Determination and Correlation of Solubility Data and Dissolution

May 22, 2014 - Solvent screening plays a key role in the optimization of the drug crystallization process based on the solubility data and dissolution...
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Determination and Correlation of Solubility Data and Dissolution Thermodynamic Data of Cefixime Trihydrate in Seven Pure Solvents Tianwei Zhang, Quan Liu, Zhiping Xie, Xiaopeng Song, and Junbo Gong* School of Chemical Engineering and Technology, State Key Laboratory of Chemical Engineering, Tianjin University, Tianjin 300072, People’s Republic of China

ABSTRACT: Solvent screening plays a key role in the optimization of the drug crystallization process based on the solubility data and dissolution thermodynamic data. In this article, the solubility of cefixime trihydrate in ethanol, propan-2-ol, butan-1-ol, butan-2-ol, pentan-1-ol, ethyl acetate, and acetone from 278.15 to 323.15 K at atmospheric pressure is reported. It is found that the solubility of cefixime trihydrate in all seven solvents increases with temperature. The modified Apelblat equation fits well with the experimental solubility data in all selected solvents with the average percent deviation less than 3.5 %. The mixing properties including the mixing free Gibbs energy, enthalpy, and entropy of cefixime trihydrate were calculated based on the van’t Hoff equation. The results indicate that the dissolution process of cefixime trihydrate in all tested solvents is endothermic, entropically driven and not spontaneous.

1. INTRODUCTION Cefixime trihydrate (CAS Registry No. 125110-14-7) chemically (6R,7R)-7[(Z)-2-(2-amino-4-thiazolyl)-2-(carboxymethoxyimino]-acet-amido)-8-oxo-3-vinyl-5-thia-1-azabicyclo(4,2,0) octa-2-ene-2 carboxylic acid trihydrate (C16H21N5O10S2) is an oral third generation cephalosporin antibiotic used to treat infections caused by bacteria such as pneumonia, bronchitis, and gonorrhea and ear, lung, throat, and urinary tract infections. It is a white to slightly yellowish crystalline powder.1,2 Figure 1 gives its chemical structure. Reaction crystallization is the major method in the industrial manufacturing process of cefixime trihydrate. The solubility

data are important physicochemical parameters influencing solution thermodynamics, crystallization kinetics and crystal interface structure in processes of solution crystallization and further recrystallization.3 However, solubility data of cefixime trihydrate in pure solvents has not been reported yet. In this work, the solubility of cefixime trihydrate in ethanol, propan-2-ol, butan-1-ol, butan-2-ol, pentan-1-ol, ethyl acetate, and acetone from (278.15 to 323.15) K at atmospheric pressure was measured by a gravimetric method.4 The van’t Hoff equation, modified Apelblat equation, and Wilson and NRTL models were applied to correlate the experimental data, based on the pure component thermodynamic properties (including mole volume, melting temperature, and enthalpy of fusion).5,6 The standard dissolution enthalpy, entropy, and the free Gibbs energy changes of cefixime trihydrate in these solvents were calculated from the measured solubility data using the modified version of the van’t Hoff equation. Received: January 19, 2014 Accepted: May 12, 2014 Published: May 22, 2014

Figure 1. Sketch of molecule structure of cefixime trihydrate. © 2014 American Chemical Society

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2. EXPERIMENTAL SECTION Materials. Table 1 shows the description of materials used in the paper, including ethanol, propan-2-ol, butan-1-ol, butan2-ol, pentan-1-ol, ethyl acetate, and acetone.

kept at a certain temperature controlled by a thermostatical bath (SW23, Julabo, Germany) with a stability of 0.05 K. The solutions were stirred for 12 h to make sure the solid−liquid equilibrium was attained and then settled for another 2 h without stirring. Five mL of upper clear solution was sampled by filtration through a 0.2 μm pore size syringe filter and evaporated in a vacuum drying oven at 50 °C for 48 h. The samples were then measured for several times every 0.5 h to make sure that the weight kept constant. All of the masses were measured using a balance (Model AB204, Mettler Toledo, Switzerland) with the precision of ± 0.0001 g. The experiment was repeated three times and the arithmetic average value was used as the final result to calculate the mole fraction solubility (x1) based on the following equation

