The Phase Rule and Its Applications Part 4

VAPOUR PRESSURES OF WHITE AND RED PHOSPHORUS.

------------------------------------------------------------------------- Vapour pressure of liquid white phosphorus. Vapour pressure of red phosphorus.

-------------------------------------------------+----------------------- Temperature. Pressure Temperature. Pressure Temperature. Pressure in cm. in atm. in atm.

------------+----------+-------------+-----------+-------------+--------- 165 12 360 3.2 360 0.1 180 20.4 440 7.5 440 1.75 200 26.6 494 18.0 487 6.8 219 35.9 503 21.9 510 10.8 230 51.4 511 26.2 531 16.0 290 76.0 -- -- 550 31.0 -- -- -- -- 577 56.0 -------------------------------------------------------------------------

These values are also represented graphically in Fig. 10.

[Ill.u.s.tration: FIG. 10.]

At all temperatures above about 260, transformation of the white into the red modification takes place with appreciable velocity, and this velocity increases as the temperature is raised. Even at lower temperatures, _e.g._ at the ordinary temperature, the velocity of transformation is increased under the influence {47} of light,[69] or by the presence of certain substances, _e.g._ iodine,[70] just as the velocity of transformation of white tin into the grey modification was increased by the presence of a solution of tin ammonium chloride (p. 40). At the ordinary temperature, therefore, white phosphorus must be considered as the less stable (metastable) form, for although it can exist in contact with red phosphorus for a long period, its vapour pressure, as we have seen, is greater than that of the red modification, and also, its solubility in different solvents is greater[71] than that of the red modification; as we shall find later, the solubility of the metastable form is always greater than that of the stable.

The relationships which are met with in the case of phosphorus can be best represented by the diagram, Fig. 11.[72]

In this figure, BO_{1} represents the conditions of equilibrium of the univariant system red phosphorus and vapour, which ends at O_{1}, the melting point of red phosphorus. By heating in capillary tubes of hard gla.s.s, Chapman[73] found that red phosphorus melts at the melting point of pota.s.sium iodide, _i.e._ about 630,[74] but the pressure at this temperature is unknown.

At O_{1}, then, we have the triple point, red phosphorus, liquid, and vapour, and starting from it, we should have the {48} vaporization curve of liquid phosphorus, O_{1}A, and the fusion curve of red phosphorus, O_{1}F.

Although these have not been determined, the latter curve must, from theoretical considerations (_v._ p. 58), slope slightly to the right; _i.e._ increase of pressure raises the melting point of red phosphorus.

[Ill.u.s.tration: FIG. 11.]

When white phosphorus is heated to 44, it melts. At this point, therefore, we shall have another triple point, white phosphorus--liquid--vapour; the pressure at this point has been calculated to be 3 mm.[75] This point is the intersection of three curves, viz. sublimation curve, vaporization curve, and the fusion curve of white phosphorus. The fusion curve, O_{2}E, has been determined by Tammann[76] and by G. A. Hulett,[77] and it was found that increase of pressure by 1 atm. raises the melting point by 0.029. The sublimation curve of white phosphorus has not yet been determined.

As can be seen from the table of vapour pressures (p. 46), the vapour pressure of white phosphorus has been determined up to 500; at temperatures above this, however, the velocity with which transformation into red phosphorus takes place is so great as to render the determination of the vapour pressure {49} at higher temperatures impossible. Since, however, the difference between white phosphorus and red phosphorus disappears in the liquid state, the vapour pressure curve of white phosphorus must pa.s.s through the point O_{1}, the melting point of red phosphorus, and must be continuous with the curve O_{1}A, the vapour pressure curve of liquid phosphorus (_vide infra_). Since, as Fig. 10 shows, the vapour pressure curve of white phosphorus ascends very rapidly at higher temperatures, the "break" between BO_{1} and O_{1}A must be very slight.

As compared with monotropic substances like benzophenone, phosphorus exhibits the peculiarity that transformation of the metastable into the stable modification takes place with great slowness; and further, the time required for the production of equilibrium between red phosphorus and phosphorus vapour is great compared with that required for establishing the same equilibrium in the case of white phosphorus. This behaviour can be best explained by the a.s.sumption that change in the molecular complexity (polymerization) occurs in the conversion of white into red phosphorus, and when red phosphorus pa.s.ses into vapour (depolymerization).[78]

This is borne out by the fact that measurements of the vapour density of phosphorus vapour at temperatures of 500 and more, show it to have the molecular weight represented by P_{4},[79] and the same molecular weight has been found for phosphorus in solution.[80] On the other hand, it has recently been shown by R. Schenck,[81] that the molecular weight of red phosphorus is at least P_{8}, and very possibly higher.

