Phosphoric acid and its anions
Phosphorus has a central role in life's processes.
Phosphorus (P) has atomic number 15 with electrons (1s22s22p63s23p33d0). It can have an expanded octet, because it can shift it's outer-shell 3s2 electrons to an unoccupied 3d obital (to give 1s22s22p63s13px13py1
3pz13d1). As the atom is large, it can thus form five bonds (PV) (e.g., PF5, PCl5). This is sp3d hybridization and results in a triangular bipyramidal shape of electrons and is nonpolar. Nitrogen cannot expand its octet since it has no 3d orbitals in its outer shell, and additionally, it is too small to allow five atoms to surround it. Phosphorus has several allotropes (e.g., white cubic P4, red amorphous, black ß-metallic). Phosphorus readily reacts exothermically with oxygen (see below) to form phosphates in dimeric and polymeric forms using P-O-P linkages.
Pure, anhydrous phosphoric acid (H3PO4, melting point 42.35 °C, boiling point 212 °C, density 1880 kg ˣ m−3), usually called just phosphoric acid, is a colorless, monoclinic, crystalline compound. a It is miscible with water with the clear, colorless, viscous, and gummy, 85% by-weight (melting point 21 °C, boiling point ~ 260 °C, density 1687 kg ˣ m−3) being the commonly found concentrated acid. It can be manufactured by treating phosphate rock with mineral acid;, e.g., calcium hydroxyapatite with sulfuric acid, with the resultant calcium sulfate filtered out.
Ca5(PO4)3OH + 5 H2SO4 → 3 H3PO4 + 5 CaSO4↓ + H2O
Ca10(PO4)6F2 + 10 H2SO4 + 20 H2O → 6 H3PO4 + 2 HF + 10 CaSO4.2H2O↓
and phosphorus pentoxide, P4O10
Caustic phosphorus pentoxide is produced by burning white phosphorus in plentiful air. It is very deliquescent, and the strongest known dehydration agent below 100 °C. These reactions are not reversible,
P4 (white) + 5 O2 → P4O10 (hexagonal) ΔH° = –3010 kJ ˣ mol−1 c
P4O10 + 6 H2O → 4 H3PO4 ΔH° = –377 kJ ˣ mol−1 a
In contrast to sulfuric acid, phosphoric acid is less reactive and not an oxidant. The dissociation constants of the HnXO4 acids increase progressively on moving from X ≡ Si n = 4 pKa1 = 9.7, to X ≡ P n = 3 pKa1 = 2.1 , to X ≡ S n = 2 pKa1 = -1.0 , to X ≡ Cl. n = 1 pKa1 = -7.0. This lower reactivity is because an increase in the electronegativity of X leads to an increased attraction of electrons from the oxygen atoms onto X, which in turn weakens the O-H linkages, and increases the strength of the acid. Phosphoric acid is tribasic with three dissociation constants, only one of which may be considered strongish (see the top of page right).
H3PO4 + H2O 
H3O+ + H2PO4− pKa1 = 2.14
H2PO4− + H2O H3O+ + HPO42− pKa2 = 7.20
HPO42− + H2O H3O+ + PO43− pKa3 = 12.37p
All three charged species are strongly solvated (ΔGhydr of PO43−, HPO42−, and
H2PO4− are −2773 kJ ˣ mol−1, −1089 kJ ˣ mol−1, and −473 kJ ˣ mol−1, respectively) [128]. Mixtures of dihydrogen phosphates and hydrogen phosphates act as buffers in the range pH 6.2 to 8.2. At pH = 7.0, 25 °C, the concentrations of the orthophosphoric acid and its three anions have the ratios,
Phosphoric acid species as a function of pH
[H2PO4−] / [H3PO4] ≈ 7.5 ˣ 104
[HPO42−] / [H2PO4−] ≈ 0.62
[PO43−] / [HPO42−] ≈ 2.14 ˣ 10−6
Sodium, potassium, rubidium, caesium, and ammonium phosphates are generally soluble, but phosphates of other cations are usually insoluble or only slightly soluble. Some hydrogen phosphates, such as Ca(H2PO4)2, are soluble. Pure H3PO4 dissociates very slightly to give the tetrahydroxy phosphonium cation and giving it a higher than expected conductivity,
2 H3PO4 P(OH)4+ + H2PO4−
The hydrogen bond networks of aqueous H3PO4 have been established over the entire concentration range, by suse of molecular dynamics simulations [4229]. The hydrogen bond network of aqueous H3PO4 was found to be fundamentally different from that of H2O, with each phosphoric acid molecule tending to form more and stronger hydrogen bonds than water leading to much more connected and clustered networks. These hydrogen-bond networks persist in the H3PO4/H2O mixtures even at relatively high water contents.