Table 1. Sources and Mass Fraction Purity of Materials materials cefixime trihydrate ethanol propan-2-ol butan-1-ol butan-2-ol pentan-1-ol ethyl acetate acetone

source Guangzhou Baiyunshan Pharmaceutical Co., Ltd. China Tianjin Kewei Chemical Co, China Tianjin Kewei Chemical Co, China Tianjin Kewei Chemical Co, China Tianjin Kewei Chemical Co, China Tianjin Kewei Chemical Co, China Tianjin Kewei Chemical Co, China Tianjin Kewei Chemical Co, China

mass fraction purity

purification method

analysis method

> 99.7 %

none

HPLCa

> 99.7 %

none

GCb

> 99.8 %

none

GCb

> 99.5 %

none

GCb

> 99.5 %

none

GC

b

> 99.6 %

none

GCb

> 99.6 %

none

GCb

> 99.6 %

none

GCb

x1 =

m1/M1 m1/M1 + m2 /M 2

(1)

where m1 and m2 represent the mass of the solute and the solvent, respectively, and M1 and M2 are the molecular masses of solute and solvent, respectively. The obtained solids were then analyzed by powder X-ray diffraction to confirm that the solid phase in equilibrium with the liquid is cefixime trihydrate.

a High performance liquid chromatography. bGas liquid chromatography. Both the analysis method and the mass fraction purity were provided by the suppliers.

3. THERMODYNAMIC MODELS van’t Hoff Equation. For an ideal solution, the van’t Hoff equation relates the logarithm of mole fraction of a solute as a linear function of the reciprocal of the absolute temperature.

Melting Properties Evaluation. The thermal analysis (DSC/TG) of cefixime trihydrate in Figure 2 exhibits a water

ln x1 = −ΔHfus/(RT ) + ΔSfus/R

(2)

where x1 is the mole fraction solubility, ΔHfus and ΔSfus are the mole enthalpy and entropy of fusion of the solute, respectively, T is the corresponding absolute temperature, and R is the gas constant. In practice, ΔHfus and ΔSfus are replaced with ΔHd (enthalpy of dissolution) and ΔSd (entropy of dissolution) by taking the mixing effect into consideration, respectively.8,9 ln x1 = −ΔHd /(RT ) + ΔSd /R

(3)

Modified Apelblat Equation. The modified Apelblat Equation is a semiempirical model, which can also be used to correlate the solubility and the temperature as follows:10 ln x1 = A + B /T + C ln T

(4)

where A, B, and C are empirical constants. The values of A and B represent the variation in the solution activity coefficient and provide an indication of the effect of solution nonidealities on the solubility of solute, while the value of C reflects the effect of temperature on the fusion enthalpy.11 Local Composition Models. According to the phase equilibrium criteria, the fugacity of the compound in the liquid ( f1l) and solid ( f1s) phases must be the same at constant temperature T and pressure P

Figure 2. DSC curve of cefixime trihydrate.

loss of 11 % in the temperature range (25−110) °C (the theoretical water content of cefixime trihydrate is 10.65 %) and a decomposition before cefixime trihydrate showing a clear melting peak since the mass of the samples declines with the increasing temperature from 200 °C. So, the melting temperature (Tm) and enthalpy of fusion (ΔfusH) of cefixime trihydrate cannot be obtained through thermal analysis. In this work, a group contribution method7 was used to determine Tm and ΔfusH. Solubility Measurements. The solubility of cefixime trihydrate in ethanol, propan-2-ol, butan-1-ol, butan-2-ol, pentan-1-ol, ethyl acetate, and acetone from (278.15 to 323.15) K were measured by the gravimetric method. Excess solid cefixime trihydrate was added to different solvents and

f1l (T , P , x1) = f1s (T , P)

