Phosphoric acids

The production of an acid solution by dissolving in water the products of the combustion of phosphorus was demonstrated by Boyle, and the acid was prepared in a similar manner by Marggraf, who described its properties. It was extracted from the calcium phosphate of bones by Scheele. Lavoisier obtained it from phosphorus and nitric acid. Three forms differing in their properties and in their mode of preparation were recognised early in the nineteenth century.

The usual form, as prepared by Boyle and others, when partly neutralised by soda gave a yellow precipitate with a solution of silver nitrate. When a solution of this ordinary acid was heated in a gold crucible until water ceased to be evolved, a thick pasty mass was left which gave a white silver salt and coagulated albumin. When ordinary sodium phosphate, Na₂HPO₄, was heated to 240° C. it was converted into a salt which gave a white precipitate with silver nitrate. It was also shown by Graham that phosphoric acid could be obtained as a vitreous mass by long heating at 215° C., and that this, when dissolved in water, did not coagulate albumin or give a precipitate with barium chloride in acid solution. When the acid was still more strongly heated it gave a tough vitreous mass, a solution of which coagulated albumin and gave a precipitate with barium chloride. Salts of the same acid were obtained by heating sodium biphosphate, namely, NaH₂PO₄. A vitreous mass was left which was known as "Graham's salt," and is now known as metaphosphate, NaPO₃ (q.v.) in a polymerised condition. The acid itself was prepared by decomposing the lead salt with H₂S, and also by heating the ortho- or pyro-acid to over 300° C., and later by several other methods (q.v.).

Graham proved that the three acids, ortho-, H₃PO₄, pyro-, H₄P₂O₇, and meta-, HPO₃, differed by the quantity of combined water. This water determined the basicity of the acid. The hydrogen could be replaced in stages by a metal, and e.g. in the case of orthophosphoric acid different salts, the primary, secondary and tertiary phosphates, could be produced.

The acid which is produced finally by the oxidation of phosphorus in the presence of sufficient water and after heating has probably the constitutional formula OP(OH)₃. The term " ortho," in accordance with Graham's description, was applied to " ordinary " phosphoric acid. Later, on the hypothesis of the quinquevalent nature of phosphorus, it was considered that the hypothetical acid P(OH)₅ would, strictly speaking, be the "ortho" acid. However, the present theories of valency do not indicate the possible existence of such an acid, but rather that OP(OH)₃ should be the most highly hydroxylated compound.

The acid may be made by means of a great variety of reactions. Only a few methods, of technical or historical importance, will be described here.

1. The decomposition of naturally occurring phosphates. From this source the original supplies both of technical and refined phosphoric acid are derived. The decomposition is effected by sulphuric acid, supplied in the quantities required by the equation
   
   Ca₃(PO₄)₂ + 3H₂SO₄ = 3CaSO₄ + 2H₃PO₄
   
   The decomposition may be carried out in a large vat of pitch pine saturated with tar oil, and provided with a vertical wooden shaft bearing arms or paddles and rotating on a pivot which is protected with cast-iron. In the vat are placed weak liquors from a previous decomposition and steam is blown in through a leaden pipe. Stirring is then commenced, and a charge of 6 cwt. of finely-ground high-grade phosphate (at least 70 per cent. Ca₃(PO₄)₂) is added alternately with 5 carboys of " chamber acid " of density 1.5 to 1.6 (free from arsenic). After the reaction is completed the whole charge is run on to slightly inclined filter-beds made of ashes supported on clinkers and contained in rectangular wooden tanks. The phosphoric acid which runs off first has a density of 1.150. The deposited gypsum is kept covered with water supplied as a spray until the density of the effluent falls to 1.010. The gypsum sludge, containing small amounts of free phosphoric acid and phosphate of lime, is dried by waste heat and used for mixing with superphosphate and for other purposes. The solution of phosphoric acid is concentrated by evaporation in lead-lined wooden tanks which are heated by lead pipes carrying superheated steam, concentration being continued up to a density of 1.325 to 1.50. Calcium sulphate deposited in this part of the process is removed and washed.
2. The preparation of the acid by the combustion of phosphorus and solution of the " flowers of phosphorus " in water has an historical interest only. It is obviously too expensive for large-scale work, nor does it yield a pure product.
3. Oxidation of red phosphorus by nitric acid was used before the end of the eighteenth century. An excess of nitric acid of density 1.20 to 1.25, namely, about 16 parts, is added to 1 part of phosphorus in a flask carrying a reflux condenser which is fitted in by a ground-glass joint. The phosphoric acid may be concentrated in a platinum or gold dish and is then free from most of the impurities mentioned later, with the possible exception of arsenic derived from the red phosphorus. [In process (1) arsenic, if present, is generally introduced with the sulphuric acid.] In both cases it will be converted into arsenic or arsenious acid. It may be removed by saturation with sulphur dioxide, which reduces arsenic to arsenious acid, followed by boiling to remove the excess of SO₂, precipitation of the arsenic as sulphide by hydrogen sulphide, filtration and removal of the excess of H₂S by means of a current of air.
   
   Concentrated phosphoric acid may be further purified by crystallisation.
4. Furnace Methods.—Phosphoric acid can be prepared from the pentoxide, which is sublimed at high temperatures from a mixture of calcium phosphate, sand and coke. Phosphorus is first produced and then burns to the pentoxide. Reduction proceeds according to the equation
   
   Ca₃(PO₄)₂ + 3SiO₂ + 5C = 3CaSiO₃ + 2P + 5CO
   
   An electrically-heated furnace or an oil-fired furnace built of carborundum bricks and kept at a temperature of 1500° to 1700° C. is suitable. A regenerative system of heating is used. The mixture of carbon, sand and phosphate is introduced at the top of a slanting flue and meets the ascending heated gases in its descent to the hearth, where it melts and reacts according to the equation given above. The escaping gases are taken round and burnt in a set of channels which surround the furnace.
   
   If phosphorus is burnt in air to the pentoxide, the absorption of this in water is rather difficult. Oxidation by steam according to the equation
   
   2P + 5H₂O = P₂O₅ + 5H₂
   
   gives hydrogen as a by-product which may be converted into ammonia and combined with the phosphoric oxide (Liljenroth process).

Impurities

The acid prepared by commercial methods contains numerous impurities, some of which are difficult to remove. They include bases such as Na, K, Ca, Al, Fe, Mn totalling 0.5 to 3.0 per cent., Pb up to 14 parts per million, Ag from 1 to 2.5 parts per million, H₂SO₄ from 0.1 to 1.0 per cent., HF in about the same amount, and HCl from 0.01 to 0.04 per cent.

Preparation of the Crystalline Acid

Two compounds have been crystallised from concentrated solutions of phosphoric acid—the anhydrous acid, H₃PO₄, and the hemi-hydrate 2H₃PO₄.H₂O. According to Joly a solution having the composition H₃PO₄ + 0.3H₂O, when inoculated with a crystal of H₃PO₄, deposits the hemi-hydrate. The mother 'liquor then has the composition 2H₃PO₄.H₂O and solidifies to a mass of crystals when inoculated with this hydrate. Another method of obtaining the crystalline acid has been described in the following terms: "Crystals of anhydrous phosphoric acid were prepared by maintaining the ordinary Commercial Pure acid in an open vessel at a temperature of about 95° C. until it reached a specific gravity of approximately D_4°^25° 1.85. The solution was then cooled below 40° C., inoculated with a crystal of orthophosphoric acid, allowed to stand until crystallisation was complete and the mother liquor then separated from the crystals by centrifuging in a porcelain-lined centrifuge. The crystals recovered in this way were then melted at a temperature of about 50°, sufficient water was added to bring to a specific gravity of D_4°^25° 1.85, the solution inoculated as before and the process repeated thrice. The crystals were finally dried by allowing them to stand for several months over phosphorus pentoxide. Crystals of the semi-hydrate were prepared by adding the proper amount of water to a weighed portion of fused anhydrous phosphoric acid, cooling below 29° and inoculating with a crystal of the hydrate.