On concentration of phosphoric acid, condensed linear polyphosphoric acids (Hn+2PnO3n+1, n = 2 - 15) form by the loss of water molecules, e.g.,
2 H3PO4 (HO)2P(=O)OP(=O)(OH)2+ H2O pyrophosphoric acid
3 H3PO4 (HO)2P(=O)OP(=O)(OH)OP(=O)(OH)2+ 2 H2O triphosphoric acid
4 H3PO4 (HO)2P(=O)OP(=O)(OH)OP(=O)(OH)OP(=O)(OH)2+ 3 H2O tetraphosphoric acid
Pyrophosphoric acid (left) and triphosphoric acid
Several different sets of pKa's for the polyphosphates have been suggested. Typically, pyrophosphate has two strongly acidic and two weakly acidic hydroxyl groups, pKa1 = -0.44, pKa2 = 2.64, pKa3 = 6.76 , pKa4 = 9.41, and triphosphate has three strongly acidic and two weakly acidic hydroxyl groups, pKa1 = -0.51, pKa2 = 1.20, pKa3 = 2.30 , pKa4 = 6.50, pKa5 = 9.24. Each phosphorus atom has just a single strong acid hydroxyl group. Pyrophosphate (H4P2O7) (extremely) slowly hydrolyzes in dilute solution.
In larger polyphosphates, each phosphorus atom bears a phosphonyl group (P=O) and a strongly acidic hydroxyl group. In addition, the two terminal P atoms of linear polyphosphates are each bonded to a second weakly acidic hydroxyl group. Cyclic metaphosphoric acids (HPO3)n are formed from low-molecular polyphosphoric acids by ring closure. They generally have a comparatively small number of ring atoms (n = 3 - 8) with each phosphorus atom bound to one strongly acidic hydroxyl group and one phosphonyl group (P=O). On concentration, these polyphosphates dehydrate further to form two-dimensional to three-dimensionally cross-linked, glassy metaphosphoric acid networks.
Poly H2PO4−
Adenosine triphosphate, ATP4− Mg2+
Despite their negagive charge, dihydrogen phosphates may form chains of hydrogen bonded molecules under some circumstances, see diagram right [4316]. Condensed phosphates may exist as linear (see ATP below), cyclic (see P4O10 above) or branched structures (the ultraphosphates [4325]).
Phosphate esters and anhydrides are key to much of metabolic biochemistry. They are relatively stable, except in the presence of specific enzymes that use their negative charge in their specificity. b They can link nucleotides whilst retaining their negative charge, so stabilizing the diesters against random hydrolysis and enabling them to be retained by membrane barriers.
The genetic materials DNA and RNA are phosphodiesters, and ATP (see left) is life's energy currency. Many intermediary metabolites (e.g., creatine phosphate, glucose-6-phosphate, phosphoenolpyruvate) are phosphate esters, phosphates, or pyrophosphates and are essential in biochemical syntheses and degradations.
ATP has pKa values of 0.9, 1.5, 2.3, and 7.7 (three strong and one weak acid). in contrast, ADP has pKa values of 0.9, 2.8, and 6.8 (two strong and one weak acid), both ignoring the basicity of the amino group on the adenine group (pKa ~ 4.15 ) and the acidity of the hydroxyl group on the ribose group (pKa = 12.98)e.
Phosphorous acid, HPO(OH)2 (usually shown as H3PO3, melting point 73.6 °C, boiling point 200 °C with decomposition, density 1651 kg ˣ m−3), is prepared by the hydrolysis of phosphorus trichloride with water or steam or the hydration of phosphorus trioxide (P4O6), d
PCl3 + 3 H2O → HPO(OH)2 + 3 HCl
P4O6 + 6 H2O → 4 HPO(OH)2
When burnt with a restrictive oxygen supply, white phosphorus forms phosphorus trioxide (see above left, which slowly oxidized to phosphorus pentoxide by air at room temperature. Phosphorus trioxide disproportionates above 210 °C to form the linear diphosphorus tetraoxide (P2O4, OPOPO2. the mixed anhydride of phosphonic and orthophosphoric acid),
2 P4O6 → 3 P2O4 +2 P
P4 (white) + 3 O2 → P4O6 ΔH° = –1646 kJ ˣ mol−1 d
P2O4 + 3 H2O → HPO(OH)2 + H3PO4
Phosphorous acid has two acidic groups, one strong and one weak, giving rise to the phosphites (properly called the phosphonates).
