Raman- and infrared-spectroscopic investigations of dilute aqueous phosphoric acid solutions

Article abstract of DOI:10.1039/c0dt00417k

Phosphoric acid in water and heavy water has been studied by Raman and infrared spectroscopy over a broad concentration range (0.00873-1.560 mol kg^-1) at 23 °C. The vibrational modes of the PO₄ skeleton (C_3v symmetry) of H₃PO₄(aq) and D ₃PO₄(D₂O) have been assigned. In addition to the P-O stretching modes a deformation mode has been detected, δPO-H(D) at 1250 and 935 cm^-1, respectively. In addition to the modes of the phosphoric acid and heavy phosphoric acid a mode of the dissociation product H₂PO₄^- and D₂PO₄ ^- has been detected at 1077 cm^-1 and 1084 cm^-1 respectively. H₃PO₄ and D₃PO₄ is hydrated in aqueous solution which could be verified by Raman spectroscopy following the νPO and ν_sP(OH)₃ mode as a function of temperature. These modes show a pronounced temperature dependence inasmuch as νPO shifts to higher wavenumbers with temperature increase and ν_sP(OH)₃ to lower wavenumbers. In the range between 300-600 cm^-1 the deformation modes have been observed. In very dilute H₃PO₄ solutions however, the dissociation product is the dominant species. The dissociation degree, α for H₃PO ₄(aq) and D₃PO₄(D₂O) as a function of dilution has been measured at 23 °C. In these dilute H₃PO ₄(aq) and D₃PO₄(D₂O) solutions no spectroscopic features for a dimeric species of the formula H₆P ₂O₈ and D₆P₂O₈ could be detected. Quantitative Raman measurements have been carried out to follow the dissociation of H₃PO₄ and D₃PO₄ over a very broad concentration range and also as a function of temperature. From the dissociation data, the pK₁ value for H₃PO₄ has been determined to 2.14(1) and for D₃PO₄ to 2.42(1) at 23 °C. In the temperature interval from 24.5 to 99.7 °C the pK ₁ values for H₃PO₄(aq) have been determined and thermodynamic data have been derived.

Full text of DOI:10.1039/c0dt00417k

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PAPER
www.rsc.org/dalton | Dalton Transactions
Raman- and infrared-spectroscopic investigations of dilute aqueous
phosphoric acid solutions†
Wolfram W. Rudolph*
Received 4th May 2010, Accepted 14th July 2010
DOI: 10.1039/c0dt00417k
Phosphoric acid in water and heavy water has been studied by Raman and infrared spectroscopy over a
-
1
◦
broad concentration range (0.00873–1.560 mol kg ) at 23 C. The vibrational modes of the PO
skeleton (C3v symmetry) of H PO (aq) and D PO (D O) have been assigned. In addition to the P–O
4
3
4
3
4
2
-
1
stretching modes a deformation mode has been detected, dPO–H(D) at 1250 and 935 cm , respectively.
In addition to the modes of the phosphoric acid and heavy phosphoric acid a mode of the dissociation
-
-
-1
-1
product H
PO is hydrated in aqueous solution which could be verified by Raman spectroscopy following the
nP O and n P(OH) mode as a function of temperature. These modes show a pronounced temperature
dependence inasmuch as nP O shifts to higher wavenumbers with temperature increase and n P(OH)
to lower wavenumbers. In the range between 300–600 cm the deformation modes have been observed.
In very dilute H PO solutions however, the dissociation product is the dominant species. The
2
PO
4
and D
2
PO
4
has been detected at 1077 cm and 1084 cm respectively. H
3
PO
4
and
D
3
4
s
3
s
3
-
1
3
4
dissociation degree, a for H
3
PO
(aq) and D
and D
been carried out to follow the dissociation of H
4
(aq) and D
PO
could be detected. Quantitative Raman measurements have
PO and D PO over a very broad concentration range
3
PO
4
(D
2
O) as a function of dilution has been measured at
◦
23 C. In these dilute H
3
PO
4
3
4
(D
2
O) solutions no spectroscopic features for a dimeric
species of the formula H
6
P
2
O
8
6
P
2
O
8
3
4
3
4
and also as a function of temperature. From the dissociation data, the pK
1
value for H
3
PO has been
4
◦
determined to 2.14(1) and for D
3
PO
4
to 2.42(1) at 23 C. In the temperature interval from 24.5 to
◦
99.7 C the pK
1
values for H
3
PO (aq) have been determined and thermodynamic data have been
4
derived.
1
5–33
1
. Introduction
present.
acid:
The first dissociation equilibrium of the phosphoric
1
2,3
Unquestionably, the industrial and biological importance of
phosphate systems brought about extensive investigations of
physicochemical properties of aqueous solutions of phosphoric
acid and phosphates. Among many techniques, Raman and
-
+
H
3
PO
4
+ H
2
O ꢀ H
2
PO
4
+ H O
3
(1)
is well known from thermodynamic studies and from conductivity
work at room temperature
higher temperatures and pressures.
studies, the structure of the species has been proposed and dimeric
species such as H
others denied the need to invoke such species.
The structure of phosphoric acid in aqueous solution has
4–13
16,19,22
infrared spectroscopy has been used quite extensively.
The
and have also been extended to
26,31
spectroscopic material published however, showed disagreement
concerning the peak positions of the fundamental modes, depo-
larization degrees, and other band parameters. In some cases, the
number of modes contradicted the predicted ones deduced from
group theory for H
have a simple spectrum, there is much confusion in the literature
over the assignment of the modes. In a standard work and earlier
publications the modes of the H
modes of its dissociation product H
Simultaneous to these vibrational studies, a number of inves-
tigations on phosphoric acid solutions were done using methods
such as potentiometry, conductivity, ultrasonic absorption and
vapour pressure measurements. The main purpose concerned the
determination of the dissociation of the phosphoric acid and
therefore raised questions concerning the nature of the species
From a number of these
-
20,21,28
6
P
2
O
6
and H
5
P
2
O
6
have been deduced
while
1
6,22,26,30
3
PO . Although the phosphoric acid should
4
34
been obtained by an earlier X – ray diffraction study on two
14
concentrated aqueous H
˚
3
PO solutions. A peak in the range
4
4–7
~3.75 A in the correlation functions revealed the presence of
3
PO
4
(aq) were confused with the
-
2
PO
4
(aq).
H
3
PO
with about four water molecules. The existence of a hydration
shell around H PO in aqueous solution had been inferred from
earlier diffusion measurements. A recent neutron diffraction and
4
–H
2
O interactions and each H
3
PO molecule interacts
4
3
4
15
35
isotopic substitution study (NDIS) was applied on hydrogen
phosphate solutions and showed the existence of strong hydrogen
bonds formed between phosphate anions and water molecules
and a hydration number of 11–15 was found. Density functional
theory/molecular dynamics simulation of aqueous solutions
of orthophosphate species H PO
into hydrogen transfer and hydration properties of these aqueous
species. A first hydration shell of PO
displayed a flexible first coordination shell between 13 and 7
water molecules decreasing from PO
36
3
-n
Institut f u¨ r Virologie im MTZ, TU Dresden, Fetscherstr. 74, D-01307,
Dresden, Germany. E-mail: wolfram.rudolph@tu-dresden.de
(n = 0–3) provided insights
n
4
†
Electronic supplementary information (ESI) available: Geometry of
the H PO molecules (C symmetry) and the numbering of the atoms
which is used for the definition of the parameters in Table 2. See DOI:
0.1039/c0dt00417k
3-
2-
-
4
, HPO
4
, and H
2
PO
4
3
4
3
3
-
-
1
4
to H
2
PO . The H-bond
4
9
642 | Dalton Trans., 2010, 39, 9642–9653
This journal is © The Royal Society of Chemistry 2010

View Article Online
interactions between the oxygen atoms of the phosphates and
the surrounding water molecules explained the diminished effect
on the structure of water with increasing hydrogenation of the
were determined with a pycnometer of 5.000 mL volume at (23 ±
0.1) C.
