Solubility of Acetaminophen and Ibuprofen in Polyethylene Glycol ...

J Solution Chem (2011) 40:2032–2045
DOI 10.1007/s10953-011-9767-2
Solubility of Acetaminophen and Ibuprofen
in Polyethylene Glycol 600, N-Methyl Pyrrolidone
and Water Mixtures
Shahla Soltanpour · Abolghasem Jouyban
Received: 24 July 2010 / Accepted: 10 April 2011 / Published online: 17 November 2011
© Springer Science+Business Media, LLC 2011
Abstract The solubility of acetaminophen and ibuprofen in binary and ternary mixtures
of N-methyl pyrrolidone, polyethylene glycol 600 and water at 25 °C were determined and
the solubilities are mathematically represented by the Jouyban–Acree model. The density
of the solute-free solvent mixtures was measured and employed to train the Jouyban–Acree
model and then the densities of the saturated solutions were predicted. The overall mean
relative deviations (OMRDs) for fitting the solubility data of acetaminophen and ibuprofen
in binary mixtures are 3.2% and 6.0%, respectively. The OMRDs for fitting the solubilities
in ternary solvent mixtures for acetaminophen and ibuprofen are 15.0% and 28.6%, respectively,
and the OMRD values for predicting all solubilities of acetaminophen and ibuprofen
by a trained version of the Jouyban–Acree model are 9.4% and 17.8%, respectively. The
prediction OMRD for the density of saturated solutions is 1.9%.
Keywords Jouyban–Acree model · Acetaminophen · Ibuprofen · Solubility · N-methyl
pyrrolidone
1 Introduction
Solutions, especially concentrated solutions, of pharmaceutical compounds have many advantages
compared to solid forms. Solutions are easy to use and make excellent vehicles
for carrying the uniform pharmaceutical compounds. They provide rapid pharmacological
S. Soltanpour
Liver and Gastrointestinal Diseases Research Center, Tabriz University of Medical Sciences, Tabriz
51664, Iran
Present address:
S. Soltanpour
Faculty of Pharmacy, Zanjan University of Medical Sciences, Zanjan 45139, Iran
A. Jouyban ()
Drug Applied Research Center and Faculty of Pharmacy, Tabriz University of Medical Sciences, Tabriz
51664, Iran
e-mail: ajouyban@hotmail.com

J Solution Chem (2011) 40:2032–2045 2033
action, because it is not necessary to disintegrate and dissolve the compounds in the gastrointestinal
fluids. Despite these advantages, some pharmaceutical compounds are not marketed
in solution form due to their low solubility and/or chemical instability. Many pharmaceutically
active compounds have low solubility and require relatively high volumes of the solvent
for dissolution. Because of safety, compatibility, stability and economic considerations,
the number of solvents to be used for making the liquid solutions is limited. Furthermore,
using high volumes of solvents for solubilizing pharmaceuticals is not advised because there
are some restrictions, e.g. for injections. One solution for overcoming this solubility problem
is the addition of water-miscible co-solvents or surfactants to the formulation [1].
N-methyl pyrrolidone (NMP) is a chemically stable and powerful polar solvent. These
properties are very useful in some chemical reactions in which an inert medium is needed.
Despite the stability of NMP, it can play an active role in certain reactions such as hydrolysis,
oxidation, condensation, etc. NMP is a very strong solubilizing agent and is currently
used in some commercially available pharmaceutical products [2]. NMP has various applications
in pharmaceutical and medicinal fields such as a permeation enhancer in transdermal
formulations [3, 4], improving the transdermal flux of both hydrophilic and hydrophobic
drugs [5], is a solubilizing agent for poorly soluble drugs [6], provides entrapment of poorly
water-soluble drugs in hybrid nanoparticles [7], enhances aqueous phase transdermal transport
[5], increases the skin permeation of drugs [8] and is a co-surfactant in microemulsion
systems [9]. Furthermore, various medical devices like self-hardening bone graft substitutes
[10], dental barrier membranes [11] and subcutaneous drug delivery systems [12, 13]
contain small amounts of NMP. The pharmaceutical applications of NMP have been reviewed
in a recent work [14].
Polyethylene glycols (PEGs), called macrogols in the European pharmaceutical industry,
are produced by polymerization of ethylene oxide [15, 16]. PEGs with a mean molecular
weight up to 400 are non-volatile liquids at room temperature. PEG 600 shows a melting
point of 17 to 22 °C, so it may be a liquid at room temperature but a paste at lower temperatures.
Solubility of PEGs in water is an important property, which makes them suitable in
different applications. Liquid PEGs up to 600 are freely miscible with water [17]. The liquid
PEGs have a slightly bitter taste, but it can be adjusted easily by suitable additives (sweeteners)
and solid PEG grades have no taste. Solid PEGs are not soluble in liquid PEGs, but
blending them with liquid PEGs leads to a white, pasty ointment with good solubility in
water, good dissolving properties and suitable vehicles for many substances and ointment
bases [18–20]. Solid PEGs are preferred bases for suppositories [21]. Producing tablets requires
variable excipients with different functions, several of them covered by PEGs. They
may act as carriers, solubilizers, absorption improvers for active substances, lubricants and
binders [22]. The relatively low melting point favors a sintering or compression technique.
At the same time the PEG has a plasticizing effect, which facilitates the shaping of the tablet
mass in the compression process and may counteract capping. The flexibility of sugar-coated
tablets is increased by PEGs and, since PEG acts as an anticaking agent, the cores are prevented
from sticking together. With film formers in sugar-free coating processes, PEGs act
as a softener. PEGs 300 and 400 are listed as the active ingredients in ophthalmic demulcents
[23]. With the two OH groups at the end of the PEG molecules, all typical reactions of
alcohols, such as ester, carbonate and carbamate formation are possible. Methylether-capped
PEGs, are available to avoid chain-building reactions, since these PEGs are only able to react
at one end of the molecule. The PEG conjugation of drugs, e.g. anticancer drugs, makes
them safer therapeutic agents which target malignant tissues with more selectivity [24, 25].
