Atomic Weight of Phosphorus

In his tables published in 1818 Berzelius gave 31.36 as the atomic weight of phosphorus. Other values obtained before and after this time did not agree even so well as this with the value accepted to-day. The reactions principally employed in this early period were the displacement of gold and silver from their chloride and sulphate respectively by elementary phosphorus. These reactions, on the assumption that one atom of phosphorus precipitates f of an atom of gold and 5 atoms of silver, led to the weighted mean just quoted. The reactions are, however, in reality rather complex. It happened that the right condition, i.e. an excess of silver sulphate, was chosen to give the ratio P:5Ag. If, however, the metal is completely deposited the ratio is P:4Ag nearly.

Schrotter determined the ratio of the element to its pentoxide by burning a weighed quantity of amorphous phosphorus in dry oxygen and weighing the oxide. The method is fraught with many difficulties. Unconsumed phosphorus was carried forward, and the combustion had to be completed in the successive bulbs in which the product was collected and weighed. It is also probable that backward diffusion or other contact with water vapour introduced an error. The minimum atomic weight deduced from these experiments was 30.94, the maximum 31.06 and the mean 31.03. But on account of the known incompleteness of the combustion the value 31.00 was assigned.

This experimental result happened to agree with that of Dumas, who by means of the ratio PCl₃ to AgCl found P =31.04, a result which, taking the probable accuracy as 1 in 300, is not affected by recalculating from Dumas' ratios with our fundamental atomic weights.

Determinations of the molecular weight of phosphine by the method of limiting densities led to atomic weights of 30.98 and 30.91. The compressibility of phosphine was not known, however, with sufficient accuracy to allow a reliable calculation of the limiting density.

In an attempt to settle the question by a comparison of all the best methods known at the time, v. der Plaats decomposed silver nitrate with phosphorus, burned red phosphorus to the pentoxide and also determined the ratio of silver to its orthophosphate. The results, based on Ag = 107.90, are—

Ratio determined	P:5Ag	Ag3PO4:3Ag	2P:P2O5
Atomic weight	30.93	30.99	30.98

The concordance is not sufficiently good to justify a recalculation to our fundamental value Ag = 107.88.

In the more recent determinations which have led to the accepted value of the atomic weight the method of decomposition of the halides has been followed with the aid of all the present knowledge as to the proper conditions for the conversion of halogen hydrides into silver halides. An interesting method has also been worked out by which silver phosphate is converted into the bromide. The results obtained by this method, which will be described first, give additional weight to those obtained from the phosphorus halides.

Atomic Weight from the Ratio Silver Bromide to Silver Phosphate Silver orthophosphate, prepared by several methods, one of which is indicated below, was converted into silver bromide, the equations involved being:—

3AgNO₃ + Na₂HPO₄ = Ag₃PO₄ + 2NaNO₃ + HNO₃. (1)
Ag₃PO₄ + 3HBr = 3AgBr + H₃PO₄. (2)

The silver nitrate was prepared by dissolving precipitated silver in nitric acid, which had been twice redistilled and condensed in a platinum condenser. The silver was precipitated from the commercial nitrate by means of ammonium formate. After washing, it was fused with sugar charcoal, scrubbed, cleaned with ammonia and nitric acid, dissolved in the redistilled nitric acid, the solution evaporated to saturation, precipitated with more nitric acid, centrifuged and the nitrate recrystallised. The hydrobromic acid was prepared by passing hydrogen through the purest bromine and then combining the mixed gases over heated platinised asbestos. The condensed acid was twice boiled with more bromine and once with bromine liberated by means of potassium permanganate, then distilled through a quartz condenser. The Na₂HPO₄ was treated with hydrogen sulphide, boiled, filtered free of a green precipitate (due to iron), then recrystallised fifteen times. It contained about 0.01 milligram of arsenic in 10 grams, an amount entirely insufficient to affect the results. By nephelometry no chloride or other substances were found which could be precipitated by silver nitrate in nitric acid solution. NaNH₄HPO₄ was prepared and purified in a similar manner.