H3PO3 + H2O H3O+ + H2PO3− pKa1 = 1.3
H2PO3− + H2O H3O+ + HPO32− pKa2 = 6.7
A small proportion of HPO(OH)2 reversibly forms P(OH)3.
HPO(OH)2P(OH)3
Phosphine
Phosphine (PH3, see trigonal structure left and compare with NH3) is prepared by disproportionating phosphorous acid at around 200 °C. Phosphine is structurally similar to ammonia (NH3), but phosphine (melting point -133.8 °C, boiling point -87.8 °C, density 569 kg ˣ m−3 when liquid at 21 °C) is odorless, flammable, corrosive, toxic, much less polar (with opposite polarity), and less soluble in water. Particularly notable is that the P atom is slightly positively charged in PH3, compared with the substantial negative charge on ammonia's N atom due to the difference in N (3.04) and P (2.19) electronegativities .
4 H3PO3 → PH3↑ + 3 H3PO4 ~200 °C
Unlike NH3, PH3 is not basic. It only forms very weak hydrogen bonds as its P-H bonds are nonpolar. It has been supposedly found in the atmosphere of Venus, where it has been taken, by some, as a possible sign of life. l
Phosphinic acid H3PO2 (hypophosphorous acid, H2(PO)OH, density 1493 kg ˣ m−3, melting point 26.5 °C, boiling point 130 °C with decomposition) is prepared by the reaction of white phosphorus with a hot aqueous solution of an appropriate hydroxide, e.g., Ca(OH)2
2 P4 + 3 Ca(OH)2 + 6 H2O → PH3 + 3 Ca(H2PO2)2
Ca(H2PO2)2 + H2SO4 → CaSO4 + 2 H3PO2
Phosphinic acid gives rise to the hypophosphites (properly called the phosphinates). A small proportion of H3PO2 reversibly forms phosphinous acid, HP(OH)2,
H2(PO)OH HP(OH)2
Phosphinic acid has a single ionizable strong acid group,
H3PO2 + H2O H3O+ + H2PO2− pKa = 1.2
Hypophosphites are reducing agents, giving phosphorous acid,
HPO32− + 2 H2O + 2 e− H2PO2− + 3 OH− E° = -1.65 V
The redox series for the phosphorus acids is given below. The missing compound (H3PO, oxidation state -1, phosphine oxide) is unstable forming PH3 and H3PO2 acid even at low temperature,
2 H3PO → PH3 + H3PO2
.
The redox series for the phosphorus acids
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does not possess long-range order
The small white hydroxide ions are located in hexagonal channels (down the c-axis, seen bottom left) and surrounded by calcium ions, shown green. These hydroxyl ion channels, running straight through the center of the basal plane of its hexagonal lattice, are partially responsible for hydroxyapatite's useful properties. k These hexagonally-placed Ca2+ ions supposedly prevent any interfacial water molecules from forming hydrogen bonds with the hydroxide ions.f The 'crystals' grow fastest along the c-axis. Spherical (distorted, ~ 9 nm) Posner clusters,h,i Ca3Ca6(PO4)6 (as stable stand-alone particles, see structure below) start new hydroxyapatite crystal formation and surround the hexagonal channels. Their central linear, triple calcium ions (Ca3), go backward giving a three-fold rotation axis parallel to the c-axis. A phosphate ion phosphorus atom is placed approximately at the vertices of an octahedron, with 8 Ca2+ ions placed on the 8 external faces of this octahedron (forming a distorted cube, similar to the diamond structure) and the remaining ninth Ca2+ ion placed centrally. The ionic structure is somewhat irregular and does not form a stable regular cube or regular octahedron on relaxation in vacuo, which may well prevent long-range ordering. It hydrates well in aqueous solutions, and this tends to enable its retention of a more regular structure.
