Determination of dissociation constants of
p-hydroxybenzophenone in aqueous organic
mixtures — Solvent effects
M.I. Sancho, A.H. Jubert, S.E. Blanco, F.H. Ferretti, and E.A. Castro
Abstract: The apparent acidity constant of p-hydroxybenzophenone, which is a practically insoluble drug in water but
of great pharmaceutical interest, was determined by reversed-phase high-performance liquid chromatography in organic
solvent – water mixtures (acetonitrile–water, ethanol–water, and methanol–water), varying the reaction medium
permittivity in the interval 56 to 70, at constant ionic strength (0.050) and temperature (30 °C). A combined glass elec-
trode calibrated with aqueous standard buffers was used to obtain pH readings based on the concentration scale (w
The pKa values from chromatographic data were obtained using the Hardcastle–Jano equation. Moreover, excellent lin-
ear relationships between the pKa values and solvation properties of the reaction medium (relative permittivity and
Acity) were used to derive acid dissociation constants in aqueous solution. It has been concluded that the pKa values
extrapolated from such solvent–water mixtures are consistent with each other and with previously reported measure-
ments. In addition, the molecular structures of all the chemical species involved in the acid–base dissociation equilib-
rium studied were calculated with a B3LYP/6–311++G(d,p) method that makes use of the polarizable continuum model
(PCM). Taking into account the theoretical pKa values, the conclusions obtained match our experimental determina-
Key words: solvent effects, p-hydroxybenzophenone, acidity constant, solvation parameters, structure, DFT calculation.
Résumé : Faisant appel à la chromatographie liquide à haute performance en phase inversée et opérant à une tempéra-
ture de 30 °C, à une force ionique de 0,050 et dans des mélanges de solvants organiques et d’eau (acétonitrile–eau,
éthanol–eau et méthanol–eau) dont la permittivité du milieu se situe entre 56 et 70, on a déterminé la constante
d’acidité apparente de la p-hydroxybenzophénone, un médicament pratiquement insoluble, mais d’un grand intérêt phar-
maceutique. On a utilisé une combinaison d’une électrode de verre calibrée avec des tampons aqueux de référence pour
obtenir des lectures de pH sur l’échelle de concentration (w
chromatographiques, en utilisant l’équation de Hardcastle–Jano. De plus, on a utilisé les excellentes relations linéaires
entre les valeurs de pKa et les propriétés de solvatation du milieu réactionnel (permittivité relative et Acité) pour obte-
nir les constantes de dissociation acide en solutions aqueuses. On en conclut que les valeurs de pKa extrapolées à par-
tir des mélanges solvants organiques et eau sont en accord entre eux ainsi qu’avec les mesures rapportées
antérieurement. De plus, les structures moléculaires de toutes les espèces chimiques impliquées dans l’équilibre de dis-
sociation acide–base étudié ont été calculées à l’aide de la méthode B3LYP/6-311++G(d,p) qui utilise le modèle du
continu polarisable (MCP). En prenant en considération les valeurs de pKa théoriques, les conclusions obtenues sont en
accord avec nos données expérimentales.
spH). On a obtenu les valeurs de pKa à partir de données
Mots-clés : effets de solvant, p-hydroxybenzophénone, constante d’acidité, paramètres de solvatation, calculs par la
théorie de la fonctionnelle de densité.
[Traduit par la Rédaction]
Sancho et al.469
The knowledge of pKa values of organic compounds in
aqueous solutions with weak acid or basic properties is fun-
damental to the development of chemical and biological
studies, specially those related to chemical stability (1, 2)
and preformulation of new pharmaceuticals (3). Numerous
compounds with potential biological applications frequently
present very low solubility in aqueous media, while in or-
ganic solvents the solubility is elevated. Because of this, the
determination of the ionization constants in water – organic
solvent mixture and the calculation of these constants in
pure water by means of extrapolations techniques become
very useful (4, 5). It must be noted that the variation of nu-
Can. J. Chem. 86: 462–469 (2008)doi:10.1139/V08-040© 2008 NRC Canada
Received 14 November 2007. Accepted 20 February 2008.
Published on the NRC Research Press Web site at
canjchem.nrc.ca on 11 April 2008.
M.I. Sancho, S.E. Blanco, and F.H. Ferretti. Area de
Química–Física, Facultad de Química, Bioquímica y
Farmacia, Universidad Nacional de San Luis, Chacabuco y
Pedernera, 5700 San Luis, Argentina.
A.H. Jubert. CEQUINOR, Dpto. de Química, Facultad de
Ciencias Exactas, Universidad Nacional de La Plata, 1900
Buenos Aires, Argentina.
