Correlation of Solubility and Prediction of the Mixing Properties of

Research Note pubs.acs.org/IECR

Correlation of Solubility and Prediction of the Mixing Properties of Ginsenoside Compound K in Various Solvents Runyan Li,† Hao Yan,† Zhao Wang,† and Junbo Gong*,†,‡ †

School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, People’s Republic of China Tianjin Key Laboratory of Modern Drug Delivery and High-Efficiency, Tianjin University, Tianjin 300072, People’s Republic of China

‡

S Supporting Information *

ABSTRACT: The solubilities of ginsenoside compound K in pure solvents and binary mixture solvents were determined at several temperatures from 278.15 K to 318.15 K by a static analytical method. The experimental solubility data in pure solvents were correlated by the van’t Hoff plot, the modified Apelblat equation, the λh (Buchowski) equation, the Wilson model, and the NRTL model, with the Wilson model giving the best correlation results. Based on the Wilson model and experimental data, the mixing Gibbs free energies, enthalpies, and entropies of solutions and activity coefficients in pure solvents were predicted, and other thermodynamic properties (infinite-dilution activity coefficients and excess enthalpies) were calculated as well. In addition, the solubility was maximal at a certain water mole fraction in acetone + water mixture and acetonitrile + water mixture, whereas in a methanol + water system, the solubility decreases as the water concentration increases monotonically. The solubilities in mixture solvents were correlated by the solvent components using the Wilson model. The partial molar Gibbs free energies with negative values were obtained, which indicates the changing of the solubility.

1. INTRODUCTION Ginsenoside compound K (C36H64O8, CAS Registry No. 39262-14-1) is the main metabolite detected in blood after oral administration of protopanaxadiol saponins.1,2 It is also called 20-O-b-D-glucopyranosyl-20(S)-protopanaxadiol, and its chemical structural is given in Figure 1. Many methods,

However, there is little information on the crystallization method to isolate the compound K,8 and the solubility data of compound K have not been reported in the literature up to now. In this work, the solubility of compound K in three pure organic solventsmethanol, acetone, and acetonitrilewas measured by a static method in the temperature range from 278.15 K to 318.15 K. Furthermore, the solubility of compound K in water is very low, so the solubilities in water + methanol, water + acetone, water + acetonitrile cosolvents were determined at 10° intervals, from 278.15 K to 318.15 K, using the static method as well. The van’t Hoff plot, modified Apelblat equation, λh (Buchowski) equation, Wilson model, and NRTL model were chosen to obtain correlation of the experimental data in pure solvents. In addition, the solubilities in solvent mixtures were correlated to the fraction of water using the Wilson model. In order to understand the solubility behavior, the mixing Gibbs free energies, enthalpies, and entropies of solutions in pure solvents and the partial molar Gibbs free energies in solvent mixtures were derived. In addition, other thermodynamic properties (infinite-dilution activity coefficients and excess enthalpies) were calculated.

Figure 1. Chemical structure of ginsenoside compound K.

including heating, acid treatment, base treatment, enzymatic conversion, and biotransformation, have been used to produce compound K; the most effective method is microbial biotransformation.3 Because of its high bioactivity, for example, anti-inflammatory, anti-antiallergic, hepatoprotective activities,4,5 the compound has received increasing attention. As a result, the purification method to obtain the high yield and high-purity product of compound K is particularly important. It is well-known that solution crystallization is a key step to separation and purification in the pharmaceutical, food, and chemical industries, which influences crystal habit, purity, yield, crystal size, etc. The solubility of the material in solvents is probably the most important property that should be known for crystallization.6 Besides, for the poorly water-soluble compound, the water + organic solvents have been evaluated to increase the solubility to obtain the high-quality product.,7 © 2012 American Chemical Society

2. EXPERIMENTAL SECTION 2.1. Materials. Ginsenoside compound K was supplied by Zhejiang Hisun Pharmaceutical Co., Ltd., China. It is identified by powder X-ray diffraction (PXRD), and the mass fraction purity, determined by HPLC (Agilent C18, Agilent TechReceived: Revised: Accepted: Published: 8141