The melting-points, as registered by different investigators, are in fair agreement, thus:

H₃PO₄ between 38.6° C and 42.35° C, 2H₃PO₄.H₂O between 27.0° C and 29.35° C .

Hydrates of Phosphoric acid

The thermal diagram of H₃PO₄ and H₂O is shown in fig., on which there are two melting-points, m₁ that of H₃PO₄ and m₂ that of 2H₃PO₄.H₂O, and two eutectics, e₁ that of H₃PO₄ and 2H₃PO₄.H₂O and e₂ that of 2H₃PO₄.H₂O and ice. The solubilities according to Smith and Menzies are marked in the table opposite by an asterisk. These investigators reported also a distinct solubility curve corresponding to a hydrate 10H₃PO₄.H₂O, which started from the eutectic e₁ and ended with a transition point at 25.85° C.

Phosphoric acid crystallises in four- or six-sided prisms belonging to the rhombic system.

The determination of the molecular weight by depression of the freezing-point indicates some electrolytic dissociation. A value of 93 has been found for the molecular weight. The acid apparently forms double molecules in glacial acetic acid which dissociate in process of time.

The molar heat of fusion of H₃PO₄ is 2.52 Cals., that of 2H₃PO₄.H₂O 7.28 Cals. The heat of solution was found to be positive, 2.69 Cals. per mol of the crystalline acid dissolved and 5.21 Cals. per mol of the liquid acid.

The heat of dilution was found to be—

Mols water per mol H3PO4	11.19	13.88	19.88	29.99
Heat of dilution, Cals	33.13	19.93	12.26	8.23

The heat of formation from the elements includes that of water, and was found to be—

H3PO4	H3PO4	H3PO4
crystalline	fused	dissolved
302.56 Cals.	300.04 Cals.	305.29 Cals.

The following tables summarise the principal determinations of the densities at certain definite temperatures. If the percentages of H₃PO₄ are divided by 1.38 the quotient gives percentages of P₂O₅.

Densities of aqueous solution of phosphoric acid At 15° C

Per cent. H3PO4	5	10	20	30	40	50	60
Density	1.0276	1.0567	1.1196	1.1889	1.2651	1.3486	1.4395

Densities of aqueous solution of phosphoric acid At 17.5° C

Per cent. P2O5	5	10	20	30	40	50	60	68
Density	1.037	1.079	1.169	1.271	1.383	1.521	1.677	1.809

Densities of aqueous solution of phosphoric acid At 25° C

Per cent. H3PO4	5	10	15	20	25	30	35	40	45	50	55	60	65	70	75	80	85	90	91
Density	1.027	1.055	1.085	1.116	1.149	1.183	1.219	1.256	1.294	1.336	1.381	1.429	1.477	1.527	1.579	1.633	1.690	1.753	1.766

The vapour pressures of solutions at 0° C. are

Grams H3PO4 in 100 grams H2O	0.945	22.32	124.9	390.2
Ph2o	4.612	4.377	2.710	0.636 mm.

Vapour pressures of water at 100° C. were lowered in a high ratio by phosphoric acid, as appears from the following data:

Grams H3PO4 in 100 grams H2O	20.75	149.16	330.52
Lowering of vapour pressure	30.1	290.9	507.3 mm.

The crystalline acid has an appreciable specific conductivity of about 1×10^-4 reciprocal ohms (mhos), while the fused acid at the same temperature has a conductivity of 1×10^-2 mhos. Specific conductivities of the more concentrated solutions show a maximum at about 43 per cent., as appears from the following data:—

Conductivities of concentrated solutions of phosphoric acid

H3PO4, per cent.	1.4	2.87	5.28	16.09	30.71	43.26	52.83	71.29	92.07	100.0
Specific conductivity, k	0.014	0.02533	0.04245	0.08064	0.12816	0.14916	0.13750	0.07876	0.02203	0.01406

The molar conductivity (=1000k/c) thus varies from 97.50 in the 1.4 per cent, solution to 26.28 in the 43.26 per cent, solution and 1.31 in the 92.07 per cent, solution. Degrees of ionisation are low in the concentrated acids.

The conductivities of the more dilute solutions up to 0.1 molar have been determined to 156° C.

Equivalent conductivities of dilute solutions of phosphoric acid

H3PO4, mols per litre	0	0.0002	0.002	0.010	0.0125	0.050	0.080	0.100
λ at 18° C	338	330.8	283.1	203	191.2	122.7	104	96.5
λ at 25° C	378	367.2	311.9	222	208.1	132.6	112.4	104.0

The temperature coefficient was positive as usual at ordinary temperatures and reached a maximum at temperatures which varied with the ion concentration. Thus, in the case of the 0.0002 molar solutions, the maximum had not been reached at 156° C. (λ = 804.7), while in the 0.1 molar solution it occurred at about 75° C. Other results were expressed by the formula—

λ=λ₀e^-0.0822t(1+0.01455t)

It is clear that the degree of dissociation is less at the higher temperatures; thus for a 0.1 molar solution it is estimated as 38.5 per cent, at 18° C. and 11.5 per cent, at 156° C.

The viscosities of concentrated solutions of phosphoric acid are high; those of moderately concentrated solutions are given below:—

Viscosities of solutions of phosphoric acid

H3PO4, mols per litre	0.25	0.50	1.00	2.00
η relative at 18° C. (water = 1)	1.064	1.143	1.311	1.739
H3PO4, equivalents per litre	0.125	0.25	0.50	1.00
η relative at 25° C. (water = 1)	1.0312	1.0656	1.1331	1.2871

The refractive index of a solution of the acid of density 1.180 was at 7.5° C.—

Spectral line	A	D	H
n	1.3584	1.3630	1.3746

The molar refraction was 23.6. The equivalent refracting power of the H₂PO₄^- ion has been calculated as 21.6. Refractivities may conveniently be used in determining the concentration of aqueous solutions and also in testing for freedom from the meta- and pyro-acids.

