Part 16 (1/2)
{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.