Fig. 102Fig.102.
Fig. 104Fig.104.
Fig. 103Fig.103.
Formation of Double Salt.—We have already learned in the preceding chapter that if the temperature is outside[357]thetransition interval, it is possible to prepare a pure saturated solution of the double salt. If, now, we suppose the double salt to contain the two constituent salts in equimolecular proportions, its saturated solution must be represented by a point lying on the line which bisects the angle AOB;e.g.point D, Fig. 103. But a double salt constitutes only a single phase, and can exist, therefore, in contact with solutions of varying concentration, as represented by EDF.
Let us compare, now, the relations between the solubility curve for the double salt, and those for the two constituent salts. We shall suppose that the double salt is formed from the single salts when the temperature is raised above a certain point (as in the formation of astracanite). At a temperature below the transition point, as we have already seen, the solubility of the double salt is greater than that of a mixture of the single salts. The curve EDF, therefore, must lie above the point C, in the region representing solutions supersaturated with respect to the single salts (Fig. 104). Such a solution, however, would be metastable, and on being brought in contact with the single salts would deposit these and yield a solution represented by the point C. At this particular temperature, therefore, the isothermal solubility curve will consist of only two branches.
Fig. 105Fig. 105.
Suppose, now, that the temperature is that of the transition point. At this point, the double salt can exist together with the single salts in contact with solution. The solubility curveof the double salt must, therefore, pass through the point C, as shown in Fig. 105.
From this figure, now, it is seen that a solution saturated with respect to double salt alone (point D), is supersaturated with respect to the component A. If, then, at the temperature of the transition point, excess of the double salt is brought in contact with water,[358]and if supersaturation is excluded,the double salt will undergo decomposition and the component A will be deposited. The relative concentration of the component B in the solution will, therefore, increase, and the composition of the solution will be thereby altered in the direction DC. When the solution has the composition of C, the single salt ceases to be deposited, for at this point the solution is saturated for both double and single salt; and the system becomes invariant.
This diagram explains very clearly the phenomenon of the decomposition of a double salt at the transition point. As is evident, this decomposition will occur when the solution which is saturated at the temperature of the transition point, with respect to the two single salts (point C), does not contain these salts in the same ratio in which they are present in the double salt. If point C lay on the dotted line bisecting the right angle, then the pure saturated solution of the double salt would not be supersaturated with respect to either of the single salts, and the double salt would, therefore, not be decomposed by water. As has already been mentioned, this behaviour is found in the case of optically active isomerides, the solubilities of which are identical.
At the transition point, therefore, the isothermal curve also consists of two branches; but the point of intersection of the two branches now represents a solution which is saturated notonly with respect to the single salts, but also for the double salt in presence of the single salts.
We have just seen that by a change of temperature the two solubility curves, that for the two single salts and that for the double salt, were made to approach one another (cf.Figs. 104 and 105). In the previous chapter, however, we found that on passing the transition point to the region of stability for the double salt, the solution which is saturated for a mixture of the two constituent salts, is supersaturated for the double salt. In this case, therefore, point C must lie above the solubility curve of the pure double salt (Fig. 106), and a solution of the composition C, if brought in contact with double salt, will deposit the latter. If the single salts were also present, then as the double salt separated out, the single salts would pass into solution, because so long as the two single salts are present, the composition of the solution must remain unaltered. If one of the single salts disappear before the other, there will be left double salt plus A or double salt plus B, according to which was in excess; and the composition of the solution will be either that represented by D (saturated for double salt plus A), or that of the point F (saturated for double salt plus B).
Fig. 106Fig. 106.
In connection with the isothermal represented in Fig. 106, it should be noted that at this particular temperature a solution saturated with respect to the pure double salt is no longer supersaturated for one of the single salts (point D); so that at the temperature of this isothermal the double salt is not decomposed by water. At this temperature, further, the boundary curve consists of three branches AD, DF, and FB, which give the composition of the solutions in equilibrium with pure A, double salt, and pure B respectively; while the points D and F represent solutions saturated for double salt plus A and double salt plus B.
On continuing to alter the temperature in the same directionas before, the relative shifting of the solubility curves becomes more marked, as shown in Fig. 107. At the temperature of this isothermal, the solution saturated for the double salt now lies in a region of distinct unsaturation with respect to the single salts; and the double salt can now exist as solid phase in contact with solutions containing both relatively more of A (curve ED), and relatively more of B (curve DF), than is contained in the double salt itself.