Posner's cluster,
aggregates randomly in solution as Ca3Ca6(PO4)6.30H2O
Amorphous calcium phosphates have variable chemical but essentially identical glass-like physical properties.j Hydroxyapatite Ca10(PO4)6(OH)2 (HAP, hydroxylapatite) embedded in a matrix of collagen makes up an essential part of human bones (in the form of ~5 nm thick and 20 nm long platelets) and teeth (the enamel is made up of hydroxyapatite rods ~ 20 - 40 nm in diameter). It is the most abundant inorganic material in our bodies (~10% by weight) after water (~60% by weight) and can be made chemically from lime (calcium hydroxide) and phosphoric acid,
10 Ca(OH)2 + 6 H3PO4 → Ca10(PO4)6(OH)2↓+ 18 H2O
precipitating as the amorphous form before conversion to pseudo-hexagonal crystals (P63/m, a = b = 9.432 Å, c = 6.881 Å). g In biological systems, there is a large drop in pH.
10 Ca2+ + 6 HPO42− + 10 H2O → Ca10(PO4)6(OH)2 + 8 H3O+
This acidity may be compensated by other reactions, such as the conversion of monoclinic tetracalcium phosphate (TTCP, Ca4(PO4)2O) to hydroxyapatite, n
3 Ca4(PO4)2O + 3 H2O → Ca10(PO4)6(OH)2 + 2 Ca2+ + 4 OH−
Apatites (Ca5(P04)3X, where X = OH−, F−, Cl−, etc.) form a family of compounds with a wide range of components with similar hexagonal structures. The exact structures of biological apatites remain undefined with Ca:P molar ratios ranging from 1.5 to 1.66, and they contain other materials such as the partial replacement of Ca2+ by Mg2+, OH− by F−, or PO43− by CO32−. Thus, its calcium-deficient and partially carbonated form
(Ca,Z)10(PO4,Y)6(OH,X)2
(where Z = Na+, K+, Mg2+, Sr2+, etc., Y = CO32−, HPO42−, and X = Cl−, F−) is found in bone. The cleaved and crystal surfaces of hydroxyapatite are hygroscopic and immediately attract water and carbon dioxide from the atmosphere.
Hydroxyapatite has a high nucleation rate at low super-saturation (favoring ultrafine particles). However, it then has an accommodating and low crystal growth rate favoring a versatile microstructure with varying 'defects' (e.g., making it hydrophobic or hydrophilic), giving it great utility in supporting life and acting as a metabolic reservoir for mineral ions. The dominant mode of growth is different on different crystal faces and is dependent on the crystallographic direction of growth. m
Hydroxyapatites are formed from calcium and phosphate ions that are abundant in bodily fluids and can quickly be built up, broken down, and repaired on demand. Like water, hydroxyapatite has a memory in so far as the history of its formation affects its properties. Hydroxyapatite's interaction with biological molecules depends on their surface exposure and chemistry.
Posner's cluster geometry
Bone is a nanocomposite with hydroxyapatite nanoparticles held within a collagen protein matrix, both extending throughout the whole shape and the whole saturated with essential and active water (10-20% by weight) provided by pores down to 5 nm in size. The nanoparticles consist of 50-150 nm thick stacks of 2.5-4 nm thick crystal platelets, arranged with their flat faces parallel and their c-axes parallel to the collagen fibrils. Chiral Posner’s clusters (see right, Ca3Ca6(PO4)6 ) are found within the crystal structure of hydroxyapatite Ca10(PO4)6(OH)2 with the addition of a Ca2+ ion and two hydroxide ions. There is little doubt that these biocompatible and antibacterial clusters are intimately concerned with bone metabolism. However, although the clusters are found intact and achiral in vitro, modeling within water fails to confirm this.
Water is bound to the crystal surfaces and connects between the collagen helices, with a high amount of bound water ndicating good bone quality. The strength of bones is derived from a hierarchical organization of coupled hydroxyapatite and collagen across length scales spanning from nm to cm [4275]. Water is the essential 'glue' for this integration of strong mineral hydroxyapatite with its reinforcing rods of flexible collagen polymer. As a result, bones are lightweight, strong, and stiff. Without the collagen (by baking), the bone would be very brittle, and without the calcium phosphate (by dissolving in dilute acid), the bone would be soft and bendable.
