Formation of monofluorophosphate from fluoride in phosphoric acid - Water and phosphoric acid - sulfuric acid - water mixtures

Article abstract of DOI:10.1139/V07-027

When dissolved in concentrated phosphoric acid, sodium fluoride reacts rapidly to form monofluorophosphate. In less concentrated acid, the reaction does not proceed to completion, and the reaction kinetics become very much slower. The equilibrium and rate

Full text of DOI:10.1139/V07-027

346
Formation of monofluorophosphate from fluoride
in phosphoric acid – water and phosphoric acid –
sulfuric acid – water mixtures
Kenneth E. Newman, Raymond E. Ortlieb, Nicole Pawlik, and Jason Reedyk
Abstract: When dissolved in concentrated phosphoric acid, sodium fluoride reacts rapidly to form monofluorophosphate.
In less concentrated acid, the reaction does not proceed to completion, and the reaction kinetics become very much
slower. The equilibrium and rate constants for the reaction have been determined. In ternary mixtures of phosphoric
acid, sulfuric acid, and water, the formation of monofluorophosphate is considerably enhanced, and the kinetics are
rapid. The results are interpreted in terms of the very low water activity coefficients in strong-acid solutions.
Key words: monofluorophosphate, monofluorophosphoric acid, 19F NMR, 31P NMR, phosphoric acid, sulufric acid,
equilibria, kinetics.
Résumé : Lorsqu’il est dissout dans de l’acide phosphorique concentré, le fluorure de sodium réagit rapidement pour
former le monofluorophosphate. Dans de l’acide moins concentré, la réaction n’est pas complète et la cinétique de la
réaction est ralentie. On a déterminé les constantes d’équilibre et de vitesse de la réaction. Dans des mélanges ternaires
d’acide phosphorique, d’acide sulfurique et d’eau, la formation du monofluorophosphate est très accélérée et la ciné-
tique est rapide. On interprète les résultats en fonction des très faibles coefficients d’activité de l’eau dans des solutions
fortement acides.
Mots-clés : monofluorophosphate, acide monofluorophosphorique, RMN du 19F, RMN du 31P, acide phosphorique, acide
sulfurique, équilibre, cinétique.
[Traduit par la Rédaction]
Newman et al. 351
Introduction
ter, at temperatures between 150 and 400 °C (2). The anhy-
drous acid itself can be made under much less forcing condi-
tions, namely room temperature reaction of anhydrous
metaphosphoric acid (HPO3) and gaseous hydrogen fluoride
(3).
MFP salts find uses in the treatment of osteoporosis, con-
trol of corrosion (particularly in steel reinforcing in con-
crete), and as fungicides and bactericides. However, the
major use of MFP salts is as anticaries agents in toothpastes.
The hydrolysis of MFP to fluoride is extremely slow at near
neutral pH values, although it is hydrolyzed readily by
phosphatase enzymes, including those found in saliva (4).
The addition of an acid has also been shown to significantly
enhance the reaction rate (5).
Mono-, di-, and hexafluorophosphates, along with their
corresponding acids, were first synthesized and character-
ized by Lange and co-workers in a series of papers starting
in 1926 (1). As part of this extended study, they reported
that sodium fluoride, when dissolved in concentrated phos-
phoric acid, gave a mixture of HF and monofluoro-
phosphoric acid (MFP), H2PO3F.2 The ratio of MFP to HF
increased with increasing phosphoric acid concentration.
The patent literature suggests that sodium monofluorophos-
phate (Na2PO2F) is commercially manufactured using very
forcing conditions. For example, the 1993 patent of
Swidersky et al. involves mixing H3PO4, NaOH, and NaF in
stoichiometric amounts, together with a small amount of wa-
Phosphoric acid is manufactured by the reaction of the ore
(apatite), Ca5(PO4)3(OH), with concentrated sulfuric acid in
the temperature range of 70–80 °C (the so-called “wet pro-
cess”) according to the simplified reaction [1] (6).
Received 31 July 2006. Accepted 5 February 2007. Published
on the NRC Research Press Web site at canjchem.nrc.ca on
5 May 2007.
K.E. Newman,1 R.E. Ortlieb, N. Pawlik, and J. Reedyk.
The King’s Centre for Molecular Structure, The King’s
University College, 9125 50th Street, Edmonton, AB
T6B 2H3, Canada.
[1]
Ca5(PO4)3(OH) + 5H2SO4 = 5CaSO4(s)
+ 3H3PO4 + H2O
The ore is invariably contaminated with fluoroapatite,
Ca5(PO4)3(F), with the total fluoride content of the feedstock
in the range of 3.5%–4%. The strongly acidic reaction con-
ditions favor the formation of HF, which dissolves silica and
silica-like impurity minerals in the ore. Products of this reac-
tion are various fluorosilicates, including the volatile silicon
1Corresponding author (e-mail: ken.newman@kingsu.ca).
2Given the strongly acidic media of interest in this paper, the
extent of protonation of monofluorophosphate will not
always be obvious. Thus, we will refer to the species as
MFP regardless of its form except where noted.
Can. J. Chem. 85: 346–351 (2007)
doi:10.1139/V07-027
© 2007 NRC Canada

