The Phase Rule and Its Applications Part 17

C_{6}H_{5}.C.H C_{6}H_{5}.C.H and ), N.OH HO.N

or to difference in configuration, _i.e._ stereoisomerism (_e.g._ optically active substances), or to polymerism (_e.g._ acetaldehyde and paraldehyde).

In all such cases, although the different solid forms correspond to a single definite const.i.tution, in the liquid state a condition of equilibrium between the two modifications is established. As a general name for these different cla.s.ses of substances, the term "dynamic isomerides"

has been introduced; and the different kinds of isomerism are cla.s.sed together under the t.i.tle "dynamic isomerism."[279]

By reason of the importance of these phenomena in the study more especially of Organic Chemistry, a brief account of the equilibrium relations exhibited by systems composed of dynamic isomerides may be given here.[280]

In studying the fusion and solidification of those substances which exhibit the relationships of dynamic isomerism, the phenomena observed will vary somewhat according as the reversible transformation of the one form into the other takes place with measurable velocity at temperatures in the neighbourhood of the melting points, or only at some higher temperature. If the transformation is very rapid, the system will behave like a one-component system, but if the isomeric change is comparatively slow, the behaviour will be that of a two-component system.

Temperature-Concentration Diagram.--The relationships which are met with here will be most readily understood with {197} the help of Fig. 59.

Suppose, in the first instance, that isomeric transformation does not take place at the temperature of the melting point, then the freezing point curve will have the simple form ACB; the formation of compounds being for the present excluded. This is the simplest type of curve, and gives the composition of the solutions in equilibrium with the one modification ([alpha] modification) at different temperatures (curve AC); and of the solutions in equilibrium with the other modification ([beta] modification) at different temperatures (curve BC). C is the eutectic point at which the two solid isomerides can exist side by side in contact with the solution.

[Ill.u.s.tration: FIG. 59.]

Now, suppose that isomeric transformation takes place with measurable velocity. If the pure [alpha]-modification is heated to a temperature _t'_ above its melting point, and the liquid maintained at that temperature until equilibrium has been established, a certain amount of the [beta]-form will be present in the liquid, the composition of which will be represented by the point _x'_. The same condition of equilibrium will also be reached by starting with pure [beta]. Similarly, if the temperature of the liquid is maintained at the temperature _t"_, equilibrium will be reached, we shall suppose, when the solution has the composition _x"_. The curve DE, therefore, which pa.s.ses through all the different values of _x_ corresponding to different values of _t_, will represent the change of equilibrium with the temperature. It will slope to the right (as in the figure) if the transformation of [alpha] into [beta] is accompanied by absorption of heat; to the left if the transformation is accompanied by evolution of heat, in accordance with van't Hoff's Law of movable equilibrium. If transformation occurs without heat effect, the equilibrium will be independent of the {198} temperature, and the equilibrium curve DE will therefore be perpendicular and parallel to the temperature axis.

We must now find the meaning of the point D. Suppose the pure [alpha]- or pure [beta]-form heated to the temperature _t'_, and the temperature maintained constant until the liquid has the composition _x'_ corresponding to the equilibrium at that temperature. If the temperature is now allowed to fall sufficiently slowly so that the condition of equilibrium is continually readjusted as the temperature changes, the composition of the solution will gradually alter as represented by the curve _x'_D. Since D is on the freezing point curve of pure [alpha], this form will be deposited on cooling; and since D is also on the equilibrium curve of the liquid, D is the only point at which solid can exist in stable equilibrium with the liquid phase. (The vapour phase may be omitted from consideration, as we shall suppose the experiments carried out in open vessels.) All systems consisting of the two hylotropic[281] isomeric substances [alpha] and [beta] will, therefore, ultimately freeze at the point D, which is called the "natural" freezing point[282] of the system; provided, of course, that sufficient time is allowed for equilibrium to be established. From this it is apparent that _the stable modification at temperatures in the neighbourhood of the melting point is that which is in equilibrium with the liquid phase at the natural freezing point_.