For achieving an optimized solvent mixture for dissolving a certain amount of a drug in a
given volume of the solvent, the trial-and-error approach is usually employed, which is timeconsuming
and expensive; therefore, employing cosolvency models could be an appropriate

2034 J Solution Chem (2011) 40:2032–2045
solution. Among the developed cosolvency models, the Jouyban–Acree model is one of
the most versatile. It provides accurate mathematical descriptions and shows how the solute
solubility varies with both temperature and solvent composition. The model for representing
the solubility of a solute in binary solvent mixtures at various temperatures is:
[
]
w 1 w 2
2∑
log 10 C m,T = w 1 log 10 C 1,T + w 2 log 10 C 2,T +
J i (w 1 − w 2 ) i (1)
T
i=0
where C m,T is the solute’s molar solubility in the binary solvent mixtures at temperature T ,
w 1 and w 2 are the mass fractions of the solvents 1 and 2 in the absence of the solute,
and C 1,T and C 2,T denote the molar solubility of the solute in the neat solvents 1 and 2,
respectively. The J i terms are constants of the model and are computed by regressing
(log 10 C m,T − w 1 log 10 C 1,T − w 2 log 10 C 2,T ) against w 1w 2 w
, 1 w 2 (w 1 −w 2 )
,and w 1w 2 (w 1 −w 2 ) 2
.
T T T
This model was used to calculate multiple solubility maxima [26] and also to correlate other
physico-chemical properties in solvent mixtures [27–32] and promises accurate mathematical
representations.
Equation 1 can be used to model the solubility data of a solute in a binary solvent at various
temperatures. It requires C 1,T and C 2,T data and also a minimum number of solubility
data in mixed solvents for the training process, which restricts its applications for prediction
purposes. A number of attempts have been made to overcome this limitation. These includes
the presentation of trained versions of the Jouyban–Acree model for specific cosolvents. The
trained version of the model can be employed for predicting the solutes solubility in aqueous
and non-aqueous solvent mixtures at various temperatures by using only C 1,T and C 2,T
data. For PEG 400 {1} (to avoid reader confusion the solvent numbers used in the equations
are reported in {})–water {2} mixtures, Eq. 1 was trained using experimental solubilities of
drugs and the obtained model is [33]:
log 10 C m,T = w 1 log 10 C 1,T + w 2 log 10 C 2,T
+ w 1w 2 [
394.82 − 355.28(w1 − w 2 ) + 388.89(w 1 − w 2 ) 2] , (2)
T
for propylene glycol {1}–water {2} mixtures is [34]:
log 10 C m,T = w 1 log 10 C 1,T + w 2 log 10 C 2,T + w 1w 2 [
37.030 + 319.490(w1 − w 2 ) ] , (3)
T
for ethanol {1}–water {2} mixtures is [35]:
log 10 C m,T = w 1 log 10 C 1,T + w 2 log 10 C 2,T
+ w 1w 2 [
724.21 + 485.17(w1 − w 2 ) + 194.41(w 1 − w 2 ) 2] , (4)
T
and its updated version [36]:
log 10 C m,T = w 1 log 10 C 1,T + w 2 log 10 C 2,T
+ w 1w 2 [
724.21 + 485.17(w1 − w 2 ) + 194.41(w 1 − w 2 ) 2]
T
− 0.314w 1 w 2 log 10 P (5)
in which log 10 P is the logarithm of the octanol–water partition coefficient of the drug.
The model for dioxane {1}–water {2} mixtures is [37]:
log 10 C m,T = w 1 log 10 C 1,T + w 2 log 10 C 2,T
+ w 1w 2 [
958.44 + 509.45(w1 − w 2 ) + 867.44(w 1 − w 2 ) 2] (6)
T

J Solution Chem (2011) 40:2032–2045 2035
for glycerol {1}–water {2} mixtures is [38]:
( )
w1 w 2
log 10 C m,T = w 1 log 10 C 1,T + w 2 log 10 C 2,T + 1048.364
T
− 1.232w 1 w 2 log 10 P, (7)
and for ethyl acetate {1}–ethanol {2} mixtures the trained model is [39]:
log 10 C m,T = w 1 log 10 C 1,T + w 2 log 10 C 2,T
+ w 1w 2 [
382.99 + 125.66(w1 − w 2 ) + 214.58(w 1 − w 2 ) 2] . (8)
T
It should be noted that the solvent composition of the mixtures and also the solute concentration
can be expressed using different units. Our results (not shown here) revealed that
these different expressions have no effect on the prediction capability of the model.
The accuracies of Eqs. 2–8 were evaluated using various numbers of data sets (NDS) by
computing the MRDs. The OMRDs (± SD) for the equations and their NDSs are 39.8%
(SD = 46.7, NDS = 80), 24.1% (SD = 15.1, NDS = 27), 49.4% (SD = 88.3, NDS = 26),
35.5% (SD = 22.5, NDS = 32), 27.2% (SD = 14.3, NDS = 36), 40.7% (SD = 35.8,
NDS = 5) and 13.1% (SD = 8.1, NDS = 26), respectively. As a general point, greater
NDS and less diversity of the investigated solutes resulted in greater accuracy for the model.
As it is shown in Eq. 5, addition of a term representing the solute’s structure improves the
prediction capability of the model.