◦
11,12
39,40
orthophosphates. A computer simulation on aqueous K
3
PO
4
,
Raman and IR spectroscopic measurements
37
K
2
HPO
4
, and KH
2
PO
4
solutions confirmed the strong hydration
Raman spectra were measured with equipment at the TU
effect of these ions and a partially ordered second hydration
shell.
3
9
◦
Dresden at (23 ± 0.1) C. The spectra were excited with the
4
+
87.98 nm of an Ar laser at power levels ~1200 mW. After passing
Raman and infrared spectroscopic techniques are well suited
for studying the structural aspect of the species present as well
as allowing quantification of the first dissociation step. In recent
the Zeiss double monochromator GDM 1000, with gratings
of 1300 grooves/mm, the scattered light was detected with a
cooled photo multiplier tube ITT 130 in the photon counting
mode. A scrambler in front of the slit served to compensate for
grating preference. IVV and IVH spectra were obtained with fixed
polarisation of the laser beam by changing the polarisation filter
9–12
publications from our laboratory
the structure, vibrational
spectra and dissociation of aqueous phosphoric acid solutions
at room temperature have been partially reported. From these
studies it became clear that the phosphoric acid is quite strongly
hydrated. Due to the strong hydration the characteristic modes of
(Bernotar foil) in the parallel and perpendicular arrangement
between the sample and the entrance slit to give the scattering
geometries:
the P O group and the P(OH)
3
group are influenced resulting
in a shift of the characteristic modes compared to the ones in
H
3
PO
4
systems in non-polar solvents. It could be shown that the
¢2
¢2
I
VV = I(Y[ZZ]X) = 45a + 4g
(3)
(4)
-
overlap with the modes of H
phosphoric acid caused many erroneous interpretations of both
the vibrational spectrum and the definition of the symmetry of
2
PO
4
(aq), the dissociation product of
¢
2
I
VH = I(Y[ZY]X) = 3g
the PO
4
unit (cf. e.g. ref.[11]). The present investigation builds not
The isotropic spectrum, Iiso or I was then constructed:
a
only on earlier results but also provides vibrational data on dilute
aqueous solutions of phosphoric acid. In addition deuterated
phosphoric acid was studied. In order to study the hydration on
I
iso = IVV - 4/3·IVH
(5)
The depolarization ratio, r, of the modes has been determined
H
3
PO in aqueous solution concentrations were measured to very
4
according to eqn (6):
dilute solutions and also as function of temperature. Quantitative
measurements have also been carried out to determine the first
dissociation constant as a function of dilution, of added neutral
salt and change in temperature.
¢
2
¢2
¢2
r = IVH/IVV = 3g /(45a + 4g )
(6)
The polarization analyser has been calibrated with CCl
each measuring cycle and adjusted if necessary. The depolarisation
4
before
-
1
ratio of the n
1
mode of CCl
4
at 459 cm has been measured 15 times
2
. Experimental section
and a depolarization ratio equal to 0.0036 ± 0.0005 determined.
-
1
The depolarization ratio of the CCl
4
modes at 217 and 315 cm
Commercial phosphoric acid contains traces of fluorescing sub-
stances and therefore the phosphoric acid has been prepared
(these modes are depolarised according to the theory) have been
determined to 0.75 ± 0.02.
A second set of Raman spectra were measured in the macro
with sublimated P
spectra. The P 10 has been sublimated in a home built sublimation
apparatus and then the P 10 converted with ultrapure water
PureLab Plus, Ultra-pure Water Purification Systems) in a
moisturizing apparatus according to reaction (2):
4
O10 in order to achieve high quality Raman
4
O
chamber of the T 64000 Raman spectrometer from Jobin Yvon
4
O
◦
◦
in a 90 scattering geometry at (23 ± 0.1) C. The spectra were
(
+
excited with the 487.98 nm line of an Ar laser at a power level
of ~ 1100 mW at the sample. After passing the spectrometer in
subtractive mode, with gratings of 1800 grooves/mm, the scattered
light was detected with a cooled CCD detector. A more detailed
description of the Raman measurements is given in ref.40
1
/2P O ꢀ 2H PO
4
O
10 + 3H
2
3
4
(2)
The stock solution was filtered through a G5 sintered-glass
frit (Schott & Genossen, Jena) under CO free atmosphere. A
stock solution was prepared with a concentration of 1.450 mol L
2
-
1
Quantitative Raman measurements
-
3
◦
-1
(
r = 1.0713 g cm at 23 C) equal to 1.5604 mol kg . The lower
concentrated H PO solutions were prepared with ultrapure water
free of CO by weight. A D
3
4
Quantitative Raman measurements have been carried out to deter-
mine the first dissociation constant of phosphoric acid according
-
1
2
3
PO
4
stock solution, 1.430 mol L
1.1712 g cm- at 23 C) equal to 1.390 mol kg has been
3
◦
-1
to an external quantification method previously described Ra-
11
(
3
9
prepared according to the above described procedure but using
O (Merck Chemicals, 99.9% D) instead of water. The lower
concentrated D PO solutions were prepared with D O by weight.
For further details on the preparation of H PO and D PO cf. ref.
11,12].
The phosphate content of the stock solution was determined
man spectra were measured with equipment at the TU Dresden
◦
D
2
at (23 ± 0.1) C and ~ 1.5 mL solutions have been measured in
3.5 mL quartz cuvette with a tightly fitted Teflon stopper from
Hellma, M u¨ llheim/Baden, Germany (path length 10 mm). The
3
4
2
3
4
3
4
+
[
spectra were excited with the 487.98 nm of an Ar laser at power
levels ~ 1200 mW at the sample and only the IVV scattering has
38
by gravimetry. The solution densities were determined with a
pycnometer of 5.000 mL volume at (23 ± 0.1) C.
been recorded. The stability of the apparatus has been checked,
◦
2-
including the laser power, by measuring the n
1
mode of SO
4
of a
-
1
NaH
2
PO
4
and KH
2
PO
4
solutions have been prepared with
0.740 mol L K
2
SO solution during the measuring cycle of ~1.5 h.
4
ultrapure water free of CO
2
by weight. The solution densities
The variation of the integrated band intensity of the external
This journal is © The Royal Society of Chemistry 2010
Dalton Trans., 2010, 39, 9642–9653 | 9643

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2
-
at 981 cm-1 was better than ± 1% during
PO
-] it follows:
reference mode n
1
SO
4
After rearranging eqn (8) for [H
2
4
-
a measuring cycle. The analytical band of H
2
PO
4
(aq) the mode
-
1
-
4
A1077 ⋅J1178
at 1077 cm , n
s
PO
2
has been chosen because it is the strongest
⎡
⎤
H PO
=
⎥
⎦
(9)
⎢
2
⎣
-
A1178 ⋅J1077
Raman mode of H
2
PO
4
(aq), and furthermore this mode does
PO (aq) and were integrated after
subtracting a synthetic baseline in the wavenumber limits from
not overlap with modes of H
3
4
In the IVV scattering the H
3
PO band at 1178 has a slight inten-
4
-
1
sity contribution from the band at 1160 cm of the dissociation
-
1
1
025–1128 cm . Great care was taken to measure high quality
spectra. The signal to noise ratio (S/N ratio) of the spectra of
PO solution has been determined to ~940.