Newman et al.
347
Fig. 1. Variation of normalized NMR intensities of each peak of
tetrafluoride (SiF4), as well as hexafluorosilicic acid
(H2SiF6) and (or) its salts. Phosphoric acid reactor vessels
are thus typically scrubbed to remove the volatile HF and
SiF4. The other product of reaction [1], calcium sulfate (gyp-
sum) is typically pumped as a slurry to tailings ponds; pro-
cess water is also stored for recycle in storage ponds. These
ponds are typically fairly acidic (pH < 2) with very high dis-
solved solids content, and with fluoride levels in the range
of 0.35%–1.35% (7). Probably, the fluoride is mostly in the
form of HF and SiF62–, but the latter species may partially
hydrolyze to SiF4. Fugitive emissions of gaseous HF and
SiF4 from the ponds are thus of environmental concern.
The work reported here is the first part of an extended
study to explore and understand in detail the chemistry and
fate of the fluoride impurities as they pass through the “wet
process” manufacture of phosphoric acid. The ready forma-
tion of MFP in phosphoric acid under benign conditions led
us to focus initially on the conditions that determine its for-
mation. Given the central role of sulfuric acid on the manu-
facturing process, its effect on MFP formation was clearly
important to the study.
the monofluorophosphate doublet (closed and open circles) and
hydrogen fluoride (closed squares) for a 0.0078 m of sodium
monfluorophosphate solution in a phosphoric acid – water mix-
ture of the composition x(H3PO4) = 0.254. The D2O/H2O frac-
tion was 0.41. For clarity, the data for the component of the
MFP doublet represented by the open circles were displaced ver-
tically by 0.2 units. The smooth curves are the fitted values, ob-
tained as described in the text.
Experimental
NaF (Fisher, ACS grade), Na2PO3F (Alfa Aesar, >99%),
H3PO4 (Aldrich, 100%), H3PO4 (Sigma, 85%, ACS), H2SO4
(95%–98%, ACS grade), and D2O (Cambridge Isotope Lab-
oratories, 99%) were used as received. All solutions were
prepared by weight in polyethylene or Teflon containers and
were typically 0.01 m total fluoride. Solutions typically con-
tained 10%–15% D2O, although a few solutions were pre-
pared with 40%–50% D2O. Some of the most-acidic
solutions were prepared without D2O and thus were run un-
locked. NMR spectra were obtained with a Bruker 400
Avance NMR spectrometer using a Bruker ATMA multi-
nuclear probe operating at 161.98 MHz for 31P and
376.46 MHz for 19F. All NMR spectra were run at 22.0
0.1 °C. Samples were contained in 5 mm NMR tubes with
polytetrafluoroethylene – fluorinated ethylene polypropylene
copolymer (PTFE–FEP) liners (Wilmad LabGlass, NJ, USA).
siderable variation, as the phosphoric acid concentration is
varied from 5% to 85% H3PO4.
We may define α as the fraction of the fluorine-containing
species in the form of MFP
cMFP
[2]
α =
cMFP + cHF
where ci is the concentration (expressed as either molality or
molarity). At 85% H3PO4, the value of α from the integra-
tion of the 19F spectrum is 0.81. As the phosphoric acid con-
centration is decreased, not only does α decrease, but also
the kinetics of interconversion of HF and MFP become sur-
prisingly slow. The dependence of α on phosphoric acid con-
centration was thus determined as the infinite-time values
obtained from a study of the kinetics of the reaction of 0.01
m Na2MFP in aq. phosphoric acid solutions. Figure 1 shows
a typical kinetic 19F NMR run. The integrated NMR peak in-
tensities were normalized by dividing through by the sum of
the intensities. The normalized intensities were fitted to a
first-order kinetic equation by a non-linear least-squares ap-
proach, using the “Solver” facility of Microsoft® Excel.
Each NMR peak was fitted to a unique time-zero and time-
infinity intensity, but with a common value for the rate con-
stant. For H3PO4 compositions greater than 80% [x(H3PO4)
> 0.42], the kinetics were too fast to measure by this NMR
method, and thus, only the equilibrium values could be mea-
sured. For x(H3PO4) < 0.04, the infinity values for the MFP
peaks were too small to be measured reliably and were thus
constrained to zero. Although no extended study was per-
formed, the kinetics do not appear to exhibit any strong iso-
tope effects as the D2O fraction is changed. Figure 2 shows
the values of α as a function of x(H3PO4). For the two points
Results
The 19F NMR spectrum of a 0.01 m solution of NaF in
85%3 H3PO4 solution consists of a doublet, centered at
–75.1 ppm with a coupling constant of 937 Hz, and a some-
what broad peak at ~147 ppm. The 31P NMR spectrum of a
similar solution consists of a very large peak centered at
~0 ppm, a small doublet centred at –7.4 ppm with a coupling
constant of 937 Hz, and another small peak at –12.8 ppm.
The spectra are readily interpreted in terms of a mixture of
MFP and HF. The doublet feature in each spectrum is due to
J12(19F–31P) coupling in the MFP. The large peak at ~0 ppm
in the 31P spectrum is due to H3PO4, and the small peak at
–12.8 ppm is due to a small amount of pyrophosphate
(P2O74–). These assignments are consistent with literature
values (8). It is worth noting that the 19F chemical shifts of
both MFP and HF and the MFP coupling constant show con-
3 Throughout this work, “% i” refers to the weight% of solvent species i, calculated excluding the solutes. x(i) refers to the mole fraction of
solvent species i, calculated excluding the solutes.
© 2007 NRC Canada

