{187}

In this figure, the melting-point curve, _i.e._ the temperature-concentration curve for the mixed crystals, is represented by the lower curve. Since the addition of the laevo-form to the dextro-form raises the melting point of the latter, the concentration of the laevo-form (on the right-hand branch of the curve) must, in accordance with the rule given, be greater in the solid phase than in the liquid. Similarly, since addition of the dextro-form raises the melting point of the laevo-form, the solid phase (on the left-hand branch of the curve) must be richer in dextro- than in laevo-carvoxime. At the maximum point, the melting-point and freezing-point curves touch; at this point, therefore, the composition of the solid and liquid phases must be identical. It is evident, therefore, that at the maximum point the liquid will solidify, or the solid will liquefy completely without change of temperature; and, accordingly, mixed crystals of the composition represented by the maximum point will exhibit a definite melting point, and will in this respect behave like a simple substance.

(_c_) _The freezing-point curve pa.s.ses through a minimum_ (Curve III., Fig.

49).

In this case, as in the case of those systems where the pure components are deposited, a minimum freezing point is obtained. In the latter case, however, there are two freezing-point curves which intersect at a eutectic point; in the case where 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 point the composition of the two phases is the same. At this point, therefore, complete solidification or complete liquefaction will occur without change of temperature, and the mixed crystals will accordingly exhibit a definite melting point.

[Ill.u.s.tration: FIG. 52.]

{188}

Example.--As an example of this there may be taken the mixed crystals of mercuric bromide and iodide.[273] Mercuric bromide melts at 236.5, and mercuric iodide at 255.4. The mixed crystal of definite constant melting point (minimum point) contains 59 mols. per cent. of mercuric bromide, the melting point being 216.1.

The numerical data are contained in the following table, and represented graphically in Fig. 52:--

----------------------------------------------------- Mols. per cent. of

HgBr_{2}.

Freezing point.

Melting point.

----------------------------------------------------- 100

236.5

236 90

228.8

226 80

222.2

219 70

217.8

217 65

216.6

216 60

216.1

215.5 55

216.3

216 50

217.3

216 40

221.1

218 30

227.8

223 20

236.2

231 10

245.5

242 0

255.4

254 -----------------------------------------------------

[Ill.u.s.tration: FIG. 53.]

Fractional Crystallization of Mixed Crystals.--With the help of the diagrams already given it will be possible to predict what will be the result of the fractional crystallization of a fused mixture of two substances which can form mixed crystals. Suppose, for example, a fused mixture of the composition _x_ (Fig. 53) is cooled down; then, as we have already seen, when the temperature has fallen to _a_, mixed crystals of composition, _b_, are deposited. If the temperature is allowed to fall {189} 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 ma.s.s 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 repeating this process, the composition of the successive crops of mixed crystals which are obtained approximates more and more to that of the pure component B, while, on the other hand, the composition of the liquid phase produced tends to that of pure A. By a systematic and methodical repet.i.tion of the process of fractional crystallization, therefore, a _practically_ complete separation of the components can be effected; a perfect separation is theoretically impossible.

From this it will be readily understood that in the case of substances the freezing point of which pa.s.ses through a maximum, fractional crystallization will ultimately lead to mixed crystals having the composition of the maximum point, while the liquid phase will more and more a.s.sume 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, however, where the curves exhibit a minimum, the solid phase which separates out will ultimately be one of the pure components, while a liquid phase will finally be obtained which has the composition of the minimum point.

II.--THE TWO COMPONENTS DO NOT FORM A CONTINUOUS SERIES OF MIXED CRYSTALS.

This case corresponds to that of the partial miscibility of liquids. The solid component A can "dissolve" the component B until the concentration of the latter in the mixed crystal has reached a certain value. Addition of a further amount of B will not alter the composition of the mixed crystal, but there will be formed a second solid phase consisting {190} 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 solution, vapour, can coexist; this will therefore be an invariant point.

The temperature-concentration curves will therefore no longer be continuous, but will exhibit a break or discontinuity at the point at which the invariant system is formed.

(_a_) _The freezing-point curve exhibits a transition point_ (Curve I., Fig. 54).

As is evident from the figure, addition of B raises the melting point of A, and, in accordance with the rule previously given, the concentration of B in the mixed crystals will be greater than in the solution. This is represented in the figure by the dotted curve 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 with the two different mixed crystals represented by D and E. At this temperature, therefore, the _tc_-curve for the solid phase exhibits a discontinuity; and, since the solid phase undergoes change at this point, the freezing-point curve must show a break (p. 111).

[Ill.u.s.tration: FIG. 54.]

Example.--Curves of the form given in Fig. 54 I. have been found experimentally in the case of silver nitrate and sodium nitrate.[274] The following table contains the numerical data, which are also represented graphically in Fig. 55:--

{191}

----------------------------------------------------- Molecules NaNO_{3}

Freezing point.

Melting point.

per cent.

----------------------------------------------------- 0

208.6

208.6 8

211.4

210 15.06

215

212 19.46

217.2

214.8 21.9

222

215 26

228.4

216.5 29.7

234.8

217.5 36.2

244.4

217.5 47.3

259.4

237.6 58.9

272

257 72

284

274 100

308

308 -----------------------------------------------------

The temperature of the transition point is 217.5; at this point the liquid contains 19.5, and the two conjugate solid solutions 26 and 38 molecules of sodium nitrate per cent. respectively.