From what has been said, it will be easy to predict what will be the behaviour of the system under different conditions. If pure [alpha] is heated, a temperature will be reached at which it will melt, but this melting point will be sharp only if the velocity of isomeric transformation is comparatively slow; _i.e._ slow in comparison with the determination of the melting point. If the substance be maintained in the fused condition for some time, a certain amount of the [beta] modification will be formed, and on lowering the temperature the pure [alpha] form will be deposited, not at the temperature of the melting point, but at some lower temperature depending on the concentration of the [beta] modification in the liquid phase. If isomeric transformation {199} takes place slowly in comparison with the rate at which deposition of the solid occurs, the liquid will become increasingly rich in the [beta] modification, and the freezing point will, therefore, sink continuously. At the eutectic point, however, the [beta] modification will also be deposited, and the temperature will remain constant until all has become solid. If, on the other hand, the velocity of transformation is sufficiently rapid, then as quickly as the [alpha]

modification is deposited, the equilibrium between the two isomeric forms in the liquid phase will continuously readjust itself, and the end-point of solidification will be the natural freezing point.

Similarly, starting with the pure [beta] modification, the freezing point after fusion will gradually fall owing to the formation of the [alpha]

modification; and the composition of the liquid phase will pa.s.s along the curve BC. If, now, the rate of cooling is not too great, or if the velocity of isomeric transformation is sufficiently rapid, complete solidification will not occur at the eutectic point; for at this temperature solid and liquid are not in stable equilibrium with one another. On the contrary, a further quant.i.ty of the [beta] modification will undergo isomeric change, the liquid phase will become richer in the [alpha] form, and the freezing point will _rise_; the solid phase in contact with the liquid being now the [alpha] modification. The freezing point will continue to rise until the point D is reached, at which complete solidification will take place without further change of temperature.

The diagram also allows us to predict what will be the result of rapidly cooling a fused mixture of the two isomerides. Suppose that either the [alpha] or the [beta] modification has been maintained in the fused state at the temperature _t'_ sufficiently long for equilibrium to be established. The composition of the liquid phase will be represented by _x'_. If the liquid is now _rapidly_ cooled, the composition will remain unchanged as represented by the dotted line _x'_G. At the temperature of the point G solid [alpha] modification will be deposited. If the cooling is not carried below the point G, so as to cause complete solidification, the freezing point will be found to rise with time, owing to the conversion of some of the [beta] form into the [alpha] form {200} in the liquid phase; and this will continue until the composition of the liquid has reached the point D. From what has just been said, it can also be seen that if the freezing point curves can be obtained by actual determination of the freezing points of different synthetic mixtures of the two isomerides, it will be possible to determine the condition of equilibrium in the fused state at any given temperature without having recourse to a.n.a.lysis. All that is necessary is to rapidly cool the fused ma.s.s, after equilibrium has been established, and find the freezing point at which solid is deposited; that is, find the point at which the line of constant temperature cuts the freezing point curve. The composition corresponding to this temperature gives the composition of the equilibrium mixture at the given temperature.

It will be evident, from what has gone before, that the degree of completeness with which the different curves can be realised will depend on the velocity with which isomeric change takes place, and on the rapidity with which the determinations of the freezing point can be carried out. As the two extremes we have, on the one hand, practically instantaneous transformation, and on the other, practically infinite slowness of transformation. In the former case, only one melting and freezing point will be found, viz. the natural freezing point; in the latter case, the two isomerides will behave as two perfectly independent components, and the equilibrium curve DE will not be realised.

The diagram which is obtained when isomeric transformation does not occur within measurable time at the temperature of the melting point is somewhat different from that already given in Fig. 59. In this case, the two freezing point curves AC and BC (Fig. 60) can be readily realized, as no isomeric change occurs in the liquid phase. Suppose, however, that at a higher temperature, _t'_, reversible isomeric transformation can take place, the composition of the liquid phase will alter until at the point _x'_ a condition of equilibrium is reached; and the composition of the liquid at higher temperatures will be represented by the curve _x'_F. Below the temperature _t'_ the position of the equilibrium curve is hypothetical; but as the temperature {201} falls the velocity of transformation diminishes, and at last becomes _practically_ zero. The equilibrium curve can therefore be regarded as dividing into two branches _x'_G and _x'_H. At temperatures between G and _t'_ the [alpha] modification can undergo isomeric change leading to a point on the curve G_x'_; and the [beta]

modification can undergo change leading to a point on the curve H_x'_. The same condition of equilibrium is therefore not reached from each side, and we are therefore dealing not with true but with false equilibrium (p. 5).

