Violet Phosphorus

The incipient crystallisation of red phosphorus, which has been noted already, can be carried to completion by a procedure due to Hittorf,who dissolved red phosphorus in molten lead, and on cooling obtained yellowish-red translucent plates which had a density of 2.34 and belonged to the hexagonal system of crystals. Later investigators have obtained curved rectangular leaflets which were transparent, had a steely blue lustre and belonged to the monoclinic system. The form prepared in this manner is known as "Hittorf's" or violet phosphorus, with reference to its appearance en masse (see below). The preparation was repeated by Stock and Gomolka. Red phosphorus was heated with lead in a sealed tube at 800° C. for 48 hours. After purification from lead and glass (the former was not completely removed, however), the phosphorus appeared as brown transparent plates, the density of which, corrected for the lead present, was 2.31 to 2.33. This form has also been crystallised from molten bismuth in which, however, phosphorus is less soluble.

The violet form can also be obtained from some preparations of red phosphorus by the following treatment. The finest particles are washed away in a stream of water until only dark steel-blue particles are left; these are boiled with 30 per cent, sodium hydroxide solution, washed again, boiled with 5 per cent, nitric acid, washed with hot and cold water, then with absolute alcohol and ether, and allowed to stand until dry in a vacuum desiccator with concentrated sulphuric acid. The density of this preparation is about 2.2 (2.18 to 2.23).

The preparation of violet phosphorus may conveniently be carried out as follows:—The air is displaced, by means of carbon dioxide, from a hard glass tube, which is then one quarter filled with ordinary phosphorus, the remainder of the tube containing pieces of lead, preferably those which have served for a previous preparation. The carbon dioxide is then removed, the tube sealed on the pump, and placed inside an iron tube, the space between the walls being filled with magnesia. The whole is heated in a tube furnace for 8 to 10 hours at a moderate red heat. After opening, with the usual precautions, the crystalline phosphorus is removed from the surface and the crystals from the interior are collected after dissolving the lead in 1:1 nitric acid.

Crystals of violet phosphorus apparently identical with Hittorf's phosphorus have been obtained by maintaining the element at its melting-point in a sealed tube after starting the crystallisation by a slight supercooling. The tube was opened under carbon disulphide and the crystals separated from the white phosphorus in which they were embedded. They appeared as six-sided leaflets with a characteristic angle of 76-78° and short rounded obtuse angles at the ends, the normal or supplementary angle to which was 27-28°. Violet phosphorus from molten lead yielded two kinds of crystals, one of which was identical with that prepared as above. Both were pleochroic, and were described as dark orange in a direction parallel to the long side and lighter in a direction at right-angles to this. Their density was 2.35.

Violet phosphorus, when rubbed to a very fine powder, assumes a red colour. It still exists, however, in the most stable form, i.e. the violet, because it still exerts the characteristic lower vapour pressure of this modification.

Density of Violet Phosphorus

On the whole it seems improbable that the density is much, if at all, higher than 2.30.

Melting-point of Violet Phosphorus

This determination has of course been carried out in sealed tubes. The values of different experimenters do not agree very well; they are:-630° C., Chapman; 600-610° C., Stock and Gomolka; 597° C. (when heated slowly) Stock and Stamm. Fusion and solidification proceed as if the phosphorus were not a pure substance, but a mixture. The melting-points observed were also triple points when, as usual, the phosphorus was sealed in an evacuated tube. The melting-points are lower if the temperature of the bath is raised very slowly. In a bath at constant temperature the melting-point was found to be 589.5° C. by Smits and Bokhorst, who used a graphical method in interpreting their results.

Vapour Pressure of Violet Phosphorus

The determination of the values given below was beset with considerable difficulty, especially that of securing inner equilibrium in the solid phase. The curve lies below that of liquid phosphorus, which is unstable with respect to the violet (and red) forms up to the melting-point, 589.5°, of violet phosphorus. The pressure at this triple point is 43.1 atm., while that calculated from the thermodynamical equations (v. infra) is 42.9 atm.

Vapour pressures of solid violet phosphorus

t° C	308.5	346	379.5	408.5	433.5	450.5	463.5	472.5	486.5	505	515	522.5	561	578	581	587.5	588	589	589.5
p (atm.)	0.07	0.13	0.35	0.79	1.49	2.30	3.18	3.88	5.46	8.67	10.43	11.61	24.2	34.35	36.49	41.77	42.10	42.6	43.1

Red phosphorus probably is not a unary substance, and that the difference between the vapour pressures of red and violet phosphorus below about 400° C. are probably due to the non-equilibrium conditions in the red form. Even in the case of the more uniform violet modification, however, time is required for the establishment of equilibria with vapour, and the values of the pressures even up to 500° C. are affected by an uncertainty on this account. Condensation of vapour proceeds in general more slowly than vaporisation, and especially is this the case where there is a great difference between the molecular complexities of the vapour and of the solid.