Fig. 107Fig. 107.
Transition Interval.—From what has been said, and from an examination of the isothermal diagrams, Figs. 104-107, it will be seen that by a variation of the temperature we can pass from a condition where the double salt is quite incapable of existing in contact with solution (supersaturation being excluded), to a condition where the existence of the double salt in presence of solution becomes possible; only in the presence, however, of one of the single salts (transition point, Fig. 105). A further change of temperature leads to a condition where the stable existence of the pure double salt in contact with solution just becomes possible (Fig. 106); and from this point onwards, pure saturated solutions of the double salt can be obtained (Fig. 107).At any temperature, therefore, between that represented by Fig. 105, and that represented by Fig. 106, the double salt undergoes partial decomposition, with deposition of one of the constituent salts.The temperature range between the transition point and the temperature at which a stable saturated solution of the pure double salt just begins to be possible, is known as thetransition interval(p.270). As the figures show, the transition interval is limited on the one side by the transition temperature, and on the other by the temperature at which the solution saturated for double salt and the less soluble of the single salts, contains the component salts in the same ratio as they are present in the double salt. The greater the difference in the solubility of the single salts, the larger will be the transition interval.
Isothermal Evaporation.—The isothermal solubility curves are of great importance for obtaining an insight into the behaviour of a solution when subjected to isothermal evaporation. To simplify the discussion of the relationships found here, we shall still suppose that the double salt contains the single salts in equimolecular proportions; and we shall, in the first instance, suppose that the unsaturated solution with which we commence, also contains the single salts in the same ratio. The composition of the solution must, therefore, be represented by some point lying on the line OD, the bisectrix of the right angle.
From what has been said, it is evident that when the formation of a double salt can occur, three temperature intervals can be distinguished, viz. the single-salt interval, the transition interval, and the double-salt interval.[359]When the temperature lies in the first interval, evaporation leads first of all to the crystallization of one of the single salts, and then to the separation of both the single salts together. In the second temperature interval, evaporation again leads, in the first place, to the deposition of one of the single salts, and afterwards to the crystallization of the double salt. In the third temperature interval, only the double salt crystallizes out. This will become clearer from what follows.
Fig. 109Fig. 109.
Fig. 108Fig. 108.
If an unsaturated solution of the two single salts in equimolecular proportion (e.g.pointx, Fig. 108) is evaporated at a temperature at which the formation of double salt is impossible, the component A, the solubility curve of which iscut 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 anincongruently saturated solution; but in the latter case, where both solid phases continue to be deposited, the solution is said to becongruently saturated.[360]
A "congruently saturated solution" is one from which thesolid 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.
Fig. 110Fig.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 relationships 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 transitioninterval, 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 constitute 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]
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 analogous to the formation of double salts. The isothermal solubility curves, also, have a similar form. In the case of the latter, indeed, the relationships 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 isothermalacbrepresents the solubility relations when the formation of a racemic compound is excluded, as,e.g.in the case of rubidiumd- andl-tartrates above the transition point (p.265). The solution at the pointcis, of course, inactive, andis unaffected by addition of either thed- orl- form. The lower isothermal, on the other hand, would be obtained at a temperature at which the racemic compound could be formed. The curvea′eis the solubility curve for thel- form;b′f, that for thed- form; andedf, that for the racemic compound in presence of solutions of varying concentration. The pointdcorresponds to saturation for the pure racemic compound.
Fig. 111Fig.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,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 pointc, 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 pointd(Fig. 111), and anactivesolution corresponding either toeor tof, 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.
Fig. 112Fig.112.
The curvesacbbelong 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, anda″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 (pointc); if it was a partially racemic compound, three different solutions (e,d′, andf′) will be obtained if the temperature was outside the transition interval, and two solutions,dandf, if the temperature belonged to the transition interval.
Representation in Space.
Space 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 space of the solubility relations of potassium and magnesium chlorides, and of the double salt which they form, carnallite.[365]
Fig. 113Fig.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 thesolution; along the Y-axis, the concentration of potassium 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 potassium chloride, and in the space between the two planes, there are represented the composition of solutions containing both magnesium and potassium chlorides. Anysurfacebetween 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. Alineorcurveformed 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,pointsformed 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).