The Jouyban–Acree model has theoretical justifications [40], among other cosolvency
models it shows the most accurate results [41], and by employing the solubility data in
mono-solvents, the solubility data in solvent mixtures at various temperatures can be easily
predicted [33–39]. In addition to the binary solvent mixtures, the extended models for
predicting the solubility data of drugs in ternary solvent mixtures are:
[
]
w 1 w 2
2∑
log 10 C m,T = w 1 log 10 C 1,T + w 2 log 10 C 2,T + w 3 log 10 C 3,T +
J i (w 1 − w 2 ) i
T
i=0
[
] [
]
w 1 w 3
2∑
+
J i ′
T
(w 1 − w 3 ) i w 2 w 3
2∑
+
J i ′′
T
(w 2 − w 3 ) i (9)
i=0
log 10 C m,T = w 1 log 10 C 1,T + w 2 log 10 C 2,T + w 3 log 10 C 3,T
[
] [
]
w 1 w 2
2∑
+
J i (w 1 − w 2 ) i w 1 w 3
2∑
+
J i ′
T
T
(w 1 − w 3 ) i
i=0
i=0
[
] [
]
w 2 w 3
2∑
+
J i ′′
T
(w 2 − w 3 ) i w 1 w 2 w 3
2∑
+
J i ′′′ (w 1 − w 2 − w 3 ) i (10)
T
i=0
i=0
where C 3,T is the solute molar solubility in the solvent 3 at temperature T ,andw 3 is the
mass fraction of the solvent 3 in the absence of the solute. The J
i ′ ′′
and J
i
terms are computed
using the same procedure as for the J i terms. The J
i
′′′ terms are the ternary solvent interaction
terms and are computed by regressing:
⎧
[
] ⎫
⎪⎨
log 10 Cm,T Sat − w 1 log 10 C1,T Sat − w 2 log 10 C2,T Sat − w 3 log 10 C3,T Sat − w 1 w 2
2∑
J i (w 1 − w 2 ) i
T
⎪⎬
[
] [
] i=0
w 1 w 3
2∑
⎪⎩ −
J i ′
T
(w 1 − w 3 ) i w 2 w 3
2∑
−
J i ′′
T
(w 2 − w 3 ) i ⎪⎭
i=0
i=0
i=0

2036 J Solution Chem (2011) 40:2032–2045
against w 1w 2 w 3
, w 1w 2 w 3 (w 1 −w 2 −w 3 )
,and w 1w 2 w 3 (w 1 −w 2 −w 3 ) 2
. The existence of these model constants,
which require a number of solubility data in solvent mixtures for the training process,
T T T
is a limitation for the model when the solubility predictions are the goal of the computations
in early drug discovery studies.
Experimental solubilities of acetaminophen and ibuprofen in PEG 600 {1}–water {3}
mixtures were reported in a previous work [42]. In this work, the experimental solubility
of these drugs in NMP {2}–water {3}, PEG 600 {1}–NMP {2} and PEG 600 {1}–
NMP {2}–water {3} mixtures at 25 °C are reported and the applicability of the Jouyban–
Acree model to predict the measured solubility data is shown. In addition, the applicability
of the Jouyban–Acree model for predicting the density of the saturated solutions by employing
density of solute-free solutions of mixed solvents is shown.
2 Experimental Method
2.1 Materials
Acetaminophen was purchased from Arastoo Pharmaceutical Company (Iran) and ibuprofen
was purchased from Sobhan Pharmaceutical Company (Iran). The purity of the drugs was
checked by determination of their melting points and comparing the measured solubilities in
mono-solvents with the corresponding data from the literature [43, 44]. NMP was purchased
from Merck (Germany), PEG 600 was a gift from Daana pharmaceutical company (Iran),
and double distilled water was used for preparation of the solutions.
2.2 Apparatus and Procedures
The binary solvent mixtures (100.0 g) were prepared by mixing the appropriate weights of
the solvents with the uncertainty of 0.10 g. The solubilities of acetaminophen and ibuprofen
in the solvent mixtures were determined by equilibrating excess amounts of drugs at 25 °C
using a shaker (Behdad, Tehran, Iran) placed in an incubator equipped with a temperature
controlling system maintained constant within ±0.2 °C (Nabziran, Tabriz, Iran). Because of
the high viscosity of PEG 600, after sufficient time (> 98 h), the saturated solutions of the
drugs were centrifuged at 13,000 rpm for 15 min, diluted with water for acetaminophen and
methanol for ibuprofen, and then assayed at 243 nm and 222 nm, respectively, using a UV–
vis spectrophotometer (Beckman DU-650, Fullerton, USA). Concentrations of the diluted
solutions were determined from the calibration curves. Each experimental data point represents
the average of at least three replicate experiments with the measured molar solubilities
being reproducible to within ±3.1%. Densities of the saturated solutions and the solvent
mixtures in the absence of the solute were measured using a 5 mL pycnometer.
2.3 Computational Methods
The experimental solubility data for each drug, in the binary solvents, were fitted to Eq. 1,the
model constants were computed, and the back-calculated solubilities were used to compute
the MRD values. In the next analysis, Eq. 9 was used to calculate the solubility of each drug
in the ternary solvents. In order to provide better predictions, the ternary interaction terms
of Eq. 10 were calculated using a linear regression analysis.
As discussed above, Eq. 1 should be trained using experimental solubility data. To provide
generally trained versions of the model for PEG 600 {1}–water {2} and NMP {1}–
water {2} mixtures, the generated data and collected data from the literature [42, 45–48]

J Solution Chem (2011) 40:2032–2045 2037
were used to train the model. In order to show the capability of the Jouyban–Acree model
for a predicting drug’s solubility in PEG 600 {1}–water {2} and NMP {1}–water {2} mixtures,
one data set was excluded from the training process and its solubility values were
predicted using the trained version of the model. This method is called leave one out crossvalidation.
Densities of the saturated solutions are required to convert the molar solubilities into
mole fraction solubilities. Any attempt to predict the density of the saturated solutions can
save time and the cost of the experimental efforts. In a previous paper [49], the applicability
of the Jouyban–Acree model for the prediction of the densities of liquid mixtures at
various temperatures was shown. The investigated liquid mixtures were solute free, so for
showing the model applicability in predicting the densities of the saturated solutions composed
of liquid mixtures, the model was fitted to the density of solute-free binary mixtures
and the sub-binary constants were calculated for each system. Then, by using these constants,
the model constants for ternary mixtures were obtained and the trained version of
the model was used to predict the densities of the saturated solutions and the resulting prediction
errors were within an acceptable range [42]. Therefore, the same procedure can be
used to predict the densities of saturated solutions investigated in this work. The experimental
and calculated densities were used to convert the molar solubilities to the mole fraction
scale.
The mean relative deviation (MRD) between the calculated and observed (solubility/density)
values are used to evaluate the accuracy of the model. The MRD values are
calculated using:
∑{ |Calculated − Observed|
}
Observed
MRD = 100
(11)
N
where N is the number of data points in each set.
3 Results
Tables 1 and 2 list the experimental solubilities of acetaminophen and ibuprofen in the binary
and ternary solvent mixtures along with the measured density of the saturated solutions
at 25 °C, respectively. The densities of the solute-free solvent mixtures are also listed in Table
1. The minimum solubility of acetaminophen (9.89 × 10 −2 mol·L −1 ) is observed for the
aqueous solution and is in good agreement with previous data [50–52]. The maximum solubility
of acetaminophen (8.60 mol·L −1 ) in the solvent mixtures is observed for the PEG 600
{1}–NMP {2}–water {3} (0.3 + 0.6 + 0.1 mass fractions) mixture. The aqueous solubility
of ibuprofen is 4 × 10 −4 mol·L −1 (or 6.72 × 10 −6 as mole fraction) and is comparable with
the corresponding values from the literature [53, 54]. The maximum solubility of ibuprofen
(8.95 mol·L −1 ) in the solvent mixtures studied is observed in the PEG 600 {1}–NMP {2}–
water {3} (0.1 + 0.6 + 0.3 mass fractions) mixture. There are no published experimental
data for drugs in the investigated solvent mixtures.
