Journal of Molecular Liquids 206 (2015) 110–113

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Journal of Molecular Liquids

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Solubility of naproxen in 2-propanol + water mixturesat various temperatures

Mahdis Mohammadzade a, Mohammad Barzegar-Jalali b, Abolghasem Jouyban c,d,⁎a Liver and Gastrointestinal Diseases Research Center, Tabriz University of Medical Sciences, Tabriz, Iranb Biotechnology Research Center, Tabriz University of Medical Sciences, Tabriz, Iranc Drug Applied Research Center and Faculty of Pharmacy, Tabriz University of Medical Sciences, Tabriz 51664, Irand Pharmaceutical Engineering Laboratory, School of Chemical Engineering, College of Engineering, University of Tehran, P.O. Box 11155/4563, Tehran, Iran

⁎ Corresponding author at: Liver and Gastrointestinal DUniversity of Medical Sciences, Tabriz, Iran.

E-mail address: ajouyban@hotmail.com (A. Jouyban).

http://dx.doi.org/10.1016/j.molliq.2015.01.0520167-7322/© 2015 Elsevier B.V. All rights reserved.

a b s t r a c t

a r t i c l e i n f o

Article history:Received 4 January 2015Received in revised form 27 January 2015Accepted 28 January 2015Available online 29 January 2015

Keywords:Mixed solventSolubilitySimulationJouyban–Acree model

The experimental solubility of naproxen in 2-propanol+watermixtures at different temperatures (298.2, 303.2,308.2 and 313.2 K)was reported. The solubility was correlated and/or predicted using three numerical methods;i.e., the combined van't Hoff equation and Jouyban–Acree model (method I), the extended version of theJouyban–Acree model with Abraham parameters (method II), and the minimum number of data points (N =10) were used to train the combinedmodel. The accuracies of the calculated solubilities were evaluated by com-puting themean percentage deviation (MPD). The obtainedMPDs for investigated numerical analyses varied be-tween 13 and 30%.

© 2015 Elsevier B.V. All rights reserved.

1. Introduction

Naproxen or (+)-6-methoxy-α-methyl-2-naphthaleneacetic acid(Fig. 1), a non-steroidal anti-inflammatory drug (NSAID) that iscommonly used for the reduction of pain (mild to moderate), is alsoused for reduction of fever, stiffness and inflammation of osteoarthritis,rheumatoid arthritis, psoriatic arthritis and treatment of dysmenorrhea[1,2]. Its mechanism of action is inhibition of cyclo-oxygenases 1 and 2which inhibits prostaglandin synthesis.

Naproxen is a BCS (biopharmaceutics classification system) class IIdrug whose bioavailability is rate-limited by its dissolution. The mostchallenging problem associated with naproxen formulation develop-ment is its limited aqueous solubility. To improve the lowbioavailabilityof poorly soluble drugs several solubilization techniques could be foundin the literature including the addition of pharmaceutical cosolventswhich is the commonly used technique [3–5]. In order to design theprocess of pharmaceutical dosage forms for injectable formulation,knowing some physicochemical properties such as solubility and theoccupied volumes by the drugs and other components in the solutionis needed [6,7]. The solubility behavior of drugs in cosolvent mixturesat different temperatures is used in pre-formulation studies, purification

iseases Research Center, Tabriz

methods and pharmaceutical dosage form design, among other applica-tions [4,8].

The solubility of naproxen was reported in ethyl acetate + ethanol[9], ethanol + propylene glycol [10], propylene glycol + water [11],ethanol + water [12] and polyethylene glycol 200 + water [13]mixtures and in the mono-solvents 1-butanol [14], 1-octanol [15]and 1,4-dioxane [16].

Solubility measurement is a laborious and time consuming procedureand mathematical models could be used as an alternative approach. Anumber of models have been developed to predict the solubility ofdrugs in mixed solvent [4,17,18]. The Jouyban–Acree model is one ofthe well-established models providing the most accurate computationsfor solubility of a solute with respect to temperature and composition ofthe solvent mixture and is [19]:

logCsatm;T ¼ φ1 logC

sat1;T þ φ2 logC

sat2;T þ

φ1:φ2

T

X2i¼0

Ji: φ1−φ2ð Þi ð1Þ

in which Cm,Tsat is the solute's molar solubility in the solvent mixtures at

temperature T, φ1 and φ2 are the volume fractions of the solvents 1 and2 in the absence of solute, C1,Tsat and C2,T

sat are themolar solubility of the sol-ute in the neat solvents 1 and 2, respectively, and Ji denotes the con-stants of the model which are computed by a regression analysis.Eq. (1) requires experimental values of C1,Tsat and C2,T

sat at each temperatureof interest and could be considered as a limiting factor for its practicalapplications in the pharmaceutical industry. To cover this limitation, it

Fig. 1. Chemical structure of naproxen.