The crystalline forms and other properties of the different phosphates of sodium were described by Graham. The ordinary phosphate of soda "is a highly alkaline salt, although generally viewed as neutral in composition. Mitscherlich found that a solution of this salt required the addition of half as much acid as it already possesses to deprive it of an alkaline reaction." By heating, the salt was found to contain 25.2 molecules of water to 1 molecule of phosphoric oxide. One of these molecules was retained to a higher temperature than the others. " The phosphate of soda contains 3 atoms base; namely, 2 atoms soda and 1 atom water. When this last atom was lost the sodium salt changed into that of a different acid, namely, a pyrophosphate." In modern symbols—

Na₂HPO₄.12H₂O → Na₂HPO₄ + 12H₂O
2Na₂HPO₄ → Na₄P₂O₇ + H₂O

Sodium biphosphate was known as a dimorphous salt . . of the 4 atoms of water which the crystals contain, they lose, I find, 2 atoms at the temperature of 212° (F.), and not a particle more till heated up to about 375°." After heating to 212° " it contains 3 atoms base, namely, one atom soda and 2 atoms water united to a double atom of phosphoric acid. The salt cannot sustain the loss of any portion of this water without assuming a new train of properties." Several other forms were obtained by heating to higher temperatures, and at a low red heat a glass was obtained which was deliquescent, not crystallisable from solution, and which gave the reactions of " phosphoric acid ignited per se" In modern symbols—

2NaH₂PO₄.2H₂O → 2NaH₂PO₄ + 2H₂O at 212° F.
2NaH₂PO₄ → Na₂H₂P₂O₇ + H₂O at 400° F.
2NaH₂PO₄ → 2NaPO₃ + 2H₂O at dull red heat

When at least half as much alkali as it already contained was added to ordinary phosphate of soda and the solution was concentrated, tufts of slender prismatic needles appeared. This salt was highly alkaline in reaction. "It is a fact of extraordinary interest that the acid of this sub-phosphate is not convertible into pyrophosphoric acid by the action of heat on the salt." In modern terms Na₃PO₄ is unchanged on ignition.

The heat of neutralisation, Q_n, of phosphoric acid (1 mol) with NaOH (n mols) in dilute solution has been determined with the following results:—

n mols	0.5	1.0	2.0	3.0	6.0
Qn Cals	7.3	14.8	27.1	34.0	35.3

Thus heat was evolved in a uniform manner as the alkali increased from 0 to 0.5 and 0.5 to 1.0 in the neutralisation of the first hydrogen. It was also evolved in a uniform manner but at a lower rate between 1.0 and 2.0 alkali, showing that the affinity of dissociation of the second hydrogen is lower than that of the first, and at a lower rate still during the neutralisation of the third hydrogen, showing that this has an even lower dissociation affinity. Heats corresponding to the neutralisation of the first, second and third hydrogens were 14.8, 12.3 and 6.9 Cals. Heats of neutralisation by the alkaline earths in very dilute solution were in the same order, e.g. for ½Ca(OH)₂, etc., 14.8, 9.7 and 5.3 Cals. respectively.

The heat of dissociation, Q_d, probably is positive, since dissociation diminished with rise of temperature. This agrees with the fact that the heat of neutralisation, Q_n, of the first hydrogen ion, viz. 14.8 Cals., is somewhat greater than that of a completely dissociated strong monobasic acid, viz. 13.5 Cals. The following calculation also shows a quantitative agreement:—



in which x is the electrical conductivity and Q_d = 1.530 Cals. At 21.5° C. Therefore (1 - α)Q_d = 1.242, in which the value of the amount of undissociated phosphoric acid, (1-α), has been introduced. Now Q_n = 13.520 + (1 - α) Q_d. Therefore Q_n = 14.76 Cals. calculated.

The heat of dissociation of the first hydrogen as calculated from the change of the constant with temperature was found to be 2.00 Cals. at 25° to 37.5° C., which, when combined with the preceding value of a, gives Q = 15.14 Cals.

The molar refractivities during neutralisation, M(μ-l)/D, when plotted against the percentage of alkali added gave curves which showed discontinuities at the points corresponding to primary and secondary salt.

Most important confirmation of the discontinuities at these points was obtained by plotting the static acidities (H⁺) expressed as their negative logs (pH) against the alkali added. The discontinuities in these graphs were clearly marked. Parts of these neutralisation curves were obtained first by the physiological chemists on account of the use of phosphates as mixtures of regulated acidity (" buffers ") for comparison with the acidities and alkalinities of physiological fluids.

Other series of results within the range which is suitable for " buffer " mixtures have been determined. The points of inflection were also determined by the conductivity method.

The neutralisation curves have been expressed by three constants corresponding to the first, second and third dissociations, viz.:—

, ,

The value of the first constant was determined as 1.1×10^-2 by measurements of the conductivity of the free acid. The second constant was determined as 1.95×10^-1 by conductivity measurements in solutions of NaH₂PO₄. This value was confirmed by calculations from the neutralisation curve as determined by means of the hydrogen electrode. The value of the third constant, viz. 3.6×10^-13, was first determined by measurements of the conductivity of ammonium phosphates and also by the distribution of the ammonia between water and chloroform. It was shown that this result was incompatible with the observed values of hydrion concentration during the later stages of neutralisation by a strong alkali. A calculation based on these values gave K₃ = 3.0×10^-12 in decimolar solutions.

A review of all the data revealed a slight drift in the constants of this acid (as of others) with changes in concentration, etc. The constants were corrected for alterations in the " activities " of the HPO₄⁼ and other ions in the more dilute solutions for which ionic strengths could be calculated. These corrections, applied to the results of Michaelis and Garmendia, and to new results, gave constants which were hardly affected by changes in concentration, namely K₂ = 5.9×10^-8, K₃ = 1×10^-12. The value of K₁ corrected for ionic strength, was 0.9×10^-2 at c = 0.1 and 0.8×10^-2 at limiting (low) concentration. A redetermination, with the aid of the quinhydrone electrode, in solutions of c = 0.06 down to c = 0.005 molar gave K₁ =0.8×10^-2, K₂ = 7.4×10^-8, K₃ = 0.8×10^-12.

It is suggested that the following rounded constants will represent values in phosphate solutions of concentrations from 0.1 molar downwards with sufficient accuracy for many purposes:—

K₁ = 1.0×10^-2; K₂ = 1.5×10^-7; K₃ = 2.0×10^-12

Neutralisation Curve of Orthophosphoric Acid.

The complete titration tabulated was obtained by means of the hydrogen electrode in a 0.01277 molar solution of phosphoric acid to which was added 0.0919 normal sodium hydroxide at 20° C., the titration to NaH₂PO₄ requiring 13.9 c.c. of the alkali.

The basicity of the acid has also been determined by conductivity titrations.

The constitution of phosphoric acid is deduced from the basicity, which shows three hydroxyl groups, and thus a saturated character, with no hydrogen directly attached to phosphorus; this explains the lack of oxidising properties, which indicates the absence of —O—O— chains, and the direct formation of the acid from POCl₃. The acid chloride and the resulting acid probably have the same structure, which is represented under the older theories as containing quinquevalent phosphorus, O=P=Cl₃, or on the newer as being tercovalent with a " mixed bond," or .

Phosphoric acid is a co-ordinated compound with the co-ordination number 4, and may accordingly be written H₃[PO₄]. Although the trivalent ion seldom is actually present, except perhaps in solid Na₃PO₄, etc., it is written according to Lowry as . Such a compound as Na₂HPO₄ is of course equally a co-ordination compound and may be written as on this scheme.

Mono-, di- and tri-esters are known, e.g. ethyl phosphates, which have not been prepared in tautomeric forms. The trimethyl and triethyl phosphates have vapour densities corresponding to simple molecules OP(OC₂H₅)₃, etc.

The chemical reactions of phosphoric acid can be classified mainly under salt and ester formation, hydration, dehydration and complex formation. Towards reducing and oxidising agents the aqueous solution is comparatively inert.