The S/N ratio for the lower concentrated solutions dropped and
for a solution 0.0124 mol kg a value of ~180 has been reached.
solutions (0.00696–0.870 mol kg ) have been
measured in the wavenumber range from 780–1280 cm and 12
-
product H
2
PO
4
, namely nasPO
PO
2
(cf. ref. [11]). The band nasPO
2
is of
much lower intensity than n
s
2
and the intensity ratio J1077/J1160 =
a 0.183 mol kg-
1
H
3
4
3
4/1 and the corrected band intensity, A1178 may be expressed as
*
follows: A1178 = A 1178 - 0.029·A1077 and substituting this expression
-
1
into eqn (9) it follows:
-
1
Twelve NaH
2
PO
4
-
1
A1077 ⋅J1178
1178- 0.029⋅A1077 ) ⋅J1077
−
4
⎡
⎤
=
-
1
H
2
PO
(10)
solutions of H
3
PO
4
(aq) (0.00873–0.2515 mol kg ). The measuring
PO solution,
solution and so
forth. Two independent measuring series have been carried out
for the NaH PO - and H PO - solutions. The integrated band
⎣⎢
⎦⎥
*
(A
cycle was as follows: first, measurement of the H
3
4
2
-
second, the SO
4
(aq) and then the NaH
2
PO
4
with A*1178 as the uncorrected integrated band intensity of the
-
1
-
mode at 1178 cm . With the equilibrium concentration of H
on hand and m , the stoichiometric solute concentration known,
the hydrolysis degree, a in H PO (aq) is defined as:
2
PO
4
2
4
3
4
T
intensity, A1077 as a function of concentration has been determined
3
4
and from this calibration curve the equilibrium concentration of
a = [H
-]/m
PO
(11)
-
-
2
4
T
H
2
PO
1077 = 63.0297·mH2PO4-; R = 0.9996). An identical procedure has
been employed for NaD PO - and D PO solutions (0.00644–
.5293 mol kg ). The integrated band intensity, A1084 as a
4
, [H
2
PO
4
] determined in the phosphoric acid solutions
2
-
(
A
and it follows therefore [H PO ] = a·m .
2
4
T
2
4
3
4
-
1
0
FT-IR- measurements
-
1
function of NaD
2
PO concentration (0.00505–0.0505 mol kg ;
4
Infrared (IR) solution spectra were measured between 400–
4000 cm with a FTIR spectrometer described in refs. [11,40]
between KBr disks protected with a thin (20 mm) polyethylene
PE) film. The thin PE-film protects the KBr windows and is easily
1
D
1 solutions) was plotted and from this linear calibration curve of
-
1
-
-
2
2
PO
4
, [D
2
PO
4
] has been determined (A1084 = 77.6237·mD2PO4-;
R = 0.9990). (The equilibrium species concentration i is denoted
as [i].)
(
subtracted from the measured spectrum.
The Raman temperature measurements have been carried out in
a home built Raman oven similar to the one described in ref. [41].
Density Fuctional Theory calculations
The H
3
PO solutions have been sealed in quartz tubes and only
4
the IVV-scattering has been measured. The quantification has been
The optimization of the molecular geometry and the calculation of
the vibrational spectra was performed with the Density Functional
carried out according to a previously described external reference
1
1,12
-1
-1
method.
Briefly, for a 0.2515 mol kg (0.248 mol L ) H
PO and H
3
PO
4
-
Theory (DFT) method B3LYP using the basis set B3LYP 6-
solution, the equilibrium concentration of H
3
4
2
PO
4
52
3
11+G(3d,f) using Gaussian 03. The optimization procedure led
were obtained from the ratios of the integrated band areas of
to a stable configuration with C
frequencies appeared. Calculations have been carried out on the
single H PO molecule in vacuo and in the presence of the solvent
water) by placing H PO within the solvent reaction field. The
3
symmetry and no imaginary
-
1
-1
the 1178 cm mode of H
3
PO
4
(nP O) and the 1077 cm mode
-
-1
of H
2
PO
4
(n
s
PO
2
). The J - value of the band at 1077 cm
3
4
-
of the species H
2
PO
4
has been determined for three NaH
2
PO
4
(
3
4
solutions with known amounts of perchlorate as internal standard
Polarized Continuum Model (PCM) creates the solute cavity via
a set of interlocking spheres centred on the atoms, and uses
a numerical representation of the polarization of the solvent
-
1
(
NaClO
has been determined in three H
HCl (suppression of dissociation) and ClO
NaClO has been used as internal standard substance in both
4
). Similarly, the J - value of the band at 1178 cm of H
3
PO
4
3
PO solutions with additional
4
-
4
as internal standard.
(ref. 53).
4
cases. The relative molar scattering factors for these modes, J1178
3
. Results and discussions
and J1077 are equal to 0.340 and 1.000 respectively. The sum of the
-
equilibrium concentrations [H
the stoichiometric concentration of H
3
PO
4
] and [H
2
PO
4
] is equal to m ,
T
3.1. Raman and infrared spectra of dilute H
3
PO
4
and D
3
PO
4
-
1
3
PO
4
(in mol kg ):
In the gas phase the H
according to DFT calculations and a detailed account of the
3
PO
4
molecule possesses C symmetry
3
m
T
= [H
3
PO
4
] + [H
2
PO
4
-]
(7)
PO
42
data will be presented in a forthcoming paper. The wavenumber
positions for the H PO molecule in vacuo are presented in Table 1
and for H PO with an explicit solvation shell (hydration shell)
in Table 2. The geometry parameters of the H PO in vacuo and
PO with solvation, H PO (aq), are presented in Table 3 and in
Furthermore, the integrated band intensities for the H
3
4
mode at 1178 cm- and the H
expressed as follows: A1178 = J1178 [H
1
PO
PO
-
mode at 1077 cm can be
-1
3
4
2
4
-
3
4
3
4
] and A1077 = J1077 [H
2
PO
4
].
3
4
The ratio of the integrated intensities, A1077/A1178 was calculated:
H
3
4
3
4
Figure S1† the structure and the numbering of the atoms is given.
These DFT results will be discussed after the discussion of the
measured vibrational data.
-
4
A1077
[H PO ]⋅J
2
1077
1078
=
(8)
A1078 [H PO ]⋅J
2
4
9
644 | Dalton Trans., 2010, 39, 9642–9653
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3 4
Table 1 DFT Raman and infrared data for H PO in the gas phase
Raman
Depol.
n˜ max/cm- Intensity degree Character Intensity IR Normal modes
1
1
3
3
4
4
8
9
1
1
1
3
3
57.9
10.4
76.1
54.2
58.4
39.4
19.8
053.9
064.1
318.4
821.7
824.0
1.3
0.2
0.8
0.8
1.8
21.1
1.4
1.6
1.3
0.75
0.02
0.75
0.60
0.75
0
0.75
0.75
0.75
0.11
0.75
0.05
e
a
e
a
e
a
e
a
e
a
e
a
69.0
87.7
42.0
14.5
64.5
19.7
335.1
93.7
54.6
316.4
173.2
21.3
rOH
rOH
rOH + dOPO
d
d
n
n
s
OPO
asOPO
s
P(OH)
asP(OH)
3
3
dPOH
dPOH
9.7
34.6
126.3
nP
n
n
O
asOH
s
OH
3 4
Table 2 DFT Raman and infrared data for H PO with solvation shell
Fig. 1 Upper panel: Raman spectrum (IVV and IVH scattering) of a
0.183 mol kg- (0.181 mol L ) H
1
-1
PO
(aq). The modes of H
PO
(aq)
at
Raman
3
4
3
4
-1
in the P–O stretching region are: n
s
P(OH)
3
at 890 cm , nasP(OH)
3
Depol.