111M. Mohammadzade et al. / Journal of Molecular Liquids 206 (2015) 110–113

could be combined with the van't Hoff equation [20] by replacing theC1,Tsat and C2,T

sat values with the corresponding terms from van't Hoff equa-tion. The combined version is [21]:

logCsatm;T ¼ φ1 A1 þ

B1

T

� �þ φ2 A2 þ

B2

T

� �þ φ1:φ2

T

X2i¼0

Ji: φ1−φ2ð Þi: ð2Þ

The A1, B1, A2, B2 and Ji terms are the model constants and could becomputed using a no intercept least square analysis.

Solubility of drugs is influenced by the interactions in the solutionsbetween solvents and the solute represented by physical and chemicalparameters similar to those proposed by Acree and Abraham [22]. TheAbrahammodel includes five parameters for each solute and six solventcoefficients which were previously calculated for a number of solvents[23]. The general Abraham model is:

logCS

CW

� �¼ cþe � Eþs � Sþa � Aþb � Bþv � V ð3Þ

where Cs and Cw are the solubilities of solute (in molarities) in theorganic solvent andwater, respectively, E is the excess molar refraction,S the is dipolarity/polarizability of solute, A denotes the solute'shydrogen-bond acidity, B indicates the solute's hydrogen-bond basicityand V is theMcGowan volume of the solute. The c, e, s, a, b and v are theAbraham solvent coefficients and E, S, A, B and V are the Abraham soluteparameters [23].

The Jouyban–Acree model and the Abraham solvation parameterscould be combined for providing a globally trained model to predictthe solubility of drugs in mixed solvents. The trained model for solubil-ity of drugs in cosolvent+water mixtures at various temperatures [24]is:

logCsatm;T ¼ φ1 logC

sat1;T þ φ2 logC

sat2;T þ

φ1:φ2

T

�1639:07−561:01 c1−c2ð Þ2

h i−1344:81 E e1−e2ð Þ2

h i−18:22 S s1−s2ð Þ2

h i−3:65 A a1−a2ð Þ2

h iþ 0:86 B b1−b2ð Þ2

h iþ 4:40 V v1−v2ð Þ2

h i8<:

9=;

þ φ1:φ2 φ1−φ2ð ÞT

�−1054:03þ 1043:54 c1−c2ð Þ2

h iþ 359:47 E e1−e2ð Þ2

h i−1:20 S s1−s2ð Þ2

h iþ 30:26 A a1−a2ð Þ2

h i−2:66 B b1−b2ð Þ2

h i−0:16 V v1−v2ð Þ2

h i

8>>>><>>>>:

9>>>>=>>>>;

þφ1:φ2 φ1−φ2ð Þ2T

�2895:07−1913:07 c1−c2ð Þ2

h i−901:29 E e1−e2ð Þ2

h i−10:87 S s1−s2ð Þ2

h iþ24:62 A a1−a2ð Þ2

h iþ 9:79 B b1−b2ð Þ2

h i−24:38 V v1−v2ð Þ2

h i8<:

9=;

ð4Þ

in which c1, e1, s1, a1, b1 and v1 terms are the Abraham solvent coeffi-cients of solvent 1 (2-propanol in this work) with the numerical valuesof 0.063, 0.320, 1.024, 0.445, −3.824 and 4.067, respectively and c2, e2,s2, a2, b2 and v2 are those of solvent 2 (water in this work) with the nu-merical values of −0.994, 0.577, 2.549, 3.813, 4.841 and −0.869, re-spectively. The numerical values of Abraham solvent coefficients were

computed for a number of solvents and listed in some publications ofAbraham et al. [25]. This extended version provided another predictiontool for solubility of drugs in aqueous binary solvent mixtures [24]. Thefirst two terms of Eq. (4) represent the idealmixing behaviors of the sat-urated solutions of the analyte in the mono-solvents, and the othermodel constants and variables present the effects of solvent composi-tion and temperature on non-ideal mixing behavior of the saturated so-lution and the interactions between solvent 1 and solvent 2 and thesolute in the mixed solvent system. These model constants for a singleanalyte have been explained in more detail in earlier reports [26,27].Concerning modeling of the solubility of different solutes in cosolvent +watermixtures at various temperatures, we included the Abraham soluteparameters and Abraham solvent coefficients for representing the effectsof different chemical structures of drugs and physico-chemical propertiesof binary solvents on the solubilities.

Therefore, the objectives of this work are the following.

1) Reporting the experimental solubility of naproxen in binary mixturesof 2-propanol and water at 298.2, 303.2, 308.2, and 313.2 K.

2) Predicting the solubility of naproxen at different temperatures usinga combination of Jouyban–Acree model with van't Hoff equation in2-propanol + water.