Equations 9 and 10 were used to fit the data sets of acetaminophen and ibuprofen; the
constants and MRD values are shown in Table 3. In the binary mixtures of acetaminophen
the lowest MRD value is for PEG 600 {1}–NMP {2} mixtures with 1.0% and the highest
MRD value belongs to NMP {2}–water {3} mixtures with 7.4%. For ibuprofen in binary
mixtures the lowest MRD is for PEG 600 {1}–NMP {2} mixtures with 0.8% and the highest
MRD value belongs to PEG 600 {1}–water {3} mixtures with 9.3%. In the binary mixtures,
the overall MRD (OMRD) values are 3.2% and 6.0%, respectively, for acetaminophen and
ibuprofen. The MRD values for ternary mixtures are 15.0% and 28.6%, respectively, for

2038 J Solution Chem (2011) 40:2032–2045
Table 1 Experimental molar solubilities (C m,T ) of acetaminophen in PEG 600 {1}–NMP {2}–water {3}
mixtures at 25 °C and densities of the saturated and solute-free solutions
w 1 w 2 w 3 C m,T
(mol·L −1 )
Density of the saturated
solutions (g·mL −1 )
Density of solute-free
solvent mixtures (g·mL −1 )
1.00 0.00 – 1.4531 1.1556 1.1291
0.90 0.10 – 1.5118 1.1536 1.1198
0.80 0.20 – 1.7102 1.1412 1.1119
0.70 0.30 – 2.1035 1.1330 1.1021
0.60 0.40 – 2.4669 1.1248 1.0962
0.50 0.50 – 2.8706 1.1165 1.0863
0.40 0.60 – 3.1281 1.1103 1.0745
0.30 0.70 – 3.4581 1.1021 1.0667
0.20 0.80 – 3.8479 1.0918 1.0509
0.10 0.90 – 4.2377 1.0815 1.0391
0.00 1.00 – 5.0451 1.0703 1.0293
– 0.00 1.00 0.0989 1.0162 0.9837
– 0.10 0.90 0.4595 1.0216 0.9978
– 0.20 0.80 0.7507 1.0288 1.0017
– 0.30 0.70 1.1614 1.0360 1.0056
– 0.40 0.60 1.6455 1.0414 1.0096
– 0.50 0.50 2.1397 1.0486 1.0135
– 0.60 0.40 2.8358 1.0559 1.0155
– 0.70 0.30 3.4999 1.0613 1.0175
– 0.80 0.20 3.7783 1.0649 1.0214
– 0.90 0.10 4.1124 1.0667 1.0253
– 1.00 0.00 5.0451 1.0703 1.0293
0.10 0.10 0.80 0.5670 1.0897 1.0300
0.20 0.10 0.70 0.8370 1.0939 1.0465
0.10 0.20 0.70 0.8788 1.0877 1.0382
0.10 0.30 0.60 1.4698 1.0794 1.0465
0.20 0.20 0.60 1.0592 1.0836 1.0527
0.30 0.10 0.60 1.0209 1.0877 1.0650
0.40 0.10 0.50 1.3097 1.1165 1.0836
0.30 0.20 0.50 1.7168 1.1103 1.0733
0.20 0.30 0.50 1.9882 1.0980 1.0630
0.10 0.40 0.50 2.6145 1.0918 1.0527
0.50 0.10 0.40 1.6271 1.1495 1.0918
0.40 0.20 0.40 1.7983 1.1412 1.0877
0.30 0.30 0.40 2.2297 1.1330 1.0733
0.20 0.40 0.40 2.2437 1.1289 1.0650
0.10 0.50 0.40 2.3550 1.1145 1.0547
0.60 0.10 0.30 2.1810 1.1454 1.1062
0.50 0.20 0.30 2.4107 1.1412 1.1000
0.40 0.30 0.30 2.8282 1.1392 1.0918
0.30 0.40 0.30 3.1205 1.1392 1.0774

J Solution Chem (2011) 40:2032–2045 2039
Table 1 (Continued)
w 1 w 2 w 3 C m,T
(mol·L −1 )
Density of the saturated
solutions (g·mL −1 )
Density of solute-free
solvent mixtures (g·mL −1 )
0.20 0.50 0.30 3.1692 1.1371 1.0691
0.10 0.60 0.30 3.1831 1.1268 1.0630
0.70 0.10 0.20 2.2048 1.1186 1.1165
0.60 0.20 0.20 2.6780 1.1103 1.1103
0.50 0.30 0.20 3.3043 1.1042 1.1042
0.40 0.40 0.20 3.3600 1.0959 1.0897
0.30 0.50 0.20 3.4852 1.0877 1.0774
0.20 0.60 0.20 4.4595 1.0794 1.0691
0.10 0.70 0.20 4.0656 1.0691 1.0630
0.80 0.10 0.10 2.4833 1.1836 1.1186
0.70 0.20 0.10 2.5263 1.1745 1.1124
0.60 0.30 0.10 3.4901 1.1691 1.1042
0.50 0.40 0.10 3.5548 1.1618 1.0897
0.40 0.50 0.10 7.9486 1.1564 1.0836
0.30 0.60 0.10 8.5972 1.1418 1.0774
0.20 0.70 0.10 6.3619 1.1309 1.0691
0.10 0.80 0.10 6.3202 1.1273 1.0547
Table 2 Experimental molar solubilities (C m,T ) of ibuprofen in PEG 600 {1}–NMP {2}–water {3} mixtures
at 25 °C and density of the saturated solutions
w 1 w 2 w 3 C m,T (mol·L −1 ) Density of the saturated
solutions (g·mL −1 )
1.00 0.00 – 1.4425 1.1364
0.90 0.10 – 1.9340 1.1083
0.80 0.20 – 2.3699 1.0980
0.70 0.30 – 2.7695 1.0918
0.60 0.40 – 3.2418 1.0856
0.50 0.50 – 3.5324 1.0753
0.40 0.60 – 3.6501 1.0712
0.30 0.70 – 3.7954 1.0650
0.20 0.80 – 4.0860 1.0609
0.10 0.90 – 4.5582 1.0527
0.00 1.00 – 5.5121 1.0444
– 0.00 1.00 0.0004 0.9873
– 0.10 0.90 0.0201 0.9888
– 0.20 0.80 0.1532 0.9950
– 0.30 0.70 0.3333 1.0032
– 0.40 0.60 0.6057 1.0156
– 0.50 0.50 0.9955 1.0218
– 0.60 0.40 1.4799 1.0279

2040 J Solution Chem (2011) 40:2032–2045
Table 2 (Continued)
w 1 w 2 w 3 C m,T (mol·L −1 ) Density of the saturated
solutions (g·mL −1 )