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Figure 2. Experimental and modeling solubility of ginsenoside compound K in pure solvents ((■) methanol, (●) acetone, and (▲) acetonitrile; solid line represents correlation results): (a) van’t Hoff plot, (b) λh equation, (c) modified Apelblat equation, (d) Wilson model, and (e) NRTL model.

temperature (Tm1) and enthalpy of fusion (ΔfusH1) of compound K were determined by differential scanning calorimetry (DSC) (Mettler−Toledo, Model DSC 1/500, Switzerland). The size of samples were 5−10 mg, with the heating rate was 5 K/min. The dry nitrogen flow as protective gas was ∼100 mL/min. The uncertainties of the measurements are estimated to be ±2%.

nologies, USA), was higher than 99.0%. Methanol, acetone, and acetonitrile were analytical-grade (purchased from Tianjin Kewei Chemical Co, China) with purity of >99.0% without further purification. Deionized water was prepared in our laboratory and used throughout. 2.2. Apparatus and Procedure. 2.2.1. Differential Scanning Calorimetric (DSC) Measurements. The melting 8142

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Van’t Hoff Equation. The relationship between the mole fraction solubility of a solute and the temperature can be expressed by the van’t Hoff equation in a real solution.11 Considering the solvent effect, the solubility is described by relating the logarithm of mole fraction of a solute with the absolute temperature:

2.2.2. Single-Crystal X-ray Diffraction. Data collection of all the solvates were performed on Rigaku R-AXIS Rapid II and Bruker CCD area detector diffractometer using graphitemonochromated Mo Kα radiation (λ = 0.71073 Å). The structures of the solvates were solved by direct methods using SHELXS-97, besides the semiempirical absorption correction was used. Meanwhile, the refinement method, full-matrix leastsquares on F2, used SHELXS-97 as well. All hydrogen atoms were placed and refined with relative isotropic displacements. 2.2.3. Solubility Measurements. The solubilities of compound K in the pure solvents and binary solvent mixtures were measured using the gravimetric method.9 Excess solid compound K was added to different solvents and kept at a certain temperature controlled by a thermostatical bath (SW 23, Julabo, Germany) with a stability of 0.05 K. The solutions were stirred for 6 h to make sure the solid−liquid equilibrium was attained for that the average sample concentrations at 5 and 6 h differed by 2%. Then, ∼10 mL of upper clear solution was sampled after filtration by the 0.2-μm pore size syringe filter and evaporated in a vacuum drying oven at 55 °C for 24 h. After dried, the samples were measured for several times every 0.5 h to make sure that the weight was unaltered. In this drying condition, we ensure that the solvent can completely evaporate and no solute molecules escaped. The experiment was repeated three times and used the arithmetic average value as the final result. All of the masses were measured using a balance (Model AB204, Mettler−Toledo, Switzerland) with an accuracy of ±0.0001 g. The estimated uncertainty of the solubility values is acetone > acetonitrile. The solubility of compound K in methanol is ∼5 times larger than that in acetone, and is even 2 orders of magnitude larger than that in acetonitrile. This is because that the physicochemical properties of the solvent, for instance, polarity, intermolecular interaction, and the ability of solvent to form a hydrogen bond with the drug molecules, influence the dissolution of drugs in pure solvents.10 Methanol has both hydrogen-bond accepting and donating functionalities, and acetone is only the hydrogen-bond acceptor. Besides, the polarity of methanol is more than that of acetone, so the solubility in methanol is higher. The significantly lower solubility in acetonitrile is due to the weak interaction between acetonitrile and compound K. 3.2.1. Correlation of the Solubility Data. The solubility of compound K in pure solvents can be fitted by many thermodynamic approximation methods.