It has already been shown that even the first dissociation of phosphoric acid is much lower than the dissociation of the halogen acids and sulphuric acid. Consequently its catalytic action (due mainly to hydrion concentration) on various chemical reactions is much slighter; e.g. the relative strength of phosphoric acid in the inversion of cane sugar was 6.21 when that of HCl was 100. It is largely expelled from its salts by the stronger mineral acids in ordinary aqueous solution, although in the presence of only small quantities of water, or at higher temperatures, these conditions are reversed owing to (a) the great affinity for water, (b) the low volatility, of phosphoric acid. Thus while on the one hand phosphoric acid is produced by the interaction of dilute sulphuric acid with calcium phosphate at temperatures below the boiling-point, on the other hand sulphuric acid is completely expelled by evaporation at 150° to 200° C. with concentrated phosphoric acid.

The direct action of phosphoric acid on ethyl alcohol at about 200° C. is one of dehydration, and the acid is therefore conveniently used in the preparation of ethylene, as it is not, like sulphuric acid, reduced under these conditions. Glycerophosphoric acid, which probably is mainly monoglycerylphosphoric acid, is made by heating glycerol with concentrated phosphoric acid at 100° C., neutralising with baryta and decomposing the barium salt with sulphuric acid. Similar condensations have been reported with sugars, e.g. mannitol, etc.

Phosphoric acid is not affected by the ordinary reducing agents in solution, including nascent hydrogen. The reduction of phosphorus pentoxide and phosphates by carbon at high temperatures.

Ordinary oxidising agents have no effect, but with the meta- or pyro- acid hydrogen peroxide gave perphosphoric acid.

The formation of complexes with other acids is extremely character istic of phosphoric acid and its anhydride. The phosphotungstates and phosphomolybdates are well-crystallised compounds which are used in analytical chemistry. The yellow precipitate (NH₄)₃PO₄.12MoO₃ is the ammonium salt of a phosphomolybdic acid, H₃PO₄.12MoO₃, which is prepared by adding aqua regia in small quantities to the ammonium salt. Phosphotungstic acid, H₃PO₄.12WO₃.xH₂O, may be prepared as greenish crystals by evaporation of the mixed acids in the correct proportions and extraction with ether. These acids, with the borotungstic, silicotungstic acids, etc., are usually formulated as co-ordination compounds. The phosphorus is represented as the central atom with a co-ordination number of 6, thus:

H₇[P(W₂O₇)₆], H₇[P(Mo₂O₇)₆]

Phosphoiodic acids, such as P₂O₅.18I₂O₅.4H₂O, and their salts, phosphotelluric acids and their salts, e.g. (NH₄)₂P₂TeO₁₀, have also been prepared.

A complex acid is probably present when silica dissolves in phosphoric acid, as it does to the extent of about 5 per cent, at 260° C. Concentrated phosphoric acid at 100° to 200° C. etches the surface of glass, and it has been found to attack quartz at 300° C. Phosphoric acid at high temperatures also destroys the glaze on porcelain. Platinum is not affected unless a reducing agent is present, which may give phosphorus and a phosphide.

It is no doubt on account of this formation of complexes that concentrated phosphoric acid is capable of dissolving such inert metals as tungsten and zirconium, as well as silicon and carborundum. The less noble metals are attacked by phosphoric acid, but iron tends to become passive. The basic oxides, ferric oxide and alumina are dissolved by the concentrated acid.

The ions of phosphoric acid, together with those of carbonic acid, play an important part as regulators of acidity, or natural "buffer" mixtures, in physiological fluids, especially in the blood. Salts which take part in this regulation are NaH₂PO₄ and Na₂HPO₄, NaHCO₃ and Na₂CO₃. The pH value of blood is 7.3 to 7.4 at blood temperature (37° to 38° C.) and about 7.5 at 18° C.; the ratio of monohydrogen phosphate, i.e. Na₂HPO₄, to dihydrogen phosphate, i.e. NaH₂PO₄, at this point is about 4:1. Even the small amount of phosphate present in the blood and cell protoplasm has a considerable effect in regulating the pH to its " resting " value— slightly on the alkaline side of neutrality. Any steady increase in the content of acid is countered by the formation of more NaH₂PO₄, which, being more readily diffusible than Na₂HPO₄, passes into the kidneys. Acidity of the urine is thereby increased and the cell protoplasm or blood loses some of its alkali reserve. The necessity of constant small amounts of phosphate for the body metabolism is evident.

Phosphoric acid is poisonous only at a high concentration, when it shows the usual corrosive effects of acids. The salts, and even the acid in low concentration, favour the growth of moulds and fungi, provided that the hydrogen-ion concentration also is favourable.

Phosphoric esters are also present in the blood, and their hydrolysis by means of an enzyme, phosphatase, which has been found in the bones, is probably one step in the process of ossification. The properties of these esters have been largely determined by Robison and his collaborators.

Many pharmaceutical preparations contain phosphoric acid or phosphates, or glycerophosphoric acid, which, as already stated, is made by heating glycerine with the ortho- or meta-acid. Lecithin is an ester of glycerophosphoric acid which contains choline, (CH₃)₃≡N(OH)-CH₂-CH₂OH, and two molecules of a fatty acid radical (stearyl or oleyl).

Acid phosphates are used in baking powders, " self-raising " flours and for " improving " flours. The acid is also an ingredient of some non-alcoholic beverages.

Sugar phosphates, mainly the hexose mono- and di-phosphates, play an important part in alcoholic fermentation. The calcium salts of these esters have been prepared.

The acid, or calcium superphosphate, is used in the sugar-refining industry as a defecator to coagulate gums and other organic impurities and cause them to form a scum.

It has been employed instead of sulphuric acid in the hydrolysis of cellulose to give sugars. As a dehydrating agent in organic preparations, such as that of ethylene from ethyl alcohol, it is sometimes preferred to sulphuric acid.

Other miscellaneous uses are: In dental cements and filling pastes, with kaolin, other silicates, chalk and magnesia. Solutions containing the acid and ferrous phosphate will give a protective coating to iron and steel. Carbon is activated by being dipped in a solution of metallic salts and phosphoric acid and then igniting. Solutions containing ammonium phosphate with the sulphate and a soluble zinc salt may be used for fireproofing materials. Phosphates are sometimes included in photographic toning and fixing baths.

When heated in open vessels of gold or platinum the acid loses water, being converted successively, and to some extent concurrently, into the pyro- and meta-acids, thus:—

2H₂PO₄ → H₄P₂O₇ + H₂OnH₂PO₄ → (HPO₂)_n + nH₂O

According to Graham the pyro-acid was formed largely even at 100° C., while Watson found that conversion was complete between 255° and 260° C. Exposure to a current of moist air raised the temperature of dehydration, while dry air lowered it. Thus air saturated with water vapour at 68° C. will leave 0.2 per cent, of water in the ortho-acid kept at 181° C., and will dehydrate it and produce 0.02 per cent, of H₄P₂O₇ at 191° C. When air which has been dried by passing through 96 per cent, sulphuric acid at 12° C. is drawn through phosphoric acid at 186° C. this acid is dehydrated to 86.8 per cent, of H₄P₂O₇. Other dehydrating agents have a similar effect. Phosphorus oxychloride reacts in the following manner:—

5H₃PO₄ + POCl₃ = 3H₄P₂O₇ + 3HCl

A mixture of the ortho- and meta-acids may be condensed together to form the pyro-acid by heating on the water-bath, thus:—

H₃PO₄ + HPO₃ = H₄P₂O₇

Metaphosphoric acid is the final product obtained when phosphoric acid is heated in the air and was produced in this way by Berzelius. The minimum temperature required for dehydration is about that of molten lead, 327° C. The meta-acid begins to be formed at about 300° C. and dehydration can be completed at 316° C. or by heating until fumes are continuously evolved.