– 0.70 0.30 2.5152 1.0321
– 0.80 0.20 4.1862 1.0362
– 0.90 0.10 5.2942 1.0403
– 1.00 0.00 5.5121 1.0444
0.10 0.10 0.80 0.0479 1.0609
0.20 0.10 0.70 0.0583 1.0671
0.10 0.20 0.70 0.2131 1.0774
0.10 0.30 0.60 0.3148 1.0465
0.20 0.20 0.60 0.2593 1.0506
0.30 0.10 0.60 0.0759 1.0568
0.40 0.10 0.50 0.0941 1.0733
0.30 0.20 0.50 0.2376 1.0568
0.20 0.30 0.50 0.4464 1.0424
0.10 0.40 0.50 0.5118 1.0238
0.50 0.10 0.40 0.2352 1.1042
0.40 0.20 0.40 0.3623 1.0918
0.30 0.30 0.40 0.5939 1.0733
0.20 0.40 0.40 0.7891 1.0568
0.10 0.50 0.40 1.1342 1.0424
0.60 0.10 0.30 1.2976 1.1165
0.50 0.20 0.30 1.4656 1.1062
0.40 0.30 0.30 1.6200 1.0712
0.30 0.40 0.30 1.7925 1.0527
0.20 0.50 0.30 1.9696 1.0341
0.10 0.60 0.30 8.9499 1.6336
0.70 0.10 0.20 1.9396 1.1392
0.60 0.20 0.20 2.5026 1.1227
0.50 0.30 0.20 3.5560 1.1103
0.40 0.40 0.20 3.4915 1.0939
0.30 0.50 0.20 3.0475 1.0815
0.20 0.60 0.20 4.3769 1.0691
0.10 0.70 0.20 7.1919 1.0527
0.80 0.10 0.10 3.2472 1.0873
0.70 0.20 0.10 2.4663 1.0745
0.60 0.30 0.10 2.5953 1.0636
0.50 0.40 0.10 2.9222 1.0509
0.40 0.50 0.10 3.7739 1.0400
0.30 0.60 0.10 3.5923 1.0309
0.20 0.70 0.10 3.0475 1.0218
0.10 0.80 0.10 3.1564 1.0127

J Solution Chem (2011) 40:2032–2045 2041
Table 3 The constants of the Jouyban–Acree model and the mean relative deviations (MRD) of backcalculation
for the solubility of acetaminophen and ibuprofen in binary and ternary solvent mixtures
Drug N Solvent system J 0 J 1 J 2 MRD%
Acetaminophen 11 PEG 600 {1}–NMP {2} 25.595 21.946 −190.757 1.0
Acetaminophen a 11 PEG 600 {1}–water {3} 525.287 178.733 110.211 1.3
Acetaminophen 11 NMP {2}–water {3} 573.236 −520.733 480.948 7.4
Acetaminophen 36 PEG 600 {1}–NMP {2}–water {3} 1549.527 4400.519 3805.727 15.0
OMRD 6.2
Ibuprofen 11 PEG 600 {1}–NMP {2} 108.590 −180.307 −77.088 0.8
Ibuprofen a 11 PEG 600 {1}–water {3} −196.127 693.573 2546.005 9.3
Ibuprofen 11 NMP {2}–water {3} 1549.194 −1575.793 1968.898 8.0
Ibuprofen 36 PEG 600 {1}–NMP {2}–water {3} 2867.939 3246.069 7430.691 28.6
OMRD 11.7
a Solubility data taken from a previous work [42]
acetaminophen and ibuprofen. The MRD values for ternary solvent mixtures are higher
than those of the binary solvent mixtures. After calculating the sub-binary and ternary constants
for each drug (details are shown in Table 3), the trained versions of the Jouyban–
Acree model were used to predict the solubility of acetaminophen and ibuprofen in both
binary and ternary solvent mixtures. The OMRD values for predicting the acetaminophen
and ibuprofen solubility in binary and ternary solvent mixtures are 6.2% and 11.7%, respectively.
In addition to those trained versions of the Jouyban–Acree model, two generally trained
models for PEG 600 {1}–water {2} and NMP {1}–water {2} mixtures, using data sets
taken from previous work [42, 45–48], are presented in this work. The trained version for
PEG 600 {1}–water {2} mixtures is:
log 10 C m,T = w 1 log 10 C 1,T + w 2 log 10 C 2,T + 213.21 w 1w 2
T
and the trained version for NMP {1}–water {2} mixtures is:
(12)
log 10 C m,T = w 1 log 10 C 1,T + w 2 log 10 C 2,T
+ w 1w 2 [
668.67 − 678.59(w1 − w 2 ) + 1220.13(w 1 − w 2 ) 2] . (13)
T
The back-calculated MRDs of Eqs. 12 and 13 and the references of the data sets are shown
in Table 4. In PEG 600 {1}–water {2} mixtures the lowest (18.4%) and highest (127.9%)
MRDs are observed for lamotrigine and clonazepam, respectively. Also in NMP {1}–
water {2} mixtures the lowest and highest MRDs belong to lamotrigine (25.6%) and clonazepam
(149.9%), respectively. The OMRD values for Eqs. 12 and 13 are 56.9% and 58.1%,
respectively. Comparing the MRD values of Eqs. 12 and 13 with those of Eq. 1 (listed in
Table 3) reveal that the MRD values of Eq. 1 are less than those of Eqs. 12 and 13. Butthe
main advantage of Eqs. 12 and 13 is that they need experimental solubility data of drugs
in mono-solvents, but for computing the constants of Eq. 1 at least three solubility data in
mixed solvents are required. Therefore, with the advantage and weakness of Eqs. 12 and 13,
the MRD values of these equations are acceptable.