B + C ln T T

(3)

where A, B, and C are empirical constants. The values of A and B reflect the variation in the solution activity coefficient and provide an indication of the effect of solution nonidealities on the solubility of solute. The value of C represents the effect of temperature on the fusion enthalpy.16 Local Composition Model. At the given temperature and pressure, the fugacity of a compound in the liquid phase (fl1) and in the solid phase (fs1) must be the same at phase equilibrium. f1l = f1s

(4)

In the liquid−solid systems, the fugacity in the liquid phase (fl1) can be also be described by the activity coefficient: x1γ1f1l = f1s

(5)

where γ1 is the activity coefficient of the solute. According to the activity coefficient method, the equilibrium solubility of the compound is expressed by the rigorous thermodynamics equation.17 ln x1 = −ln γ1 + +

1 R

∫T

T

m1

ΔfusH1 ⎛ 1 1⎞ 1 − ⎟− ⎜ R ⎝ Tm1 T ⎠ RT ΔCp1 T

dT

∫T

T

ΔCp1 dT

m1

(6)

where Tm is the melting temperature of the solute, ΔfusH is the enthalpy of fusion of the solute, and ΔCp is the difference in heat capacities between the melting and solid states. Besides, the two terms contain ΔCp on the right side can be neglected, so eq 6 become the simplified equation.18 8143

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Research Note

ΔfusH1 ⎛ 1 1⎞ − ⎟ ⎜ R ⎝ Tm1 T⎠

is worthwhile to mention that the optimized α12, which is given in the Supporting Information, ranges from 0.15 to 0.30, while the values of α12 generally vary a range of 0.2−0.47 for vapor− liquid equilibrium.22 However, in choosing the proper value of α12, there exists an ambiguity sometimes. Marina et al.23 indicated that the better accuracies could be obtained with α12 = −1 satisfies all systems. Moreover, the positive values of ln γ1 illustrate that the solutions are positive deviation systems from Raoult’s law and the interactions between solute and solvent are repulsive.24 3.2.2. Mixing Properties in Pure Solvents. In the nonideal system, the excess property is the difference of the mole properties between the real solution and ideal solution under the same temperature and pressure, which can be expressed as25

(7)

As a result, the activity coefficient, enthalpy of fusion and melting temperature should be known for calculating the solubility of the solute based on eq 7. The Wilson model, NRTL model, UNIQUAC model, and UNIFAC19 model were used to calculated the activity coefficient; in this work, the Wilson model and NRTL model were employed. Wilson Model. Wilson’s expression for the activity coefficient of compound in the pure solvent is20 ⎞ ⎛ Λ12 Λ 21 ln γ1 = −ln(x1 + Λ12x 2) + x 2⎜ − ⎟ x 2 + Λ 21x1 ⎠ ⎝ x1 + Λ12x 2 (8)

where Λ12 and Λ21 are the model parameters. Λ12 =

M E = ΔM − ΔM id

⎛ Δλ ⎞ ⎛ λ − λ11 ⎞ V2 V2 ⎟= exp⎜ − 12 exp⎜ − 12 ⎟ ⎝ ⎝ RT ⎠ V1 RT ⎠ V1

Recasting eq 15, it becomes

ΔM = M E + ΔM id

(9)

⎛ λ − λ 22 ⎞ ⎛ Δλ ⎞ V1 V ⎟ = 1 exp⎜ − 21 ⎟ exp⎜ − 21 ⎝ ⎠ ⎝ RT ⎠ V2 RT V2

(10)

where Δλ12 and Δλ21 are the cross interaction energy parameters, which can be fitted by the experimental solubility, and V2 and V1 are the mole volumes of the solute and solvent. NRTL Model. The activity coefficient of this model is given by21 2 ⎤ ⎡ τ21G21 τ12G12 ⎥ ln γ1 = x 22⎢ + 2 2 (x 2 + G12x1) ⎦ ⎣ (x1 + G21x 2)

τ12 =

g12 − g22 RT

=

G21 = exp( −α12τ21)

and

Δg12 RT

and

τ21 =

g21 − g11 RT

1 ARDP = N

∑ i=1

x1, i − x1, i

ΔSid = −R(x1 ln x1 + x 2 ln x 2)

(18)

ΔH id = 0

(19)

(20)

