pressure of the water vapour which they emit varies with the degree of hydration or the concentration of water in the mi

entioned that the term "solid" is used in its popular sense. Strictly speaking,

f essential importance to remember that a solid solution constitutes only on

ing limited chiefly to the phenomena of occlusion or adsorption of gases by charcoal.[257] We shall, therefore

d by the two phases gas-solid, th

when the pressure reaches a certain value,

g.

his point combination can take place. There will now be three phases present, viz. solid component, compound, and vapour. The system is therefore univariant, and if the temperature is maintained constant, the vapour pressure will be constant, irrespective of the amount of compound formed, i.e. irrespective of the relative amounts of gas and solid. T

absorbed and may al

sure will still vary with the concentration of the gaseous component in the solid phase. This is represented by the curve AB in Fig. 47. When, however, the pressure has reached a certain

tain concentration the solid solution can s

learn more fully. If, now, two immiscible solutions are formed, then the system will become univariant, and at constant temperature the pc-curve will be a strai

g.

nion that a compound is formed, but rather that the gas undergoes very great condensation, acts as a quasi-metal (to which he gave the name hydrogenium), and forms a homogeneous alloy with the palladium, later investigat

f the equilibrium between hydrogen and palladium on the basis of the Phase Rule classification given above. If a compound

om this point of view, a brief account of the results obtained will be given he

f the gas pressure with the concentration of the hydrogen in the palladium at the temperatures 120°, 170°, and 200°. As can be seen, the curve consists of three parts, an ascending portion which passes gradually and continuously into an almost horizontal but slightly asc

g.

e; the higher the temperature, the lower is the concentration at which the middle passes into the terminal portion of the curve. Such a behaviour would, however, agree with the assumption of the formation of two solid solutions, the "miscibility" of which increases with the temperature, as in the case of the liquid solutions of phenol and water (p. 97). Nevertheless, although the assumption of the formation of two solid solutions is more satisfactory than that of the formation of a compound, it does not entirely explain the facts. If two solid solutions are formed, the pressure curve should be horizo

ome unexplained phenomena, the behaviour found by Hoitsema would appear t

ids in Solids.

es, the depression was too small; in some instances, indeed, the freezing point may be raised. To explain these irregularities, van't Hoff assumed that the dissolved substance crystallized out along with the solid solvent

tallization together of isomorphous substances, and known as isomorphous mixtures. Indeed, it has been contended[264] that these isomorphous mixtures should not be considered as solid solutions at all, although no sharp line of demarcation can be drawn between the two classes. The differences, however, in the behaviour of th

chapter, we are dealing with the fusion curves of two substances, where, however, the liquid solution is in equilibrium not with one of the pure components, but with a solid solution or mixed crystal. The simple scheme (Fig. 29, p. 117) which was obtained in the case of two components which cry

es; the consideration of the formation of mixed crystals of isodimorphous substances

Crystals of Isomo

ponents in these two phases is not, in general, the same, two curves will be required for each system, one relating to the liquid phase, the other relating to the solid. The temperature at which solid begins to be deposited from the liquid solution will be called the freezing point of the mixture, and the temperatur

can form an Unbroken S

solid phase present, viz. the solid solution or mixed crystal. If the components are completely miscible in the solid state, they will also be completely miscible in the liquid state, and there can therefore be only one liquid phase. The system can at

g.

s lie between the freezing points of t

ng point curve is therefore a straight line joining the melting points of the two components. This behaviour, however, is rather exceptional, the freezing-point curve lying generally above, sometimes also below, the straight line joining the melting points of the pu

les of

ic ald

. Freezing point. De

i

31.