In the leave one out cross-validation method, one drug was excluded from the training
sets and Eq. 1 was trained with the rest of the data sets, and then by using the trained ver-

2042 J Solution Chem (2011) 40:2032–2045
Table 4 The details of data sets and the mean relative deviations (MRD) of the back-calculation and leave
one out methods
Drug N Solvent system Reference MRD%
(backcalculation)
MRD%
(leave one
out)
Acetaminophen 11 PEG 600 {1}–water {3} [42] 30.0 34.4
Ibuprofen 11 PEG 600 {1}–water {3} [42] 52.4 53.2
Pioglitazone HCl 12 PEG 600 {1}–water {3} [48] 54.9 59.7
Diazepam 11 PEG 600 {1}–water {3} [46] 57.9 74.3
Lamotrigine 11 PEG 600 {1}–water {3} [46] 18.4 20.4
Clonazepam 11 PEG 600 {1}–water {3} [46] 127.9 172.9
OMRD 56.9 69.2
Acetaminophen 11 NMP {2}–water {3} This work 34.1 40.9
Ibuprofen 11 NMP {2}–water {3} This work 58.6 62.1
Pioglitazone HCl 14 NMP {2}–water {3} [45] 56.9 70.2
Diazepam 11 NMP {2}–water {3} [47] 41.8 49.2
Lamotrigine 11 NMP {2}–water {3} [47] 25.6 30.1
Clonazepam 11 NMP {2}–water {3} [47] 149.9 198.8
Phenobarbital 11 NMP {2}–water {3} [47] 39.7 44.0
OMRD 58.1 70.8
sion, the solubility of the excluded drug was predicted. The details of the MRD values for
the leave one out method are shown in Table 4. In PEG 600 {1}–water {2} mixtures the
lowest and highest MRDs belong to lamotrigine (20.4%) and clonazepam (172.9%), respectively,
and for NMP {1}–water {2} mixtures the lowest and highest MRDs belong again to
lamotrigine (30.1%) and clonazepam (198.8%), respectively. The OMRD values for PEG
600 {1}–water {2} and NMP {1}–water {2} mixtures are 69.2% and 70.8%, respectively.
For predicting the density of the saturated solutions, the densities of solute free binary
and ternary solvent mixtures were measured. Then, by the density of the binary mixtures,
the constants of Eq. 14 were computed:
[
]
w 1 w 2
2∑
log 10 ρ m,T = w 1 log 10 ρ 1,T + w 2 log 10 ρ 2,T + w 3 log 10 ρ 3,T +
J i (w 1 − w 2 ) i
T
+
[
w 1 w 3
T
2∑
i=0
] [
J i ′ (w 1 − w 3 ) i w 2 w 3
+
T
2∑
i=0
i=0
J ′′
i (w 2 − w 3 ) i ]. (14)
Then by using these sub-binary constants, the ternary constants of Eq. 15 were computed:
log 10 ρ m,T = w 1 log 10 ρ 1,T + w 2 log 10 ρ 2,T + w 3 log 10 ρ 3,T
[
] [
]
w 1 w 2
2∑
+
J i (w 1 − w 2 ) i w 1 w 3
2∑
+
J i ′
T
T
(w 1 − w 3 ) i
+
[
w 2 w 3
T
i=0
2∑
i=0
i=0
] [
J i ′′ (w 2 − w 3 ) i w 1 w 2 w 3
+
T
2∑
i=0
J ′′′
i (w 1 − w 2 − w 3 ) i ]. (15)

J Solution Chem (2011) 40:2032–2045 2043
The final trained version is:
log 10 ρ m,T = w 1 log 10 ρ 1,T + w 2 log 10 ρ 2,T + w 3 log 10 ρ 3,T + 0.290 (w 1w 2 )
T
+ 1.403 (w 1w 3 )
+ w 2w 3 [
0.266 − 0.504(w2 − w 3 ) + 0.336(w 2 − w 3 ) 2]
T T
+ w 1w 2 w 3 [
3.108 − 7.474(w1 − w 2 − w 3 ) ] . (16)
T
Equation 16 was used to predict the densities of the saturated solutions. The prediction
MRDs were 1.4% and 2.4%, respectively, for acetaminophen and ibuprofen and the OMRD
was 1.9%. The experimental and calculated densities were used to convert the molar solubility
to the mole fraction solubility, and the OMRD value for the difference of mole fraction
solubilities from experimental and predicted densities was 1.9%.
4 Discussion
Experimental solubilities of acetaminophen and ibuprofen are reported in aqueous and nonaqueous
mixtures of PEG 600 and NMP. Aqueous mixtures data could be used in liquid
drug formulation whereas non-aqueous data could be used in other formulations such as
softgels. The Jouyban–Acree model fits well to the experimental solubility data for drugs
at all compositions of the solvent mixtures. Also, it fits well to the experimental solubilities
of drugs in ternary solvents with given fractions of the cosolvents. These findings are
also supported by the small MRD values of the back-calculated and experimental solubility
data. Although the MRDs are very low, especially for sub-binary solvents, it should be
kept in mind that the constants are computed using the solubility of acetaminophen and/or
ibuprofen, which need experimental measurements. Generally, the overall MRDs observed
in these predictions show that the Jouyban–Acree model provided more accurate predictions
in the presence of one or two cosolvents. According to the density prediction results, it’s not
necessary to measure the density of all saturated solutions, and by measuring the density of
the solute-free solvent mixtures and with trained version of the Jouyban–Acree model, the
density of the saturated solutions could be predicted within an acceptable MRD.
Acknowledgements The authors would like to thank the Research Affairs of Tabriz University of Medical
Sciences for the partial financial support under grant No. 5/4/5452, and also Daana pharmaceutical company
for supplying the drug powders and materials used in this work.