⎡ ∂(G E /T ) ⎤ H E = − T 2⎢ ⎥ ⎣ ∂T ⎦

RT

where Δg12 and Δg21are the cross interaction energy parameters, and α12 is the parameter related to the nonrandomness in the mixture. The values of α12 were optimized to correlate the NRTL model. The solubility of compound K was correlated by the abovementioned models, and the comparison results between the measured results and calculated ones are given in the Supporting Information and are plotted in Figure 2. The parameters of the five models are given in the Supporting Information, which were obtained by minimizing the average relative deviation percentage (ARDP): x1,cali

(17)

Besides, the excess entropy and enthalpy can be obtained from GE:27

Δg21 (13)

N

ΔGid = RT (x1 ln x1 + x 2 ln x 2)

G E = RT (x1 ln γ1 + x 2 ln γ2)

(12)

=

id

where x1 is the mole fraction of solute and x2 is the mole fraction of solvent. According to the Wilson model, the excess Gibbs energy in the pure solvent is26

(11)

where G12, G21, τ12, and τ21 are model parameters, and these can be expressed as G12 = exp( −α12τ12)

(16)

where M and ΔM represent the excess property and the mixing property in ideal solution, respectively. For ideal solution, the mixing Gibbs free energy, mixing enthalpy, and mixing entropy in pure solvent can be denoted by25 E

and Λ 21 =

(15)

⎛ Δλ12 Λ12 Δλ 21Λ 21 ⎞ = x1x 2⎜ + ⎟ x 2 + x 2 Λ 21 ⎠ ⎝ x1 + x 2 Λ12

SE =

HE − GE T

(21)

(22)

Using the Wilson model, the infinite-dilution activity coefficient (ln γ∞ 1 ) and the infinite-dilution reduced excess enthalpy 28 (HE,∞ 1 ) of compound K also can be obtained. ln γ1∞ = −ln Λ12 + 1 − Λ 21

(23)

⎛V ⎞ ⎛H ⎞ ⎛ Δλ ⎞ H1E , ∞ = ⎜ E ⎟ = Δλ12 + Δλ 21⎜ 1 ⎟ exp⎜ − 12 ⎟ ⎝ RT ⎠ ⎝ V2 ⎠ ⎝ x1x 2 ⎠x → 0

100 (14)

where N is the number of experimental points, x1,i and xcal 1,i are the experimental solubility value and calculated solubility value, respectively. The overall ARDPs of the five models are 2.296% (van’t Hoff), 2.084% (λh), 1.629% (Apelblat), 1.087% (Wilson), and 1.383% (NRTL). As a result, the Wilson model is the best one for correlating the solubility of compound K in pure solvents. It

1

(24)

Substituting the Wilson model and the solubility data into eqs E,∞ 15−24, the calculated values of ΔG, ΔH, ΔS, ln γ∞ 1 , and H1 of compound K are listed in the Supporting Information. The value of ΔG decreases with increasing solubility, which indicates that dissolution is more favorable. Furthermore, the 8144

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negative ΔG value (Figure 3) verifies that the dissolution of compound K is a spontaneous process. In addition, the ΔH

Figure 3. (a and b) Predicted mixing Gibbs free energy at measured solubility points based on the Wilson model: (■) methanol, (●) acetone, and (▲) acetonitrile.

values are positive in all pure solvents, indicating that the processes are endothermic dissolution and the intermolecular interactions between the solute and solvent are repulsive. The compound K systems are not highly nonideal, since the 25 difference between ln γ1 and ln γ∞ 1 is small. 3.3. Solubility of Compound K in Solvent Mixtures. The influences of temperature and solvent composition on the solubility of compound K in binary solvent mixtures can be seen in the Supporting Information and Figure 4. Similar to the solubility in the pure solvents, it increases as the temperature increases in the entire region. Furthermore, in acetone + water and acetonitrile + water mixtures, the solubility increases strongly with increasing mole fraction of water at first, reaches a maximum, and then decreases to a low value. Whereas, in a methanol + water cosolvent, in the range of studied temperatures, the solubility decreases while the water concentration increases monotonically. The influencing mechanisms are extremely complex (for instance, the polarity of the solvent, solute−solvent interaction, ion−dipole interaction, dipole−dipole interaction, hydrogen bonding−hydrophobic moiety interaction).29 The existence of the maxima results in complex thermodynamic properties, including the influence of

