Protolytic equilibria of picric acid in a mixture of protophobic and protophilic polar solvents non-donors of H-bonds

Article abstract of DOI:10.1134/S1070363211060132

A new differentiating medium for the study of prototropic equilibria is proposed: acetonitrile with a small addition of DMSO. From the dependence of the picric acid pK^a on the content of DMSO in this medium the optimum composition of the mixture was found ensuring the stability of the pK ^a values with minimal addition of DSMO: 4 wt %. It was experimentally confirmed that the addition of water in an amount up to 0.1 wt % has virtually no effect on the measured pK^a value in a mixture with the optimum composition. Pleiades Publishing, Ltd., 2011.

Full text of DOI:10.1134/S1070363211060132

ISSN 1070-3632, Russian Journal of General Chemistry, 2011, Vol. 81, No. 6, pp. 1153–1158. © Pleiades Publishing, Ltd., 2011.
Original Russian Text © D.O. Ruzanov, D.V. Samoilov, K.V. Gensh, Yu.E. Zevatskii, N.P. Novoselov, 2011, published in Zhurnal Obshchei Khimii, 2011,
Vol. 81, No. 6, pp. 960–965.
Protolytic Equilibria of Picric Acid
in a Mixture of Protophobic and Protophilic Polar Solvents
Non-Donors of H-bonds
D. O. Ruzanova, D. V. Samoilovb, K. V. Genshc, Yu. E. Zevatskiia, and N. P. Novoselovc
a St. Petersburg State Institute of Technology (Technical University),
Moskovskii pr. 26, St. Petersburg, 198013 Russia
b JSC Novbythim, St. Petersburg, Russia
e-mail: samoylov@newchem.ru
c St. Petersburg State University of Technology and Design,
ul. Bolshaya Morskaya 18, St. Petersburg, 191186 Russia
Received January 25, 2011
Abstract—A new differentiating medium for the study of prototropic equilibria is proposed: acetonitrile with a
small addition of DMSO. From the dependence of the picric acid pKa on the content of DMSO in this medium
the optimum composition of the mixture was found ensuring the stability of the pKa values with minimal
addition of DSMO: 4 wt %. It was experimentally confirmed that the addition of water in an amount up to
0.1 wt % has virtually no effect on the measured pKa value in a mixture with the optimum composition.
DOI: 10.1134/S1070363211060132
DMSO
Organic solvents belonging to dipolar aprotic or
polar, non-donor of hydrogen bond (NDHB) are a
suitable medium for many chemical processes [1]. The
polar NDHB solvents are classified by their chemical
properties as weakly basic protophobic (e.g., propylene
carbonate, acetonitrile, acetone, and particularly
nitromethane and nitrobenzene) and the more basic
protophilic (like dimethyl sulfoxide, dimethylform-
amide, and hexamethylphosphoramide) ones [2, 3].
acetonitrile, logMeCN
γ
+
or, equivalently, the dif-
= 7.85 – (–3.4) = 11.25.
tr
H
ference logwtrγHMeСN
+
– logwtrγHDMSO
+
For the same reason, in the weakly basic proto-
phobic solvents, unlike protophilic ones, even traces of
water may distort the nature of the acid–base
equilibrium in any part of the paH* scale.
Dipolar aprotic solvents show a pronounced dif-
ferentiating effect, changing differently the strength of
the acids of different nature. The length of the pH scale
of both protophobic and protophilic NDHB solvents is
usually about 30 logarithmic units [1, 2]. However, the
large difference in the basicity of the solvents of two
main types suggests that even at a small additive of a
protophilic NDHB solvent to a protophobic one, one
can expect that in such a mixture the proton will be
solvated totally by the protophilic solvent only.