37.28°

43.12°

46.80°

52.94°

58.82°

65.07°

67.91°

0 69.

ollowing rule: At any given temperature, the concentration of that component by the addition of which the freezing point is depressed, is greater in the liquid than in the solid phase; or, conversely, the concentration of that component by the addition of which the freezing point is raised, is greater in the solid than in the liquid phase. An illustration of this rule is afforded by the two substances chloro- and bromo-cinnamic aldehyde alre

ion of two components, A and B, having the composition represented by the point x (Fig. 50), is allowed to cool, the system will pass along the line xx′. At the temperature of the point a, mixed crystals will be deposited, the composition of which will be that represented by b. As the temperature continues to fall, more and more solid will be

g.

tinuing to add heat, the temperature of the mass will rise, more of the solid will melt, and the composition of the two phases will change as represented by the curves da and cb.

will not necessarily coincide with the freezing-point curve, although it may approach very near to it; complete coincidence can

rve passes through a maxi

g.

n the pure components crystallize out. For, since the curve passes through a maximum, it is evident t

rve of mixtures of d- and l-carvoxime[272] (C10H14N.OH). The freezing points and melting points of the diffe

cent

ime. Per

reezing point.

72.0

72.

73.

75.4°

79.0

84.6

88.2

0 90

91.4

86.4

77.

72.

72.0

in the solid phase than in the liquid. Similarly, since addition of the dextro-form raises the melting point of the l?vo-form, the solid phase (on the left-hand branch of the curve) must be richer in dextro- than in l?vo-carvoxime. At the maximum point, the melting-point and freezing-point curves touch; at this point, therefore, the composition of the solid a

rve passes through a mini

e mixed crystals are formed there is only one continuous curve. On one side of the minimum point the liquid phase contains relatively more, on the other side relatively less, of the one component than does the solid phase; while at the minimum

g.

Mercuric bromide melts at 236.5°, and mercuric iodide at 255.4°. The mixed crystal of definite constant me

in the following table, and rep

per ce

ing point. M

36.5°

28.8

22.2

17.8

16.6

6.1°

16.3

17.3

21.1

27.8

36.2

45.5

5.4°

g.

e is allowed to fall to x′, and the solid then separated from the liquid, the mixed crystals so obtained will have the composition represented by e. If, now, the mixed crystals e are completely fused and the fused mass allowed to cool, separation of solid will occur when the temperature has fallen to the point f. The mixed crystals which are deposited have now the composition represented by g, i.e. they are richer in B than the original mixed crystals. By repeati

e maximum point, while the liquid phase will more and more assume the composition of either pure A or pure B, according as the initial composition was on the A side or the B side of the maximum point. In those cases, ho

o not form a Continuous

l not alter the composition of the mixed crystal, but there will be formed a second solid phase consisting of a solution of A in B. At this point the four phases, mixed crystals containing excess of A, mixed crystals containing excess of B, liquid

rve exhibits a transition

AD. On the other hand, addition of A lowers the melting point of B, and the two curves BC and BE are obtained for the liquid and solid phases respectively. At the temperature of the line CDE the liquid solution of the composition represented by C is in equilibrium

g.

in the case of silver nitrate and sodium nitrate.[274] The following table co

ules

ezing point.

.6° 2

1.4°

215°

217.2°

222

8.4°

34.8°

44.4°

59.4°

272

84°

308°

t the liquid contains 19.5, and the two conjugate solid solutio

g.

g.

rve exhibits a eutectic p

e addition of the other, until at last a point is reached at which the liq

um and thallium nitrates[275] and of naphthalene and monochloracetic acid.[276] Th

quid solution.

ce

Per cent. a

ne. Per c

100

96.0 1

0 79.0

29.4 7

3 68.7

4 57.6

3 46.7

7 32.3

4 15.6

100

by D and E respectively. If, therefore, a fused mixture containing the two components A and B in the proportions represented by C is

g.

g.

the relationships are somewhat more complicated. As before, the area above the freezing-point curve gives the conditions under which homogeneous liquid solutions can exist; but below the melting-point curve two different mixed crystals can coexist. This will be best understood from Figs. 57 and 58. D and E represent, as we have seen, the composition of two mixed crystals which are in equilibrium with the liquid solution at the temperature of the point C. These two mixed crystals represent,

mixed crystals the composition of which is represented by x′ and x″ respectively. From this, then, it can be seen that in the case of substances which form two solid solutions, the mixed crystals which are desp

n the alloy between the temperature at which it separates out from the fused mass and the ordinary temperature. Thus, for example, one of the alloys of copper and tin which separates