The solutions which were allowed to interact were about 0.03 N in order to avoid inclusions in the precipitates. The latter were well washed, and allowed to stand in water for at least 24 hours. Silver orthophosphate was stable in the presence of the moderate amounts of acid produced by some of the reactions which were tried. If silver nitrate is poured into excess of disodium hydrogen phosphate the precipitate settles rapidly, but precipitation is incomplete. If disodium ammonium phosphate is poured into silver nitrate the precipitate settles rapidly and the solution remains nearly neutral, according to the equation

Na₂NH₄PO₄ + 3AgNO₃ = Ag₃PO₄ + 2NaNO₃ + NH₄NO₃

By a combination of methods, for an account of which the original paper should be consulted, pure Ag₃PO₄ was obtained and dried by heating in a platinum boat in a current of dry air free from carbon dioxide. After weighing, it was dissolved in nitric acid and the solution was poured into an excess of hydrobromic acid, with the precautions usually employed in the quantitative precipitation of silver bromide.

The ratio 3AgBr:Ag₃PO₄ varied between 1.34558 and 1.34570 as extremes, the mean value being 1.34562. It was considered that the mean value was, if anything, slightly low owing to a possible occlusion of Ag₂HPO₄. It was noted that the samples of silver phosphate prepared under more acid conditions gave a ratio of 1.34558, while those under less acid conditions gave a ratio of 1.34564. If Ag is taken as 107.88 and the percentage of Ag in AgBr as 57.4453, the two mean values of the bromide-phosphate ratio give 31.043 and 31.037 respectively as the atomic weight of phosphorus.

In view of the fact that the methods to be described each have their own sources of error it seems that the phosphate results should be taken into account in assigning the atomic weight.

Ratios PBr₃:3PBr and PBr₃:3Ag.

The preceding method is open to the criticism that silver orthophosphate contains only 7.4 per cent, of phosphorus. Phosphorus tribromide is somewhat better in this respect, containing 11.5 per cent, of phosphorus; but on the other hand the preparation and quantitative decomposition of this compound in a manner suitable for atomic weight determinations present great difficulties, the nature of which is apparent from the following narrative.

Outline of Process Pure dry bromine was allowed to act on pure dry phosphorus in a vacuum; the PBr₃ was distilled into receivers which were sealed and weighed, then decomposed by breaking under an ammoniacal solution of hydrogen peroxide. The. solution was acidified with nitric acid and the bromine precipitated and weighed as silver bromide.

The Reagents The water, nitric acid and ammonia were purified by redistillation and the usual methods, and the silver by the methods in common use for its preparation as a standard element in atomic weight determinations. The hydrogen peroxide was a c.p. sample free from sulphuric and halogen acids. The nitrogen used in the preparation of the PBr₃ was prepared by passing air and ammonia over heated copper gauze. The phosphorus was twice distilled with steam in an all-glass apparatus. The bromine was distilled from concentrated potassium bromide (which removes all but a trace of chlorine), then converted into potassium bromide by action on a solution of potassium oxalate. To remove iodine the solution of potassium bromide was boiled with some of the partly purified bromine, and finally with small portions of potassium permanganate. It was then evaporated to dryness and fused. From this fused potassium bromide bromine was prepared by dissolving in water, adding sulphuric acid and enough potassium permanganate to liberate three-quarters of the halogen. This was distilled a second time from the bromide, which was nearly pure. The separated bromine was dried by resublimed phosphorus pentoxide, from which it was distilled immediately before use.

Preparation of Phosphorus Tribromide An excess of bromine was necessary on account of the solubility of phosphorus in PBr₃. Distillation of this from red phosphorus yields a product which contains too little bromine. The phosphorus (14 grams) was freed from water by pressing between hardened filter-papers and placed in a distillation flask containing dry nitrogen. The flask was then placed in boiling water and the contents subjected to a current of dry nitrogen, with shaking, to eliminate all steam from the liquid phosphorus. The flask was then evacuated and closed. It was cooled with ice-water, and the calculated amount of pure dry bromine admitted gradually from a tap funnel. After addition of nearly the theoretical amount of bromine the PBr₅ in the upper part of the flask was decomposed with hot water and more bromine admitted until the tribromide assumed a reddish colour due to excess of bromine, when such excess amounted to a few centigrams. Dry nitrogen was then admitted so as to produce a slight excess pressure, and the tribromide then fractionally distilled in a vacuum, the fractions being collected in a number of receivers placed in series. In this distillation a residue of a few grams was left in each of the first two receivers, this containing any dissolved phosphorus which was present. The bulk of the distillate in the third receiver now contained a slight excess of bromine. This was removed by bubbling through the warm liquid vapour derived from the second receiver. This process was continued for some time after the distillate became colourless. The residue in the third receiver, about 100 grams, was redistilled into several small bulbs, which were then sealed at their capillary junctions. The first and last samples collected showed equally a slight yellow tint when warm. This is probably characteristic of the pure tribromide.

