The Phase Rule and Its ApplicationsFindlay, Alexander
Science
The Phase Rule and Its Applications
Findlay, Alexander
Chemistry, Physical and theoretical; Phase rule and equilibrium; Solution (Chemistry)
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 pass 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 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 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 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
P_{4}, then the metastable vaporization curve of white phosphorus would not
pass through the melting point of red phosphorus, as was assumed above.[82]
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