Heats of Vaporisation, Sublimation and Fusion

These latent heats have been obtained from the respective pressure-temperature relations of the liquid and solid violet phosphorus. The Clausius equation

dlnp/dt = Q/RT²

in which it is assumed that the vapour (P₄) obeys the gas laws, is integrated and thrown into the form—

Tlnp = -Q/R + cT (1)

If Q, the latent heat, does not vary with the temperature, a straight line will be obtained by plotting Tlnp against T. This is so in the case of liquid violet phosphorus. The graph of liquid white phosphorus is slightly curved, and is a prolongation of that for liquid violet phosphorus. The integration constant c is obtained from the equation

c = (T₂lnp₂-T₁lnp₁)/(T₂-T₁) = tan α (2)

where α is the angle between the graph and the axis of abscissae. By introducing the c values into equation (1), the values of Q are obtained for the mean temperatures (T₂+T₁)/2.

For liquid violet phosphorus c = 9.6, Q = 9,900 calories (from 551° to 591° C.), mean temp. 571° C.

For liquid white phosphorus c = 11.1, Q = 12,100 calories (from 160° to 360° C.), mean temp. 260° C.

Thus the numerical value of Q diminishes by 2,200 calories between 260° and 571° C., and the temperature coefficient a in the equation

Q_T = Q₀ + αT

is found to be

α = dQ/dt = -7.1

This value of α is now introduced into the integrated form of the Clausius equation, and another equation is obtained which includes the variation of Q with T and which should apply to the whole vapour- pressure curve of liquid phosphorus on the assumption that it is continuous, i.e. that the liquid formed at lower pressures is really the same as that formed at higher pressures. The equations in question are

lnp = -Q₀/RT + α/R lnt + c (3)

= -Q₀/RT – 3.6lnt + c (4)

Q₀ is found to be 16,400 calories.

Putting equation (4) into the form

Tlnp + 3.6Tlnt = -Q₀/R + cT

and plotting the left-hand side against T, a straight line should be obtained, and this is very nearly the case.

The latent heat of vaporisation of liquid phosphorus at its boiling-point is calculated from equation (3) and is found to be

Q_LV = 12,500 calories at T_b = 553° C. Abs.

Hence we have

Q_LV/T_b = 22.6

which is nearly the normal value.

The heat of sublimation of violet phosphorus can be calculated from the pressure-temperature relations in a similar manner. In the first place, c is calculated by equation (2) between T₁ = 343.5+273 and T₂ = 589.5 +273 and is found to be 18.9. Since the Tlnp/T graph is found to be rectilinear over this range of temperature it follows that Q_SV does not vary much, and it was possible to write the linear equation

Tlnp = 18.9T - 13,050

If the value of Q/R is taken as 13,000 calories in round numbers the heat of sublimation of violet phosphorus works out at 25,800 calories. This is an abnormally high value as can be seen by comparing the ratio Q_SV/T_S with the normal ratio of about 30. T_S is the sublimation temperature, i.e. that temperature at which the vapour pressure of the solid is equal to 1 atmosphere. In the present case T_S was found by putting p = 1 in equation (1) and was 688° abs. or 415° C., the sublimation temperature of violet phosphorus.

Hence

Q_LV/T_b = 25,800/688 = 37.5

the abnormal ratio referred to above. The excess of heat required in this sublimation is explained as being due to the change from a polymerised form having a lower energy content into the simpler P₄ molecule. This energy change has been found in a different way as the difference between the heats of combustion of polymerised and ordinary phosphorus, i.e. 4x4,400 = 17,600 calories per mol P₄. The difference 25,800 – 17,600 = 8,200 calories is the physical latent heat of change of state solid → vapour.

Finally the molar heat of fusion Q_SL is obtained in the usual way as the difference between the latent heat of sublimation Q_SV and that of evaporation Q_LV at the triple point, 862.5° abs.—

Q_SL = 25,800 - 10,200 = 15,600 calories

Critical Constants

These have been calculated from van der Waals' and other equations of state. Thus T_c = 720.6° C., p_c = 93.3 atm. or t_c = 675° C., p_c = 80 atm. Another estimate is t_c = 695° C.; this value has been used to calculate the critical pressure by an extrapolation of the vapour-pressure curve from t = 634° C. The value of p_c so found is 88.2 atm. Or 82.2 atm.