Aqueous vapour pressures in equilibrium with the meta-acid are much lower than those over the pyro-acid. The pressure over the pyro-acid became appreciable at 100° c. and reached 100 mm. somewhat above 160° c., while that over the meta-acid became appreciable at 190° c. and reached 100 mm. a little over 240° C.

The complex metaphosphates, (MPO₃)_x, probably contain a complex anion. The di-, tri-, etc. phosphoric acids however (pyrophosphoric acid and its series) are not polymers but condensation products, belonging to the series mH₃PO₄-(m-1)H₂O, and give tetra-, penta- and hexa-valent ions from H₄P₂O₇, H₅P₃O₁₀ and H₆P₄O₁₃. The salts were made by melting together (NaPO₃)₆ and Na₄P₂O₇ in various proportions. They were transformed into orthophosphates in warm water.

The production of this lowest hydrate of phosphoric anhydride by heating phosphoric acid, or the production of metaphosphates by heating dihydrogen phosphates, has already been outlined. In those methods of preparation, NH₄ may take the place of H; thus HPO₃ has been prepared by heating (NH₄)₂HPO₄ and NaPO₃ by heating Na(NH₄)₂PO₄ or microcosmic salt, NaNH₄HPO₄. The free acid can also be produced by the combined oxidation and dehydration of H₃PO₃, as for example by bromine, thus

2H₃PO₃ + 2Br₂ = 4HBr + 2HPO₃

The acid appears as a transparent, vitreous, tough mass, which usually is deliquescent and dissolves in water with much heat. At a red heat it volatilises without decomposition giving a vapour with a density corresponding to a molecular weight of 76.8 to 78.2, the theoretical value for (HPO₃)₂ being 80.

The properties of the vitreous acid varied considerably according to the mode of preparation. The degree of hydration never corresponded exactly to HPO₃, which requires 88.7 per cent, of P₂O₅, but reached a constant value at about 78 per cent., and the acid then volatilised unchanged. After a short heating the acid contained 83.89 per cent, of HPO₃ and 16.13 per cent, of water, and was readily soluble in water. After heating at dull redness for periods of several hours the acid dissolved at first readily and then with difficulty and with a characteristic crackling sound. This sound was due to the splitting of small particles with a glassy fracture. The product was not yet pure HPO₃, but contained water in the ratios HPO₃/H₂O = 89.29/10.71 and 89.9/10.1. After heating for 24 hours at a dull red heat the acid dissolved very slowly (several days) without crackling.

The lowering of the freezing-point of aqueous solutions shows that metaphosphoric acid is polymerised. In a fresh solution containing initially 0.852 mol of HPO₃ the molecular weight lay between (HPO₃)₂ and (HPO₃)₃. Pure metaphosphoric acid is best prepared from Pb(PO₃)₂ (from Pb(NO₃)₂ and NaPO₃ aq.). The precipitate is suspended in water and decomposed by a current of H₂S. The lowering of the freezing-point of the acid freshly prepared in this manner indicated a molecular weight of 102, which, as the acid was ionised, indicated the presence of some complex molecules. Evaporation of this solution gave one in which the acid had a molar weight of 172.

The heat of formation of the solid acid from its elements is given as 224.9 to 226.6 Cals., and that of the acid in solution as 236.4 Cals. On adding the heat of formation of 1 mol of water the sum of the heats (for H₂O and HPO₃) is found to be almost the same as that evolved in the formation of orthophosphoric acid.

Esters of metaphosphoric acid are known. Ethyl metaphosphate, C₂H₅PO₃, was prepared by heating dry ethyl acetate with phosphoric oxide and extracting the product with ether and warm alcohol, from which the ester was precipitated by ether.

Aqueous Solutions of Metaphosphoric Acid

The physical properties of the solutions are not well defined, as the acid is in process of de-polymerisation and hydration (see below). The refractive index was investigated by Gladstone. Heats of neutralisation were those of a monobasic acid; when one equivalent of alkali was added the heat evolved was 14.4 Cals., 14.84 Cals. The electrical conductivity of the simple acid HPO₃, calculated from that of the changing acid which contained both (HPO₃)_n and H₃PO₄, was found to be of the same order as that of a strong monobasic acid (e.g. HIO₃).

The Hydration of Metaphosphoric Acid

The change of metaphosphoric into orthophosphoric acid was observed by Graham. In solutions of ordinary metaphosphoric acid two changes are proceeding, the depolymerisation of (HPO₃)_n and hydration with formation of H₃PO₄. The change of osmotic pressure on standing was shown by the freezing-point method. The lowering in a normal solution of the acid changed from 0.697° to 1.452° in 12 days, that in a double-normal solution from 1.425° to 3.150° in the same time. The conductivity at 18° C. did not alter much for the first 20 hours; it then fell steadily. The first period lasted longer at 18° C. than at 25° C., and presumably at lower temperatures would be greatly extended. During this period depolymerisation may be the main reaction. The subsequent decrease in conductivity is due to the conversion of the highly dissociated HPO₃ into the less dissociated H₃PO₄. The velocity of the change was such that a half-normal solution kept at 0° C. was completely converted in 150 days, at 31° C. in 5 days and at 95° C. in less than an hour. The change was accelerated by strong mineral acids.

There is general agreement that during the change the titre to methyl orange remains constant. This will be the case whether pyro-phosphoric acid is formed as an intermediate product or not. The titre to phenolphthalein increases, and this also agrees equally well with both suppositions. The velocity constant was found to correspond to a unimolecular reaction. The change, however, consists of at least two, if not three parts, and several observers have found that there is no simple constant—thus, the velocity did not agree with either a unimolecular or a bimolecular reaction; the constant increased with time; the velocity was not proportional at each moment to the amount of unchanged substance.

It cannot be assumed that, because pyrophosphoric acid is produced as an intermediate product in the dehydration of H₃PO₄ that it will also be produced during the hydration of HPO₃. The amounts observed may be present in the original HPO₃ or be produced by the heat developed when this is placed in water. The pyro-acid has been detected in the last fractional precipitates of silver phosphates, etc. Since there is some evidence that metaphosphoric acid is hydrated more rapidly than pyrophosphoric acid the latter may accumulate up to a certain maximum concentration.

The foregoing results have been elucidated by the observation that hydration of the simple molecules HPO₃ leads to a preponderance of orthophosphoric acid, while hydration of the hexapolymer, (HPO₃)₆, leads to a considerable proportion of each acid, ortho- and pyro-.

Metaphosphates become hydrated in neutral and alkaline as well as in acid solution, according to the equations

NaPO₃ + H₂O = NaH₂PO₄
NaPO₃ + NaOH = Na₂HPO₄

At a temperature of 73° C. the velocity constant whether referred to a unimolecular or a bimolecular reaction diminished with time; after an hour rather less than three-quarters of the original metaphosphate remains. The product is mainly orthophosphate, as was proved by titration with methyl orange and phenolphthalein, although small quantities of pyrophosphate were formed by a side reaction. The pyro-acid was determined by titration to bromophenol blue in the presence of zinc sulphate, which leads to a complete precipitation of pyrophosphate, the ortho-acid being unaffected, thus

Na₂H₂P₂O₇ + 2ZnSO₄ = Zn₂P₂O₇ + Na₂SO₄ + H₂SO₄

The hydration of hexametaphosphate, (NaPO₃)₆, also proceeded as a unimolecular reaction. In neutral or alkaline solution ortho- phosphate is formed; in acid solution ortho- and pyro-acids in about equal amounts.