-1
-1
1
008 cm (very weak), and nP O at 1178 cm . The very weak, broad
mode dPO–H at 1250 cm is almost not visible in the Raman effect. Lower
n˜ max/cm- Intensity degree Character IR Intensity Normal modes
1
-
1
-1
-1
2 4
panel: Raman spectrum of a 0.112 mol kg (0.111 mol L ) NaH PO
175.1
322.3
363.9
452.1
459.2
849.8
898.0
993.4
1026.3
1245.8
3274.3
3293.5
1.9
0.1
1.6
3.6
1.8
40.9
2.1
2.1
2.6
0.75
0.02
0.75
0.75
0.65
0
0.75
0.71
0.75
0.11
0.75
0.04
e
a
e
e
a
a
e
a
e
a
e
a
166.5
237.0
71.5
107.2
20.6
rOH
◦
-
rOH
solution at 23 C. The modes of H
2
PO
4
(aq) in the P–O stretching region
-
1
-1
rOH + dOPO
are : n
1
s
P(OH)
2
at 877 cm , nasP(OH)
2
at 942 cm (very weak), n
s
PO
2
at
d
d
n
n
asOPO
-1
-1
077 cm , and nasPO
2
at 1160 cm (very weak).
s
OPO
32.9
s
P(OH)
3
-1
the O PO
3
unit occur below 550 cm and the P–O stretching
506.9
234.2
92.0
526.8
726.0
77.3
asP(OH)
3
dPOH
-
1
modes above 750 cm . In the older literature the PO group of
4
dPOH
phosphoric acid has been assigned to contradicting point groups
21.9
60.7
338.9
nP
O
4
6
8
such as T
d
, C2v and also C3v
n
n
asOH
Before a more detailed analysis of individual H
discussed, it is instructive to compare the H PO
of a 0.183 mol kg (0.181 mol L ) solution with a spectrum
3
PO
4
bands are
s
OH
3
4
(aq) spectrum
-
1
-1
Table 3 Geometrical parameters for H
solvation sphere (symmetry C
3
PO
4
in gas phase and with
-
1
-1
of 0.112 mol kg (0.111 mol L ) NaH
2
PO solution (Fig. 1).
4
3
)
From this comparison it is obvious that with the exception of
-
1
Molecule with
solvation shell
the very weak mode at 1008 cm , all other modes in the P–O
Parameter
Molecule in gas phase
-1
stretching region of the spectrum (800–1400 cm ) are more or less
-
overlapped with the modes of H
2
PO
4
(aq). The spectral data for
a
a
a
12; P O b. length
13; P–O b. length
56; O–H b. length
156; angle P–O–H
315; angle O–P–O
215; angle O P–O
1.463
1.590
0.964
112.5
102.0
1.474
1.582
0.989
113.7
102.6
-
1
-
a 0.112 mol kg
H
2
PO (aq) are given in Table 4 and in Fig. 1,
4
lower panel, where only the P–O stretching modes are presented.
From this comparison it becomes clear that the band at
◦
◦
a
a
a
◦
◦
-
1
◦
◦
1077 cm in the H PO (aq) spectrum has to be assigned to n PO
3
4
s
2
116.2
115.7
◦
◦
-
d
2138; dihedral angle
33.5
39.3
of H
2
PO (aq) the dissociation product according to reaction (1).
4
W (a.u.)
-644.33557540
-644.37647586
Table 4 Raman data of the PO
4
modes of H
2
PO -
4
(aq) in dilute NaH
2
PO
4
◦
solutions at 23 C
The PO
4
unit of the molecule of the isolated H
3
PO molecule
4
possesses C3v symmetry considering the OH groups as point
masses. In solution, such an assumption seems reasonable because
the normal modes of PO–H such as nOH, dPO–H, and g PO–H are
1
n
max/cm- Intensity fwhh cm-1 Depolarization degree Assignment
371*
2
3
45
60
54
19.5
26
20
26
40
0.75
0.75
0.60
0.007
0.75
0.038
0.75
0.10
r, t, wO P(OH)2
2
3
5
8
9
93*
15*
77
mostly decoupled from the O PO
skeleton has 5 atoms which corresponds to 9 normal modes
n.m.). The irreducible representation of the vibrational modes
is as follows: Cvib(C3v) = 3a (Ra, i.r.) + 3e(Ra, i.r.). All the modes
with the character a , and e are Raman active and infrared allowed.
The modes with the character a are: n (a ) = n P(OH) , n (a ) =
nP O and n (a ) = d P(OH) . These modes are polarized in the
Raman effect. The modes n (e) = nasP(OH) , n (e) = dasP(OH)
and n (e) = rOP(OH) have the character e and are expected to
3
skeleton modes. The O PO
3
3.5
100
2.94
89.1
2.63
0.5
dP(OH)
2
+ dPO
2
n
n
n
n
s
P(OH)
asP(OH)
PO
2
(
42
2
1077
s
2
1
1
1
160
240
asPO
2
1
+
dPO–H
1
1
s
3
2
1
*For the C2V symmetry of the *O
modes are expected; broad double band, depolarized and the broad
polarized deformation mode constitute accidental overlapped bands. This
very weak broad mode is not observable in dilute solutions
2
PO
2
skeleton modes 5 deformation
3
1
s
3
4
3
5
3
,
+
6
3
be depolarized in the Raman effect. The deformation modes of
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(
This mode is also used for analytical purposes; see experimental
-
section.) The other strong band in H
2
PO
4
(aq) spectrum at
77 cm- assigned to n
of the phosphoric acid at 890 cm . The influence of H
on the spectrum of H PO (aq) has already been established. It
had been found that the successive addition of HCl suppresses the
1
P(OH) overlaps strongly with the mode
8
s
2
-
1
-
2
PO (aq)
4
11
3
4
-
1
-1
band at 1077 cm . In a spectrum of a 0.310 mol L
solution with 1.44 mol L HCl added the mode at 1077 cm
H
3
PO
4
(aq)
-
1
-1
had almost completely disappeared and furthermore, the mode at
1
8
90 cm- becomes symmetrical (see Fig. 1 ref. [11]). The intensity
-
-1
contribution of the H
PO (aq) at 890 cm overlap almost completely and cannot
be separated in a meaningful way. The term “890 cm band has
been coined and may express this situation. The peak position
n˜ max) and the full width at half height (fwhh) of the “890 cm
sum) band are presented in Fig. 2. The distinct concentration
2
PO
4
(aq) mode at 877 cm and n
s
P(OH)
3
-
1
of H
3
4
-
1”
8
-
1”
(
(
dependence of n˜ max and of the fwhh are clearly due to the
dissociation of H PO (aq) which is a function of dilution. For
a meaningful band separation of these severely overlapped bands
3
4
Fig. 3 Isotropic Raman spectra of 3 dilute phosphoric acid solutions.