Below the temperatures G and H, isomeric transformation does not occur in measurable time. We shall not, however, enter into a detailed discussion of the equilibria in such systems, more especially as they are not systems in true equilibrium, and as the temperature at which true equilibrium can be established with appreciable velocity alters under the influence of catalytic agents.[283] Examples of such systems will no doubt be found in the case of optically active substances, where both isomerides are apparently quite stable at the melting point. In the case of such substances, also, the action of catalytic agents in producing isomeric transformation (racemisation) is well known.

[Ill.u.s.tration: FIG. 60.]

Transformation of the Unstable into the Stable Form.--As has already been stated, the stable modification in the neighbourhood of the melting point is that one which is in equilibrium with the liquid phase at the natural freezing point. In the case of polymorphic substances, we have seen (p. 39) that that form which is stable in the neighbourhood of the melting point melts at the higher temperature. That was a {202} consequence of the fact that the two polymorphic forms on melting gave identical liquid phases. In the present case, however, the above rule does not apply, for the simple reason that the liquid phase obtained by the fusion of the one modification is not identical with that obtained by the fusion of the other. In the case of isomeric substances, therefore, the form of lower melting point _may_ be the more stable; and where this behaviour is found it is a sign that the two forms are isomeric (or polymeric) and not polymorphic.[284] An example of this is found in the case of the isomeric benzaldoximes (p. 203).

Since in Fig. 59 the [alpha] modification has been represented as the stable form, the transformation of the [beta] into the [alpha] form will be possible at all temperatures down to the transition point. At temperatures below the eutectic point, transformation will occur without formation of a liquid phase; but at temperatures above the eutectic point liquefaction can take place. This will be more readily understood by drawing a line of constant temperature, HK, at some point between C and B. Then if the [beta]

modification is maintained for a sufficiently long time at that temperature, a certain amount of the [alpha] modification will be formed; and when the composition of the mixture has reached the point H, fusion will occur. If the temperature is maintained constant, isomeric transformation will continue to take place in the liquid phase until the equilibrium point for that temperature is reached. If this temperature is higher than the natural melting point, the mixture will remain liquid all the time; but if it is below the natural melting point, then the [alpha]

modification will be deposited when the system reaches the condition represented by the point on the curve AC corresponding to the particular temperature. As isomeric transformation continues, the freezing point of the system will rise until it reaches the natural freezing point D.

Similarly, if the [alpha] modification is maintained at a temperature above that of the point D, liquefaction will ultimately occur, and the system will again reach the final state represented by D.[285]

{203}

Examples.--_Benzaldoximes._ The relationships which have just been discussed from the theoretical point of view will be rendered clearer by a brief description of cases which have been experimentally investigated. The first we shall consider is that of the two isomeric benzaldoximes:[286]--

C_{6}H_{5}.C.H C_{6}H_{5}.C.H HO.N N.OH

Benzantialdoxime Benzsynaldoxime ([alpha]-modification). ([beta]-modification).

Fig. 61 gives a graphic representation of the results obtained.

The melting point of the [alpha] modification is 34-35; the melting point of the unstable [beta]-modification being 130. The freezing curves AC and BC were obtained by determining the freezing points of different mixtures of known composition, and the numbers so obtained are given in the following table.

{204}

---------------------------------------------------- Grams of the [alpha] modification in 100 gm. of mixture. Freezing point.

----------------------------------+----------------- 26.2 101 49.2 79 73.7 46 91.7 26.2 95.0 28.6 96.0 30.0 ----------------------------------------------------

[Ill.u.s.tration: FIG. 61.]