348
Can. J. Chem. Vol. 85, 2007
Fig. 2. Equilibrium fraction (α) of monofluorophosphate as a
function of the mole fraction of H3PO4. ᭹: Experimental values;
Fig. 4. Equilibrium fraction (α) of monofluorophosphate in
H3PO4 – H2SO4 – H2O mixtures. ٗ: 15% H2O, plotted vs. %
H2SO4; ᭹: 50% H2SO4, plotted vs. % H3PO4; ᭿: ~ 43% H3PO4,
plotted vs. % H2SO4 (see text for information on this series).
________
: Fitted values (see Discussion for details).
Fig. 3. Apparent first-order rate constants for the interconversion
of HF and MFP as a function of the mole fraction of H3PO4.
The line represents the best straight-line fit, excluding the open-
circle data point.
composition varied slightly (from 42.3 to 45.5), which ac-
counts for the slightly scattered results. It is remarkable that
sulfuric acid has such a large effect on MFP formation. For
example, a H3PO4–H2SO4 – H2O (42:38:20) mixture yields
100% MFP, whereas a H3PO4 – H2O (42:58) mixture yields
only 10% MFP. The results are even more dramatic in the
low-water (15%) mixtures where a H3PO4 – H2SO4 – H2O
(20:60:15) mixture yields 100% MFP, whereas in a 20%
H3PO4 solution in the absence of H2SO4, the yield is ~ 1%.
The kinetics in the sulfuric acid solution were typically too
fast to measure by our relatively slow NMR method.
Discussion
Formation of MFP in H3PO4 – H2O mixtures
Theory
For the reaction of HF to give MFP, we can write
[3]
H3PO4 + HF ꢀ H2PO3F + H2O
In terms of the reaction conditions of interest here, both
phosphoric acid and water are the predominant species (the
solvent), whereas HF and MFP are considered solutes. We
have written both of the reactants in their protonated forms
because phosphoric acid is a weak acid in water and HF is
even weaker. We have no reliable knowledge about the ion-
ization state of MFP. Certainly, it is a stronger acid (in wa-
ter) than phosphoric acid. However, in the strongly acidic
solvents of interest here, we will assume that it is also
protonated.
In general, an equilibrium constant is only a “constant” in
any given solvent or solvent mixture. For example, in mix-
tures of ethanol–water, weak acids become considerably
weaker as the alcohol content of the solvent increases. One
approach to this problem is to define our equilibrium con-
stant K(P–W) for reaction [3] in solvent mixture P–W as
in the figure at x(H3PO4) ≈ 0.51, one was obtained using
NaF as the initial reactant, the other using Na2MFP. The ori-
gin of the smooth line through the data will be discussed
later. Figure 3 shows the apparent first-order rate constants
for the kinetics of formation of MFP as a function of
x(H3PO4). Quite remarkably, the values obtained were linear
with R2 = 0.997.4
For the phosphoric acid – sulfuric acid – water mixtures,
it is more difficult to survey adequately the solvent composi-
tion range. In addition to the H3PO4 – H2O binary mixtures
(i.e., the 0% H2SO4 isopleth), measurements were also made
along the following ternary diagram isopleths: ~43% phos-
phoric acid, 15% H2O, and 50% H2SO4. The results are
shown in Fig. 4. In the ~ 43% H3PO4 series, the weight
4 Most texts on error analysis give a definition for R, see for example ref. 9.
© 2007 NRC Canada

