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 P8, and very possibly higher.
In the case of phosphorus, therefore, it is more than possible that we are dealing, not simply with two polymorphic
forms of the same substance, but with polymeric forms, and that there is no transition point at temperatures above the absolute zero, unless we assume 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 P4, then the metastable vaporization curve of white phosphorus would not pass through the melting point of red phosphorus, as was assumed 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