Ca10(PO4)6(OH)2 + 14 H3O+ → 10 Ca2+ + 6 H2PO4− + 16 H2O
Bone growth and repair is contolled by cells, including the osteoblasts and osteocytes. There is a regulated balance of activity (homeostasis) between bone-forming osteoblasts that also secrete extracellular matrix proteins such as type I collagen and bone-resorbing osteoclasts. o
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a K. Schrödter, G. Betttermann, T. Saffel, F. Wahl, T.Klein and T. Hofmann, Phosphoric acid and phosphates, Ullmann's Encyclopedia of Industrial Chemistry, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, vol 26 (2015) DOI: 10.1002/14356007.a19_465.pub3. [Back]
b F. H. Westheimer, Why nature chose phosphates, Science, 235, (1987) 1173-1178. [Back]
c I.-H. Jung and P. Hudon, Thermodynamic assessment of P2O5, Journal of the American Ceramic Society, (2012) 1-8, DOI: 10.1111/j.1551-2916.2012.05382.x. [Back]
d G. Bettermann, W. Krause, G. Riess and T. Hofmann, Phosphorus compounds, Inorganic, Ullmann's Encyclopedia of Industrial Chemistry, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, vol 27 (2012) DOI: 10.1002/14356007.a19_527. [Back]
e H. Åström, E. Limén and R. Strömberg, Acidity of secondary hydroxyls in ATP and adenosine analogues and the question of a 2',3'-hydrogen bond in ribonucleosides, Journal of the American Chemical Society, 126 (2004) 14710-14711. [Back]
f D. Zahn and O. Hochrein, Computational study of interfaces between hydroxyapatite and water, Physical Chemistry Chemical Physics, 5 (2003) 4004-4007. [Back]
g M. I. Kay, R. A Young and A. S. Posner, Crystal structure of hydroxyapatite, Nature, 204 (1964) 1050-1052. [Back]
h L. Wang, S. Li, E. Ruiz-Agudo, C. V. Putnis and A. Putnis, Posner’s cluster revisited: direct imaging of nucleation and growth of nanoscale calcium phosphate clusters at the calcite-water interface, CrystEngComm, 14 (2012) 6252-6256; M. W. Swift and M. P. A. Fisher, Posner molecules: From atomic structure to nuclear spins, Physical Chemistry Chemical Physics, 20 (2018) 12373-12380. [Back]
i G. Mancardi, C. E. H. Tamargo, D. Di Tommaso and N. H. de Leeuw, Detection of Posner’s clusters during calcium phosphate nucleation: a molecular dynamics study, Journal of Materials Chemistry B, 5 (2017) 7274-7284. [Back]
j S. V. Dorozhkin. Amorphous calcium (ortho)phosphates, Acta Biomaterialia, 6 (2010) 4457-4475; S. V. Dorozhkin, Calcium orthophosphates (CaPO4): occurrence and properties, Morphologie, 101 (2017) 125-142. [Back]
k V. Uskoković, The role of hydroxyl channel in defining selected physicochemical peculiarities exhibited by hydroxyapatite, Royal Society of Chemistry Advances, 5 (2015) 36614-36633. [Back]
l J. S. Greaves, A. M. S. Richards, W. Bains, P. B. Rimmer, H. Sagawa , D. L. Clements, S. Seager , J. J. Petkowski, C. Sousa-Silva, S. Ranjan, E. Drabek-Maunder, H. J. Fraser, A. Cartwrigh, I. Mueller-Wodarg, Z. Zhan, P. Friberg, I. Coulson, E. Lee and J. Hoge. Phosphine gas in the cloud decks of Venus, Nature Astronomy, (2020) Article in press, DOI: 10.1038/s41550-020-1174-4; but see Editors cautionary note, 20 Nov and; A. P. Lincowski et al, Claimed detection of PH3 in the clouds of Venus is consistent with mesospheric SO2, arXiv:2101.09837v1 [astro-ph.EP] 25 Jan 2021. [Back]
m V, Uskoković, Disordering the disorder as the route to a higher order: Incoherent crystallization of calcium phosphate through amorphous precursors, Crystal Growth & Design, 20 (2019) 4340-4357. [Back]
n V, Uskoković and D. P. Uskoković, Nanosized hydroxyapatite and other calcium phosphates: Chemistry of formation and application as drug and gene delivery agents, Journal of Biomedical Materials research. Part B, Applied Biomaterials, 96 (2011) 152-191 DOI: 10.1002/jbm.b.31746. [Back]
o A. Salhotra, H. N. Shah, B. Levi and M. T. Longaker, Mechanisms of bone development and repair, Nature Reviews, Molecular Cell Biology, 21 (2020) 696-711. [Back]
p The third dissociation constant of phosphoric acid in H2O and D2O from 75 to 300 °C has been reported [4251]. [Back]
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