Liquid Phosphorus

Values of the densities and specific volumes up to the boiling- point have been determined and are as follows:—

Densities and specific volumes of liquid phosphorus

t° C	30	40	56.5	100	200	280	290
Density	1.7684	1.74924	1.7444	1.6949	1.6027	1.52867	1.4850
Specific Volume	0.5654	0.5719	0.5733	0.5899	0.6238	0.6544	0.6733

Hence the expansion of the liquid is expressed by the formula

v_t = v₅₀[1 + 0.0₃5167(t - 50) + 0.0₆370(t - 50)²]

In another investigation, on 0.7669 gram of phosphorus contained in an evacuated glass dilatometer, the increase of volume between 50° and 235° C. was found to be expressed by:

v_t = 0.5733[l +0.0₃505(t - 50) + 0.0₆118(t - 50)²]

The agreement between the two expressions is good at the lower temperatures, and the differences at higher temperatures are about the same value as the coefficient of expansion of glass. Thus at 200° C. the second equation gives the specific volume as 0.6180 c.c. per gram. Without the correction for expansion of glass the apparent specific volume becomes 0.621 c.c.

The specific volume at the boiling-point, determined by the method of Ramsay, was 0.6744 c.c. The corresponding atomic volume. Is 20.9 ± 0.4. This constant thus lies between 20 and 21, with a tendency to diminish on keeping the phosphorus at this boiling temperature, owing to the formation of the denser Pβ molecules, which are shown by the cherry-red colour of the liquid.

The vapour pressures of liquid phosphorus are tabulated overpage in three sections, namely—

1. Commencing below the triple point, which is practically the same as the melting-point, and up to about 150° C.
2. From about 150° C. to nearly 360° C. Over this range three sets of measurements are available.
3. From about 500° C. to the melting-point of violet phosphorus the pressures of the metastable or supercooled liquid are known, and the pressure curve of liquid violet phosphorus has been followed up to over 600° C.

These results have been expressed by various interpolation formulae. That originally proposed by Smits and Bokhorst was

log p (mm.) = -3585.96/T – 3.59 log T + 19.2189

This was found to give pressures lower than those experimentally determined between 44° and 150° C. by MacRae and Voorhis, who have altered the constants to fit this range also, as follows:—

logp(mm.) = -2898/T – 1.2566 log T + 11.5694

These formulae express the pressures of the liquid from 44° C. to 634° C.

The latent heat of vaporisation of liquid yellow phosphorus at its boiling-point has been given as 4 Cals. or 3.89 Cals.

The values of the surface tension σ and density D at two temperatures were determined with the object of calculating the molar surface energy σ(M/D)^2/3, and its change with temperature.

Then, by comparison with the normal temperature coefficient, the molar weight in the liquid state can be deduced.

t° C	D	σ	σ(M/D)2/3	Δ(Molar surface energy)/Δt.
78.3	1.714	43.09	748.2	2.205
132.1	1.664	35.56	629.6

The molar weight M used in this calculation corresponded to a molecule P₄, and since the temperature coefficient calculated on this assumption is normal, the molar weight in the liquid state is thus found to be the same as in the gaseous state. The molar weight in the dissolved state at the boiling-point of carbon disulphide, and at the freezing-point of benzene, also corresponds very closely to P₄.