Figure 4. Experimental solubility of ginsenoside compound K in binary mixture solvents at different temperatures ((■) 278.15 K, (●) 288.15 K, (▼) 298.15 K, (□) 308.15 K, and (○) 318.15 K): (a) methanol + water mixture, (b) acetone + water mixture, and (c) acetonitrile + water mixture.

both enthalpy and entropy effects, and no definite explanation has been obtained.30 On the other hand, acetone and acetonitrile act as overall water−structure−breaker and destroy the three-dimensional hydrogen-bonded network.31 This enhances the ability of the solvents to form the hydrogen bond with the drug molecule. However, when the water concentration in the binary mixture solvents increases 8145

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Because of the strong interaction between the two solvents in the system, the mixing effect on the solution is too weak when adding the solute into the solvents. As a result, the partial molar Gibbs free energy was used to indicate the mixing property.

continuously, water clusters are formed. The process of cavity formation is endothermic for against the cohesive forces of the solvent, so the solubility back down afterward.7 The interaction between solute and solvent can be clearly understood through the single crystal structures of compound K in the different mixture solvents (Figure 5), which the single crystals were

ΔG1 = G1E + G1id = RT (x1 ln γ1 + x1 ln x1)

where x1 is the mole fraction of solute. The correlated solubilities were compared with the experimental data and the overall ARDP are summarized in the Supporting Information. The overall ARDP of 35 experimental points is relatively high in the binary solvate systems, which is due to the solubilities are so small in the solvents. It can be seen that several results produced high deviations at low temperature and at certain solvent compositions, such as xwater = 0.5425 and 0.6400 in a methanol + water mixture, xwater = 0.4463 and 0.6168 in an acetone + water mixture, and xwater = 0 and 0.6030 in an acetonitrile + water mixture. (See Figure 6.) The overall ARDP would reduce to a small value when excluding these data, but these data were not excluded from the calculations to avoid the bias. In addition, the Wilson model parameters are listed in the Supporting Information. The calculated values of ln γ1 and ΔG1 are shown in the Supporting Information, according to eqs 25−27. The results show that the partial molar Gibbs free energy diminishes with the increasing of the mole fraction of water in the methanol + water mixture and acetonitrile + water mixture at first, but it increases as the water proportion increases in the acetone + water binary up to xwater = 0.7632 and in the acetonitrile + water binary up to xwater = 0.6030. The minimum value of ΔG1 indicates the most favorable dissolution and the highest solubility in the solution. On the other hand, the changing trend of active coefficient is the same as that of the solubility. These results are very useful for optimizing the crystallization of compound K. The high yield of the two polymorphisms can be obtained in the pure methanol and in the acetone + water cosolvent with xwater = 0.7632.

Figure 5. The chemical structures of ginsenoside compound K in different binary mixture solvents: (a) acetone + water mixture and (b) acetonitrile + water mixture.

4. CONCLUSIONS Differential scanning calorimetry (DSC) was used to measure the melting temperature (Tm) and the enthalpy of fusion (ΔfusH) of ginsenoside compound K, to be 435.57 K and 5151.22 J/mol, and 451.19 K and 18 879.25 J/mol in different solvents, respectively. The result shows that there are two polymorphisms of compound K in the used solvents. The solubility of compound K in three pure solvents and three binary solvent mixtures were measured. Experimental data on the solubility of compound K in pure organic solvents, methanol, acetone, and acetonitrile were obtained by a static method in the temperature range from 278.15 K to 318.15 K. The solubilities of compound K are dependent on the temperature, and, at constant temperature, have the following order: methanol > acetone > acetonitrile. The van’t Hoff plot, the modified Apelblat equation, the λh (Buchowski) equation, the Wilson model, and the NRTL model were chosen to correlate the experimental data. The fitting results of Wilson model is the best. In order to understand the solubility behavior, the mixing Gibbs free energies, enthalpies, and entropies of solutions in pure solvents were derived based on Wilson model parameters. The results show that the dissolution of compound K is a spontaneous endothermic process and the solutions are positive deviation systems from Raoult’s law.

