Physical Properties of Phosphorus

The volume which is occupied by the atom of phosphorus when it is combined with one or two other elements to form liquid compounds has been deduced from the molar volumes of such compounds on the assumption that the other elements possess constant and characteristic atomic volumes in these compounds. Thus, from the molar volumes of PCl₃ and PBr₃ at their boiling-points Kopp assigned to phosphorus the atomic volume 25.2. The exact determinations by Thorpe of the densities and coefficients of expansion of PCl₃, PBr₃, POCl₃, PSCl₃, POBrCl₂ and PCl₂(OC₂H₅) gave values for the atomic volume of phosphorus which ranged between 24.0 and 26.1, the mean being about 25.3. The value derived from the density of liquid PH₃ (q.v.), using Kopp's value for hydrogen, is 29.1. These variations do not depend on experimental errors, nor, in the comparison of such compounds as PCl₃ and PBr₃, can they be ascribed to differences in constitution. It has been suggested that the differences between the molar volumes of the liquid compounds at their boiling-points (or other temperatures at which the vapour pressures are equal) and the sums of the atomic volumes of the liquid elements at the same vapour pressures are also some function of the affinities which come into play during the combinations. The volumes measured at the respective boiling-points are:—Cl, 22.76; Br, 26.8; P, 20.5; therefore P+3Cl = 88.8 and P+3Br = 100.9. According to Thorpe also PCl₃ = 93.34 and PBr₃ = 108.8. The combination with chlorine under conditions of equal vapour pressure is accompanied by an expansion of 4.5 units, and that with bromine by 7.9 units, in excess of the values which would obtain if Kopp's additive law held good. The comparison has been extended to the oxyhalides and the pentahalides with the result that the changes of volume on combination were found to be different in each case.

In attempting to determine the structure of such compounds as POCl₃ the molar volume of the compound at its boiling-point may be diminished by that of PCl₃, leaving 7.8, which is Kopp's value for oxygen linked to two elements, and leads to a formula Cl₂=P-O-Cl. If, however, the molar volume of POCl₃ is diminished by the atomic volumes of P and 3Cl, the remainder, 12.2, is the atomic volume of doubly-linked oxygen, which leads to a formula Cl₃≡P=O.

It is improbable that phosphorus is trivalent in POCl₃, and further, in such compounds it is exercising its maximum valency. Since the atomic volume calculated on the assumption of a double bond between the phosphorus and the oxygen agrees most closely with the atomic volume of elementary phosphorus, it is probable that in the liquid element as well as in POCl₃ phosphorus is exercising this maximum valency, which includes " mixed bonds," thus

The volumes which liquid compounds would occupy if they remained in this state at temperatures not far removed from the absolute zero represent the closest packing possible at ordinal external pressure and under the influence of the internal or intrinsic pressure alone of non-oriented molecules, i.e. those which are not arranged in a space-lattice. These volumes can be obtained by shorter or longer extrapolations from the actual observed liquid volumes.

The formula of Cailletet and Mathias gives the mean isobaric densities of a liquid and its saturated vapour as a rectilinear function of the temperature. Thus

(D_L+D_V)/2 = D₀/2 + αT

in which the meaning of the symbols is obvious, and D₀/2 is half the limiting density at the absolute zero obtained by the extrapolation.

The specific volumes v₀ (=1/D₀) are found in the case of many liquids to have a mean value equal to 0.26 of v_c (the critical volume), while according to van der Waals' equation they should be equal to 0.33 of v_c (v_c=3b). In either case the volumes v₀ at maximum contraction are corresponding volumes and should therefore be additively related to those of the constituent elements. It has been shown that the most closely additive relations are obtained if the limiting volumes are calculated by the equation

D_L-D_V = D₀(1-T/T_c)^0.3

From the differences in molar volumes mV₀ (or M/D₀) of homologous series, etc., the atomic volumes _AV₀ of each element are calculated in the usual way. The value assigned to phosphorus is 12.7. The atomic volumes are added together to give Σ_AV₀, and the sums are compared with the molar volumes found, mV₀.