-
1
From the isotropic spectrum Iiso(H
3 4
PO ) the background spectrum
(
877 and 890 cm ) additional information would be necessary. The
I
iso(H
2
O) has been subtracted. Given are the measured, background
-
-1
intensity of the H
2
PO
4
(aq) mode, n
s
PO at 1077 cm however,
2
-1
corrected spectra, the two band components at 877 and 890 cm and
the sum curve (from bottom to top: 0.00873, 0.0613, and 0.183 mol kg )
at 23 C.
does not overlap with any of the bands of phosphoric acid.
-1
From its known intensity and under consideration of the J-
◦
-
values for the H
2
PO
4
(aq) bands, the band intensity of the mode
J
1
077
at 877 cm- may be calculated:
1
.
A877
=
⋅A1077 =1.122⋅A1077
J877
Representative spectra of dilute phosphoric acid solutions together
with the result of the band fit and the component bands at 877
and 890 cm- are presented in Fig. 3.
1
Fig. 4 The relative integrated band intensity, A
i
of the H
3
PO
4
mode
PO at
-1
-
nP O at 1178 cm (filled squares) and the mode of H
2
PO
4
, n
s
2
1
1
077 cm- (open squares) versus the stoichiometric H
3
PO
4
concentration
◦
at 23 C.
1
160 cm- which is of very weak band intensity. Nevertheless,
1
-
1
band intensity correction for nP O at 1178 cm (H
3
PO
4
) has to
Fig. 2 Position of the band maximum, nmax (upper panel) and fwhh
be taken into account (see experimental section).
-1
-
(
lower panel) of the “890 cm - band” versus the stoichiometric H
3
PO
4
In D PO (aq) solutions, the dissociation product D PO (D O)
3
4
2
4
2
◦
concentration at 23 C.
-1
is detectable by the mode n
s
PO
2
(D O) which occurs at 1084 cm .
2
As mentioned, the spectral features of the dissociation product
-
-
Furthermore, the integrated band intensities, A
i
of the mode
H
2
PO
ref. 6,14). The vibrational spectra of H
T
analog in fairly dilute phosphoric acid solution are discussed (m <
4
/D
2
PO
4
have led to confusion in the older literature (cf.
-
1
-
-1
nP O for [H
3
PO
4
] at 1178 cm and for [H
2
PO
4
] at 1077 cm
3
PO and its deuterated
4
versus the stoichiometric phosphoric acid concentration is pre-
-
1
-1
9–12
sented in Fig. 4. The A
i
-value of the mode at 1178 cm of
1.10 mol kg ) because in concentrated solutions,
the bands
the equilibrium concentration of H
3
PO
4
, [H
3
PO
4
], rises steadily
shift and broaden considerably and coalesce. The phosphoric acid
molecules occur in these concentrated solutions as associated
-
while A
i
for [H
2
PO
4
] levels off. This behaviour is an expression
8–12
of the decreasing dissociation degree a of the phosphoric acid
with increasing concentration. The band intensity of the nP
is completely overlapped with a mode of H
species.
0.01 mol kg ) the bands of the dissociation product H
dominate the spectrum of H PO (aq).
T
On the other hand, in very dilute solutions (m <
-
1
PO
-(aq)
O
2
4
-
2
PO
4
(aq), nasPO
2
at
3
4
9
646 | Dalton Trans., 2010, 39, 9642–9653
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◦
4 3 4
Table 5 Raman data of the PO modes of H PO (aq) at 23 C
max/cm- Intensity fwhh cm-1 Depolarization degree Assignment
1
n
3
3
4
8
1
1
1
57
94.5
99
90.1
008
178
255
1.3
3.4
9.3
100
0.9
22.5
2
45
60
54
19.5
18
53
40
0.75
0.75
0.65
0.005
0.75
0.095
0.12
rO P(OH)
3
d
d
n
n
asP(OH)
3
s
P(OH)
P(OH)
asP(OH)
3
s
3
3
nP
O
dPO–H
◦
3 4
Table 6 Raman data of the modes in dilute D PO solutions at 23 C
max/cm- Intensity fwhh cm-1 Depolarization degree Assignment
1
n
3
3
4
8
9
1
1
64
74
94
70
35
018
194
1
3
9.2
100
2.5
0.9
20
44
58
52
17.5
~34
18
0.75
0.75
0.62
0.006
0.14
0.75
0.095
rO P(OD)
3
d
d
n
asP(OD)
3
s
P(OD)
P(OD)
3
s
3
dPO–D
Fig. 6 Infrared (top) and Raman spectrum (IVV and IVH scattering) of a
n
asP(OD)
3
.560 mol kg- (1.450 mol L ) H
1
-1
◦
1
3 4
PO solution at 23 C.
50
nP
O
With the knowledge of the H
spectrum of H PO (aq) a detailed discussion of the spectrum of
phosphoric acid is given. An overview Raman spectrum (100–
2
PO
-(aq) influence on the
4
3
4
-
1
-1
-1
1
400 cm ) of a 0.756 mol kg (0.728 mol L ) H
shown in Fig. 5 and the spectroscopic results for H
summarized in Table 5 and for D PO (D O) in Table 6. The Raman
and infrared spectra in the P–O stretching region (700–1400 cm )
3
PO
4
solution is
3
PO
4
(aq) are
3
4
2
-
1
of a 1.560 mol kg- (1.450 mol L ) H
and for a 1.393 mol kg (1.430 mol L ) D PO (D O) in Fig. 7.
1
-1
PO
(aq) are given in Fig. 6
3
-1
4
-
1
3
4
2
Fig. 7 Infrared (top) and Raman spectrum (IVV and IVH scattering) of a
.393 mol kg-
1
D
PO
◦
1
3
4
solution at 23 C.
O) these modes occur at 364, 374 and 494 cm- (see
1
In D
3
PO
4
(D
2
Table 6).
-
1
Fig. 5 Raman spectrum of a 0.756 mol kg- (0.728 mol L ) H
2
panel: IVV and IVH scattering; the inset shows the deformation modes at an
expanded scale. Lower panel: isotropic spectrum.
1
-1
The P–O stretching mode at 890 cm is the band with the highest
intensity in the Raman spectrum and is also strongly polarized.
This mode is assigned to the symmetrical stretching mode of the
3 4
PO
at
C. The arrow indicates the mode at 1077 cm-1 of H
3 PO . Upper
2 4
◦
-
-
1
P(OH) group, n P(OH) . The mode at 1008 cm is of much lower
3
s
3
intensity than n
s
P(OH)
3
. The mode is depolarized and assigned to
In the overview Raman spectrum of H
band regions become visible, the deformation region and the P–O
stretching region. The deformation modes in H PO (aq) show an
3
PO
4
(aq) (Fig. 5) two
the antisymmetic stretch of the the P(OH)
intensity ratio A890/A1008 for the modes n
is ~ 110 : 1. In the infrared absorption spectrum the intensity ratio
890/A1008 reverses to that in the Raman effect because n P(OH)
is very weak and nasP(OH) is of strong intensity (see Fig. 6).
The nP O mode in H PO (aq) should be observed analogous
to comparable phosphoryl compounds OPX (X = Cl, Br, OR
3
group, nasP(OH)
3
. The
s
P(OH) and nasP(OH)
3
3
3
4
accidental overlap so that only two instead of three modes are to
be observed: a depolarized double mode, very poorly resolved with
A
s
3
3
-
1
maxima at 357 and 395 and a polarized mode at 499 cm . The
deformation modes are of low intensities (see Table 5 and Fig. 5).