obtained through slow evaporation the saturated solutions. The results show that water plays a very important role in forming the chemical structures in acetone + water and acetonitrile + water mixtures, which indicates preferential solvation of compound K in the two systems. It can be found that the Wilson model gives the best fit in pure solvents. Therefore, it was used to correlate the solubility with the fraction of water in the binary solvent systems. The activity coefficient of this model can be expressed as19 ln γ1 = 1 − ln(x1 + Λ12x 2 + Λ13x3) Λ 21x 2 x1 − x1 + Λ12x 2 + Λ13x3 x 2 + Λ 21x1 + Λ 23x3 Λ32x3 − x3 + Λ31x1 + Λ32x 2 (25) −

where Λij =

⎛ λij − λii ⎞ Vj ⎛ Δλij ⎞ exp⎜ − exp⎜ − ⎟= ⎟ Vi RT ⎠ Vi ⎝ ⎝ RT ⎠

(27)

Vj

(26)

where i = 1, 2, 3, j = 1, 2, 3, and Δλ12, Δλ21, Δλ13, Δλ31, Δλ23, and Δλ32 are the cross interaction energy parameters. 8146

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solutions with the fraction of water, whereas the solubilities decrease with the water content increases in the water + methanol mixture. The solubilities in solvent mixtures were correlated with the fraction of water obtained using the Wilson model. Because of the strong interactions between the two solvents, the partial molar Gibbs free energies, which are corresponding to the solubility, were calculated. Finally, the appropriate crystallization conditions were determined according to the results.

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ASSOCIATED CONTENT

S Supporting Information *

Experimental solubility, optimized parameters for the models, and predicted values of the mixing properties in pure solvents and binary mixture solvents. This material is available free of charge via the Internet at http://pubs.acs.org/.

■

AUTHOR INFORMATION

Corresponding Author

*Tel.: 86-22-27405754. Fax: +86-22-27374971. E-mail: junbo_ [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This material is based upon work supported by National Natural Science Foundation of China (Nos. 20836005 and 21176173) and Tianjin Municipal Natural Science Foundation (Nos. 10JCYBJC14200 and 11JCZDJC20700). The analysis tools used in this study were supported by State Key Laboratory of Chemical Engineering (No. SKL-ChE-11B02).

■

Figure 6. Calculated values of ΔG1 in binary mixture solvents at different temperatures ((■) 278.15 K, (●) 288.15 K, (▼) 298.15 K, (□) 308.15 K, and (○) 318.15 K): (a) methanol + water mixture, (b) acetone + water mixture, and (c) acetonitrile + water mixture.

Furthermore, the solubility of compound K in water is very low, so that the solubility in water + methanol, water + acetone, water + acetonitrile cosolvents were measured using the gravimetric method as well. It indicates that there are two maxima in the water + acetone and water + acetonitrile

NOTATIONS A = empirical constant for the modified Apelblat equation ARDP = average relative derivation percentage B = empirical constant for the modified Apelblat equation C = mpirical constant for the modified Apelblat equation f = fugacity Δg12 = cross interaction energy parameter for the NRTL model (g12−g22) (J/mol) Δg21 = cross interaction energy parameter for the NRTL model (g21−g11) (J/mol) ΔG = mixing Gibbs free energy (J/mol) GE = excess Gibbs free energy (J/mol) h = model parameter for the λh equation ΔH = mixing enthalpy (J/mol) HE = excess enthalpy (J/mol) HE,∞ = infinite-dilution reduced excess enthalpy (J/mol) ΔHsoln = van’t Hoff enthalpy of solution ΔfusH = enthalpy of fusion at the melting point (J/mol) N = number of experimental data R = gas constant; R = 8.3145 J/(mol K) ΔS = mixing entropy (J/(mol K)) SE = excess entropy (J/(mol K)) ΔSsoln = van’t Hoff entropy of solution T = temperature (K) Tm = melting temperature (K) V = molar volume (cm3/mol) x = mole fraction in the solution