A bulb and contents, after weighing, was broken by shaking under a solution of ammoniacal hydrogen peroxide in a stout flask closed by a glass stopper. The decomposition of the PBr₃ was complete in 5 minutes, but the flask was allowed to stand for 24 hours with occasional shaking in order to effect complete absorption of the fumes of NH₄Br. The cooled solution was filtered through a small paper, which was burned at as low a temperature as possible. All the broken glass was thus collected and weighed. The filtrate was acidified with nitric acid, introduced by a thistle funnel at the bottom of the solution, in order to avoid any loss of bromine set free locally and temporarily. The bromine, present as hydrobromic acid, was then determined in two ways—

1. By finding the amount o£ silver which combined with it completely.
2. By weighing the silver bromide precipitated.

Both determinations were carried out with the same solution.

1. A quantity of silver which was equivalent to the bromine present within a few tenths of a milligram was dissolved in nitric acid with the usual precautions, the solution treated with an excess of nitric acid and added to the solution prepared from the PBr₃ with constant agitation. After standing, portions of the clear solution were tested in a nephelometer for excess of bromide or of silver. The bromide was always found to be in slight excess. The solution was then adjusted with N/100 AgNO₃, shaken, allowed to stand, and the adjustment repeated until the amounts of silver and of bromine were again equivalent. After standing for a week, a nephelometer test showed that there was again an excess of bromide, apparently due to the diffusion of occluded bromide out of the precipitate. The deficiency of silver was again made up, the final end-point being reached in about a fortnight.
2. The precipitated AgBr was washed by decantation with water and collected on a Gooch-Munroe-Neubauer crucible, which was then heated gradually to 200° C. and kept at that temperature for 18 hours or more. After cooling, the bromide was weighed by substitution for a similar counterpoise. The precipitate was then transferred to a porcelain crucible and fused. The loss in weight on fusion seldom amounted to more than 0.001 per cent, of the weight of the precipitate. The clear yellow colour of the fused bromide was an additional guarantee of purity, since a very small percentage of impurity is sufficient to produce a perceptible darkening. The amounts of AgBr which were dissolved in the filtrate and wash water were also determined.

The concordance of the two methods (a) and (b) could be checked by means of the ratio Ag:AgBr, which as a mean of seventeen results was 0.574462. This is almost identical with the value 0.574453 which had already been considered to be the most probable. Three series of determinations were carried out, each including five to eight separate experiments, and there were thirty-six in all. The means of each of the sets carried out according to methods (a) and (b) are given in the following tables. The atomic weight of phosphorus is calculated from these results using Ag = 107.880 and Br = 79.916.

A given percentage error in the experimental work is multiplied nine times in the calculation of the atomic weight, i.e. an experimental error of 0.01 per cent, affects the calculated atomic weight of phosphorus by 0.027 unit. The highest individual value was 31.040, the lowest 31.013, which corresponds almost exactly to 0.01 per cent, accuracy in the experimental work. Of the thirty-six results, however, twenty-seven fell between 31.035 and 31.021, a fluctuation only half as great. The variations in the mean results are about 0.002 per cent., which corresponds to about 0.006 unit in the atomic weight. The means of the means agree to 0.003 unit. Giving a slightly greater weight to method (a) the investigators deduce from these results an atomic weight of 31.027.

Ratios PCl₃:3AgCl and PCl₃:3Ag.

Since the percentage of phosphorus is considerably higher in the chloride than in the bromide it was considered that the atomic weight might be deduced with even greater accuracy from the former compound. The methods used were similar, although not identical; the most important points of difference will be noted.

Chlorine prepared from manganese dioxide and pure HCl was liquefied and the dry gas evolved from the liquid was admitted to the dry phosphorus in a vacuum. In this case phosphorus pentachloride was formed in considerable quantity and was removed only by several distillations. It could not be inferred with such confidence that the trichloride was free from pentachloride as that the tribromide was free from bromine. The trichloride was decomposed and oxidised in the manner already described. In the subsequent estimation of the silver chloride less difficulty was experienced in freeing this from occluded chloride, but more difficulty in determining accurately the amount of silver chloride remaining in solution. It was found possible, however, to diminish the solubility by adding an excess of silver nitrate solution and partly washing the precipitated chloride with this solution.