Newman et al.
349





c(H2PO3F) γ(H2PO3F) x(H2O)
α
γ(H2PO3F) x(H2O)
[4]
K(P−W) =
=






c(HF)
γ(HF) x(H3PO4)
1 − α γ(HF) x(H3PO4)

where the γ terms are the conventional concentration-dependent activity coefficients, which can be ignored, providing the con-
centrations are low enough. This equilibrium constant changes when the solvent composition is changed because the standard
chemical potentials of the reactants and products are solvent-dependent. This is often referred to as the “primary medium ef-
fect”. One approach to this problem is to use “free energies of transfer”. Thus, we can write, for the thermodynamic cycle in-
volving reaction [3] in two different solvents, W and P–W
[5]
[10] ∆tGo[P(P–W) ← P(W)] = [µ(P) – RT ln xp]P–W
– [µ(P) – RT ln(xp = 0)]W
where ∆tGo(P–W ← W) are called the free energies of trans-
fer of the species from solvent W (in this case, water) to the
solvent mixture P–W. Straightforward analysis of the ther-
modynamic cycle allows us to write the standard free energy
of reaction in solvent mixture P–W as
This equation yields
[11] ∆tGo[P(P–W) ← P(W)] = RT ln γP – RT ln γP(0)
[6]
∆
rxnGo(P−W) = ∆rxnGo(W) +
∆ tGo(P−W ← W)
where γP(0) is the limiting activity coefficient of P in pure
W.
Solvent-activity coefficients are frequently expressed in
terms of an equation of the form (10)
∑
products
−
∆tGo(P−W ← W) = −RT ln K(P−W)
∑
reactants
The great utility of this equation is that, in principle, the
various free energy of transfer terms can be obtained for in-
dividual species by thermodynamic measurements such as
vapor pressure or solubility. Thus, we can obtain the solvent-
composition dependence of the equilibrium constant.
2
[12] ln γw = Axp
and
[13] ln γP = A(1 – xP)2
For the reaction of interest, it is not obvious how one
would measure the free energy of transfer of HF from H2O
to H3PO4. Even if one could find a suitable experimental
technique, HF reacts too rapidly in phosphoric acid. It is
also not immediately obvious how one would measure this
quantity for H2PO3F. However, for the purposes of this anal-
ysis, we wish to explore the crucial role of the free energy of
transfer terms for the two-solvent components, i.e., H2O and
H3PO4. The free energy of transfer of species W from W to
solvent mixture P–W can be written more formally as
By combining eqs. [9], [11], [12], and [13], we readily ob-
tain
[14] ∆tGo[W(P–W) ← W(W)] – ∆tGo[P(P–W)
← P(W)] = 2RT AxP
Combining eqs. [6] and [14] (ignoring contributions from
free energy of transfer of the two solutes) we obtain
[15] ln K(P–W) = ln K(W) – 2AxP
predicting a linear dependence of ln K with phosphoric acid
mole fraction.
[7]
∆tGo[W(P–W) ← W(W)] = [µ(W) – RT ln xw]P–W
Comparison with experiment
– [µ(W) – RT ln(xw = 1)]W
The values of K(P–W), obtained from the data in Fig. 2
using eq. [4], vary from 0.28 to 4.5 over the solvent compo-
sition range x(H3PO4) = 0.049–0.51. A plot of ln(K) vs.
x(H3PO4) is predicted to be linear by eq. [15]. To see how
well the values for α obey this prediction, they were fitted by
a non-linear least-squares approach, using Microsoft® Excel
Solver, to eq. [4] with the γ terms set to unity and with ln(K)
as a linear function of x(H3PO4). Thus, the two fitting pa-
rameters were the slope and intercept. Figure 2 shows a
comparison between observed and calculated values of α.
The large variation of K with solvent composition is the
The usual definition for activity coefficients in binary sol-
vent mixtures is
[8]
µ(W) = µo(W) + RT ln xw + RT ln γw
with ln γw → 1, as xw → 1; thus, eq. [7] becomes (as we
might expect)
[9]
∆tGo[W(P–W) ← W(W)] = RT ln γw
Applying a similar approach to eqs. [7] and [8] to the
transfer of species P from W to a P–W mixture, we obtain
© 2007 NRC Canada