The chemical properties of metaphosphoric acid, apart from those which are due to the fact that dehydration has proceeded to a maximum, do not differ essentially from those of the other hydrates of phosphorus pentoxide. The acid dissolves freely in certain oxygenated organic compounds—aldehydes, ketones and anhydrides, e.g. benzaldehyde, benzophenone and acetic anhydride. It was chlorinated but not dehydrated by phosphorus pentachloride:—

HPO₃ + 2PCl₅ = 3POCl₃ + HCl

The polymers of metaphosphates are considerably more stable than those of the acid itself and consequently a great variety of these salts has been reported, having the general formula (MPO₃)_n, in which n varies from 1 to 6 or possibly up to 10. The heating of Na₂H₂P₂O₇ yielded a soluble salt, "Graham's salt," and an insoluble salt, "Maddrell's salt." A sodium salt having the formula Na₃P₃O₉.6H₂O may be crystallised from the melt obtained by fusing Na₂HPO₄.12H₂O either alone or with ammonium nitrate. From the sodium salt there may be prepared by double decomposition salts of many of the heavy metals, e.g. Pb₃P₃0₉.3H₂O. These may be decomposed by H₂S, etc. giving the free acids, which slowly decompose, yielding the ortho-acid. One structure which has been assigned to the complex acid H₃P₃O₉ is



Trimetaphosphates are often moderately soluble, e.g. Ag₃(PO₃)₃.H₂O and Ba₃(PO₃)₆.6H₂O. They often crystallise with 9 molecules of water, e.g. Zn₃(PO₃)₆.9H₂O, and also up to 15, e.g. Mg₃(PO₃)₆.15H₂O. The electrical conductivities of their solutions agree well with those which should be shown by the salts of a tribasic acid.

Monometaphosphates

The insoluble salt obtained by heating microcosmic salt, NaNH₄HPO₄, was apparently polymerised meta-phosphate, while soluble salts obtained by neutralising metaphosphoric acid with sodium carbonate belonged to two series and quickly changed into orthophosphate when moist.

A salt which proved to have the simple molecular weight by the freezing-point method was prepared by the action of ethyl hexametaphosphate dissolved in alcohol on sodium ethoxide:—

(C₂H₅PO₃)₆ + 6C₂H₅ONa = 6(C₂H₅)₂NaPO₄
(C₂H₅)₂NaPO₄ = NaPO₃ + (C₂H₅)₂O

The sodium salt was crystallised as a granular substance. It precipitated salts of barium, silver and lead.

Dimetaphosphates of copper, manganese, cobalt and zinc are said to be formed when an oxide or nitrate of these metals is heated with an excess of phosphoric acid between 316° and 400° C. The zinc salt had the formula ZnP₂O₆.4H₂O, and when treated with alkali sulphides gave the alkali salts K₂P₂O₆.2H₂O, etc. Other authorities, however, have adduced reason for supposing that these salts are tri- or tetra-metaphosphates.

Tetrametaphosphates

These salts are said to be formed when orthophosphates of metals of high atomic weight—silver, barium, lead—are heated with an excess of phosphoric acid at about 300° C. The free acid, H₄P₄O₁₂, prepared by decomposing the silver salt with H₂S, was rapidly hydrated to H₄P₂O₇.

Pentametaphosphates

Alkali and ammonium salts of H₅P₅O₁₅ have been prepared—the latter by heating (NH₄)₂P₂O₆ to 200° or 250° C. The melt was dissolved in water and the salt precipitated by alcohol as an amorphous white mass. K₄NH₄P₅O₁₅.6H₂O was obtained in the crystalline state. Calcium, strontium and barium salts, when added to solutions of pentametaphosphates, gave gummy or flocculent precipitates.

Hexametaphosphates were made by heating to a red heat NaH₂PO₄ or NaNH₄HPO₄, i.e. in a platinum crucible at about 700° C., with rapid cooling. When the solution from this melt was added to silver nitrate, one of the products was a crystalline salt, probably Ag₆P₆O₁₈.

The conductivities of these salts and of the pentametaphosphates showed that only some of the kations were dissociated, and that there were probably complex anions, e.g. Na₄[Na₂(PO₃)₆]. Complex ferro- and ferri-metaphosphates are also known, M₄[Fe(PO₃)₆], M₃[Fe(PO₃)₆].

The ethyl ester has been prepared by boiling ethyl alcohol with P₂O₅ for some hours. A viscous liquid insoluble in ether but soluble in chloroform was obtained, the molar weight of which in naphthalene corresponded to (C₂H₅)₆P₆O₁₈.

The polymetaphosphates are distinguished by giving gelatinous precipitates with salts of most metals, and by decolorising red solutions containing Fe(CNS)₃.

Still more complex metaphosphates have been reported as resulting from the fusion of salts of bivalent metals with NaNH₄HPO₄.

Sodium tetraphosphate, Na₆P₄O₁₃, and decaphosphate, Na₁₂P₁₀O₃₁, were also said to be among the products obtained by fusing complex metaphosphates with pyrophosphates. The acid H₆P₄O₁₃ was crystallised from a syrupy liquid obtained by adding more phosphorus pentoxide to a solution obtained by adding the pentoxide to water.

The complex basic phosphates such as 5CaO.3P₂O₅, which was made by passing the vapour of phosphorus pentoxide over anhydrous calcium oxide, are supposed to be derived from more hydrated condensed acids such as H₁₀P₆O₂₀.

Orthophosphates

Solubility The tribasic phosphates of the alkali metals and ammonia are soluble, while those of the alkaline earth metals and the common metals are insoluble. They are usually prepared by double decomposition between disodium hydrogen phosphate and a salt of the required metal, thus

2Na₂HPO₄ + 3Pb(O₂C.CH₃)₂ = Pb₃(PO₄)₂ + 4CH₃CO₂Na + 2CH₃CO₂H
Na₂HPO₄ + 3AgNO₃ = Ag₃PO₄ + 2NaNO₃ + HNO₃

Formation of the yellow precipitate of Ag₃PO₄ is a common test for orthophosphates. On account of the acid which is liberated precipitation is not complete. Acid phosphates of the alkaline earth metals, e.g. CaHPO₄, are precipitated from solutions which are nearly neutral. Monoammonium phosphates, MNH₄PO₄, which are so much used in quantitative analysis, are precipitated from neutral or slightly acid solution then made ammoniacal (MgNH₄PO₄),or neutral or slightly acid solution (ZnNH₄PO₄ in presence of sodium acetate and acetic acid, pH =6.l-6.9).

The nature of the original salts may be deduced from the nature of the residue. CaHPO₄ may be distinguished from Ca₃(PO₄)₂ by washing with ammonia; in the former case the washings will contain soluble phosphate. Mg₃(PO₄)₂ may be detected in ignited Mg₂P₂O₇ by wetting with AgNO₃ solution, which, if the former is present, imparts a yellow colour due to Ag₃PO₄.