The nature of the proton solvation is the main factor
determining the pKaS value of an acid (HA ↔ H+ + A–)
in a polar NDHB solvent S. Another factor is the
medium effect in going from water to the solvent S:
ΔрKа = рKаS – рKа (in water)
= logwγHS + logwγAS – logwγHS ,
(1)
A
where γHS, γAS, and γHSA are the activity coefficients
of the transfer of ion (molecule) from water into the
solvent. For example, the difference between the
values of pKaS in acetonitrile and dimethyl sulfoxide
(DMSO) for a large series of neutral and anionic acids
is ranged from 10.0 to 11.5 [4]. As a rough
approximation, this corresponds to the logarithm of
activity coefficient of proton transfer from DMSO to
w
w
w
Another important feature of the polar NDHB
solvents is rather pronounced formation in them of the
associates between an acid and its conjugate anion or
between a base and the conjugate cation (A– + HA ↔
A–···HA; BH+ + B ↔ BH+···B). This phenomenon is
known as homoassociation. The occurrence of these
processes, along with the processes of heteroas-
1153

1154
RUZANOV et al.
Table 1. Characteristics of the most widely used solvents at 25°Ca
μ, D2
1.85
3.96
3.86
3.79
3.92
2.88
4.98
3.17
DN
AN
PA, kJ mol–1
691.0
рKS
14.0
33.3
29.4
23.9
33.3
32.5
–
ETN
logH OγHS+ b
2
Solvent
εr
Water
78.5
46.4
36.7
37.8
35.9
20.6
65.0
2.7
18.0
29.8
26.6
27.8
14.1
17.0
15.1
2.7
54.8
19.3
16.0
13.6
18.9
12.5
18.3
20.5
1.000
0.444
0.404
0.401
0.460
0.355
0.472
0.481
0
Dimethylsulfoxide
N,N-Dimethylformamide
N, N'-dimethylacetamide
Acetonitrile
884.4
–3.40
–2.52
–
887.0
908.0
779.2
+7.85
≈7.0
+6.5c
+15d
Acetone
812.0
Propylene carbonate
Nitromethane
814.2
754.6
–
a
εr is a relative dielectric permeability, μ is a dipole moment, D; DN is Gutmann donor numbers, AN is an acceptor number determined by
31P NMR spectroscopy, PA is protonation enthalpy in the gas phase, pKaS is the index of the autoprotolysis rate constant, ETN is
normalized Reihardt parameter. b The values of logH O
γ
were calculated according to the tetraphenylborate hypothesis. c Data from [9].
S+
H
2
tr
d Data from [10].
sociation (BH+ + A– ↔ BH+···A–; HX + A– ↔ XH···A–),
is due to the lack of hydrogen bonds in the NDHB
solvents.
equilibrium in acetone there is a possibility of
incomplete dissociation of salts in acetonitrile.
Therefore, we investigated the properties of
acetonitrile with small additions of DMSO, a solvent,
which is more basic than water. Thus, in acetonitrile
the protonation constants of DMSO and H2O are 6×105
and 3×102, respectively [24]. It is expectable that such
a solvent will retain the general solvation properties of
acetonitrile, but a proton solvated with DMSO will
serve as the lyonium ion, while the influence of the
water traces becomes irrelevant, if this solvent is not
used for the study of the acids weaker than water. In
addition, DMSO will solvate the trace amounts of
water remaining after purification and/or coming into
the solvent from the atmosphere, and thereby
preventing to some extent the hydration of anions.
These considerations have found experimental
evidence in a series of studies of protolytic and ionic
equilibria in analogous mixed solvent: acetone con-
taining 5 mole percent DMSO [25–27].
Acetonitrile is one of the most common solvents.
The strongly pronounced differentiating effect of this
solvent toward the dissociation of dissolved elec-
trolytes is well known [5, 11]. However, high
hygroscopic ability of the water absorption combined
with the low basicity of acetonitrile leads to the fact
that even in a very carefully dehydrated solvent there
is a danger of hydration of the proton, that is, the
existence of a lyonium ion not as H(MeCN)+m, but as
H3O+, H5O2+, etc. Despite the strong complication of
the experimental quantitative study of ionic equilibria
in pure acetonitrile due to the great influence of the
negligible amounts of water on the mechanism of the
proton solvation [12], the reliability of the acidity scale
in acetonitrile is well known thanks to a series of
papers by Kolthoff and co-workers [13–18], and the
Kaljurand’s group [19–22].
