Part 24 (2/2)

If an unsaturated solution of the two single salts in equimolecular proportion (_e.g._ point _x_, Fig. 108) is evaporated at a temperature at which the formation of double salt is impossible, the component A, the solubility curve of which is {279} cut by the line OD, will first separate out; the solution will thereby become richer in B. On continued evaporation, more A will be deposited, and the composition of the solution will change until it attains the composition represented by the point C, when both A and B will be deposited, and the composition of the solution will remain unchanged. The result of evaporation will therefore be a mixture of the two components.

If the formation of double salt is possible, but if the temperature lies within the transition interval, the relations will be represented by a diagram like Fig. 109. Isothermal evaporation of the solution X will lead to the deposition of the component A, and the composition of the solution will alter in the direction DE; at the latter point the double salt will be formed, and the composition of the solution will remain unchanged so long as the two solid phases are present. As can be seen from the diagram, however, the solution in E contains less of component A than is contained in the double salt. Deposition of the double salt at E, therefore, would lead to a relative decrease in the concentration of A in the solution, and to counterbalance this, _the salt which separated out at the commencement must redissolve_.

Since the salts were originally present in equimolecular proportions, the final result of evaporation will be the pure double salt. If when the solution has reached the point E the salt A which had separated out is removed, double salt only will be left as solid phase. At a given temperature, however, a single solid phase can exist in equilibrium with solutions of different composition. If, therefore, isothermal evaporation is continued after the removal of the salt A, double salt will be deposited, and the composition of the solution will change in the direction EF. At the point F the salt B will separate out, and on evaporation both double salt and the salt B will be deposited. In the former case (when the salt A disappears on evaporation) we are dealing with an _incongruently saturated solution_; but in the latter case, where both solid phases continue to be deposited, the solution is said to be _congruently saturated_.[360]

A ”congruently saturated solution” is one from which the {280} solid phases are continuously deposited during isothermal evaporation to dryness, whereas in the case of ”incongruently saturated solutions,” at least one of the solid phases disappears during the process of evaporation.

[Ill.u.s.tration: FIG. 110.]

Lastly, if the temperature lies outside the transition interval, isothermal evaporation of an unsaturated solution of the composition X (Fig. 110) will lead to the deposition of pure double salt from beginning to end. If a solution of the composition Y is evaporated, the component A will first be deposited and the composition of the solution will alter in the direction of E, at which point double salt will separate out. Since the solution at this point contains relatively more of A than is present in the double salt, both the double salt and the single salt A will be deposited on continued evaporation, in order that the composition of the solution shall remain unchanged. In the case of solution Z, first component B and afterwards the double salt will be deposited. The result will, therefore, be a mixture of double salt and the salt B (congruently saturated solutions),

It may be stated here that the same relations.h.i.+ps as have been explained above for double salts are also found in the resolution of racemic compounds by means of optically active substances (third method of Pasteur). In this case the single salts are doubly active substances (_e.g._ strychnine-_d_-tartrate and strychnine-_l_-tartrate), and the double salt is a partially racemic compound.[361]

Crystallization of Double Salt from Solutions containing Excess of One Component.--One more case of isothermal crystallization may be discussed.

It is well known that a double salt which is decomposed by pure water can nevertheless be obtained pure by crystallization from a solution containing excess of one of the single salts (_e.g._ in the case of carnallite). Since the double salt is partially decomposed by water, the temperature of the experiment must be within the transition {281} interval, and the relations will, therefore, be represented by a diagram like Fig. 109. If, now, instead of starting with an unsaturated solution containing the single salts in equimolecular proportions, we commence with one in which excess of one of the salts is present, as represented by the point Y, isothermal evaporation will cause the composition to alter in the direction YD', the relative amounts of the single salts remaining the same throughout. When the composition of the solution reaches the point D', pure double salt will be deposited. The separation of double salt will, however, cause a relative decrease in the concentration of the salt A, and the composition of the solution will, therefore, alter in the direction D'F. If the evaporation is discontinued before the solution has attained the composition F, only double salt will have separated out. Even within the transition interval, therefore, pure double salt can be obtained by crystallization, provided the original solution has a composition represented by a point lying between the two lines OE and OF. Since, as already shown, the composition of the solution alters on evaporation in the direction EF, it will be best to employ a solution having a composition near to the line OE.