Precipitated phosphates of the zinc group and of the alkaline earth metals and magnesium dissolve in acetic acid, whereas those of iron, aluminium and chromium remain undissolved, a fact which is much used in qualitative analysis. The hydrion concentrations, expressed as pH, at which the various precipitates appear have been determined. All phosphates dissolve in excess of dilute strong acids, in many cases only that amount of acid being required which will convert the precipitate into a primary or dihydrogen phosphate (cf. CaH₄(PO₄)₂).

The precipitates obtained with magnesia mixture (magnesium chloride in ammoniacal solution), or ferric chloride in an acid solution to which sodium acetate has been added, are often used as tests for phosphate, and in the latter case the phosphate is removed from solution as ferric phosphate. Another common test is the formation of yellow ammonium phosphomolybdate when a nitric acid solution of ammonium molybdate is added to phosphate solution.

It is also possible to eliminate phosphate as insoluble phosphometastannic acid by adding tin to a nitric acid solution of phosphoric acid.

Pyro- and Meta-phosphates

The behaviour of the pyro- and meta-phosphates towards the foregoing reagents and others which may be used in distinguishing these salts are tabulated below:—Common and distinctive reactions of orto-, Pyro- and meta-phosphates

Reagent.	Ortho-	Pyro-	Meta-
Silver nitrate, neutral or slightly alkaline solution.	Yellow precipitate, dissolving in acetic acid.	White crystalline precipitate, not dissolving in acetic acid	White gelatinous precipitate, not dissolving in acetic acid.
Barium chloride, neutral or alkaline	White precipitate.	White precipitate.	White precipitate.
Do. acid	No precipitate	No precipitate	White precipitate
Albumin, acid solution	No reaction	No reaction	Coagulated
Ammonium molybdate with nitric acid	Yellow crystalline precipitate on warming	No precipitate in cold or on gentle warming	No precipitate in cold or on gentle warming
Zinc acetate to acid solution	No precipitate	White precipitate, soluble in excess of pyrophosphate.	No precipitate
Salts of chromium	Precipitate, soluble in cold acetic acid.	Precipitate, insoluble in acetic acid	Precipitate, insoluble in acetic acid
Special tests	Lead acetate gives white Pb3(PO4)2, almost insoluble in acetic acid	Magnesium chloride gives white precipitate, soluble in excess of MgCl2 or pyrophosphate	Magnesium salts give no precipitate
		Luteo cobaltic chloride, Co(NH3)6Cl3, gives a reddish-yellow crystalline precipitate, Co(NH3)6NaP2O7.11½H2O	Bismuth salts in alkaline solution give a white precipitate

The titrations are based upon the degrees of dissociation of the first, second, etc. hydrogen ion.

Orthophosphoric Acid may be titrated with sodium or potassium hydroxide free from carbonate. The equivalent point indicating NaH₂PO₄ occurs at pH=ca. 4.2, which is within the transition range of methyl yellow, methyl orange and bromophenol blue. The end-point tint should be matched against that of a comparison solution containing about the same concentration of NaH₂PO₄.

The acid may also be titrated as dibasic, using phenolphthalein, thymolphthalein or thymol blue, the end-point tint being matched against a solution of Na₂HPO₄.

The results are closer to the theoretical if the solutions are saturated with sodium chloride.

Pyrophosphoric Acid may be titrated as a dibasic acid to pH = 4.0 using methyl yellow, etc. as before; also as a tetrabasic acid using phenolphthalein, thymolphthalein or thymol blue in the presence of barium salt. Electrometric titrations have also been performed.

Metaphosphoric Acid may be titrated with methyl orange, etc. irrespective of its progressive hydration. The phenolphthalein titre, however, varies with time.

These acids may easily be converted into the ortho-form by boiling alone or in the presence of some nitric acid, and then determined by one of the methods described in the following.

1. With Silver Nitrate.— This depends upon the precipitation of silver orthophosphate in solutions of low and controlled acidity. In the assay of commercial 85 per cent, phosphoric acid of density 1.710 the syrup is diluted to a convenient volume and an aliquot part is taken which contains about 0.1 gram of H₃PO₄. It is neutralised to phenolphthalein with approximately decinormal alkali (free from chloride). 50 c.c. of decinormal silver nitrate are then added while the solution is kept neutral to litmus by stirring in zinc oxide or a suspension of the hydroxide. The whole or a measured part of the filtered solution is acidified with nitric acid and, after the addition of ferric alum, the unused silver nitrate is titrated with standard decinormal ammonium thiocyanate in the usual manner. Alkali phosphates may also be determined in this way.
   
   Silver phosphate is also quantitatively precipitated in the presence of sodium acetate and acetic acid, the phosphoric acid then being titrated as a tribasic acid according to the equation
   
   H₃PO₄ + 3AgNO₃ + 3CH₃COONa = Ag₃PO₄ + 3NaNO₃ + 3CH₃COOH
   
   This reaction is also used in the method of Holleman as modified by Wilkie. A phosphate solution containing phenolphthalein is reddened by the addition of alkali, then just decolorised with nitric acid. An excess of standard silver nitrate is then added and decinormal sodium acetate and alkali to slight pink colour, followed by 2 c.c. of decinormal H₂SO₄. The solution is diluted and filtered and the excess of silver determined by titration with decinormal ammonium thiocyanate.
2. With Molybdate.—Precipitation of phosphate in nitric acid solution by means of ammonium molybdate serves not only as a qualitative test, but also for the quantitative separation of phosphate in a preliminary or even final manner. Insoluble phosphates are previously dissolved in nitric acid, while the phosphoric acids are nearly neutralised with ammonia and then acidified with nitric acid. The nitric acid solution of ammonium molybdate (3 per cent.) is added hot, the mixture boiled and the precipitate collected on a filter. The precipitate may now be treated in various ways:—
   1. The precipitate is redissolved in ammonia, reprecipitated with nitric acid and ammonium molybdate, washed with a solution of ammonium nitrate and nitric acid, and dried for a long time at 160° to 180° C. preferably in a current of air. The precipitate is then (NH₄)₃PO₄.12MoO₃ containing theoretically 3.782 per cent. P₂O₅ and 1.65 per cent, phosphorus. Under the conditions given the practical factor for conversion to per cent. P₂O₅ is 3.753. If the precipitate is greenish it should be heated again with a small crystal of NH₄NO₃ and a little ammonium carbonate which gives the correct yellow.
   2. On gentle ignition the precipitate is converted into a blue-black substance 24MoO₃.P₂O₅ which contains 3.947 per cent. P₂O₅.
   3. The precipitate is dissolved in 2.5 per cent, ammonia, the solution nearly neutralised with hydrochloric acid and precipitated with a solution of magnesium salts.
   4. The well-washed precipitate is dissolved in a known quantity in excess of standard alkali, the excess alkali being titrated with standard nitric acid using phenolphthalein:—
      
      2[(NH₄)₃PO₄ + 12MoO₃] + 46NaOH + H₂O = 2(NH₄)₂HPO₄ + (NH₄)₂MoO₄ + 23Na₂MoO₄ + 23H₂O
      
      1 c.c. decinormal NaOH corresponds to 0.000309 gram P₂O₅.
   5. The molybdate method has been adapted to the determination of small quantities of phosphorus colorimetrically. The solution in nitric acid is evaporated to dryness to render the silica insoluble, and the residue taken up with nitric acid. After the addition of an excess of ammonium molybdate the colour is matched against a standard of nearly the same concentration in phosphate. The maximum colour is developed after a few minutes, while that in the presence of silicic acid requires some hours. Darker solutions precipitate in time while lighter ones fade.
      