350
Can. J. Chem. Vol. 85, 2007
Table 1. Fitting parameters for the determina-
tion of α in H3PO4 – H2SO4 – H2O mixtures
from eqs. [11] and [12].
cause of the sigmoid shape of Fig. 2. The values obtained
for ln K(W) and 2A in eq. [15] were –2.7 and –8.5, respec-
tively. No attempt was made to assess the uncertainties in
these parameters because the data were obtained over a nar-
row range of x .
P1
–9.298 × 10–2
1.298 × 10–3
1.189 × 10–1
–2.473 × 10–3
1.529 × 10–1
–1.753 × 10–3
The activitypcoefficients of both W and P in phosphoric
acid mixtures can be obtained from vapor-pressure measure-
ments. The calculation is straightforward because, for this
system, the vapor contains no phosphoric acid. The 20 °C
vapour-pressure data (11) after conversion to water activity
coefficients were fitted to eq. [12] to obtain a value of –10.7
for 2A.5
P2
S11
S12
S21
S22
Note: The fit included 65 data points (as shown
in Figs. 2 and 4). The standard deviation between
observed and calculated points is 0.04.
Thus, we conclude that the majority of the large increase
in equilibrium constant for the formation of MFP, going
from pure water to pure phosphoric acid, is due to the ex-
treme thermodynamic non-ideality of the mixture. In partic-
ular, the reaction is strongly promoted by the low water
activities, which manifest themselves in the negative value
for A in eqs. [12] to [15]. However, the previously men-
tioned analysis has not included free energy of transfer terms
for the two solutes. We also caution that experimental mea-
surements on which the previously mentioned analysis was
performed are not of the highest precision.
Fig. 5. A triangular graph that shows contour plot of the fraction
α of MFP formed in H3PO4 – H2SO4 – H2O mixtures (see text
for details). Moving from left to right across the figure, the con-
tours represent fractions of 0.95, 0.8, 0.6, 0,4, 0.2, and 0.1. The
ellipses represent the composition regions where the measure-
ments were taken.
Formation of MFP in H3PO4 – H2SO4 – H2O
To obtain an analytical and graphical representation of the
variation of α with solvent composition for the H3PO4 –
H2SO4 – H2O mixtures, the experimental values for α were
fitted using a non-linear least-squares approach to equations
of the form:
α
x(H2O)
[16] Kapp
=
1 − α x(H3PO4)
with
[17] ln Kapp = PwP(1 + S11wS + S12wS2)
1
+ P wP2(1 + S21wS + S22wS2)
2
and with wP and wS being the wt% of phosphoric and
sulphuric acids in the ternary solvent mixture, respectively.
The optimal values for the fitting parameters are shown in
Table 1.
acid to depress the thermodynamic activity of water. From
the water-activity data for the simple binary mixture
H2SO4 – H2O (12), we obtain a value of –24.3 for 2A.6 This
is, of course, simply a manifestation of the strong dehydrat-
ing ability of this acid. This effect is used to advantage in
many chemical processes such as the production of concen-
trated nitric acid (13). HNO3 – H2O mixtures form an
azeotrope, and thus the acid cannot be concentrated by sim-
ple distillation. It is concentrated by extractive distillation
using concentrated sulphuric acid. It is interesting to note
that phosphoric acid has also been suggested as an extractive
distillation agent to concentrate nitric acid. (14).
There is no particular theoretical reason for choosing the
previously mentioned equations, which are simply conve-
nient representations of the data. With the addition of extra
terms, slightly improved fits can be obtained. Figure 5 shows
the triangular contour plot from the fit. Whilst the accuracy
of the fit may be doubtful in the solvent region that is low in
both H2O and H3PO4 (i.e., the H2SO4 apex), the form of the
graph is unmistakable. Formation of MFP is determined
most strongly by the water content of the solution: the lower
the water content, the larger the formation of MFP. Quite re-
markably, this is a much stronger determinant than the phos-
phoric acid content of the solution. Thus, we conclude that,
as in the case of the binary solvent mixture H3PO4 – H2O,
the reaction is being driven by the strong ability of sulphuric
Acknowledgements
We acknowledge helpful discussions with Mr. Ken Larlee
of Agrium Inc. (Redwater, AB) and with all of the members
5 Vapor-pressure data are probably not extensive enough to justify including higher-fitting terms to this equation. Including these terms does
not make a significant difference to the results given here.
6 To get a good fit, it is necessary to take into account that for the first deprotonation step, sulfuric acid is strong; thus, we define the mole
fraction of water as xw = nw /(nw + 2ns ) where n is the number of moles of i, and i is water or sulfuric acid.
© 2007 NRC Canada