Formation of Mixed Crystals.--If the two single salts A and B do not crystallize out pure from solution, but form an unbroken series of mixed crystals, it is evident that an invariant system cannot be produced. The solubility curve will therefore be continuous from A to B; the liquid solutions of varying composition being in equilibrium with solid solutions also of varying composition. If, however, the series of mixed crystals is not continuous, there will be a break in the solubility curve at which two solid solutions of different composition will be in equilibrium with liquid solution. This, of course, will const.i.tute an invariant system, and the point will correspond to the point C in Fig. 108. A full discussion of these systems would, however, lead us too far, and the above indication of the behaviour must suffice.[362]

{282}

Application to the Characterization of Racemates.--The form of the isothermal solubility curves is also of great value for determining whether an inactive substance is a racemic compound or a conglomerate of equal proportions of the optical antipodes.[363]

As has already been pointed out, the formation of racemic compounds from the two enantiomorphous isomerides, is a.n.a.logous to the formation of double salts. The isothermal solubility curves, also, have a similar form. In the case of the latter, indeed, the relations.h.i.+ps are simplified by the fact that the two enantiomorphous forms have identical solubility, and the solubility curves are therefore symmetrical to the line bisecting the angle of the co-ordinates. Further, with the exception of the partially racemic compounds to be mentioned later, there is no transition interval.

In Fig. 111, are given diagrammatically two isothermal solubility curves for optically active substances. From what has been said in the immediately preceding pages, the figure ought really to explain itself. The upper isothermal _acb_ represents the solubility relations when the formation of a racemic compound is excluded, as, _e.g._ in the case of rubidium _d_- and _l_-tartrates above the transition point (p. 265). The solution at the point _c_ is, of course, inactive, and _is unaffected by addition of either the _d_- or _l_- form_. The lower isothermal, on the other hand, would be obtained at a temperature at which the racemic compound could be formed.

The curve _a'e_ is the solubility curve for the _l_- form; _b'f_, that for the _d_- form; and _edf_, that for the racemic compound in presence of solutions of varying concentration. The point _d_ corresponds to saturation for the pure racemic compound.

[Ill.u.s.tration: FIG. 111.]

From these curves now, it will be evident that it will be possible, in any given case, to decide whether or not an inactive body is a mixture or a racemic compound. For this purpose, {283} two solubility determinations are made, first with the inactive material alone (in excess), and then with the inactive material plus excess of one of the optically active forms. If we are dealing with a mixture, the two solutions thus obtained will be identical; both will have the composition corresponding to the point _c_, and will be inactive. If, however, the inactive material is a racemic compound, then two different solutions will be obtained; namely, an inactive solution corresponding to the point _d_ (Fig. 111), and an _active_ solution corresponding either to _e_ or to _f_, according to which enantiomorphous form was added.

_Partially racemic compounds._[364] In this case we are no longer dealing with enantiomorphous forms, and the solubility of the two oppositely active isomerides is no longer the same. The symmetry of the solubility curves therefore disappears, and a figure is obtained which is identical in its general form with that found in the case of ordinary double salts (Fig.

112). In this case there is a transition interval.

[Ill.u.s.tration: FIG. 112.]

The curves _acb_ belong to a temperature at which the partially racemic compound cannot be formed; _a'dfb'_, to the temperature at which the compound just begins to be stable in contact with water, and _a”ed'f'b”_ belongs to a temperature at which the partially racemic compound is quite stable in contact with water. Suppose now solubility determinations, made in the first case with the original material alone, and then with the original body plus each of the two compounds, formed from the enantiomorphous substances separately, then if the original body was a mixture, identical solutions will be obtained in all three cases (point _c_); if it was a partially racemic compound, three different solutions (_e_, _d'_, and _f'_) will be obtained if the temperature was outside the transition interval, and two solutions, _d_ and _f_, if the temperature belonged to the transition interval.

{284}

_Representation in s.p.a.ce._

s.p.a.ce Model for Carnallite.--Interesting and important as the isothermal solubility curves are, they are insufficient for the purpose of obtaining a clear insight into the complete behaviour of the systems of two salts and water. A short description will, therefore, be given here of the representation in s.p.a.ce of the solubility relations of pota.s.sium and magnesium chlorides, and of the double salt which they form, carnallite.[365]

[Ill.u.s.tration: FIG. 113.]

Fig. 113 is a diagrammatic sketch of the model for carnallite looked at sideways from above. Along the X-axis is measured the concentration of magnesium chloride in the {285} solution; along the Y-axis, the concentration of pota.s.sium chloride; while along the T-axis is measured the temperature. The three axes are at right angles to one another. The XT-plane, therefore, contains the solubility curve of magnesium chloride; the YT-plane, the solubility curve of pota.s.sium chloride, and in the s.p.a.ce between the two planes, there are represented the composition of solutions containing both magnesium and pota.s.sium chlorides. Any _surface_ between the two planes will represent the various solutions in equilibrium with only one solid phase, and will therefore indicate the area or field of existence of bivariant ternary systems. A _line_ or _curve_ formed by the intersection of two surfaces will represent solutions in equilibrium with two solid phases (viz. those belonging to the intersecting surfaces), and will show the conditions for the existence of univariant systems. Lastly, _points_ formed by the intersection of three surfaces will represent invariant systems, in which a solution can exist in equilibrium with three solid phases (viz. those belonging to the three surfaces).

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