(5)

In the equilibrium system, the fugacity in the liquid phase ( fl1) can be expressed by the activity coefficient x1γ1(T , P , x1)f1l (T , P) = f1s (T , P)

(6)

where γ1 is the activity coefficient of the solute in the liquid phase. 1916

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Table 2. Mole Volumes of Pure Components (293.15 K, 0.1 MPa) cefixime trihydrate

ethanol

propan-2-ol

butan-1-ol

butan-2-ol

pentan-1-ol

ethyl acetate

acetone

498.2

58.52

76.78

91.94

92.12

108.5

98.59

73.40

Vm/10−6/m3·mol−1

first-order groups. Thus, the estimation is performed at three successive levels by the following equations

Based on further assumptions, a simplified and well-known equation was obtained12,13 ln x1 =

⎞ ΔfusH ⎛ T − 1⎟ − ln γ1 ⎜ RT ⎝ Tm ⎠

Tm = Tm0 ln(∑ NT i m1i + (7)

i

where x1, Tm, ΔfusH, R, and T represent the mole fraction solubility of the solute, the melting point of the solute, the solute enthalpy of fusion at its melting point, the gas constant, and the absolute temperature of the solution, respectively. In our study, the solute activity coefficient γ1 were calculated by two well-established activity coefficient models, the Wilson and the NRTL model. Wilson Model. Wilson’s expression for the activity coefficient of compound in the pure solvent is

(8)

Λ12 =

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

(9)

Λ 21 =

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

(10)

i

+

k

(13)

∑ MjHfus2j j

(14)

where Tm0 and Hfus0 are adjustable parameters, with the values of 147.450 K and −2.806 kJ·mol−1, respectively. Tm1i and Hf us1i represent the contributions of the first-order groups for the corresponding properties. Similarly, Tm2j, Hfus2j and Tm3k, Hfus3k represent the contributions of the second-order and third-order groups, respectively. The melting temperature and enthalpy of fusion of cefixime trihydrate estimated by this method are 500.15 K and 23.902 kJ·mol−1, respectively. Although the calculated solubility data agree well with the experimental data in this study, these estimated properties cannot be considered as the real physical properties of cefixime trihydrate. Mole Volumes of Pure Components. Table 2 gives the mole volumes of solvents obtained from literatures15 and that of cefixime trihydrate calculated by its density, 1.019 g·cm−3, which was measured using a pycnometer method.16 Solubility Data. The measured mole fraction solubility data of cefixime trihydrate in the seven pure solvents at temperatures from (278.15 to 323.15) K are presented in Table 3 and plotted in Figure 3. For each solvent, the solubility of cefixime trihydrate increases with the rise of temperature ranking as acetone > ethanol > butan-1-ol ≈ propan-2-ol ≈ butan-2-ol > ethyl acetate > pentan-1-ol at temperature below 298.15 K and acetone > ethanol > butan-1-ol > propan-2-ol > butan-2-ol > ethyl acetate > pentan-1-ol at temperature above 298.15 K. It is found that polarity of solvents is not the only factor that affect the solubility of cefixime trihydrate because the polarity order of solvents is ethanol (65.4) > butan-1-ol (60.2) > pentan-1-ol (56.8) > butan-2-ol (55.2) > propan-2-ol (54.6) > acetone (35.5) > ethyl acetate (23).17 Since both hydrophilic groups (carboxyl group, imino group) and hydrophobic groups (carbon−carbon double bond, phenyl group) exist in cefixime trihydrate, the hydrogen bond interaction between the solute and solvent also influence its dissolution capability. Regression Analysis of Solubility Data. The Van’t Hoff equation, modified Apelblat equation, Wilson and NRTL model were employed to correlate the solubility data by Matlab software which gave both the parameters in each model and the calculated solubility of cefixime trihydrate. To minimize the objective function f = (x1cal-x1exp), a nonlinear least-squares method was applied in this work. The calculated mole fraction solubility data x1cal are presented in Table 3 and the model parameters during the optimization procedure are listed in Table 4. The average percent deviation (APD %), defined as