In the case of phosphorus, therefore, it is more than possible that we are dealing, not simply with two polymorphic {50} forms of the same substance, but with polymeric forms, and that there is no transition point at temperatures above the absolute zero, unless we a.s.sume the molecular complexity of the two forms to become the same. The curve for red phosphorus would therefore lie below that of white phosphorus, for the vapour pressure of the polymeric form, if produced from the simpler form with evolution of heat, must be lower than that of the latter. A transition point would, of course, become possible if the sign of the heat effect in the transformation of the one modification into the other should change.

If, further, the liquid which is produced by the fusion of red phosphorus at 630 under high pressure also exists in a polymeric form, greater than P_{4}, then the metastable vaporization curve of white phosphorus would not pa.s.s through the melting point of red phosphorus, as was a.s.sumed above.[82]

We have already seen in the case of water (p. 31) that the vapour pressure of supercooled water is greater than that of ice, and that therefore it is possible, theoretically at least, by a process of distillation, to transfer the water from one end of a closed tube to the other, and to there condense it as ice. On account of the very small difference between the vapour pressure of supercooled water and ice, this distillation process has not been experimentally realized. In the case of phosphorus, however, where the difference in the vapour pressures is comparatively great, it has been found possible to distil white phosphorus from one part of a closed tube to another, and to there condense it as red phosphorus; and since the vapour pressure of red phosphorus at 350 is less than the vapour pressure of white phosphorus at 200, it is possible to carry out the distillation from a _colder_ part of the tube to a _hotter_, by having white phosphorus at the former and red phosphorus at the latter. Such a process of distillation has been carried out by Troost and Hautefeuille between 324 and 350.[83]

Relationships similar to those found in the case of phosphorus are also met with in the case of cyanogen and {51} paracyanogen, which have been studied by Chappuis,[84] Troost and Hautefeuille,[85] and Dewar,[86] and also in the case of other organic substances.

Enantiotropy combined with Monotropy.--Not only can polymorphic substances exhibit enantiotropy or monotropy, but, if the substance is capable of existing in more than two crystalline forms, both relationships may be found, so that some of the forms may be enantiotropic to one another, while the other forms exhibit only monotropy. This behaviour is seen in the case of sulphur, which can exist in as many as eight different crystalline varieties. Of these only monoclinic and rhombic sulphur exhibit the relationship of enantiotropy, _i.e._ they possess a definite transition point, while the other forms are all metastable with respect to rhombic and monoclinic sulphur, and remain so up to the melting point; that is to say, they are monotropic modifications.[87]

E. _Liquid Crystals._

Phenomena observed.--In 1888 it was discovered by Reinitzer[88] that the two substances, cholesteryl acetate and cholesteryl benzoate, possess the peculiar property of melting sharply at a definite temperature to milky liquids; and that the latter, on being further heated, suddenly become clear, also at a definite temperature. Other substances, more especially _p_-azoxyanisole and _p_-azoxyphenetole, were, later, found to possess the same property of having apparently a double melting point.[89] On cooling the clear liquids, the reverse series of changes occurred.

The turbid liquids which were thus obtained were found to possess not only the usual properties of liquids (such as the {52} property of flowing and of a.s.suming a perfectly spherical shape when suspended in a liquid of the same density), but also those properties which had hitherto been observed only in the case of solid crystalline substances, viz. the property of double refraction and of giving interference colours when examined by polarized light; the turbid liquids are _anisotropic_. To such liquids, the optical properties of which were discovered by O. Lehmann,[90] the name _liquid crystals_, or crystalline liquids, was given.