Greek Letters

α12 = nonrandomness parameter γ = activity coefficient

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γ∞ = infinite-dilution activity coefficient λ = model parameter for the λh equation Δλ12 = cross interaction energy parameter for Wilson equation (λ12 − λ11) (J/mol) Δλ21 = cross interaction energy parameter for Wilson equation (λ21 − λ22) (J/mol)

aspartate in water from T = (278 to 348) K. J. Chem. Thermodyn. 1999, 31, 85−91. (16) Wei, D. W.; Pei, Y. H. Solubility of Diphenyl Carbonate in Pure Alcohols from 283 to 333 K. J. Chem. Eng. Data 2008, 53, 2710−2711. (17) Prausnitz, J. M.; Lichtenthaler, R. N.; Azevedo, E. G. Molecular Thermodynamics of Fluid Phase Equilibria, 3rd ed.; Prentice Hall: Englewood Cliffs, NJ, 1999. (18) Long, B. W.; Li, J.; Song, Y. H.; Du, J. Q. Temperature Dependent Solubility of α-Form L-Glutamic Acid in Selected Organic Solvents: Measurements and Thermodynamic Modeling. Ind. Eng. Chem. Res. 2011, 50, 8354−8360. (19) Manifar, T; Rohani, S. Measurement and Development of Solubility Correlations for Tritolylamine in Twelve Organic Solvents. Ind. Eng. Chem. Res. 2005, 44, 970−976. (20) Wilson, G. M. Vapor-liquid Equilibrium. XI. A New Expression for the Excess Free Energy of Mixing. J. Am. Chem. Soc. 1964, 86, 127−130. (21) Renon, H.; Prausnitz, J. M. Local Compositions in Thermodynamic Excess Functions for Liquid Mixtures. AIChE J. 1968, 14, 135−144. (22) Wei, D. W.; Pei, Y. H. Measurement and Correlation of Solubility of Diphenyl Carbonate in Alkanols. Ind. Eng. Chem. Res. 2008, 47, 8953−8956. (23) Marina, J. M.; Tassios, D. P. Effective Local Compositions in Phase Equilibrium Correlations. Ind. Eng. Chem. Process Des. Dev. 1973, 12, 67−71. (24) Nordstrom, F. L.; Rasmuson, C. Prediction of Solubility Curves and Melting Properties of Organic and Pharmaceutical Compounds. Eur. J. Pharm. Sci. 2009, 36, 330−344. (25) Smith, J. M.; Ness, H. C. V.; Abbott, M. M. Introduction to Chemical Engineering Thermodynamics; McGraw−Hill: New York, 2001. (26) Kondepudi, D. K. Introduction to Modern Thermodynamics; John Wiley & Sons, Ltd: Chichester, England, 2008. (27) Yan, H.; Wang, Z.; Wang, J. K. Correlation of Solubility and Prediction of the Mixing Properties of Capsaicin in Different Pure Solvents. Ind. Eng. Chem. Res. 2012, 51, 2808−2813. (28) Gow, A. S. Calculation of Vapor−Liquid Equilibria from Infinite-Dilution Excess Enthalpy Data using the Wilson or NRTL Equation. Ind. Eng. Chem. Res. 1993, 32, 3150−3161. (29) Chaudhari, P.; Sharma, P.; Barhate, N.; Kulkarni, P.; Mistry, C. Solubility enhancement of hydrophobic drugs using synergistically interacting cyclodextrins and cosolvent. Curr. Sci. 2007, 92, 1586− 1591. (30) Granberg, R. A.; Rasmuson, K. C. Solubility of Paracetamol in Binary and Ternary Mixtures of Water + Acetone + Toluene. J. Chem. Eng. Data 2000, 45, 478−483. (31) Blandamer, M. J.; Burgess, J. Kinetic reactions in aqueous mixtures. Chem. Soc. Rev. 1975, 4, 55−75.

Subscripts

1 = solute (ginsecoside compound K) 2, 3 = solvent (methanol, acetone, acetonitrile and water) Superscripts

cal = calculated data id = ideal solution l = liquid s = solid

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REFERENCES

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dx.doi.org/10.1021/ie300945p | Ind. Eng. Chem. Res. 2012, 51, 8141−8148