Here Δλ12 and Δλ21 are the cross interaction energy parameters and V1 and V2 are the mole volumes of solute and solvent, respectively.9 NRTL Model. In the binary system, the activity coefficient in this model is given by6

(11)

Here G12 = exp( −α12τ12) G21 = exp( −α12τ21) τ12 = (g12 − g22)/(RT ) τ21 = (g21 − g11)/(RT )

∑ OkHfus3k) k

where

⎡ τ G 2 τ12G12 2 ⎤ 21 21 ⎥ ln γ1 = x 2 2⎢ + (x 2 + G12x1)2 ⎦ ⎣ (x1 + G21x 2)2

j

ΔfusH = Hfus0 + (∑ NH i fus1i +

ln γ1 = −ln(x1 + Λ12x 2) + x 2(Λ12 /x1 + Λ12x 2 − Λ 21/x 2 + Λ 21x1)

∑ MjTm2j + ∑ OkTm3k)

(12)

where Δg12 (= g12 − g22) and Δg21 (= g21 − g11) represent different interaction energies, parameter α12 is a measurement of the nonrandomness of the mixture, which generally varies between 0.20 and 0.47.14 In the current study, the values of α12 were optimized to correlate the solubility data in the six pure solvents and 0.20 was adopted.

4. RESULTS AND DISCUSSION Melting Properties Evaluation. Marrero and Gani7 consider the molecular structure of a compound to be a collection of three types of groups; the first-orders groups are intended to describe a wide variety of organic compounds, while the role of the second and third-order groups is to provide more structural information about molecular fragments of compounds whose description is insufficient through the 1917

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Table 3. Experimental and Calculated Solubility of Cefixime Trihydrate in Seven Pure Solvents (0.1 MPa)a T/K