E.A. Castro.1INIFTA, Dpto. de Química, Facultad de
Ciencias Exactas, Universidad Nacional de La Plata, 1900
Buenos Aires, Argentina.
1Corresponding author (email@example.com).
merous physicochemical properties of solutes with the sol-
vent and pH form a very attractive field of research, of great
interest and applicability (6–9).
Benzophenones (BPs) are aromatic ketones usually ob-
tained from natural products (10) or by methods of organic
synthesis (11). The great importance of these compounds re-
sults from the varied biological and physicochemical proper-
ties that they possess. Due to these properties, BPs are used
in the pharmaceutical industry as sunscreen lotions (12), in
medicine (13–15), and in the polymer industry (16). Other
applications are the design of optical materials (17), the de-
velopment of asymmetric catalysts (18), and the preparation
of UV-protecting coats (19). The effects of substituents on
their conformations (20, 21) and the metal complexing abil-
ity in hydroxylic solvents were studied (22, 23) for a better
understanding of the physicochemical properties of BPs.
Nevertheless, it should be noticed that several structural
characteristics of BPs in solution have not been completely
In this paper and with the aim of contributing to clarify
the influence of solvents on the acid–base properties of
p(OH)BP, the pKa value of the compound was determined
by means of high performance liquid chromatography
(HPLC) in different organic–aqueous solutions, with a
permittivity range of 56–70, and using methanol, ethanol,
and acetonitrile as organic modifiers. Also, diverse correla-
tions are proposed between the pKa values and solvation pa-
rameters of the reaction medium, which allow for a
calculation of the pKa of the compound in pure water. In ad-
dition, the structures of ionized and non ionized p(OH)BP in
organic solvents and water were calculated by means of a
parameter nonlocal exchange functional combined with the
Lee–Yang–Parr dynamic correlation functional) (24, 25) that
makes use of the PCM model (polarizable continuum model)
(Becke hybrid three-
Chemicals and reagents
p(OH)BP from Fluka was purified by repeated crystalliza-
tion from ethanol–water. The purity control was performed
determining its spectroscopic properties (27). NaH2PO4and
NaHCO3from Merck were used without further purification.
Methanol (MeOH), ethanol (EtOH), and acetonitrile (ACN),
all HPLC grade, from Merck, were degassed and filtered
through 0.22 µm nylon filters (Millipore) before use. Milli-Q
water was used to prepare the aqueous buffer solutions. All
the solutions were prepared by weighting with an accuracy
of ±0.0001 g.
The HPLC instrument consisted of a Gilson 322 series
pump (Gilson Inc., Middleton, WI, USA), a Rheodyne 7725i
sample injector (Cotati, CA, USA), and a Gilson 152 UV–
vis detector, equipped with a Phenomenex column tempera-
ture controller. The system was controlled by UniPoint sys-
tem software v2.10 (Gilson). The analysis was carried out
with a reverse-phase Luna (C18(2), 250mm × 4.6 mm, 5 µm)
column from Phenomenex (Torrance, CA, USA). Chromato-
graphic studies were performed under isocratic (actually
policratic) elution with a mobile phase of aqueous buffer:or-
ganic modifier at different ratios, using amphiprotic solvents
(MeOH, EtOH), and a low basic aprotic solvent (ACN) as
organic modifier with a flow rate of 1.0 mL/min. Column
temperature was maintained at a constant 30 °C. The injec-
tion volume was 20 µL, and the detector was set at 280 nm.
The capacity factor (k) was measured from chromatographic
data in the usual way, that is, k = (TR– To)/To. The mobile
phase holds up times were measured by injecting a solution
of K2Cr2O7(0.001 mol/L).
The buffers solutions employed were NaH2PO4–Na2HPO4
covering the pH range from 4.50 to 8.00 and NaHCO3–
Na2CO3covering the pH range from 8.00 to 9.00. The ionic
strength was maintained at constant value (0.05 mol/L) by
adding appropriate amounts of KCl. The pH measurements
were performed on an Orion SA 520 pH meter provided
with a 91–01 Orion combined glass electrode.
Special precautions must be taken when the pH is mea-
sured in a mixed-solvents mobile phase. It is well-known
that when the aqueous buffer is added to the mobile-phase
mixed solvent, the measured pH of the mixture will be dif-
ferent from the pH measured in the pure aqueous buffer.
This problem was recognized and discussed by Rosés et al.