[Ill.u.s.tration: FIG. 55.]

[Ill.u.s.tration: FIG. 56.]

(_b_) _The freezing-point curve exhibits a eutectic point_ (Curve II., Fig.

54). {192}

In this case the freezing point of each of the components is lowered by the addition of the other, until at last a point is reached at which the liquid solution solidifies to a mixture or conglomerate of two mixed crystals.

Examples.--Curves belonging to this cla.s.s have been obtained in the case of pota.s.sium and thallium nitrates[275] and of naphthalene and monochloracetic acid.[276] The data for the latter are given in the following table and represented in Fig. 56:--

-------------------------------------------------------------------------

Liquid solution.

Solid solution.

------------------------------------------------------------ Temperature.

Per cent.

Per cent.

Per cent.

Per cent.

naphthalene.

acid.

naphthalene.

acid.

------------------------------------------------------------------------- 62

--

100

--

100 60

4.0

96.0

1.7

98.3 55

21.0

79.0

2.1

97.9 53.5

29.4

70.0

--

-- 55

31.3

68.7

59.6

40.4 60

42.4

57.6

80.3

19.7 65

53.3

46.7

89.2

10.8 70

69.7

2.3

95.4

4.6 75

84.4

15.6

96.6

3.4 79.9

100

--

100

-- -------------------------------------------------------------------------

At the eutectic point the liquid solution is in equilibrium with two different mixed crystals the composition of which is represented by D and E respectively. If, therefore, a fused mixture containing the two components A and B in the proportions represented by C is cooled down, it will, when the temperature has reached the point C, solidify completely to a _conglomerate_ of mixed crystals, D and E.

[Ill.u.s.tration: FIG. 57.]

[Ill.u.s.tration: FIG. 58.]

Changes in Mixed Crystals with the Temperature.--In the case of the different types of systems represented in Fig. 49, a h.o.m.ogeneous liquid solution of the two components will exist at temperatures above the freezing-point curve, a h.o.m.ogeneous mixed crystal at temperatures below the melting-point curve, while at any point between the freezing-point and melting-point {193} curves the mixture will separate into a solid phase and a liquid phase. In the case, however, of the two types shown in Fig. 54 the relationships are somewhat more complicated. As before, the area above the freezing-point curve gives the conditions under which h.o.m.ogeneous 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, in the one case, a saturated solution of B in A (point D), and the other a saturated solution of A in B (point E). Just as we saw that the mutual solubility of two liquids varied with the temperature, so also in the case of two solids; as the temperature alters, the solubility of the two solid components in one another will change. This alteration is indicated diagrammatically in Figs. 57 and 58 by the dotted curve similar to the solubility curves for two mutually soluble liquids (p. 101).

Suppose, now, that a mixed crystal of the composition _x_ is cooled down, it will remain unchanged until, when the temperature has fallen to _t'_, the h.o.m.ogeneous mixed crystal breaks up into a conglomerate of two mixed crystals the composition of {194} 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 desposited from the liquid fused ma.s.s need not remain unchanged in the solid state, but may at some lower temperature lose their h.o.m.ogeneity. This fact is of considerable importance for the formation of alloys.[277]

A good example of this will soon be met with in the case of the iron and carbon alloys. The alloys of copper and tin also furnish examples of the great changes which may take place in the alloy between the temperature at which it separates out from the fused ma.s.s and the ordinary temperature.

Thus, for example, one of the alloys of copper and tin which separates out from the liquid as a solid solution breaks up, on cooling, into the compound Cu_{3}Sn and liquid:[278] a striking example of a solid substance partially liquefying on being cooled.

{195}

CHAPTER XI

EQUILIBRIUM BETWEEN DYNAMIC ISOMERIDES

It has long been known that certain substances, _e.g._ acetoacetic ester, are capable when in solution or in the fused state, of reacting as if they possessed two different const.i.tutions; and in order to explain this behaviour the view was advanced (by Laar) that in such cases a hydrogen atom oscillated between two positions in the molecule, being at one time attached to oxygen, at another time to carbon, as represented by the formula--

CH_{3}.C--CH.CO_{2}C_{2}H_{5} . ^ .

O

When the hydrogen is in one position, the substance will act as an hydroxy-compound; with hydrogen in the other position, as a ketone.

Substances possessing this double function are called _tautomeric_.

Doubt, however, arose as to the validity of the above explanation, and this doubt was confirmed by the isolation of the two isomerides in the solid state, and also by the fact that the velocity of change of the one isomeride into the other could in some cases be quant.i.tatively measured.

These and other observations then led to the view, in harmony with the laws of chemical dynamics, that tautomeric substances in the dissolved or fused state represent a _mixture_ of two isomeric forms, and that equilibrium is established not by _intra_- but by _inter_-molecular change, as expressed by the equation--

CH_{3}.CO.CH_{2}.CO_{2}C_{2}H_{5} CH_{3}.C(OH):CH.CO_{2}C_{2}H_{5}

{196} In the solid state, the one or other of the isomerides represents the stable form; but in the liquid state (solution or fusion) the stable condition is an equilibrium between the two forms.

A similar behaviour is also found in the case of other isomeric substances where the isomerism is due to difference of structure, _i.e._ structure isomerism (_e.g._ in the case of the oximes