3) Predicting the solubility of naproxen at different temperatures using aglobally trained Jouyban–Acreemodel employing the Abraham soluteparameters and Abraham solvent coefficients.

2. Experimental

2.1. Materials

Naproxen (230.29 g·mol−1) was purchased from Daana Pharma-ceutical Company (Tabriz, Iran) and used without further purification.The claimed value for the purity of the solute in its certificate was98.5%. 2-Propanol (mass fraction purity of 0.997) was obtained fromMerck company (Germany). Ethanol with a purity of 96% v/v (or0.935 in mass fraction) was supplied by Jahan Teb Alcohol (Arak, Iran)and used for dilution of naproxen solutions prior to spectrophotometricanalysis. Distilled water was used throughout this work.

2.2. Solubility determination procedure

Available solubility determination methods were reviewed in a re-cent work [28]. The solubility of naproxen was determined using thesaturation shake-flaskmethod. Briefly, 2-propanol+water binarymix-tureswere prepared bymixing appropriate volumes of solvents (0.00 to1.00 in volume fractions) varying by 0.10 intervals. The solvent volumesweremeasured using a pipette (Silber, Germany)with an uncertainty of0.06 mL. Excess amount of naproxen was added to each flask and theflasks were placed in an incubator–shaker (Heidolph Unimax 1010,Germany)with a temperature controlling systemhaving an uncertaintyof 0.1 K. All the experiments were carried out at temperatures rangingfrom 298.2 to 313.2 K. The solutions were shaken until the solubilityequilibrium was reached and the saturation is verified by the presenceof un-dissolved drug. The saturated solutionswere filtered using regen-erated cellulosemembrane filters (0.45 μm, Albet Lab Science, Spain). Inorder to analyze concentrations with UV/Vis spectrophotometer, aliquotsof solutions were diluted by distilled water–ethanol 50:50 mixture. Bothcentrifuging anddiluting stepswere performed at temperature of interestusing an incubator (Kimia Idea PardazAzarbayjan (KIPA) Co., Tabriz, Iran)with an uncertainty of 0.1 K. The absorbance of the diluted solutions wasrecorded at 262 nm using a UV–vis spectrophotometer (Cecil CE 7250,UK) and themolar concentrationswere determined using UV absorbancecalibration curve. Each experimental data is an average of at least three re-peated measurements.

R2

= 0.9674

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

Experimental

Met

hod

I

R2

= 0.9677

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

Experimental

Met

hod

II

112 M. Mohammadzade et al. / Journal of Molecular Liquids 206 (2015) 110–113

2.3. Computational method

The A, B and Ji constants of Eq. (2) for the solubility of naproxen in 2-propanol + water mixtures at various temperatures were obtainedusing a no intercept least square analysis (method I). The computedconstants were used to back-calculate the solubility using Eq. (2). Thepreviously trained version of Jouyban–Acree model employing theAbraham solvation parameters (i.e., Eq. (4)) was used to predict the sol-ubility of naproxen in 2-propanol + water mixtures (method II). Theexperimental solubility data at the lowest and highest temperatureswere fitted to Eq. (2) and the model constants, i.e., A, B and Ji valueswere calculated. Then the solubility at other temperatures was predict-ed using an interpolation technique (method III).

Themeanpercentage deviations (MPDs)were calculated as an accu-racy criterion of the computations using:

MPD ¼ 100N

X CCalculatedm;T −CExprimental

m;T

��� ���CExprimentalm;T

0@

1A ð5Þ

where N is the number of data points in each set.

3. Results and discussion

Volume fractions of the binary solvent mixtures and experimentalsolubilities at investigated temperatures (298.2, 303.2, 308.2 and313.2 K) are listed in Table 1. The solubility of naproxen at all tempera-tures is increased at higher temperatures as it is expected and thesolubility is increased at a given temperature with the addition of 2-propanol, reached a maximum value and then decreased with furtheraddition of 2-propanol. The measured aqueous solubility of naproxenis 0.00030mol·L−1 at 298.2 Kwhich is in agreementwith the literaturedata (i.e., 2.84 × 10−4 mol·L−1 [8] and 3.32 × 10−4 mol·L−1 [11]).Eq. (2) was used to fit the experimental data points (numerical methodI) and the obtainedmodel for representing the solubility of naproxen in2-propanol + water mixtures at various temperatures is:

logCsatm;T ¼ φ1 6:221−2115:417

T

� �þ φ2 4:780−2580:108

T

� �

þ1010:056φ1:φ2

T

� �þ 452:392

φ1:φ2 φ1−φ2ð ÞT

� �

−763:449φ1:φ2 φ1−φ2ð Þ2

T

! ð6Þ

which is a significant correlation with F and p values of 5056 andb0.0005 with the MPD of 12.5 ± 9.3%.