(28), among other authors. When the pKa value of ionogenic
analytes must be measured, it is advisable to perform the
measurement of the pH after mixing aqueous buffers and or-
ganic modifiers (29), with the electrode previously cali-
brated with aqueous standard buffers. Such pH value is
from data expressed in thew
namically meaningful dissociation constant, also expressed
in the same scale (w
K ). In all the experimental determina-
tions carried out in this work, the pH measurements were
made following this recommendation, i.e., the pH of the mo-
bile phase was measured after mixing the aqueous buffers
with the organic solvents (MeOH, EtOH, and ACN) with the
electrode previously calibrated with aqueous buffers, and the
spH scale was used to obtain the experimentalw
spH, and the respective pKa values obtained
spH scale leads to a thermody-
The structure of p-hydroxybenzophenone adopted for car-
rying out the calculations is shown in Fig. 1. The calcula-
tions were performed following known procedures (22). The
initial molecular geometries were modelled by the AM1
(Austin Model vs. 1) method (30). Afterwards, these initial
geometries were optimized with the Gaussian 03 (31) pro-
grams package. Since diffuse functions are crucial for theo-
retical treatment of anions (32), the B3LYP/6–311G++(d,p)
method (24, 25) was chosen to perform the final optimiza-
tion of the molecular structures. To analyse the solvent ef-
fects on the optimized structures in the gas phase, the PCM
model (26) was used. The corresponding frequencies were
calculated to make sure that the obtained structures were
true minima. In all the calculations, the default convergence
criteria were used.
Results and discussion
Determination of pKa
The acid–base equilibrium in aqueous solution studied
can be represented by the general equation
© 2008 NRC Canada
Sancho et al.463
AH + H2O ? A–+ H3O+
where AH is the weak acid p(OH)BP and A–is the pertinent
conjugate base p(O–)BP. The above reaction is characterized
by the ionization equilibrium constant (Ka), conventionally
A H O
A H O
A H O
A H O
A H O
In this equation, aA−, aH O
of the species in equilibrium. The brackets stand for the mo-
lar concentration and γ for the molar activity coefficients.
The Ka constant is related to a chromatographic measurable,
the capacity factor k, by the following equation (33)
+ , aAHand aH O
are the activities
k k f K
In the above equation, x = (ln 10)pH, k0and k1are the
limiting capacity factors of p(OH)BP and p(O–)BP, respec-
tively, f(1)is the molar activity coefficient ratio between the
weak acid and its conjugate base, Kap is the apparent equi-
librium constant, and the product Kap × f(1)is the effective
acid dissociation constant of the acid AH from eq. . It can
be easily demonstrated that ex= 1/[H+] and represents the in-
verse of the proton concentration in the mobile phase. This
is the most general equation for the retention factor of the
analyzed monoprotic weak acid. Under our experimental
conditions (p(OH)BP ≈ 1 × 10–4mol/L), the activity coeffi-
cient ratios are approximately equal unity, and eq.  re-
duces to eq.  (34),
Figure 2 shows the chromatographic results for p(OH)BP
aqueous buffer 39:61 (v/v). Computer-generated plots of k
K . For the determination of thew
eq.  was used. Thew
K values were obtained by fitting
the data from the measured retention factors as a function of
spH of the mobile phase, and performing a non-linear least-
square iterative procedure. The experimental data were fitted
to a rational function equation type 0 [y = (b + cx)/(1 + ax)],
spH values with a mobile phase of MeOH :
spH show typical sigmoidal curves (Figs. 3, 4, and 5)
spH value of the inflection point is the compound
K value of p(OH)BP,
using the software Origin Pro 7.5 (35). Figure 6 shows the
results of the fitting process for MeOH:buffer 39:61 (v/v)
mobile phase compositions, and Table 1 reports thew
values and limiting capacity factors for p(OH)BP obtained
in the three solvents under study.
Equation  suggests that the retention factor of the sol-
ute k is a weighted average of the retention factors of the dif-
ferent species that may exist in the mobile phase (34), and
this factor may be written as
k = X0k0+ X1k1
The term Xn(n = 0, 1) is the probability that the observed
retention factor k of the solute is equal to kn, and it is also
the probability of the presence of p(OH)BP (if n = 0) or the
presence of p(O–)BP (if n = 1) in the mobile phase expressed
as a function of the pH, i.e., it is the relative concentration of
the species (the mole fraction) at equilibrium. If X0= 1, then
© 2008 NRC Canada
464Can. J. Chem. Vol. 86, 2008
Fig. 1. Structure adopted in the calculations of p-
Fig. 2. Overlaid chromatograms showing the retention behaviour
of p-hydroxybenzophenone at differentw
over the peak) in 39% (v/v) methanol mobile phase, UV detec-
tion at 280 nm, flow rate 1 mL/min.