We shall first consider the solubility relations of the single salts. The complete equilibrium curve for magnesium chloride and water is represented in Fig. 113 by the series of curves ABF1G1H1J1L1N1. AB is the freezing-point curve of ice in contact with solutions containing magnesium chloride, and B is the cryohydric point at which the solid phases ice and MgCl2,12H2O can co-exist with solution. BFG is the solubility curve of magnesium chloride dodecahydrate. This curve shows a point of maximum temperature at F1, and a retroflex portion F1G1. The curve is therefore of the form exhibited by calcium chloride hexahydrate, or the hydrates of ferric chloride (Chapter VIII.). G1is a transition point at which the solid phase changes from dodecahydrate to octahydrate, the solubility of which is represented by the curve G1H1. At H1the octahydrate gives place to the hexahydrate, which is the solid phase in equilibrium with the solutions represented by the curve H1J1. J1and L1are also transition points at which the solid phase undergoes change, in the former case from hexahydrate to tetrahydrate; and in the latter case,from tetrahydrate to dihydrate. The complete curve of equilibrium for magnesium chloride and water is, therefore, somewhat complicated, and is a good example of the solubility curves obtained with salts capable of forming several hydrates.
The solubility curve of potassium chloride is of the simplest form, consisting only of the two branches AC, the freezing-point curve of ice, and CO, the solubility curve of the salt. C is the cryohydric point. This point and the two curves lie in the YT-plane.
On passing to the ternary systems, the composition of the solutions must be represented by points or curves situatedbetweenthe two planes. We shall now turn to the consideration of these. BD and CD are ternary eutectic curves (p.284). They give the composition of solutions in equilibrium with ice and magnesium chloride dodecahydrate (BD), and with ice and potassium chloride (CD). D is aternary cryohydric point. If the temperature is raised and the ice allowed to disappear, we shall pass to the solubility curve for MgCl2,12H2O + KCl (curve DE). At E carnallite is formed and the potassium chloride disappears; EFG is then the solubility curve for MgCl2,12H2O + carnallite (KMgCl3,6H2O). This curve also shows a point of maximum temperature (F) and a retroflex portion. GH and HJ represent the solubility curves of carnallite + MgCl2,8H2O and carnallite + MgCl2,6H2O, G and H being transition points. JK is the solubility curve for carnallite + MgCl2,4H2O. At the point K we have thehighest temperature at which carnallite can exist with magnesium chloride in contact with solution. Above this temperature decomposition takes place and potassium chloride separates out.
If at the point E, at which the two single salts and the double salt are present, excess of potassium chloride is added, the magnesium chloride will all disappear owing to the formation of carnallite, and there will be left carnallite and potassium chloride. The solubility curve for a mixture of these two salts is represented by EMK; a simple curve exhibiting, however, a temperature maximum at M. This maximum point corresponds with the fact that dry carnallite melts at this temperature with separation of potassium chloride.At all temperaturesabove this point, the formation of double salt is impossible. The retroflex portion of the curve represents solutions in equilibrium with carnallite and potassium chloride, but in which the ratio MgCl2: KCl is greater than in the double salt.
Throughout its whole course,the curve EMK represents solutions in which the ratio of MgCl2: KCl is greater than in the double salt. As this is a point of some importance, it will be well, perhaps, to make it clearer by giving one of the isothermal curves,e.g.the curve for 10°, which is represented diagrammatically in Fig. 114. E and F here represent solutions saturated for carnallite plus magnesium chloride hydrate, and for carnallite plus potassium chloride. As is evident, the point F lies above the line representing equimolecular proportions of the salts (OD).
Fig. 114Fig.114.
Summary and Numerical Data.—We may now sum up the different systems which can be formed, and give the numerical data from whichthemodel is constructed.[366]
I.Bivariant Systems.
II.Univariant Systems.—The different univariant systems have already been described. The course of the curves will be sufficiently indicated if the temperature and composition of the solutions for the different invariant systems are given.
III.—Invariant Systems—Binary and Ternary.