Molar volumes of phosphorus compounds at absolute zero

Compound	Formula	mV0	ΣAV0
Phosphorus trichloride	PCl3	69.6	70.6
Phosphorus tribromide	PBr3	78.6	79.0
Phosphorus oxychloride	POCl3	73.4	75.6
Triethyl phosphate	PO(OEt)3	140.5	139.8
Triphenyl phosphate	PO(OPh)3	230.2	226.8
Triphenyl phosphine	PPh3	206.4	206.8

Further information on the structure of phosphorus compounds is given by the parachor, which is a function of surface tension and molar volume, the molar volumes in effect being compared under conditions of equal surface tension. For a given liquid the expression



is independent of the temperature. The molar parachor



is found to be additively composed of terms due to each of the atoms (which may be called the atomic parachors) plus terms due to double or triple linkages, and to various types of cyclic structures. The mean parachor of phosphorus as calculated from some binary compounds, such as PCl₃, etc., is 37.3 (36.1 to 38.9). In another system it is 40.5.

	PCl3	PBr3	P(C6H5)3
PM	199.0	242.9	607.7
ΣPA	162.9	204.0	570.0

The parachors of phosphorus and the other atoms were summed and compared also with the molar values of POCl₃, etc. A different series of atomic parachors has also been proposed.

	POCl3	PO(OC2H5)3	PO(OC6H5)3
PM	217.6	399.1	686.5
ΣPA	220.6	403.0	687.7
PM-ΣPA	-30	-3.9	-1.2

The differences have the sign and magnitude which is associated with a " mixed " bond, and this confirms its structure. The ethyl ester of phenylmethylphosphinic acid had a parachor of 420.5; that calculated on the assumption of an ordinary double bond was 442.1, while on the assumption of a " mixed " or semipolar bond it was 417.3. The structure was therefore given as

(CH₃)(C₆H₅)(C₂H₅O)≡PO

The atomic refraction shows considerable variability with constitutive influences, whether it is determined by Gladstone's formula



or by Lorentz and Lorenz's formula



(Note.—A = atomic weight, r_G = refractivity according to Gladstone's formula, r_L, = refractivity according to Lorentz and Lorenz's formula.) The atomic refraction Ar_G of the element is 18.68 (solid), 18.89 (liquid), or 18.69 (mean of solid and liquid), while the value Ar_L was 9.10 (mean of solid and liquid).

The following values have been calculated from the molar refractivities of the principal liquid (or gaseous) compounds:—

	PH3 (liquid).	PH3 (gaseous).	P(C2H5)3	PCl3	PCl5	PBr3	P4O6	POCl3.
ArG	13.75	13.75	17.24	14.89	16.65	20.01	9.71	8.92
ArL	9.10	8.63	9.47	8.32	8.81	9.72	5.33	4.92

Atomic refractivities of phosphorus in its compounds are calculated as the difference between the molar refractivities and the sums of the refractivities of the other atoms. They vary according to the structure assigned, namely, whether oxygen is to be considered as singly- or doubly-linked. Molar refractivities appear to be affected by constitutive influences to about the same extent as molar volumes at the boiling-points, V_M, since the ratios of V_M to Mr_L for all the compounds considered range between 4.77 and 5.01, mean 4.9.

When the refractivities of gaseous compounds are calculated to standard conditions, the values of n-1 or (n-1)×10⁶ are often found to be nearly additively composed of those of their components, that is (n-1)×10⁶ is nearly equal to Σ(n_A-1)×10⁶. The following table enables this comparison to be made between observed and calculated refractivities. The property is only approximately additive, the deviations from this relation being great in some cases.

Compounds of the type POX₃ may, as already pointed out, have one or other of two constitutions or may exist in tautomeric equilibrium, but if the halogens X are replaced by hydrocarbon or other organic radicals R, the compound will be fixed in one or other of the two isomeric forms. This isomerism has been well established in the case of the compounds having the empirical formula OP(C₆H₅)₃. One of these, phenoxydiphenylphosphine, is an oily liquid, prepared by the condensation of phenol with diphenylchlorophosphine:—

C₂H₅OH + (C₆H₅)₂PCl = (C₆H₅)₂P.OC₆H₅ + HCl

The other, triphenylphosphine oxide, is a solid melting at 153.5° C., and is prepared by the action of water on triphenylbromophosphine bromide:—

H₂O + (C₆H₅)₃PBr₂ = (C₆H₅)₃PO + 2HBr

That the three ordinary valencies of phosphorus in compounds of the type POX₃ or POR₃ do not act in one plane, but are distributed in space symmetrically with respect to one another, was demonstrated by Caven, who replaced chlorine atoms in the trichloride one at a time but in different succession by various groups such as RNH— or RO—, forming, for example, the anilino-, p-toluidino- and then the p-toluidino-anilino chloride.