The eutectic point C was found to lie at 25-26, and the natural freezing point D was found to be 27.7. The equilibrium curve DE was determined by heating the liquid mixtures at different temperatures until equilibrium was attained, and then rapidly cooling the liquid. In all cases the freezing point was practically that of the point D. From this it is seen that the equilibrium curve must be a straight line parallel to the temperature axis; and, therefore, isomeric transformation in the case of the two benzaldoximes is not accompanied by any heat effect (p. 197). This behaviour has also been found in the case of acetaldoxime.[287]

The isomeric benzaldoximes are also of interest from the fact that the stable modification has the _lower_ melting point (_v._ p. 202).

_Acetaldehyde and Paraldehyde._--As a second example of the equilibria between two isomerides, we shall take the two isomeric (polymeric) forms of acetaldehyde, which have recently been exhaustively studied.[288]

{205}

In the case of these two substances the reaction

3CH_{3}.CHO <--> (CH_{3}.CHO)_{3}

takes place at the ordinary temperature with very great slowness. For this reason it is possible to determine the freezing point curves of acetaldehyde and paraldehyde. The three chief points on these curves, represented graphically in Fig. 62, are:--

m.p. of acetaldehyde - 118.45 m.p. of paraldehyde + 12.55 eutectic point - 119.9

[Ill.u.s.tration: FIG. 62.]

In order to determine the position of the natural melting point, it was necessary, on account of the slowness of transformation, to employ a catalytic agent in order to increase the velocity with which the equilibrium was established. A drop of concentrated sulphuric acid served the purpose. In presence of a trace of this substance, isomeric transformation very speedily occurs, and leads to the condition of equilibrium. Starting in the one case with fused paraldehyde, and in the other case with acetaldehyde, the same freezing point, viz. 6.75, was obtained, the solid phase being paraldehyde. This temperature, 6.75, is therefore the natural freezing point, and paraldehyde, the solid in equilibrium with the liquid phase at this point, is the stable form.

With regard to the change of equilibrium with the temperature, it was found that whereas the liquid phase contained 11.7 molecules per cent. of acetaldehyde at the natural freezing point, the liquid at the temperature of 41.6 contains 46.6 molecules per cent. of acetaldehyde. As the temperature {206} rises, therefore, there is increased formation of acetaldehyde, or a decreasing amount of polymerisation. This is in harmony with the fact that the polymerisation of acetaldehyde is accompanied by evolution of heat.

While speaking of these isomerides, it may be mentioned that at the temperature 41.6 the equilibrium mixture has a vapour pressure equal to the atmospheric pressure. At this temperature, therefore, the equilibrium mixture (obtained quickly with the help of a trace of sulphuric acid) boils.[289]

{207}

CHAPTER XII

SUMMARY.--APPLICATION OF THE PHASE RULE TO THE STUDY OF SYSTEMS OF TWO COMPONENTS

In this concluding chapter on two-component systems, it is proposed to indicate briefly how the Phase Rule has been applied to the elucidation of a number of problems connected with the equilibria between two components, and how it has been employed for the interpretation of the data obtained by experiment. It is hoped that the practical value of the Phase Rule may thereby become more apparent, and its application to other cases be rendered easier.

The interest and importance of investigations into the conditions of equilibrium between two substances, lie in the determination not only of the conditions for the stable existence of the partic.i.p.ating substances, but also of whether or not chemical action takes place between these two components; and if combination occurs, in the determination of the nature of the compounds formed and the range of their existence. In all such investigations, the Phase Rule becomes of conspicuous value on account of the fact that its principles afford, as it were, a touchstone by which the character of the system can be determined, and that from the form of the equilibrium curves obtained, conclusions can be drawn as to the nature of the interaction between the two substances. In order to exemplify the application of the principles of the Phase Rule more fully than has already been done, ill.u.s.trations will be drawn from investigations on the interaction of organic compounds; on the equilibria between optically active compounds; and on alloys. {208}

Summary of the Different Systems of Two Components.--Before pa.s.sing to the consideration of the application of the Phase Rule to the investigation of particular problems, it will be well to collect together the different types of equilibrium curves with which we are already acquainted; to compare them with one another, in order that we may then employ these characteristic curves for the interpretation of the curves obtained as the result of experiment.