By its basicity, acetonitrile is noticeably inferior
compared to DMSO and slightly to acetone. As can be
seen from Table 1, the Gutmann donor numbers (DN)
for acetonitrile, acetone and DMSO are 14.1, 17.0 and
29.8, respectively [2], and the values of the proton
affinity in a vacuum (PA) 779.2, 812.0 and 884.4 J mol–1,
respectively [23]. The acetonitrile relative permittivity
(ε25 = 36.0), is significantly higher than that of acetone
(ε25 = 20.56). Nevertheless, by analogy with the
Thus, acetonitrile with the addition of DMSO has a
differentiating ability with respect to the acid strength
typical of aprotic solvents. Furthermore, this system is
insensitive to small water admixtures. The com-
bination of these two factors makes the mixture a very
promising medium for studying the prototropic ionic
equilibria. For the study, we used the acetonitrile–
DMSO mixture with the content of the latter less than
10 wt %. The accumulation of experimental data on
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PROTOLYTIC EQUILIBRIA OF PICRIC ACID
the pKa in the chosen medium will allow obtaining the
1155
D, rel. units
values of pKa in acetonitrile (their experimental
determination is extremely difficult) by analogy with
[10, 28, 29] using the linear relations of the type
рKаAN = aрKаS + b,
(2)
where pKaS and pKaAN are the pKa values in the system
under study and acetonitrile, respectively, a and b are
empirical parameters, which are constant for the acids
similar by the structure. For the construction of such
correlations, one must initially obtain the pKa values in
the considered system for the reference acids (for
which the values in acetonitrile are known) of different
chemical classes.
λ, nm
Starting the study of protolytic equilibria in the
proposed medium it was important to establish the
optimal composition of the mixture in which the
content of acetonitrile (which determines the solvation
of ions, except for protons) is maximal and the DMSO
content is sufficient for the stability of the pKa values
at adding small amounts of water. For this purpose we
investigated a dependence of the measured pKa value
of picric acid on the content of DMSO in the mixture
from 0.18 to 6 wt % (0.01 to 3.24 mol %). The choice
of picric acid is defined by the fact that because of
spatial constraints and the charge delocalization in the
picrate anion, its homoassociation in polar NDHB
solvents is minimal [3, 4, 31]. An important argument
in favor of picric acid is the pos-sibility of using
spectrophotometric method without buffering for
determining the pKa values. To apply the method it is
necessary to study a strong enough acid (pKa in the
studied mixture not higher than 5) and the spectra of
the prototropic forms should be clearly distinguishable.
Based on the values of pKa of picric acid (3.45) in a
similar mixture of acetone–DMSO of the molar ratio
95:5 [25], this acid is expected to meet the
requirements for the study in the medium under
investigation applying the method of dilution. It is
crucial that for this method the knowledge of the paH*
scale in the selected solvent is not required.
Furthermore, the addition of DMSO (as a strong
hydrogen bond acceptor) contributes to weakening the
possible homoassociation of picric acid.
Fig. 1. Electron absorption spectra of picric acid in the
boundary forms: (1) anion, (2) protonated, (3) in the
process of dilution.
a weighed portion of the mother solution of picric acid
in the studied mixture with the concentration about
3×10–4 M was diluted with a weighted sample of the
mixed solvents and then the resulting concentration
was calculated. The degree of dilution of working
solutions ranged from 2 to 4.5. In each mixed solvent
to obtain the HA spectrum shape a small amount of
HClO4 was added. The spectra of the A– anion were
measured from the solutions of picric acid with the
addition of 1,8-diazabicyclo[5.4.0]-7-undecene (DBU);
these spectra practically coincided with the spectra of
tetraethylammonium picrate. As can be seen from the
figure, the absorption spectra of ionic and molecular
forms are well resolved.
The magnitude of the mixed dissociation constants
(pKam) was calculated from the experimental data using
formulas (3), (4):
pKаm = log (cHPic – x)/x2,
(3)
E − EHPic
x = cHPic
,
(4)
E
Pic – EHPic
where cHPic is analytical concentration of picric acid, x
is equilibrium concentration of picrate anion, E is
molar extinction coefficients of the solution of picric
acid with the concentration cHPic, EPic–, and EHPic are the
molar extinction coefficients of the picrate ion and
undissociated picric acid, respectively.