No signs of isomerism were detected in the mono-, di- or tri-substitution products. It was therefore stated that " the centres of gravity of the three chlorine atoms lie at the angles of an equilateral triangle, and if an imaginary line is drawn through the centre of this triangle and at right angles to its plane, the centres of gravity both of the phosphorus atom and of the oxygen atom are situated on this line."

Compounds of the types [PR₄]X and [OPR₃] are of the same stereochemical type, and contain an atom of phosphorus co-ordinated to four atoms or groups which are symmetrically disposed in space. When the groups denoted by R are different, the resulting compounds PR₁R₂R₃R₄X and POR₁R₂R₃ should be capable of existing in optically active forms.

The first preparation of the type PR₁R₂R₃R₄X could not be resolved, nor could an anilino-p-toluidinophosphoric acid be resolved into optically active isomers by fractional crystallisation with active bases. The first compound which was proved to contain an asymmetric phosphorus atom was phenyl-p-tolylphosphoric acid, the dl-hydrindamine of which—



was found to be a mixture of two compounds having different melting- points. The d- and l-hydrindamines when separately prepared each yielded on fractional crystallisation a less soluble fraction of lower lsevo-rotatory power and a more soluble fraction of higher laevo-rotatory power, thus showing a resolution of the acid.

The compound methylethylphenylphosphine oxide



also contains an asymmetric phosphorus atom. It was prepared by combining ethyldiphenylphosphine with methyl iodide, setting the base free with silver oxide and boiling with water:—

(C₆H₅)₂(C₂H₅)(CH₃)POH = C₆H₆ + (C₆H₅)(C₂H₅)(CH₃)PO

This compound, which could be distilled without decomposition, was combined with the calculated amount of d-bromocamphorsulphonic acid and the product crystallised from ethyl acetate. The recrystallised product had a molecular rotation, M_D, of +321°, while that of bromocamphoric acid and its salts with inactive substances was + 48°. On passing ammonia into a solution of the camphorsulphonate in benzene, the ammonium salt was quantitatively precipitated, and the solution on evaporation gave colourless crystals of the methylethylphenylphosphine oxide, which had a molecular rotation, M_D, of +39° in water and +57° in benzene.

Further evidence as to structure in space is derived from an examination of the electric moments due to the dipoles of some compounds.

Molecules which are not polar in the sense of being strong acids, bases or salts, may yet show an inner polarity when investigated by certain physical methods. The use of the dielectric constant and the refractivity in calculating the polarisation of molecules is described in certain monographs and text-books, e.g. "The Dipole Moment and Chemical StructureDebye-Deans (Blackie), 1931; "Recent Advances in Physical Chemistry Glasstone (Churchill), 1931.

The total molar polarisation, i.e. that due to 1 gramme-molecule of the compound, is given by the Mosotti-Clausius equation:—



in which e is the dielectric constant, M and D have their usual significance, N is the Avogadro number, and γ is the molecular polarisability due to induced dipoles. We are not concerned at present with the first term on the right, which is the distortion polarisation, P_D, i.e. that which is due to the dipoles which are set up in molecules by the applied field of force. The second term is the polarisation due to the permanent dipoles existing in the molecules before the field is applied. A permanent dipole is present whenever combination with partial separation of electric charges has taken place in such a way that the centre of gravity of all the positive charges does not correspond with that of the negative charges. If the distance between the charges e is d, then de = μ is the dipole moment of each molecule. Boltzmann's constant k = R/N, in which R is the universal gas constant and N is the Avogadro number, i.e. the number of molecules in a gramme- molecule. Since all these constants have known values and the temperature is known, the dipole moment μ can be calculated, and on certain assumptions it gives the configuration of the molecule. The following values have been found in the case of the hydrogen compounds of this group:—

	NH3	PH3	AsH3
μ×1018	1.55	0.55	0.15

The existence of these permanent dipole moments indicates that the hydrogen atoms are not in the same plane as the tervalent element, but that this occupies the apex of a tetrahedron, of which the three hydrogen atoms form the corners. The diminution of the moment with rise of atomic weight is attributed to a decrease in the height of the tetrahedra, and also to the distortion of the octets of electrons on the N, P and As atoms by the positive charges on the H atoms.