Newman et al.
351
7. G.A. Kennedy, M.M. Soraczak, S.J. Meischen, and J.D. Clay-
ton. Chemistry of gypsum pond systems. Florida Institute of
Phosphate Research Publication No. 05–025–100, August
1992. Available from http://www.fipr.state.fl.us/pondwatercd/
05–025–100Final.pdf [cited January 2007].
8. J.W. Emsley, J. Feeney, and L.H. Sutcliffe. High resolution nu-
clear magnetic resonance spectroscopy. Vol. 2. Pergamon
Press, Oxford. 1966. Chap. 11 and 12.
9. J.R. Taylor. An Introduction to error analysis. University Sci-
ence Books, Mill Valley, CA. 1982. Chap. 9.
10. See for example: E.A. Guggenheim. Thermodynamics. North
Holland, Amsterdam. 1988. Chap. 4.
of the King’s Centre for Molecular Structure. We thank the
King’s University College for financial support of this re-
search. R.E.O. thanks the Natural Sciences and Engineering
Research Council of Canada (NSERC) for the provision of
an Undergraduate Student Research Award (USRA).
References
1. The early work by Lange is well reviewed by W. Lange. In
Fluorine chemistry. Vol. 1. Edited by J.H. Simons. Academic
Press, NY. 1950. pp. 140–149.
11. Kirk-Othmer. Encyclopedia of chemical technology. 2nd ed.
Vol. 15. Interscience Publishers, NY. 1968. p. 236.
12. R.A. Robinson and R.H. Stokes. Electrolyte solutions. 2nd ed.
(revised). Butterworths, London. 1965.
13. J.G. Sloan. Adv. Chem. Ser. 1976, 155, 128.
14. R. Flatt and J. Bonnet. Chimia, 1958, 11,343.
2. H.-W. Swidersky, R. Werner., U. Hartmann, F. Moewius, V.
Radonz, and M. Meisel. US Patent 5-393-506, 07 October
1993.
3. W. Lange and R. Livingston. US Patent 2-408-784, 08 October
1946.
4. Y. Ericsson. Caries Res. 1, 144 (1967).
5. P.W. Heidbuchel. Pharm. Acta Helv. 66, 290 (1991).
6. P. Becker. Phosphates and phosphoric acid: raw materials,
technology, and economics of the wet process. 2nd ed. Marcel
Dekker, NY. 1989.
© 2007 NRC Canada