spH values (indicated
Fig. 3. Measured capacity factors vs.w
hydroxybenzophenone in methanol:buffer mixtures.
spH for p-
X1= 0, and only p(OH)BP is present in the mobile phase;
therefore, the observed retention factor k is exclusively due
to the neutral species and equal to k0. Thus, the distribution
of both species at a given pH can be estimated considering
X0= 1 – X1
Figure 7 shows the results of the distribution of both
p(OH)BP and p(O–)BP at a given pH for two different meth-
anol: buffer mobile phase compositions. It can be observed
that when pH ≤ 6 the neutral molecule is the prevailing spe-
cie (X0= 0.99), while at pH ≥ 11, the anion is the prevailing
specie in solution (X1= 0.99).
It is known that one of the most important factors deter-
mining the ionization equilibrium constants is the reaction
medium. The influence of the solvent upon the specific rate
of ion–ion, ion–dipole, or dipole–dipole reactions can be an-
alyzed using the expression by Kirkwood (36, 37).
In this equation, k0and k are the reaction specific rates for
media with infinite and D relative permittivity, e is the unit
of electric charge, kBis Boltzman’s constant, T is the abso-
lute temperature, ZAand ZBare the charges of the two ions,
r is the radius of the involved species, µ stands for the
dipolar moments, while the symbol ‡ refers to the activated
complex. It is evident that in the acid–base dissociation
equilibrium of eq. , the forward reaction involves two
dipolar molecules, AH and H2O, while the reverse reaction
involves the A–and H3O+ions. Consequently, applying
Kirkwood’s equation to these two reactions in equilibrium,
eq.  was obtained.
k T r
values determined for p(OH)BP in MeOH,
EtOH, and ACN:water mixtures were plotted against 1/D
(38, 39) according to eq. , and they are shown in Fig. 8.
The linear equations included in Fig. 8 indicate that when D
© 2008 NRC Canada
Sancho et al.465
Fig. 5. Measured capacity factors vs.w
hydroxybenzophenone in acetonitrile:buffer mixtures.
spH for p-
Fig. 4. Measured capacity factors vs.w
hydroxybenzophenone in ethanol:buffer mixtures.
spH for p-
Fig. 6. Plot of the capacity factor of p-hydroxybenzophenone
against ex(x = 10.ln (w
spH)) according to eq. .
increases, the correspondingw
the solvents with greater D favour the ionization reaction de-
scribed by eq. . Although permittivity is important to
measure the solvation abilities of solvents, it should be noted
that it is not very useful for describing solute–solvent spe-
cific interactions. Consequently, we selected the solvation
parameter Acity (40), which is appropriate for measuring the
hydrogen-bond donating ability (HBD capability) of a sol-
vent, i.e., the capability of the solvent to provide a proton.
The values of Acity determined for ACN, EtOH, MeOH, and
water are 0.37, 0.66, 0.75, and 1.00 (41), respectively. The
K values were plotted against the Acity parameter of the
used organic–aqueous mixtures as shown in Fig. 9. It can be
observed that when the Acity of the reaction medium in-
creases, the correspondingw
K decreases, i.e., the solvents
with greater HBD capability favour the acid dissociation re-
action of p(OH)BP. Moreover, it should also be noted that
K decreases. As expected,
the limiting capacity factors k0and k1vary reasonably in a
linear way with the Acity of the reaction media.
Considering eqs. [10–12] (Fig. 9),
pKa (MeOH) = –7.92 (0.49) Acity + 15.77 (0.45)
pKa (EtOH) = –6.79 (0.39) Acity + 14.61 (0.36)
pKa (ACN) = –2.20 (0.03) Acity + 9.99 (0.02)
and taking into account that Acity (H2O) = 1.00 , the
K (pKa in pure water) values 7.83, 7.85, and 7.80 were
obtained, respectively. These results suggest that the accuracy
of the HPLC methodology carried out in this work is very
good. In addition, when the obtainedw
pared with thew
K value of 7.51 obtained by means of UV–
vis spectroscopy (42), a reasonable agreement is observed.
Table 2 summarizes the calculated Gibbs free energies by
means of the B3LYP/6–311++G(d,p) method with the PCM
model for all the species involved in the ionization reaction
K values are com-
© 2008 NRC Canada
466 Can. J. Chem. Vol. 86, 2008
Fig. 8. Plot of thew
permittivity of solvent–water solutions at 30 °C, according to
eq. . Errors are in parenthesis.