104 xexp 1

104 xcal,vf 1

± ± ± ± ± ± ± ± ± ±

104 xcal,Apel 1

104 xcal,Wil 1

104 xcal,NRTL 1

18.90 21.53 24.55 28.01 31.98 36.54 41.77 47.77 54.64 62.52

17.50 20.52 23.95 27.80 32.12 36.96 42.33 48.32 54.92 62.30

16.82 19.88 23.36 27.30 31.74 36.72 42.29 48.50 55.38 63.02

9.341 10.89 12.67 14.70 17.02 19.67 22.67 26.08 29.94 34.30

8.541 10.19 12.10 14.27 16.76 19.56 22.75 26.31 30.31 34.85

9.064 10.72 12.61 14.74 17.15 19.85 22.86 26.22 29.94 34.04

9.500 10.84 12.50 14.56 17.12 20.30 24.26 29.20 35.40 43.17

8.062 9.866 12.02 14.58 17.56 21.06 25.19 29.96 35.49 42.06

8.001 9.838 12.02 14.60 17.63 21.16 25.28 30.03 35.51 41.85

8.982 10.26 11.75 13.48 15.49 17.83 20.55 23.71 27.38 31.65

7.575 9.086 10.84 12.86 15.15 17.78 20.78 24.14 27.97 32.25

7.666 9.187 10.94 12.96 15.25 17.86 20.82 24.14 27.88 31.06

3.884 4.968 6.323 8.010 10.10 12.69 15.86 19.76 24.51 30.29

3.841 4.939 6.291 7.989 10.10 12.74 15.80 19.69 24.61 30.30

4.349 5.523 6.956 8.699 10.80 13.34 16.32 19.89 24.13 29.06

6.982 8.122 9.505 11.18 13.23

6.203 7.591 9.251 11.20 13.49

6.177 7.582 9.252 11.22 13.52

ethanol 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

18.93 20.95 24.61 28.46 32.13 37.05 41.52 47.78 53.57 63.21

1.08 1.19 1.40 1.62 1.83 2.11 2.37 2.72 3.05 3.60

17.89 20.92 24.34 28.17 32.45 37.19 42.45 48.25 54.61 61.58

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

9.180 ± 0.523 10.47 ± 0.60 12.82 ± 0.73 14.81 ± 0.84 17.83 ± 1.02 19.54 ± 1.11 23.03 ± 1.31 25.53 ± 1.46 29.05 ± 1.66 35.01 ± 2.00

9.064 10.72 12.61 14.74 17.15 19.85 22.86 26.22 29.94 34.04

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

9.831 ± 0.560 10.22 ± 0.58 12.24 ± 0.70 15.12 ± 0.86 17.24 ± 0.98 20.01 ± 1.14 24.91 ± 1.42 29.32 ± 1.67 34.31 ± 1.96 43.68 ± 2.49

7.915 9.774 11.98 14.59 17.64 21.20 25.33 30.08 35.54 41.78

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

8.990 ± 0.512 9.950 ± 0.567 11.86 ± 0.68 14.28 ± 0.81 15.04 ± 0.86 17.32 ± 0.99 21.07 ± 1.20 23.43 ± 1.34 27.58 ± 1.57 31.60 ± 1.80

8.373 9.888 11.61 13.56 15.75 18.21 20.95 24.00 27.38 31.10

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

4.030 ± 0.230 5.100 ± 0.291 6.020 ± 0.343 7.790 ± 0.444 10.10 ± 0.58 13.64 ± 0.78 15.15 ± 0.86 19.14 ± 1.09 25.47 ± 1.45 29.97 ± 1.71

3.685 4.810 6.220 7.974 10.14 12.79 16.01 19.89 24.55 30.11

278.15 283.15 288.15 293.15 298.15

6.785 ± 0.387 7.472 ± 0.426 9.712 ± 0.554 11.60 ± 0.66 13.93 ± 0.79

6.119 7.540 9.226 11.21 13.53

propan-2-ol

butan-1-ol

butan-2-ol

pentan-1-ol

ethyl acetate

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Table 3. continued T/K

104 xexp 1

104 xcal,vf 1

104 xcal,Apel 1

104 xcal,Wil 1

104 xcal,NRTL 1

15.72 18.76 22.47 27.01 32.58

16.15 19.26 22.89 27.04 31.98

16.20 19.32 22.92 27.06 31.85

24.31 26.83 29.97 33.83 38.56 44.36 51.48 60.20 70.93 84.13

20.94 24.79 29.18 34.18 39.87 46.28 53.56 61.72 70.98 81.45

20.91 24.78 29.20 34.23 39.95 46.40 53.67 61.82 70.96 81.17

ethyl acetate 303.15 308.15 313.15 318.15 323.15

15.90 18.51 22.59 25.68 33.38

± ± ± ± ±

0.91 1.06 1.29 1.46 1.90

16.23 19.36 22.96 27.08 31.79

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

22.31 27.55 30.84 34.56 39.96 44.02 51.84 58.07 70.12 85.40

± ± ± ± ± ± ± ± ± ±

1.27 1.57 1.76 1.97 2.28 2.51 2.95 3.31 4.00 4.87

20.83 24.74 29.21 34.29 40.05 46.53 53.79 61.90 70.93 80.92

acetone

xcal,Apel , xcal,Wil , and xcal,NRTL represent the calculated solubility data by the van ’t Hoff, modified Apelblat, Wilson and NRTL models, 1 1 1 respectively. The standard uncertainty of T is u(T) = 0.01 K. The relative standard uncertainty of the solubility measurement is ur(x) = 0.06 (0.95 level of confidence). a cal,vf x1 ,