The determination n of pKa values was performed
using the spectrophotometric method in an unbuffered
system, by analyzing changes in the absorption spectra
of picric acid in the region 300–500 nm at the acid
concentration 5×10–5 to 2×10–4 M. For saving the
solvent, the dilution was performed by weight method:
For the calculation of the thermodynamic dis-
sociation constant corrections were introduced for the
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1156
RUZANOV et al.
The dependence of the pKa value on the mole
fraction of DMSO in the mixture is shown in Table 2
and graphically in Fig. 2.
pKa (HPic)
As a result of analysis of this dependence, we found
that the optimum composition of acetonitrile–DMSO
mixture is the weight ratio 96:4 (molar ratio 97.86:
2.14). Mass fraction of water in the purified solvents
did not exceed 0.033% (determined by titration ac-
cording to Fischer). The A and B coefficients for this
mixture in the Debye–Hueckel relation are equal to
1.329 and 0.418 respectively.
The dependence of the picric acid pKa value on the
content of DMSO in the acetonitrile–DMSO mixture
in the range 0–1 mol fractions of the latter with the
increment 0.1–0.2 has also been studied in [33]. The
resulting curve has a similar form with that obtained
by us (Fig. 2), but is smoother. Thus, at the DMSO
mole fraction equal to 0.1 the picric acid pKa was equal
to 5.98, while at 0.2 mole fraction decreased to 4.51.
The most likely cause of significant differences in
these results from the data of this study is the use in
[33] of incorrect pKa value of picric acid (1.0) in pure
DMSO, while in the referred Kolthoff publication [4]
is given an estimated value –1. The method used in
[33] for calculating the values of pK in mixed solvents
of different composition is based on the relation which
includes the value of pKa in the pure components of
the mixture and the data of measurements of EMF of
buffer acid/salt solutions in a 1:1 molar ratio at the
current composition of the mixture. It is therefore
logical to assume that with such an approach the
difference in the pKa in DMSO by 2 units to the lower
values leads to a shift of values in the mixtures
containing DMSO down by about the same amount.
Based on this, an estimate of “corrected” value of pKa
of picric acid from the data of [33] in a mixture of
acetonitrile with DMSO at the molar ratio 0.9: 0.1 is
about 4, which is consistent with the results of this
study.
χ
DMSO, mol %
Fig. 2. The dependence of the thermodynamic ionization
constants of picric acid in acetonitrile at various molar
content of DMSO.
concentration activity coefficients according to the
Debye–Hueckel second approximation (5):
–
–
pKa = pKаm + (2A√x)/(1 + Ba√x).
(5)
The coefficients A and B in the Debye–Hueckel
equation were calculated by the expressions (6) and (7)
with the a parameter 5 Å.
–
A = (1.82455×106√ρ)/(εT)3/2,
B = (50.2904√ρ)/(εT)1/2,
(6)
(7)
–
where ε and ρ are the dielectric constant and the
density of the mixture, respectively, T is absolute
temperature, K.
Table 2. Thermodynamic pKa values of picric acid in the
mixtures of acetonitrile with DMSO at 25.0°C found by the
spectrophotometric dilution method
ω(DMSO), wt %
χ(DMSO), mol %
рKа (HPic)
0
0
11.0a
5.81
4.72
4.36
3.75
3.38
3.30
3.24
3.22
0.18
0.50
1.00
2.00
3.00
4.00
5.00
6.00
0.097
0.26
0.53
1.06
1.60
2.14
2.69
3.24
To estimate the effect of the water additives, we
carried out measurements of the ionization constant of
picric acid in a acetonitrile–DMSO mixture 96: 4 in the
presence of 0.1, 0.5, and 1.25 wt % (3.4–13.4 mol %) of
water. In the first case, the pKa varied within error,
while in two others the found decrease was rather
significant (0.5 log units and more). However, the
possibility of spontaneous increase in the water content
above 0.1 wt % in the working solution is excluded.
a Data from [32].
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PROTOLYTIC EQUILIBRIA OF PICRIC ACID
According to data of titration by Fischer, such content
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