References
1. Coapman, S.D.: Progress for solubilizing difficulty soluble pharmaceutical actives. Patent No. 5141961,
25 August 1992
2. Strickly, A.: Solubilizing excipients in oral and injectable formulations. Pharm. Res. 21, 201–229 (2004)
3. Sasaki, H., Kojima, M., Mori, Y., Nakamura, J., Shibasaki, J.: Enhancing effect of pyrrolidone derivatives
on transdermal drug delivery I. Int. J. Pharm. 44, 15–24 (1988)
4. Yoneto, K., Li, S.K., Ghanem, A.H., Crommelin, D.J., Higuchi, W.I.: A mechanistic study of the effects
of the 1-alkyl-2-pyrrolidones on bilayer permeability of stratum corneum lipid liposome: a comparison
with hairless mouse skin studies. J. Pharm. Sci. 84, 853–860 (1955)
5. Lee, P.J., Langer, R., Shastri, V.P.: Role of N-methyl pyrrolidone in the enhancement of aqueous phase
transdermal transport. J. Pharm. Sci. 94, 912–917 (2005)
6. Uch, A.S., Hesse, U., Dressman, J.B.: Use of 1-methyl-pyrrolidone as a solubilizing agent for determining
the uptake of poorly soluble drugs. Pharm. Res. 16, 968–971 (1999)

2044 J Solution Chem (2011) 40:2032–2045
7. Ishihara, T., Goto, M., Kanazawa, H., Higaki, M., Mizushima, Y.: Efficient entrapment of poorly watersoluble
pharmaceuticals in hybrid nanoparticles. J. Pharm. Sci. 98, 2357–2563 (2008)
8. Koizumi, A., Makiko, F., Kondoh, M., Watanabe, Y.: Effect of N-methyl pyrrolidone on skin permeation
of estradiol. Eur. J. Pharm. Biopharm. 57, 473–847 (2004)
9. Bachhav, Y.G., Date, A.A., Patravale, V.B.: Exploring the potential of N-methyl pyrrolidone as a cosurfactant
in the microemulsion systems. Int. J. Pharm. 326, 186–189 (2006)
10. Hellerbrand, K., Siedler, M., Schutz, A., Pompe, C., Friess, W.: In situ hardening paste, its manufacturing
and use. Publication No. US 2009/0048145, 19 February 2009
11. Pirhonen, E., Nieuwenhuis, J., Kaikkonen, A., Nieminen, T., Weber, F.: Resorbable polymer compositions,
implant and method of making implant. Patent No. 6926903, 9 August 2005
12. Malook, S.U., Boon, P.F.G., Morgan, J.P.: Method of reducing the swelling or pain associated with
antibiotics compositions. Patent No. 4772460, 20 September 1988
13. Dornhofer, W., Embrechts, E.: Injection solution for intramascular and subcutaneous administration to
animal. Patent No. 5753636, 19 May 1998
14. Jouyban, A., Fakhree, M.A.A., Shayanfar, A.: Review of pharmaceutical applications of N-methyl-2-
pyrrolidone. J. Pharm. Pharmaceut. Sci. 13, 524–535 (2010)
15. Cheng, G., Fan, X., Tian, W., Liu, Y., Liu, G.: Study on anionic polymerization of ethylene oxide initiated
by ammonium/triisobutylaluminum. J. Polym. Res. 17, 529–534 (2010)
16. Mark, H.F. (ed.): 1,2-Epoxide Polymers: Ethylene Oxide Polymers and Copolymers. In: Encyclopedia
of Polymer Science and Engineering, pp. 225–273. Wiley, New York (1986)
17. Polyethylene Glycols (PEGs) and the pharmaceutical industry. http://www.clariant.com (2009). Accessed
on 22 November 2009
18. Polyethylene Glycol Ointment (PEG Ointment), USP 24th revision, p. 2495 (2000)
19. Macrogol Ointment (Polyethylene Glycol Ointment), 13th edn., p. 826. The Japanese Pharmacopoeia
(1996)
20. Macrogol 1500 (Polyethylene Glycol 1500), 13th edn., pp. 823–824. The Japanese Pharmacopoeia
(1996)
21. Nagatomi, A., Mishima, M., Tsuzuki, O., Ohdo, S., Higuchi, S.: Utility of a rectal suppository containing
the antiepileptic drug zonisamide. Biol. Pharm. Bull. 20, 892–896 (1997)
22. Al-Nasassrah, M., Podczeck, F., Newton, J.M.: The effect on an increase in chain lengthon the mechanical
properties of polyethylene glycols. Eur. J. Pharm. Biopharm. 46, 31–38 (1998)
23. FDA, Ophthalmic drug products for over-the-counter human use: active ingredients: ophthalmic demulcents.
Code of Federal Regulation 21, Part 349.12. URL http://www.accessdata.fda.gov/scripts/cdrh/
cfdocs/cfcfr/CFRSearch.cfmfr=349.12 (2009). Accessed 22 Nov 2009
24. Parnaud, G.: Polyethylene glycol suppresses colon cancer. Cancer Res. 59, 5143–5147 (1999)
25. Sakanoue, Y.: The efficacy of whole gut irrigation with polyethylene glycol electrolyte solution. Acta
Chim. Scand. 156, 463–466 (1990)
26. Jouyban-Gharamaleki, A., Acree, W.E. Jr.: Comparison of models for describing multiple peaks in solubility
profiles. Int. J. Pharm. 167, 177–182 (1998)
27. Jouyban-Gharamaleki, A., Khaledi, M.G., Clark, B.J.: Calculation of electrophoretic mobilities in water
organic modifier mixtures in capillary electrophoresis. J. Chromatogr. A 868, 277–284 (2000)
28. Jouyban, A., Fathi-Azarbayjani, A., Acree, W.E. Jr.: Surface tension calculation of mixed solvents with
respect to solvent composition and temperature by using Jouyban–Acree model. Chem. Pharm. Bull. 52,
1219–1222 (2004)
29. Jouyban, A., Khoubnasabjafari, M., Vaez-Gharamaleki, Z., Fekari, Z., Acree, W.E. Jr.: Calculation of
the viscosity of binary liquids at various temperatures using Jouyban–Acree model. Chem. Pharm. Bull.
