however, the liquid is metastable with respect to the stable solid form, and if the temperature is not allowed to rise above the melting point of the latter, the liquid may solidify. The stable solid modification thus obtained will melt only at a higher temperature.
D. Phosphorus.
An interesting case of a monotropic dimorphous substance is found in phosphorus, which occurs in two crystalline forms; white phosphorus belonging to the regular system, and red phosphorus belonging to the hexagonal system. From determinations of the vapour pressures of liquid white phosphorus, and of solid red phosphorus,[68] it was found that the vapour pressure of red phosphorus was considerably lower than that of liquid white phosphorus at the same temperature, the values obtained being given in the following table.
Vapour Pressures of White and Red Phosphorus.
| Vapour pressure of liquid white phosphorus. | Vapour pressure of red phosphorus. | ||||
| Temperature. | Pressure in cm. | Temperature. | Pressure in atm. | Temperature. | Pressure 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.
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 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, BO1 represents the conditions of equilibrium of the univariant system red phosphorus and vapour, which ends at O1, the melting point of red phosphorus. By heating in capillary tubes of hard glass, Chapman[73] found that red phosphorus melts at the melting point of potassium iodide, i.e. about 630°,[74] but the pressure at this temperature is unknown.
At O1, then, we have the triple point, red phosphorus, liquid, and vapour, and starting from it, we should have the vaporization curve of liquid phosphorus, O1A, and the fusion curve of red phosphorus, O1F. 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.
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, O2E, 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 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 pass through the point O1, the melting point of red phosphorus, and must be continuous with the curve O1A, 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 BO1 and O1A 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 assumption that change in the molecular complexity (polymerization) occurs in the conversion of white into red phosphorus, and when red phosphorus passes 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 P4,[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