3
4
3
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Table 7 Raman band parameters (IVV scattering) of a 0.252 mol kg- (0.248 mol L ) H
1
-1
PO
3
4
s 3
as a function of temperature: nP O, n P(OH) and the
band of the dissociation product H
2
PO -
4
H
3
PO
4
(nP O)
H
3
PO
4
(n
s
P(OH)
3
)
H
2
PO -
4
s 2
(n PO )
◦
max/cm-1
fwhh cm-1
max/cm-1
fwhh cm-1
n
max/cm-1
fwhh cm-1
T/ C
n
n
2
3
4
5
6
8
9
4.5
2.0
3.0
7.0
9.5
2.5
9.7
1178
1178
1182
1185.5
1186
1191
1193
53.5
54.0
55.0
58.0
59.5
62.0
64.0
891.2
890.5
888.5
888.0
887.0
886.5
885.5
19.5
19.5
19.3
19.3
19.3
19.5
19.8
1077.6
1077.8
1078
1078.5
1079
1080
1081
21.5
22.0
22.5
23.2
23.5
24.0
24.5
with R alkyl and aryl) between 1200–1400 cm-1 (e.g. ref. 43). The
precise peak position depends on the group X inasmuch as X with
increasing electronegativity shifts nP O to higher wavenumbers.
(nO–H) should be down shifted. However, in the dilute solutions
studied the broad and weak nOH mode is completely overlapped
with the OH stretching mode of water and shall therefore not be
discussed in this context (see footnote 1).
In liquid trimethyl ester of the phosphoric acid, OP(OCH
3
3
) ,
-
1
nP O occurs at ~1270 cm . This value should certainly be ex-
In aprotic, polar organic solvents such as acetronitrile, acetone,
pected for phosphoric acid as well. However, in dilute solutions of
tetrahydrofurane and dioxane) in which crystalline H
3
PO
4
is at
-
1
-1
H
3
PO
4
(aq) nP O occurs at 1178 cm as a relatively broad band of
least sparingly soluble the mode nP O occurs at 1240 cm in the
45
medium intensity but as a strong band in the infrared. The nP
O
infrared absorption spectrum. In aprotic solvents the acceptor
group P O cannot form H-bonds unless the solution is fairly
concentrated and therefore the wavenumber position for P O is
-
1
mode at ~1194 cm in D
3
PO
4
(D
2
O) is overlapped with the broad
-
1
deformation mode dDOD of the solvent D O at 1208 cm . From
2
the PO–H bands‡, mentioned above, the in-plane-deformation
similar to the one for the trimethylester. (In concentrated H
3
PO
4
mode of the PO–H group, dPO–H is of very weak intensity and
broad in the Raman effect and appears at 1250 cm . Although
solutions auto-association may occur; a formation of H-bonded
phosphoric acid molecules).
-
1
broad it is of medium intensity in the infrared spectrum (see
The DFT data (see Tables 1 and 2) reinforce the interpretation of
Fig. 6). In the spectrum of D
shifts to considerably lower wavenumbers due to the isotope shift:
3
PO
4
(D
2
O) the deformation mode
the presented vibrational data in going from the H
in vacuo to H PO (aq). The mode nP O shifts from 1384.4 cm
down to 1245.8 cm . Furthermore, the mode n P(OH) shifts
from 839.4 cm up to 849.8 cm . This tendency found by the
DFT calculations has been observed by vibrational spectroscopy.
Even if the static model applied by the calculations does not
reproduce the measured band positions precisely, the trend of the
modes depicts the situation of the measured spectral data correctly.
3
PO molecule
4
-
1
3
4
-
1
n(D)
n(H)
2.014
1.008
s
3
=
=
1.998 =1.414 and appears as a weak broad
-1
-1
mode at 935 cm-1 (Fig. 7). The factor of the isotope effect 1.344 is
smaller than the theoretically expected value but in the usual range
for such an isotope effect (anharmonicity of the modes). The above
mentioned n
s
P(OH) mode also shows an isotope effect but much
3
The geometric parameters of H
3
PO
4
(vacuo) and H
3
PO (aq) is
4
nP(OD)
18.0135
more moderately:
=
=
1.0592 =1.029 . In
presented in Table 3. The phosphoryl bond P O is much shorter
than the three single P–O bonds. Furthermore, the P O bond
nP(OH)
17.007
P(OD)
occurs at 870 cm- and the observed
1
D
3
PO
4
(D
2
O) n
s
3
lengthens slightly in going from H
whilest the P–O bond shortens slightly. At least in dilute solutions
the PO unit cannot be considered as a tetrahedral unit as has been
3
PO
4
(vacuo) to H
3
PO
4
(aq)
isotope shift is 1.023, again a little smaller than the theoretical
one.
The considerable wavenumber shift of the P O stretching
4
done in ref.34
mode in H
3
1
PO
4
(aq) compared with nP O for neat OP(OCH
3
)
3
at
In order to study the hydration in phosphoric acid solution in
the Raman effect it would be helpful to study the phosphoric acid
-
~
1270 cm is caused by strong H-bonds of the type P O ◊ ◊ ◊ HOH
formed in aqueous solutions of phosphoric acid. The P–OH
groups are also H-bonded with water molecules of the type P–
in apolar organic solvents such as CCl
4
or to study the temperature
effect on the modes of H PO (aq). Unfortunately, phosphoric acid
3
4
OH ◊ ◊ ◊ OH although the H-bond strength is somewhat weaker
2
is almost insoluble in this apolar solvent (cf. ref.45) and therefore
a temperature dependent Raman study has been applied.
In Table 7 the results of the temperature dependent Raman
44
compared to the ones between P O and water. As a result
of the H-bond formation the protons are somewhat weakened
and the stretching mode n
s
P–(OH)
3
shows noticeably p-bonding
-1
-1
spectra of a 0.251 mol kg (0.248 mol L ) phosphoric acid are
contributions. Therefore, higher stretching peak positions are
observed as normally considered with the normal P–O single
bonds. Due to the H-bonds formed the PO–H stretching mode
◦
presented (mol-ratio H
1
3
PO
4
-1
: H
2
O = 1 : 224). At 25 C nP O at
-1
178 cm (fwhh = 53 cm ) shifts with temperature to higher
◦
wavenumbers and broadens. At 99.7 C nP O is located at
193 cm (fwhh = 64 cm ). The symmetric stretching mode
, located at 25 C at 891 cm shifts slightly to
lower wavenumbers and at 99.7 C this mode is positioned at
-
1
-1
1
n
◦
-1
s
P(OH)
3
‡
The g PO–H mode, the out of plane deformation, is only observable in
-1
◦
the hydrate melt and the most concentrated solution at ~815 cm , the
nPO–H mode is detectable in concentrated solutions as a broad mode at
-1
8
86 cm . The antisymetric stretching mode of the P(OH)
3
group,
-1
-1
~
2880 cm the so called A band. A broad mode at 2350 cm is assigned
-1
n
asP(OH)
3
is much weaker compared with n
s
P(OH)
3
(intensity
to 2 x dPO–H, the B band and a much weaker one at 1700 cm , to 2 x
g PO–H as C band.
-
1
ratio n
s
P(OH) : nasP(OH) = 100 : 0.9) and is located at 1008 cm .
3
3
9
648 | Dalton Trans., 2010, 39, 9642–9653
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These results show that the P O group (H-bond acceptor) forms
strong H-Bonds with water and the temperature increase weakens
the H-bonds between the P O group and water and as a result
a weakening of the H-bond, P O ◊ ◊ ◊ HOH follows. Therefore,
the temperature increase resulting in a shift of nP O to higher
Quantifications in D
3
PO
4
solutions have been carried out using
-
1
-
the mode at 1084 cm of D
equilibrium concentrations of H
and D PO (D
2
PO
4
(D
2
O). To that purpose the
-
-
2
PO
4
and D
2
PO
4
in H
3
PO (aq)
4
3
4
2
O) respectively have been determined using the
calibration curves expressed in the experimental section.