Table 1Experimental molar solubility of naproxen in 2-propanol (1) +water (2) mixtures at dif-ferent temperatures.

φ1 T/K

298.2 303.2 308.2 313.2

0.00 3.00 × 10−4 3.90 × 10−4 4.70 × 10−4 5.50 × 10−4

0.10 2.80 × 10−4 4.00 × 10−4 5.20 × 10−4 7.30 × 10−4

0.20 6.20 × 10−4 1.08 × 10−3 1.37 × 10−3 2.47 × 10−3

0.30 3.37 × 10−3 6.04 × 10−3 7.15 × 10−3 8.86 × 10−3

0.40 1.36 × 10−2 1.81 × 10−2 2.19 × 10−2 2.64 × 10−2

0.50 2.67 × 10−2 3.90 × 10−2 4.97 × 10−2 6.82 × 10−2

0.60 5.64 × 10−2 6.99 × 10−2 8.93 × 10−2 1.25 × 10−1

0.70 8.12 × 10−2 1.08 × 10−1 1.35 × 10−1 1.82 × 10−1

0.80 1.14 × 10−1 1.64 × 10−1 1.87 × 10−1 2.43 × 10−1

0.90 1.64 × 10−1 2.05 × 10−1 2.48 × 10−1 3.14 × 10−1

1.00 1.24 × 10−1 1.59 × 10−1 1.92 × 10−1 2.74 × 10−1

The relative standard uncertainty for the solubilities is 4.6% or ur(x)= 0.046, the standarduncertainty for temperature is 0.1 K and the measurements were made at atmosphericpressure.

In practical applications of the solubility data of drugs in mixed sol-vents at various temperatures, one prefers to predict the data using insilico models without using any experimentally measured data points.However, such a model could not be found in the literature. As an alter-native, a number of attempts were made to predict the solubility ofdrugs using a minimum number of experimental data points includingthe discussed numerical methods of II and III. The Abraham solute pa-rameters for naproxen which were used in the following computations(Eq. (4)) are 1.49, 1.54, 0.57, 0.75 and 1.78, respectively for E, S, A, B andV [29]. The MPD for the predicted data points is 29.0 ± 24.5% (N= 36).As it is evident from Eq. (4), it requires two experimental data points foreach temperature. When the van't Hoff model trained with two datapoints (at the highest and the lowest temperatures) of 2-propranol

R2

= 0.9528

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

Experimental

Met

hod

III

Fig. 2. Simulated molar solubility data of naproxen (Cm,Tsat ) using numerical methods I–III

versus corresponding experimental data.

113M. Mohammadzade et al. / Journal of Molecular Liquids 206 (2015) 110–113

andwater are replacedwith C1,Tsat and C2,T

sat terms, and the rest of solubilitydata are predicted, the MPD is 29.2 ± 19.4% (N = 40). When Eq. (2) istrained using the minimum number of solubility data of naproxen in2-propanol + water mixtures, i.e. φ1 = 0.00, 0.30, 0.50, 0.70 and 1.00,at 298.2 and 313.2 K, and the rest of data is predicted, (i.e., numericalmethod III), the obtained MPD is 15.1 ± 14.3% (N = 36). In practice,one must decide on a balance between the demanded accuracy of thesolubility data and the time and cost which he/she is going to spendon the project. Fig. 2 illustrates the simulated solubility data of naproxenagainst their corresponding experimental values using numericalmethods I to III. As shown in this figure and concerning the closest dis-tance of the scattered points around the best fit line reflected in MPDvalues, the most accurate simulations weremade by numerical methodI employing whole data points in the simulation process, followed bynumerical methods III and II. With these findings from the figure andalso the obtained MPD values, it could be concluded that employingmore experimental data as input values resulted in more accurate sim-ulated data. Concerning the MPD values of comprehensive correlativestudies on solubility of solutes in binary solvents [17,19] and the accept-able MPD of 30% [30,31], prediction accuracy of both predictivemethods in this work could be considered as acceptable values.

4. Conclusion

The experimental molar solubilities of naproxen in 2-propanol +water mixtures at various temperatures are reported. The reporteddata extends the available solubility database of pharmaceuticals inmixed solvents [8]. The generated data is mathematically representedusing numerical method I. This sort of numerical analyses could beused for screening the measured solubility data for detecting possibleoutliers. In addition, they provide the most accurate predictions usinginterpolation technique. Some of data points are predicted employingnumerical methods II and III, in which reasonably accurate predictionsare provided. The expected MPDs for these analyses are between 13and 30% depending on the number of experimental input data in theprediction procedure.

Acknowledgment

This report is a part of the results of M. Mohammadzade's Pharm.Dthesis (No. 3767) submitted to the Faculty of Pharmacy, Tabriz Universityof Medical Sciences, Tabriz, Iran.

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