With the help of the data in the preceding table and of the solid model it will be possible to state in any given case what will be the behaviour of a system composed of magnesium chloride, potassium chloride and water. One or two different cases will be very briefly described; and the reader should have no difficulty in working out the behaviour under other conditions with the help of the model and the numerical data just given.
In the first place it may be again noted that at a temperature above 167.5° (point M) carnallite cannot exist. If, therefore, a solution of magnesium and potassium chlorides is evaporated at a temperature above this point, the result will be a mixture of potassium chloride and either magnesium chloride tetrahydrate or magnesium chloride dihydrate, according as the temperature is below or above 176°. The isothermal curve here consists of only two branches.
Further, reference has already been made to the fact that all points of the carnallite area correspond to solutions in equilibrium with carnallite, but in which the ratio of MgCl2to KCl is greater than in the double salt. A solution which is saturated with respect to double salt alone will be supersaturated with respect to potassium chloride. At all temperatures, therefore, carnallite is decomposed by water with separation of potassium chloride; hence all solutions obtained by adding excess of carnallite to water will lie on the curve EM.A pure saturated solution of carnallite cannot be obtained.
If an unsaturated solution of the two salts in equimolecular amounts is evaporated, potassium chloride will first be deposited, because the plane bisecting the right angle formed by the X and Y axes cuts the area for that salt. Deposition of potassium chloride will lead to a relative increase in the concentration of magnesium chloride in the solution; and on continued evaporation a point (on the curve EM) will be reached at which carnallite will separate out. So long as the two solid phases are present, the composition of the solution must remain unchanged. Since the separation of carnallite causes a decrease in the relative concentration of the potassium chloride in the solution, the portion of this salt which was deposited at the commencement mustredissolve, and carnallite will be left on evaporating to dryness. (Incongruently saturated solution.)
Although carnallite is decomposed by pure water, it will be possible to crystallize it from a solution having a composition represented by any point in the carnallite area. Since during the separation of the double salt the relative amount of magnesium chloride increases, it is most advantageous tocommence with a solution the composition of which is represented by a point lying just above the curve EM (cf. p.281).
From the above description of the behaviour of carnallite in solution, the processes usually employed for obtaining potassium chloride will be readily intelligible.[367]
Ferric Chloride—Hydrogen Chloride—Water.—In the case of another system of three components which we shall now describe, the relationships are considerably more complicated than in those already discussed. They deserve discussion, however, on account of the fact that they exhibit a number of new phenomena.
In the system formed by the three components, ferric chloride, hydrogen chloride, and water, not only can various compounds of ferric chloride and water (p.152), and of hydrogen chloride and water be formed, each of which possesses a definite melting point, but various ternary compounds are also known. Thus we have the following solid phases:—
From this it will be readily understood that the complete study of the conditions of temperature and concentration under which solutions can exist, either with one solid phase or with two or three solid phases, are exceedingly complicated; and, as a matter of fact, only a few of the possible equilibria have been investigated. We shall attempt here only a brief description of the most important of these.[368]
If we again employ rectangular co-ordinates for the graphicrepresentation of the results, we have the two planes XOT and YOT (Fig. 115): the concentration of ferric chloride being measured along the X-axis, the concentration of hydrogen chloride along the Y-axis, and the temperature along the T-axis. The curve ABCDEFGHJK is, therefore, the solubility curve of ferric chloride in water (p.152), and the curve A′B′C′D′E′F′ the solubility curve of hydrogen chloride and its hydrates. B′ and D′ are the melting points of the hydrates HCl,3H2O and HCl,2H2O. In the space between these two planes are represented those systems in which all three components are present. As already stated, only a few of the possible ternary systems have been investigated, and these are represented in Fig. 116. The figure shows the model resting on the XOT-plane, so that the lower edge represents the solubility curve of ferric chloride, the concentration increasing from right to left. The concentration of hydrogen chloride is measured upwards, and the temperature forwards. The further end of the model represents the isothermal surface for -30°. The surface of the model on the left does not correspond with the plane YOT in Fig. 115, but with a parallel plane which cuts the concentration axis for ferric chloride at a point representing 65 gm.-molecules FeCl3in 100 gm.-molecules of water. The upper surface corresponds with a plane parallel to the axis XOT, at a distance corresponding with the concentration of 50 gm.-molecules HCl in 100 gm.-molecules of water.