Nature of Liquid Crystals.--During the past ten years the question as to the nature of liquid crystals has been discussed by a number of investigators, several of whom have contended strongly against the idea of the term "liquid" being applied to the crystalline condition; and various attempts have been made to prove that the turbid liquids are in reality heterogeneous and are to be cla.s.sed along with emulsions.[91] This view was no doubt largely suggested by the fact that the anisotropic liquids were turbid, whereas the "solid" crystals were clear. Lehmann found, however, that, when examined under the microscope, the "simple" liquid crystals were also clear,[92] the apparent turbidity being due to the aggregation of a number of differently oriented crystals, in the same way as a piece of marble does not appear transparent although composed of transparent crystals.[93]

Further, no proof of the heterogeneity of liquid crystals has yet been obtained, but rather all chemical and physical investigations indicate that they are h.o.m.ogeneous.[94] No separation {53} of a solid substance from the milky, anisotropic liquids has been effected; the anisotropic liquid is in some cases less viscous than the isotropic liquid formed at a higher temperature; and the temperature of liquefaction is constant, and is affected by pressure and admixture with foreign substances exactly as in the case of a pure substance.[95]

[Ill.u.s.tration: FIG. 12.]

Equilibrium Relations in the Case of Liquid Crystals.--Since, now, we have seen that we are dealing here with substances in two crystalline forms (which we may call the solid and liquid[96] crystalline form), which possess a definite transition point, at which, transformation of the one form into the other occurs in both directions, we can represent the conditions of equilibrium by a diagram in all respects similar to that employed in the case of other enantiotropic substances, _e.g._ sulphur (p. 35).

{54}

In Fig. 12 there is given a diagrammatic representation of the relationships found in the case of _p_-azoxyanisole.[97]

Although the vapour pressure of the substance in the solid, or liquid state, has not been determined, it will be understood from what we have already learned, that the curves AO, OB, BC, representing the vapour pressure of solid crystals, liquid crystals, isotropic liquid, must have the relative positions shown in the diagram. Point O, the transition point of the solid into the liquid crystals, lies at 118.27, and the change of the transition point with the pressure is +0.032 pro 1 atm. The transition curve OE slopes, therefore, slightly to the right. The point B, the melting point of the liquid crystals, lies at 135.85, and the melting point is raised 0.0485 pro 1 atm. The curve BD, therefore, also slopes to the right, and more so than the transition curve. In this respect azoxyanisole is different from sulphur.

The areas bounded by the curves represent the conditions for the stable existence of the four single phases, solid crystals, liquid crystals, isotropic liquid and vapour.

The most important substances. .h.i.therto found to form liquid crystals are[98]:--

----------------------------------+------------+-------- Substance. Transition Melting point. point.

----------------------------------+------------+-------- Cholesteryl benzoate 145.5 178.5 Azoxyanisole 118.3 135.9 Azoxyphenetole 134.5 168.1 Condensation product from benzaldehyde and benzidine 234 260 Azine of _p_-oxyethylbenzaldehyde 172 196 Condensation product from _p_-tolylaldehyde and benzidine 231 -- _p_-Methoxycinnamic acid 169 185 ----------------------------------+------------+--------

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CHAPTER IV

GENERAL SUMMARY

In the preceding pages we have learned how the principles of the Phase Rule can be applied to the elucidation of various systems consisting of one component. In the present chapter it is proposed to give a short summary of the relationships we have met with, and also to discuss more generally how the Phase Rule applies to other one-component systems. On account of the fact that beginners are sometimes inclined to expect too much of the Phase Rule; to expect, for example, that it will inform them as to the exact behaviour of a substance, it may here be emphasized that the Phase Rule is a general rule; it informs us only as to the general conditions of equilibrium, and leaves the determination of the definite, numerical data to experiment.

Triple Point.--We have already (p. 28) defined a triple point in a one-component system, as being that pressure and temperature at which three phases coexist in equilibrium; it represents, therefore, an invariant system (p. 16). At the triple point also, three curves cut, viz. the curves representing the conditions of equilibrium of the three univariant systems formed by the combination of the three phases in pairs. The most common triple point of a one-component system is, of course, the triple point, solid, liquid, vapour (S-L-V), but other triple points[99] are also possible when, as in the case of {56} sulphur or benzophenone, polymorphic forms occur. Whether or not all the triple points can be experimentally realized will, of course, depend on circ.u.mstances. We shall, in the first place, consider only the triple point S-L-V.