Quantitative Raman spectroscopy allows one to calculate the
wavelength and a shift of n
s
P(OH)
3
to lower wavenumbers may be
explained and demonstrates the hydration of the phosphoric acid
first dissociation step of H
3
PO
4
(aq) and D
3
PO
4
(D O) according
2
in aqueous solution.
to eqn (1). The equilibrium constant K
1
for this reaction may be
In this context it may be mentioned that it is necessary to
study dilute solutions of phosphoric acid because with higher
defined as:
+
-
4
gH
⋅ gH
+
-
[
H O ]⋅[H PO ]
O
PO
4
phosphoric acid concentrations auto- association between H
molecules has been observed and a dimeric phosphoric acid,
(cf. ref. 20,21,28) has been proposed. However, as a result
3
PO
4
3
2
3
2
K =
⋅
= Q ⋅Q
g
(12)
1
1
[H
PO
]
g
3
4
H PO
3 4
H
6
P
2
O
8
◦
23
with the equilibrium concentrations for the species i denoted as
i] and g the activity coefficients of the species. The activity of
PO (aq) in the dilute solutions is taken as 1 and for K
of a carefully conducted study in 3 M NaC1O
was shown that at concentrations up to 0.02 m H
4
at 25
PO
C
it
[
i
3
4
it was
H
3
4
1
it follows:
(13)
unnecessary to invoke the existence of any species other than the
mononuclear phosphate species. In the dilute phosphoric acids no
spectroscopic evidence could be detected for the so called dimer,
+
-
4
[
H O ]⋅[H PO ]
3
2
2
±
K =
⋅ g
1
[
H PO ]
3
4
H
6
P
2
O
8
. At higher H
between H PO molecules are observable but no specific dimeric
structure could be detected rather a three dimensional network
3
PO concentrations however, interactions
4
3
4
or taking the dissociation degree into account:
2
9–11
a ⋅mT
2
±
of H-bonded phosphoric acid molecules.
The concentration
K =
⋅ g
(14)
1
1
- a
The quantitative results for dilute H
are given in Tables 8 and 9 and pQ
plotted in Fig. 9 as a function of the square root of the ionic
strength. This procedure is only meaningful for dilute solutions
and therefore only the most dilute solution data have been applied.
range of the existence of phosphoric acid molecules associated
with each other, so called auto-association depends on the water
activity and in phosphoric acid solutions with concentrations
3
PO
4
and D
3
PO
4
solutions
1
defined as - log10
Q
1
-
1
higher than ~1 mol L the association effect begins. In the hydrate
melt, H PO (l), phosphoric acid molecules are strongly hydrogen
bonded with each other forming a 3-dimensinal network of small
3
4
9–11
clusters which may be compared to the situation in crystalline
phosphoric acid where the structure reveals strong H-bonds
Extrapolation to zero concentration results in pK
PO (aq) and D PO (D O) at 2.14(1) and 2.42(1) respectively
at 23 C. A compilation of selected experimental constants for the
1
values for
H
3
4
◦
3
4
2
46
between the phosphoric acid molecules in the monoclinic crystal.
Table 8 Raman data on the dissociation of H
3
4
PO as a function of
3
D
.2. Quantitative Raman measurements of dilute H
PO (D O)
3
PO
4
(aq) and
◦
concentration at 23 C
3
4
2
√
kg mol-
1
[H
PO -
]
I
a
pQ
1
◦
m
T
2
4
m
Data at 23 C. It has been demonstrated that the phosphoric
acid spectra are overlapped with the modes of its corresponding
base, namely H
0
.00873
0.00534
0.00590
0.00695
0.00985
0.01126
0.01785
0.0204
0.0231
0.0278
0.0322
0.0408
0.0498
0.0733
0.0767
0.0832
0.0987
0.1058
0.1334
0.1425
0.1520
0.1667
0.1794
0.2020
0.2229
0.6151
0.5926
0.5567
0.4789
0.4502
0.3573
0.3312
0.3088
0.2784
0.2576
0.2230
0.1977
2.0664
2.0672
2.0609
2.0477
2.0377
2.0046
1.9978
1.9864
1.9697
1.9517
1.9314
1.9121
-
-1
2
PO
4
(aq). The only undisturbed mode at 1077 cm
0.00994
0.0124
0
0
-
of H
2
PO
4
(aq) has been used for quantitative Raman measure-
PO in water and the dissociation
.0204
.0249
ments of the dissociation of H
degree as a function of concentration has been given in Fig. 8.
3
4
0.0498
0
0
0
0
0
0
.0613
.0748
.0999
.125
.183
.252
Table 9 Raman data on the dissociation of D
3
4
PO as a function of
◦
concentration at 23 C
√
kg mol-
1
[D
PO -
]
I
a
pQ
1
m
T
2
4
m
0
0
0
0
0
0
0
0
0
.00644
.0129
.0258
.0516
.0775
.1035
.1295
.2609
.5293
0.003532
0.005719
0.00899
0.01407
0.01809
0.02166
0.02461
0.03810
0.05699
0.0594
0.0756
0.0948
0.1186
0.1345
0.1472
0.1569
0.1952
0.2387
0.5485
0.4434
0.3484
0.2727
0.2334
0.2093
0.1900
0.1460
0.1077
2.3674
2.3415
2.3184
2.2777
2.2590
2.2414
2.2387
2.1861
2.1626
Fig. 8 The dissociation degree, a versus the stoichimetric concentration
◦
of H
3
PO
4
at 23 C.
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Table 10 The influence of NaCl on the degree of dissociation of a
-
1
◦
0
.310 mol L
H
3
3
PO
PO
4
at 23 C. Given are the intensity ratios of the bands
-
1
-1 -
at 1178 cm (H
4
) and 1077 cm (H
2
PO
4
), alpha, the pQ1 values and
the ionic strength
NaCl/mol L-
√
1
A
1178/A1077
a
pQ
1
I
c
0
0
0
1
2
.00
.29
.89
.80
.87
1.545
1.390
1.230
1.122
1.058
0.1804
0.1966
0.2166
0.2326
0.2432
1.9096
1.8264
1.7312
1.6603
1.61576
0.2365
0.5924
0.9783
1.3683
1.7162
49
+
the hydration of the acid. On a microscopic level, the Na (aq)
ion will polarize the phosphoric acid causing the acid strength
to increase. Ion pairs with interposed water molecule(s) such as
+
Na (OH
2
)O P(OH)
–H PO solutions, direct coordination between Al and
phosphoric acid takes places and species such as Al ◊ ◊ ◊ OP(OH)3
3
may be formed. It is interesting to note, that
1
Fig. 9 The pQ as a function of the square root of ionic strength for
3
+
in AlCl
3
3
4
H
3
PO
4
(aq) (solid black squares) and D
3
PO
4
(D
2
O) (unfilled squares) at
3
+
◦
2
3 C.
1
2
are formed. In the H
association could be verified. It has been demonstrated that
there is essentially no association between orthophosphates and
3
PO
4
–KCl system, on the other hand, no
◦
28
first dissociation step of phosphoric acid at 25 C is given in ref.