where N refers to the number of experimental points, x1,i and xcal 1,i represent the experimental and calculated solubility data, respectively. The APD % of different correlation models are shown in Table 5. It can be seen that all models give correlation results with APD % less than 7.5 and the modified Apelblat equation gives a best correlation result with APD % less than 3.5 in all the solvents. The comparison between the experimental and calculated data by the modified Apelblat equation in Figure 3 also demonstrates that it can give satisfying correlation results for cefixime trihydrate. These models preformed differently because they are derived from different hypotheses. As we know, the van’t Hoff equation is more applicable when the solubility of the solute in solvent is low because it is deduced based on ideal solution. The modified Apelblat equation has a third part, C ln T, which makes it a nonlinear regression of experiment data rather than a linear one compared to the van’t Hoff equation, in most cases, it has a better fitting result than the van’t Hoff equation. Both the Wilson and NRTL equations are proposed based on the concept of local composition. The distribution of molecules is not purely random in a mixture with specific interactions and that nonideal mixing is associated with this fact. Compared with the two parameters of Wilson model, NRTL contains three parameters per binary interaction. The third parameter α is

Figure 3. Experimental and correlated solubility data of cefixime trihydrate in different solvents: ■, ethanol; ○, propan-2-ol; ▲, butan1-ol; □, butan-2-ol; Δ, pentan-1-ol; ●, ethyl acetate;▼, acetone;. The solid lines are correlated values by the modified Apelblat model.

APD% =

100 N

N

∑ i=1

x1, i − x1, i cal x1, i

(15)

was used to evaluate the correlation results to assess the applicability and accuracy of the models used in this paper,

Table 4. Parameters for the van’t Hoff, Modified Apelblat, Wilson, and NRTL models for the Solubility of Cefixime Trihydrate in Seven Pure Solvents model van’t Hoff Apelblet

Wilson NRTL

ΔH/104·J·mol−1 ΔS/104·J·mol−1 A/104 B/104 C/104 Δλ12/104·J·mol−1 Δλ21/104·J·mol−1 Δg12/104·J·mol−1 Δg21/104·J·mol−1

ethanol

propan-2-ol

butan-1-ol

butan-2-ol

pentan-1-ol

ethyl acetate

acetone

2.0532 0.0021 −0.0118 0.2994 0.0018 −0.3195 2.0802 2.4735 0.1256

2.1975 0.0021 −0.0061 0.0232 0.0009 −0.0908 2.8026 2.4989 0.2883

2.7626 0.0040 −0.0332 1.1992 0.0050 0.0379 0.6585 0.8002 0.1884

2.1792 0.0019 −0.0146 0.4076 0.0022 −0.0206 2.1094 2.4840 0.3089

3.4886 0.0060 −0.0073 −0.0518 0.0012 0.4531 0.3124 0.0531 0.6794

2.7363 0.0037 0.0243 0.7939 0.0037 0.0883 0.7439 0.9945 0.2277

2.2541 0.0030 −0.0324 1.2135 0.0049 −0.2886 1.0270 1.5492 −0.0395

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Table 5. APD % of the Four Models in Seven Pure Solvents model

ethanol

propan-2-ol

butan-1-ol

butan-2-ol

pentan-1-ol

ethyl acetate

acetone

van’t Hoff Apelblet Wilson NRTL

1.687 1.031 2.192 3.449

2.044 2.170 3.407 3.702

4.996 2.506 4.439 4.680

2.981 2.022 5.423 5.080

4.023 3.380 3.314 7.254

4.048 3.297 3.797 3.912

4.5606 2.7803 4.3437 4.4164

Table 6. Dissolution Enthalpy ΔHd, Entropy ΔSd, and Gibbs Free Energy Change ΔGd of Cefixime Trihydrate in Seven Pure Solventsa

related to the nonrandomness in the mixture, the relatively high values for parameter α show that the mixtures are nonideal. For strongly nonideal mixtures, the Wilson and NRTL equation often provide a good representation of experimental data. Dissolution Properties. The van’t Hoff equation reveals the relationship between the mole fraction solubility of a solute and the absolute temperature in a real solution, as shown in eq 2. By plotting ln x1 versus 1/T as presented in Figure 4, the