53, 519–523 (2005)
30. Jouyban, A., Chan, H.K., Barzegar-Jalali, M., Acree, W.E. Jr.: A model to represent solvent effects on
the chemical stability of solutes in mixed solvent systems. Int. J. Pharm. 243, 167–172 (2002)
31. Jouyban, A., Soltani, S., Chan, H.K., Acree, W.E. Jr.: Modeling acid dissociation constant of analytes in
binary solvents at various temperatures using Jouyban–Acree model. Thermochim. Acta 428, 119–123
(2005)
32. Jouyban, A., Rashidi, M.R., Vaez-Gharamaleki, Z., Matin, A.A., Djozan, D.j.: Mathematical representation
of analyte’s capacity factor in binary solvent mobile phases using Jouyban–Acree model. Pharmazie
60, 827–829 (2005)
33. Jouyban, A.: Solubility prediction of drugs in water–polyethylene glycol 400 mixtures using Jouyban–
Acree model. Chem. Pharm. Bull. 54, 1561–1566 (2006)
34. Jouyban, A.: Prediction of drug solubility in water–propylene glycol mixtures using Jouyban–Acree
model. Pharmazie 62, 365–367 (2007)
35. Jouyban, A., Acree, W.E. Jr.: In silico prediction of drug solubility in water–ethanol mixtures using
Jouyban–Acree model. J. Pharm. Pharmaceut. Sci. 9, 262–269 (2006)

J Solution Chem (2011) 40:2032–2045 2045
36. Jouyban, A., Soltanpour, Sh., Acree, W.E. Jr.: Improved prediction of drug solubilities in ethanol +
water mixtures at various temperatures. Biomed. Int. 1, 19–24 (2010)
37. Jouyban, A.: In silico prediction of drug solubility in water–dioxane mixtures using the Jouyban–Acree
model. Pharmazie 62, 46–50 (2007)
38. Jouyban, A., Fakhree, M.A.A., Mirzaei, Sh., Ghafourian, T., Soltanpour, Sh., Nokhodchi, A.: Solubility
prediction of paracetamol in water–glycerol mixtures at 25 and 30 °C using the Jouyban–Acree model.
Asian J. Chem. 21, 7249–7253 (2009)
39. Jouyban, A., Acree, W.E. Jr.: Prediction of drug solubility in ethanol–ethyl acetate mixtures at various
temperatures using the Jouyban–Acree model. J. Drug Deliv. Sci. Technol. 17, 159–160 (2007)
40. Acree, W.E. Jr.: Mathematical representation of thermodynamic properties. Part II. Derivation of the
combined nearly ideal binary solvent (NIBS)/Redlich-Kister mathematical representation from a twobody
and three-body interactional mixing model. Thermochim. Acta 198, 71–77 (1992)
41. Jouyban-Gharamaleki, A., Valaee, L., Barzegar-Jalali, M., Clark, B.J., Acree, W.E. Jr.: Comparison of
various cosolvency models for calculating solute solubility in water–cosolvent mixtures. Int. J. Pharm.
177, 93–101 (1999)
42. Soltanpour, Sh., Jouyban, A.: Solubility of acetaminophen and ibuprofen in binary and ternary mixtures
of polyethylene glycol 600, ethanol and water. Chem. Pharm. Bull. 58, 219–224 (2010)
43. Pacheco, D.P., Manrique, Y.J., Martinez, F.: Thermodynamic study of the solubility of ibuprofen and
naproxen in some ethanol + propylene glycol mixtures. Fluid Phase Equilib. 262, 23–31 (2007)
44. Manzo, R.H., Ahumada, A.A.: Effects of solvent medium on solubility. V. Enthalpic and entropic
contributions to the free energy changes of disubstituted benzene derivatives in ethanol:water and
ethanol:cyclohexane mixtures. J. Pharm. Sci. 79, 1109–1115 (1990)
45. Soltanpour, Sh., Jouyban, A.: Solubility of pioglitazone hydrochloride in aqueous solutions of ethanol,
propylene glycol, and N-methyl-2-pyrrolidone at 298.2 K. AAPS Pharm. Sci. Tech. 10, 1153–1157
(2009)
46. Soltanpour, Sh., Acree, W.E. Jr., Jouyban, A.: Solubility of 5-(2-chlorophenyl)-7-nitro-1,3-dihydro-1,4-benzodiazepin-2-one,
7-chloro-1-methyl-5-phenyl-3H-1,4-benzodiazepin-2-one, and 6-(2,3-
dichlorophenyl)-1,2,4-triazine-3,5-diamine in the mixtures of polyethylene glycol 600, ethanol, and water
at 298.2 K. J. Chem. Eng. Data 55, 1727–1731 (2010)
47. Shayanfar, A., Acree, W.E. Jr., Jouyban, A.: Solubility of clonazepam, diazepam, lamotrigine and phenobarbital
in N-methyl-2-pyrrolidone + water mixtures at 298.2 K. J. Chem. Eng. Data 54, 2964–2966
(2009)
48. Jouyban, A., Soltanpour, Sh.: Solubility of pioglitazone hydrochloride in polyethylene glycol 600–
ethanol–water mixtures at 25 °C. Latin Am. J. Pharm. 29, 825–829 (2010)
49. Jouyban, A., Fathi-Azarbayjani, A., Khoubnasabjafari, M., Acree, W.E. Jr.: Mathematical representation
of the density of liquid mixtures at various temperatures using Jouyban–Acree model. Indian J. Chem.
A 44, 1553–1560 (2005)
50. Jouyban, A., Chan, H.K., Chew, N.Y.K., Khoubnasabjafari, M., Acree, W.E. Jr.: Solubility prediction
of paracetamol in binary and ternary solvent mixtures using Jouyban–Acree model. Chem. Pharm. Bull.
54, 428–431 (2006)
51. Dearden, J.C., Patel, N.C.: Dissolution kinetics of some alkyl derivatives of acetaminophen. Drug Dev.
Ind. Pharm. 4, 529–535 (1978)
52. Paruta, A.N., Irani, S.A.: Dielectric solubility profiles in dioxane–water mixtures for several antipyretic
drugs. Effect of substituents. J. Pharm. Sci. 54, 1334–1338 (1965)
53. Rytting, E., Lentz, K.A., Chen, X.Q., Qian, F., Venkatesh, S.: Aqueous and cosolvent solubility data for
drug-like organic compounds. AAPS J., 7, E78–E105 (2005)
54. Fini, A., Laus, M., Orienti, I., Zecchi, V.: Dissolution and partition thermodynamic functions of some
nonsteroidal anti-inflammatory drugs. J. Pharm. Sci. 75, 23–25 (1986)