As to the general arrangement of the three univariant curves around the triple point, the following rules may be given. (1) The prolongation of each of the curves beyond the triple point must lie between the other two curves. (2) The middle position at one and the same temperature in the neighbourhood of the triple point is taken by that curve (or its metastable prolongation) which represents the two phases of most widely differing specific volume.[100] That is to say, if a line of constant temperature is drawn immediately above or below the triple point so as to cut the three curves--two stable curves and the metastable prolongation of the third--the position of the curves at that temperature will be such that the middle position is occupied by that curve (or its metastable prolongation) which represents the two phases of most widely differing specific volume.

Now, although these rules admit of a considerable variety of possible arrangements of curves around the triple point,[101] only two of these have been experimentally obtained in the case of the triple point solid--liquid--vapour. At present, therefore, we shall consider only these two cases (Figs. 13 and 14).

[Ill.u.s.tration: FIG. 13.]

[Ill.u.s.tration: FIG. 14.]

An examination of these two figures shows that they satisfy the rules laid down. Each of the curves on being prolonged pa.s.ses between the other two curves. In the case of substances of the first type (Fig. 13), the specific volume of the solid is greater than that of the liquid (the substance contracts on fusion); the difference of specific volume will, therefore, be greatest between liquid and vapour. The curve, therefore, for liquid and vapour (or its prolongation) must lie between the other two curves; this is seen from the figure to be the case. Similarly, the rule is satisfied by the arrangement of curves in Fig. 14, where the difference of specific volumes is {57} greatest between the solid and vapour. In this case the curve S-V occupies the intermediate position.

As we see, the two figures differ from one another only in that the fusion curve OC in one case slopes to the right away from the pressure axis, thus indicating that the melting point is raised by increase of pressure; in the other case, to the left, indicating a lowering of the melting point with the pressure. These conditions are found exemplified in the case of sulphur and ice (pp. 29 and 35). We see further from the two figures, that O in Fig. 13 gives the highest temperature at which the solid can exist, for the curve for solid--liquid slopes back to regions of lower temperature; in Fig. 14, O gives the lowest temperature at which the liquid phase can exist as stable phase.[102]

Theorems of van't Hoff and of Le Chatelier.--So far we have studied only the conditions under which various systems exist in equilibrium; and we now pa.s.s to a consideration of the changes which take place in a system when the external conditions of temperature and pressure are altered. For all such changes there exist two theorems, based on the laws of thermodynamics, by means of which the alterations in a system can be qualitatively predicted.[103] The first of these, usually {58} known as van't Hoff's _law of movable equilibrium_,[104] states: When the temperature of a system in equilibrium is raised, that reaction takes place which is accompanied by absorption of heat; and, conversely, when the temperature is lowered, that reaction occurs which is accompanied by an evolution of heat.

The second of the two theorems refers to the effect of change of pressure, and states:[105] When the pressure on a system in equilibrium is increased, that reaction takes place which is accompanied by a diminution of volume; and when the pressure is diminished, a reaction ensues which is accompanied by an increase of volume.

The demonstration of the universal applicability of these two theorems is due chiefly to Le Chatelier, who showed that they may be regarded as consequences of the general law of action and reaction. For this reason they are generally regarded as special cases of the more general law, known as the _theorem of Le Chatelier_, which may be stated in the words of Ostwald, as follows:[106] _If a system in equilibrium is subjected to a constraint by which the equilibrium is shifted, a reaction takes place which opposes the constraint, _i.e._ one by which its effect is partially destroyed._

This theorem of Le Chatelier is of very great importance, for it applies to all systems and changes of the condition of equilibrium, whether physical or chemical; to vaporization and fusion; to solution and chemical action.

In all cases, whenever changes in the external condition of a system in equilibrium are produced, processes also occur within the system which tend to counteract the effect of the external changes.

_Changes at the Triple Point._--If now we apply this theorem to equilibria at the triple point S-L-V, and ask what changes will occur in such a system when the external conditions of pressure and temperature are altered, the general answer to the question will be: So long as the three phases are present, no {59} change in the temperature or pressure of the system can occur, but _only changes in the relative amounts of the phases_; that is to say, the effect on the system of change in the external conditions is opposed by the reactions or changes which take place within the system (according to the theorems of van't Hoff and Le Chatelier). We now proceed to discuss what these changes are, and shall consider first the effect of alteration of the temperature at constant volume and constant pressure, and then the effect of alteration of the pressure both when the temperature remains constant and when it varies.