ΔHd solvent

−1

ΔGdb

J·mol ·K

19941.5 21821.9 25231.3 20962.9 33880.5 26027.9 20883.6

19.2842 20.2565 32.1301 16.7216 56.4142 32.5104 24.2834

J·mol

ethanol propan-2-ol butan-1-ol butan-2-ol pentan-1-ol ethyl acetate acetone

ΔSd

−1

−1

J·mol−1 13709.8 15276.0 14848.5 15559.3 15650.2 15522.2 13036.4

a Combined expanded uncertainties U are Uc(ΔHd) = 0.040ΔHd, Uc(ΔSd) = 0.060ΔSd, Uc(ΔGd) = 0.065ΔGd (0.95 level of confidence). b Calculated values at 323.15 K.

cefixime trihydrate increases with the rise of temperature in the tested solvents ranking as acetone > ethanol > butan-1-ol ≈ propan-2-ol ≈ butan-2-ol > ethyl acetate > pentan-1-ol at temperatures below 298.15 K and acetone > ethanol > butan-1ol > propan-2-ol > butan-2-ol > ethyl acetate > pentan-1-ol at temperatures above 298.15 K. It indicates that the solubility of cefixime trihydrate not only depends on the polarity of solvents, but also depends on the intermolecular interaction and the ability of solvent to form a hydrogen bond with the drug molecules. The experimental data were correlated with van’t Hoff equation, modified Apelblat equation, Wilson model, and NRTL model. It is found that all the models give correlation results with APD % less than 7.5 and the modified Apelblat equation provides the best fitting result with the APD % less than 3.5 in all solvents. In addition, the dissolution enthalpy, entropy, and molar Gibbs free energy of cefixime trihydrate in different solvents were predicted by the van’t Hoff equation. The results show that the dissolution process of cefixime trihydrate in the seven solvents is endothermic, entropy-driven and not spontaneous.

Figure 4. van’t Hoff plot of logarithm mole fraction solubility of cefixime trihydrate in different solvents: ■, ethanol; ○, propan-2-ol; ▲, butan-1-ol; □, butan-2-ol; Δ, pentan-1-ol; ●, ethyl acetate;▼, acetone.

values of enthalpy and entropy of dissolution can be obtained from the slope and the intercept, respectively. In addition, the changes of Gibbs free energy ΔGd for the dissolution of cefixime trihydrate in different solvents were calculated by the Gibbs−Helmholtz equation18 ΔGd = ΔHd − T ΔSd

■

(16)

The results and the uncertainty are listed in Table 6. As shown, ΔHd and ΔSd of cefixime trihydrate are positive in all the solvents [(278.15 to 323.15) K], which demonstrate that the dissolution process is endothermic, entropy-driven and that explains the increasing solubility of cefixime trihydrate with increasing temperature. What’s more, the change trend of ΔGd is opposite to the tendency of the solubility except for butan-2-ol. According to the classical thermodynamics theory, the lower ΔGd values are, the more favorable the dissolution capacity of cefixime trihydrate is and thus a higher solubility.

AUTHOR INFORMATION

Corresponding Author

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

The authors are grateful to the financial support of National Natural Science Foundation of China (No. NNSFC 21176173) and National high technology research and development program (863 Program No. 2012AA021202). Notes

The authors declare no competing financial interest.

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5. CONCLUSIONS The equilibrium solubilities of cefixime trihydrate in ethanol, isopropanol, 1-butanol, 2-butanol, pentan-1-ol, ethyl acetate, and acetone from (278.15 to 323.15) K were obtained by a gravimetric method. It can be summarized that the solubility of

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