K of p-hydroxybenzophenone against the
Fig. 7. Variation of Xnwith the pH at two different methanol:wa-
ter mobile phase composition. X0is the mole fraction of p-
hydroxybenzophenone, and X1is the mole fraction of the p-
aThe mobile phase composition is organic modifier: aqueous buffer (v/v).
composition at 30 °C (k0, k1= limiting capacity factors of the weak acid p(OH)BP and
conjugate base p(O–)BP, respectively; r = linear regression coefficient). Errors recovered
from data fit are in parenthesis.
K values and chromatographic parameters obtained for each mobile phase
under study. A thermodynamic cycle, shown in Fig. 10, was
used to calculate the Gibbs free energy change in solution,
?, according to the following equations
(A–) + G° (H+S)
(HA) – Ggas
(X) = Gsolv
(X) – Ggas
(for X = HA, A–, S, and H+S)
(A–) + ∆Gsolv
(HA) – ∆Gsolv
where AH and A–are p(OH)BP and p(O–)BP, respectively, S
is the solvent molecule, and H+S is the solvated proton.
Equation  can be used to calculate ∆Gsol
pKa. The calculated pKa (pKTheo) values were
?, and therefore
© 2008 NRC Canada
Sancho et al.467
4.48 × 10–34
2.27 × 10–35
6.06 × 10–36
5.36 × 10–37
Table 2. Calculated molecular magnitudes for the species involved in the ionization reac-
tion described by eq. , using the B3LYP/6–311++G(d,p) method with the PCM model.
= Gibbs energy in solution, kcal mol–1; p(OH)BP = p-hydroxybenzophenone;
p(O–)BP = p-hydroxybenzophenonate anion; H3O+, H+–ACN, H+–MeOH, H+–EtOH =
solvated proton with one molecule of water, acetonitrile, methanol, and ethanol, respec-
tively; KTheo= theoretical acidity constant).
Fig. 9. Changes of thew
K of p-hydroxybenzophenone with the Acity parameter of the reaction medium. Errors are in parenthesis.
Fig. 10. Thermodynamic cycle used to calculate the theoretical
acidity constants of p-hydroxybenzophenone in solution.
pKTheo(water) = 33.35; pKTheo(MeOH) = 34.64
pKTheo(EtOH) = 35.22; pKTheo(ACN) = 36.27
The above pKTheovalues differ from the ones experimen-
tally determined. It must be noted that the calculation of pKa
values using computational methods is difficult, as there is
no simple and accurate way to calculate the Gibbs free en-
ergy of the solvated proton. In addition, the pKTheovalues
are referred to the standard state, which is not the case for
the experimental data reported in this paper. Nevertheless, if
the calculated pKTheoare analyzed comparatively with each
other, it is observed that the theoretical ionization constants
vary as the Acity parameter of the solvents. This suggests
that the conjugate bases are specifically more solvated, ac-
cording to the Acity of the reaction medium, i.e., the pKTheo
values of p(OH)BP increase when the polarity–polarizability
and solvation abilities of the reaction media decrease. This
conclusion agrees with experimental observations that indi-
cate that the acid–base equilibria are shifted towards the for-
mations of ions when the polarity–polarizability and HBD
capability of the reaction medium increase.
The apparent acidity constant of p-hydroxybenzophenone
(very slightly soluble drug in water) was determined in di-
verse organic solvent–water mixtures using a polycratic
high-performance liquid chromatographic method based on
the Hardcastle–Jano equation. The pKa values measured in
organic–aqueous solutions were correlated with solvation
parameters (relative permittivity and Acity) of the reaction
medium. Excellent linear equations were proposed from
which the pKa values in pure water were obtained. The re-
sults allowed to infer that the pKa values of the compound
increase when the polarity–polarizability and solvation abili-
ties of the reaction medium decrease. The molecular struc-
tures of all the chemical species involved in the acid–base
dissociation equilibria studied were calculated with a
B3LYP/6–311++G(d,p) method that makes use of the
polarizable continuum model, and the pKa values were cal-
culated using a thermodynamic cycle. Considering the theo-
retical pKa values, several conclusions were presented,
which are consistent with the experimental determinations.
The methodology described in this work is very useful for
obtaining the pKa of compounds of low solubility in water
with adequate accuracy.
This work was supported by grants from the National Uni-
versity of San Luis (Argentina). M.I. Sancho thanks Consejo
Nacional de Investigaciones
(CONICET) for a Doctoral Fellowship.
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