      A colorimetric method has also been devised which is not interfered with by silicic acid. Iron, however, should be removed by means of cupferron. The solution should contain 0.002 to 0.025 milligram of P₂O₅ and 2 c.c. of nitric acid (density 1.12). To this is added 2 c.c. of a quinine solution made by dissolving 1 gram of the sulphate in a slight excess of nitric acid and adding enough baryta to precipitate all the sulphate. The colour developed after the addition of the molybdate is compared with that of a standard.
      
      A nephelometric method using a strychnine molybdate reagent has also been devised.
      
      A similar method is used for the determination of inorganic phosphates in urine. 1 to 5 c.c. of the urine, containing about 0.5 milligram of phosphorus, are diluted and treated with a solution of ammonium molybdate in 15 per cent, sulphuric acid (5 c.c.), 1 e.c. of 1 per cent, hydroquinone solution and 1 c.c. of 20 per cent, sodium sulphite solution. The blue colour is compared in Nessler glasses with that developed by the same solutions when mixed with a standard phosphate solution of which 5 c.c. contain 0-5 milligram of phosphorus.
      
      The standard phosphate is made by dissolving 4.388 grams of KH₂PO₄ in 1 litre and diluting this stock 10 times before use.
   6. The amount of molybdenum in the precipitate may also be determined by several methods. A quick volumetric method consists in reduction to molybdenum sesquioxide and titration with permanganate. The precipitate, after washing with acid ammonium sulphate solution, is dissolved in 10 per cent, ammonia, then treated with an excess of dilute sulphuric acid and filtered through zinc. The reduced solution and its washings are run directly into 50 c.c. of 20 per cent, ferric alum. The MoO₃ is reduced by the zinc to Mo₂O₃ (or Mo₂₄O₃₇) and this is again oxidised by the ferric sulphate, giving its equivalent of ferrous sulphate, which is titrated with KMnO₄. Since the precipitate contains 1P to 12MoO₃ and 3 atoms of oxygen oxidise Mo₂O₃, it follows that 36Fe≡lP. Therefore the iron value of the KMnO₄ multiplied by P/36Fe (i.e. 0.01540) gives the value of the KMnO₄ in terms of phosphorus. The factor is 0.0158 if the reduction product is Mo₂₄O₃₇.
3. Volumetrically, by Uranyl Solutions.—Phosphates which are soluble in water or acetic acid may be determined quickly with a solution of uranyl acetate or nitrate which has been standardised against pure sodium or potassium phosphate. The uranium solution is run into that of the phosphate, containing ammonium acetate and acetic acid. A greenish-yellow precipitate of uranyl ammonium phosphate is deposited. The excess of uranium which appears at the end-point is recognised by spotting on a white tile and mixing with drops of a solution of potassium ferrocyanide. The uranyl salt gives a dark brown colour of uranyl ferrocyanide.
   
   KH₂PO₄ + UO₂(CH₃CO₂)₂ + CH₃CO₂NH₄ = UO₂NH₄PO₄ + CH₃CO₂K + 2CH₃CO₂H
   
   It is possible also to use cochineal as an inside indicator, the end-point being shown by a change of colour from pink to green.
4. Magnesium Phosphate Method.—This is the most important and most accurate final method for the determination of phosphorus in all its compounds. If the phosphate is present as a salt soluble in water the solution is slightly acidified and magnesia mixture (containing magnesium chloride and ammonium chloride) is added. The solution is heated to boiling and a hot 2.5 per cent, solution of ammonia is added drop by drop until phenolphthalein is reddened and a crystalline precipitate obtained, which is ready for filtration after standing about 10 minutes. The precipitate is washed with 2.5 per cent, ammonia, filtered off on a Gooch crucible or on paper and ignited wet or dry to Mg₂P₂O₇, which contains 27.86 per cent, of phosphorus, 63.79 per cent, of P₂O₅ and 85.342 per cent, of PO₄.
   
   An ammonium phosphomolybdate precipitate is treated for conversion into MgNH₄PO₄. The washed precipitate of MgNH₄PO₄ may be determined volumetrically by solution in a known quantity in excess of standard hydrochloric acid and back-titration with decinormal alkali using methyl orange, thus
   
   MgNH₄PO₄ + 2HCl = NH₄H₂PO₄ + MgCl₂
   
   The most important materials or products in which it is necessary to determine phosphorus are phosphatic rocks of all sorts, soils, fertilisers (including basic slag), iron, steel and non-ferrous phosphor alloys. The former classes are dealt with in the appropriate sections of this Volume, so that it remains only to mention some special methods which are used in the case of phosphorus alloys.

The methods which have been used successfully in the preparation of persulphuric acids and persulphates have also been applied to perphosphoric acid and the perphosphates, i.e.—

1. The addition of H₂O₂ at low temperatures.
2. Anodic oxidation.

1. Hydrogen peroxide does not combine with orthophosphoric acid. But when metaphosphoric acid or phosphorus pentoxide were treated with 30 per cent, hydrogen peroxide at 0° C., solutions were obtained which had oxidising properties and which by analysis proved to contain per mono phosphoric acid, H₃PO₅. With pyrophosphoric acid in excess, perdiphosphoric acid, H₄P₂O₈, was obtained.
   
   Slightly acid or alkaline phosphate solutions of the alkali metals, etc., combine with varying proportions of H₂O₂ in a loose manner. Such solutions give the reactions of H₂O₂.
2. Electrolytic oxidation. The perphosphates of the alkali metals and of ammonium have been prepared in this way. As in the electrolytic production of persulphates low temperatures are advantageous and the presence of fluorides and chromates increases the yield, probably by maintaining a high anodic over-voltage. A low anodic current-density (e.g. about 0.015 amp./cm².) is favourable. The electrolyte may consist of a solution of KH₂PO₄ with fluoride and chromate. On evaporation at 100° C. after the electrolysis potassium perphosphate, K₄P₂O₈, can be crystallised.
   
   Perphosphates of ammonium may be prepared in good yields by electrolysis, but auto-oxidation and -reduction may occur with the production of ammonium phosphate and ammonium nitrate.
   
   Perphosphates of rubidium and caesium are more easily prepared, even in the absence of fluorides or chromates. The permonophosphates of these metals however require in their preparation rather higher current-densities.
   
   If the perphosphoric acids are regarded as derivatives of hydrogen peroxide their constitution with quinquevalent phosphorus will be
   
   

   Permonophosphoric Acid	Perdiphosphoric Acid

   
   
   

   Reactions and Detection

   Permonophosphoric acid is a strong oxidising agent. It liberates iodine at once from acidified potassium iodide (cf. Caro's acid) and oxidises manganous salts in the cold to permanganates. Hydrolysis in dilute solutions is represented by the equation
   
   H₃PO₅ + H₂O = H₃PO₄ + H₂O₂
   
   Perdiphosphoric acid liberates iodine only slowly from acidified potassium iodide, and can be kept for long periods in dilute solution.
   
   Oxidation of manganous salts in acid solution to red manganic salts is characteristic of true perphosphates. They should not give the characteristic tests of hydrogen peroxide with chromic acid or titanic acid. They oxidise acid aniline solutions to nitrosobenzene and gradually to nitrobenzene.
   
   Potassium perphosphate gives with silver nitrate a dark precipitate which changes to white Ag₃PO₅, then to yellow Ag₃PO₄ with evolution of ozone and oxygen.