The silver chloride was dried at 190° C. and weighed as usual in series III. In series I and II the exact amount of silver nitrate required for complete reaction was found by adjustment, using the nephelometer as already described. The means of the experiments in each series are given in the following table:—

The average atomic weight is given as 31.018. The investigators remark: "If the trichloride actually contained a trace of pentachloride it would account for the fact that the average result of this research is very slightly lower than that of the tribromide work."

The three main determinations of the atomic weight of phosphorus with their results are—

From	Ag3PO4	PBr3	PCl3
Atomic weight	31.04	31.027	31.018

In the fixing of standard atomic weights the results obtained from PBr₃ have been preferred for reasons that will be evident from the data already adduced. Although these results appear to be the least affected by systematic errors, nevertheless they involve such errors, and it seems hardly justifiable as yet to trust the results as far as units in the fifth significant figure. It may, however, be asserted with the greatest confidence that the atomic weight is known to be—

31.03 ± 0.01

Thus there is no doubt that all chemical determinations concur in assigning to phosphorus an atomic weight slightly greater than 31.00. Nevertheless phosphorus, when analysed by the method of mass spectra, has hitherto proved to be a pure element; no isotopes are present to account for the departure from the rule of whole numbers. There are two possible explanations—

1. "The whole number rule is not, and never was supposed to be, mathematically exact, for this would imply an identical packing effect in the case of all atoms, an exceedingly improbable supposition."
2. It is possible that an isotope accompanying P =31.00 in small amount has not yet been detected, as in the case of sulphur (S = 32.06), the spectrograph of which shows two faint lines at 33 and 34, originally ascribed to hydrides, but afterwards shown to be due to isotopes of higher atomic weight. Opinions founded on later work, however, have been less favourable to this hypothesis, and slight deviations from the whole number rule (on the oxygen scale) are now recognised in the case of " pure " elements, as appears from the quotation below.

The purely chemical evidence as to the atomic weight of phosphorus is supplemented by that derived from mass spectra.

"Ever since the discovery of the whole number rule it has been assumed that in the structure of atoms only two entities are ultimately concerned, the proton and the electron. If the additive law of mass was as true when an atomic nucleus is built of protons plus electrons as when a neutral atom is built of nucleus plus electrons, or a molecule of atoms plus atoms, the divergences from the whole number rule would be too small to be significant, and, since a neutral hydrogen atom is one proton plus one electron, the masses of all atoms would be whole numbers on the scale H = l. The measurements made with the first mass-spectrograph were sufficiently accurate to show that this was not true. The theoretical reason adduced for this failure of the additive law is that, inside the nucleus, the protons and electrons are packed so closely together that their electromagnetic fields interfere and a certain fraction of the combined mass is destroyed, whereas outside the nucleus the distances between the charges are too great for this to happen. The most convenient and informative expression for the divergences of an atom from the whole number rule is the actual divergence divided by its mass number. This is the mean gain or loss per proton when the nuclear packing is changed from that of oxygen to that of the atom in question. It will be called the 'packing fraction' of the atom and expressed in parts per 10,000. Put in another way, if we suppose the whole numbers and the masses of the atoms to be plotted on a uniform logarithmic scale such that every decimetre equals a change of 1 per cent., then the packing fractions are the distances expressed in millimetres between the masses and the whole numbers.

"Phosphorus.—The element was introduced in the form of phosphine, which gives the lines P, PH, PH₂, PH₃. If plenty of carbon monoxide is present its line will be practically unaffected by the presence of small quantities of Si²⁸, inevitably present and of mass so far unknown. So that the series CO:P: PH₃ can be employed to give values for phosphorus. . . . From the known values of H, C and O and the sum of the two intervals the 'packing fraction' of P can be calculated. The mean of six consistent values corresponds to a packing fraction -5.6 and therefore a mass 30.9825. No mass-spectrum has given the slightest reason for supposing that phosphorus is complex, so that it seems probable that the chemical atomic weight of 31.02 is too high."

The method of limiting densities when applied to phosphine also gives a lower result for the atomic weight of phosphorus. Phosphine was prepared from phosphonium iodide by means of potassium hydroxide, and was fractionated. The densities were investigated at pressures of 1 down to 0.25 atmosphere. Assuming a linear relation between pv and pressure, (pv)₀/(pv)₁ is calculated to be 1.0091. If the normal litre of oxygen weighs 1.4290 gram and the coefficient of deviation from Boyle's law per atmosphere is -0.00096, then PH₃ = 34.000 and P = 30.977.