The compounds in which phosphorus is trivalent are saturated in the sense that all the covalent bonds on the element are made up, with the completion of the outer octet of electrons, the phosphorus atom thus assuming the argon type with three completed shells of 2, 8, 8 electrons of which only the outermost are shown by the formulae—



If we admit the hypothesis that the three quantum orbits of the second series may contain a maximum of 6, 6 instead of 4, 4 electrons, it follows that PCl₅ also, and other quinquevalent compounds, may be written with ordinary valencies or duplet bonds only, giving shells of 10^-. If, however, 8 is the maximum possible (failing the completion of 12), then PCl₅ must be constituted either as NH₄Cl, or it must contribute two electrons to a pair of chlorine atoms, thus developing a " mixed bond." In the first case



would be potentially ionisable, a property which has been to some extent confirmed experimentally. One of the chlorines in PCl₄⁺ is held by a " mixed bond." In the second case



also contains a "mixed bond," uniting two chlorine atoms which are not connected with one another, and being united in a different manner from the other three should be more easily split off and replaced as a whole by O, e.g. to give POCl₃. The latter compounds, as well as H₃PO₄ and all others in which phosphorus is said to be quinquevalent, can be represented by formulae of similar type. They, as well as all compounds in which non-metals from Group IV onwards show valencies higher than the typical hydrogen valency towards other non-metals, must be represented as having one or more "mixed bonds," and as being co-ordination compounds, according to one definition of such compounds.

The oxy-acids of phosphorus can be represented by constitutional formulae in which there are 3 ordinary valencies and a " mixed bond " (phosphoric) or 3 ordinary valencies with a tautomeric change to 3 ordinary valencies and a " mixed bond " (phosphorous and hypophosphorous). Thus if POCl₃ is represented as or , then phosphoric acid is represented as .

The phosphorus probably is the central atom, possessing the coordination number 4, in all compounds which were considered formerly to contain quinquevalent phosphorus. The complete series between the quadrivalent hydride and oxide will appear as—



The corresponding formulae, e.g. for the phosphite ion, as written by Lowry, are—



The phosphites, and possibly the hypophosphites, are also capable of existing as tervalent forms which can be fixed as the esters, such as P(OEt)₃, and according to the evidence of X-rays these forms predominate in the solid or liquid compounds, whereas in solution they change into the unsymmetrical tautomeric forms. The evidence is discussed under that section which is devoted to the acids in question.

Although the allotropic forms of phosphorus are not so numerous as those of sulphur, they are better defined; the differences between them are more striking. Apart from plastic sulphur, which is really a supercooled liquid, the forms of sulphur are obviously varieties of the same element; the differences are found chiefly in the crystalline form, the other physical properties not differing much. The contrast in the appearance and obvious properties of ordinary white phosphorus and the other varieties is so great that a casual observer would hardly suppose that they were the same element. If the allotropic forms of phosphorus are classified by means of their striking properties, then at least five will be recognised, namely — White, Scarlet, Red, Violet and Black, which show great differences in other physical properties besides colour, and also in chemical properties. These forms will now be discussed from the view-points of their histories, preparation and physical properties, the conditions of their transformation and the evidence as to their molecular complexity.

Many commercial varieties of iron contain phosphorus, probably in the form of a phosphide. The metal is dissolved in HNO₃ (1:1), the solution evaporated to dryness, the residue taken up with hydrochloric acid and evaporated again until the silica has all been rendered insoluble. The residue is then taken up in hydrochloric acid, evaporated to dryness again, taken up in nitric acid and treated with ammonium nitrate and ammonium molybdate reagent. The precipitate is washed with dilute nitric acid until free from iron salts, then with water if it is to be weighed with a solution of potassium nitrate if it is to be titrated. This method also applies to other metals which contain phosphides. If tin is present, as in the phosphor bronzes, all the phosphoric oxide is found with the insoluble meta-stannic acid after solution of the alloy in nitric acid. This precipitate, after washing, drying and weighing, may be fused with three times its weight of potassium cyanide. The residue is extracted with water, the metallic tin filtered off, and the excess of cyanide destroyed with HCl, any copper and tin remaining in solution being precipitated with H₂S. In the filtrate, after boiling, the phosphate is determined by any of the methods already described.