[47] and for heavy phosphoric acid in ref. [48]. The isotope effect
+
◦
51
on the dissociation of phosphoric acid leads to a higher pK value
1
K at 25 C and Lambert and Watters have reported the value of
0
.80
in heavy phosphoric acid. (The primary and secondary isotope
effect is not discernable for phosphoric acid; ultrafast proton
10 for the association quotient for the pyrophosphate complex
3
-
◦
KP O in 1 M tetramethylammonium bromide at 25 C but
2
7
exchange.) The DpK
in good agreement with a DpK
by potentiometric measurements.
1
value, pK
1
(H
3
PO
4
) - pK
1
(D
3
PO
4
), is 0.28(2)
they were unable to detect association of orthophosphate with
potassium ions.
4
8
1
value equal to 0.272 determined
Temperature dependent quantitative Raman measurements on
Phosphoric acid solutions with increasing amounts of NaCl
become more acid and this fact has been presented for a
H
3
PO
4
(aq). Quantitative Raman spectroscopy has been carried
-
1
.310 mol L-1
out to observe the first dissociation step of a 0.2515 mol kg
0
H
3
PO (aq) in Fig. 10. The quantification has been
4
◦
◦
H
3
PO
Fig. 11). The equilibrium constant has been defined according to
eqn (14).
4
(aq) in the temperature range from 24.5 C to 99.7 C
carried out by the second method, namely determining the band
ratios of A1178/A1077 (see experimental section). The intensity ratios,
the degree of dissociation, the pQ
(
1
values, the concentration on
NaCl and the ionic strength of the phosphoric acid solutions have
-
1
been given in Table 10. The pK
1
value in a 3 mol L NaClO
4
◦
23
solution at 25 C had been reported by Baldwin and Sill e´ n and the
pK
1
value is 1.89 which is much lower than the pK value for zero
1
47
ionic strength equal to 2.142. The neutral salt effect (NaCl, KCl
and tetraethylammonium iodide) on the protonation of phosphate
ions in solution as a function of temperature has been studied
32
recently. The neutral salt which competes for water reduces
Fig. 11 Raman spectra of a 0.251 mol kg- (0.248 mol L ) H
1
-1
PO
solution
at
3
4
◦
as a function of temperature (in C). The most intense band, n
s
P(OH)
3
890 cm- was omitted for clarity.
1
~
In eqn (14) in which the activity coefficient of the undis-
sociated H PO has taken unity, and g is estimated from
A ⋅ I
3
4
±
1
Fig. 10 The pQ
1
values of a 0.310 mol L-
H
3
PO
4
solution with increasing
g
-1
amounts of NaCl added (0.0; 0.29; 0.89; 1.80; and 2.87 mol L NaCl) as
logg±
=
where Im is the ionic strength in molality
◦
1+ a⋅B ⋅ I
g
a function of the ionic strength, I
c
at 23 C. Note, the concentration scale
-1
˚
is in mol L .
(m), and the ion size parameter, a has been taken as 4 A
9
650 | Dalton Trans., 2010, 39, 9642–9653
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1
Table 11 Raman data on the dissociation of
a
0.251 mol kg-
with R the gas constant and the parameters A, B, and C given
above allow calculation of DH according to eqn (16) and with
-1
(
0.248 mol L ) H
3
PO
4
as a function of temperature
0
-
1
◦
-1
-1
-
(
7.76 kJ mol , DS equal to -67 J K mol according to eqn
*
PO -
T/K
A
1178
A
1077
[H
2
4
]
a
pQ
1
pK
1
◦
-1
17) and the free enthalpy DG -12.20 kJ mol according to eqn
◦
2
3
3
3
3
3
3
97.65
05.15
16.15
30.15
42.65
55.65
72.85
63.05
62.974
56.604
55.402
52.71
64.43
65.4
41.654
40.073
33.374
29.6541
25.242
27.375
23.965
0.0468
0.0454
0.0426
0.0392
0.0356
0.0321
0.0281
0.1864
0.1807
0.1695
0.1561
0.1418
0.1276
0.1119
1.9693
1.9995
2.061
2.1395
2.2303
2.3285
2.4508
2.1407
2.1713
2.2316
2.3091
2.3979
2.4941
2.6141
(18) at 25 C. These data derived from Raman measurements
are comparable to the recommended CODATA given in ref. [47].
Raman spectroscopy is now able to produce high quality data
-
2-
41
on equilibria HSO
4
/SO
4
such as published in and the present
data on phosphoric acid. Under normal conditions potentiometric
measurements are certainly more suitable than quantitative Ra-
man spectroscopic measurements but under extreme conditions
on small sample volumes such as in fluid inclusions or in complex
systems the Raman technique certainly has its merits.
*
A
1178 means the uncorrected band intensity of nP O; see text.
4
. Conclusions
Raman and infrared spectra of dilute solution of H
PO (D O) have been measured and the bands of the PO
ton have been assigned to C3V symmetry. In addition to the OPO
skeleton modes the deformation mode PO–H and PO–D at 1250
3
PO
4
(aq) and
D
3
4
2
4
skele-
3
-
1
and 935 cm respectively have been obtained. In the Raman and
infrared spectra of dilute solutions of H PO (aq) and D PO (D O)
no dimeric species of the form H and D respectively
could be detected. Quantitative Raman measurements have been
3
4
3
4
2
6
P
2
O
8
6
P
2
O
8
carried out and the first dissociation constant of H
3
PO (aq) and
4
◦
D
3
PO
4
(D
2
O) have been determined at 23 C. The calculated
value of the DpK
1
, pK
1
(H
3
PO
4
) - pK
1
(D
3
PO ) with 0.28(2) is
4
1 3 4
Fig. 12 The temperature dependence of pK of the H PO (temperature
comparable to the value determined by emf measurements and
demonstrates that the heavy phosphoric acid is a weaker acid than
its lighter counterpart. The influence of NaCl on the dissociation
of H PO has been determined and with increasing amounts of
range: 297.65–372.85 K); measured data (filled squares) and the fitted
curve.
6
1/2
1
.82482924⋅10 ⋅r
3
4
and A
g
and B
g
are defined by: A
g
=
and
3/2
8
1/2
(eT)
NaCl the phosphoric acid becomes more acidic. Temperature
5
0.2915865⋅10 ⋅r
B =
with e the static dielectric constant of
dependent Raman measurements of H
between 24.5 and 99.7 C. Including the activity coefficients and
3
PO (aq) have been carried
4
g
1/2
(
eT)
◦
water, r the density and T in K. The phosphoric acid becomes
calculating pK values as a function of temperatures allowed the
1
more molecular as the temperature increases§. The measured
calculation of the thermodynamic parameters. The acid becomes
more molecular with increasing temperature and the stretching
band of the P O group shifts to higher wavenumbers while the
symmetric stretch of the P–OH group shifts slightly to lower
wavenumbers.
-
Raman data at several temperatures for [H
degree of dissociation, logg , and pK
in Fig. 12 the pK values are plotted as a function of temperature.
2
PO
4
], alpha, the
±
1
are given in Table 11 and
1
The thermodynamic functions have been obtained by fitting the
dissociation constants to an equation of the type:
-
pK
1
= A/T + B + C·T
(15)
Acknowledgements
and the parameters of eqn (15) have been obtained: -log K
1
=
The author thanks Dr G. Irmer for the use of his Raman
spectrometer and for performing the DFT calculations. Mrs.
B. Ostermay is thanked for helping to measure the Raman spectra.
8
15.36/T - 4.6871 + 0.01373·T. The thermodynamic parameters
are defined as follows:
0
2
DH = 2.3026·R(A - CT )
(16)
(17)
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Dalton Trans., 2010, 39, 9642–9653 | 9651

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