Measurement and Correlation of Solubility of Azithromycin

Article pubs.acs.org/jced

Measurement and Correlation of Solubility of Azithromycin Monohydrate in Five Pure Solvents Xuemei Wang, Yanan Qin, Tianwei Zhang, Weiwei Tang, Boai Ma, 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: The solubility of azithromycin monohydrate in ethanol, propan-2-ol, butan-1-ol, ethyl ethanoate, and 2propanone from 278.15 K to 323.15 K was measured by a synthetic method. The measured solubility data were correlated by van’t Hoff equation, modified Apelblat equation, λh equation, Wilson, and NRTL models. It was found that the Wilson equations give the best correlation results. The mixing properties including the mixing free Gibbs energy, enthalpy, and entropy of azithromycin monohydrate were also calculated based on the Wilson model parameters. The results indicate that the dissolution process of azithromycin monohydrate in all tested solvents is spontaneous and endothermic.

1. INTRODUCTION Azithromycin (C38H72N2O12, CAS Registry No. 83905-01-5) is a macrolide antibiotic which has been widely used to treat urinary tract infections, skin structure infections, and respiratory tract infections owing to its strong antibacterial activity against both Gram-positive and Gram-negative aerobic micro-organisms.1,2 Its chemical structure is shown in Figure 1. Azithromycin is reported to have many solvates, but studies have been focused on the hydrates of azithromycin.3 In the industrial manufacturing processes of azithromycin, solution crystallization is a key step. The accurate equilibrium solubility data of azithromycin varying with temperature and solvent is of overwhelming importance to develop optimized crystallization processes and operation conditions. Solubility information is also extremely valuable for estimating the crystal characteristics (polymorph and crystal size distribution), toxicity, bioavailability, delivery, metabolism, and drug excretion of the compound.4,5 However, solubility data of azithromycin in pure solvents have not been reported yet. In this work, the solubility of azithromycin monohydrate in ethanol, propan-2-ol, butan-1-ol, ethyl ethanoate, and 2propanone were measured at temperatures ranging from 278.15 K to 323.15 K by a synthetic method.6 The van’t Hoff equation, modified Apelblat equation, λh equation, Wilson, and NRTL models were applied to correlate the experimental data, based on the pure component thermodynamic properties (including mole volume, melting temperature, © 2014 American Chemical Society

Figure 1. Sketch of the molecule structure of azithromycin.

Received: October 8, 2013 Accepted: December 27, 2013 Published: February 11, 2014 784

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and enthalpy of fusion).7,8 To understand solubility behavior, thermodynamic excess functions (GE, SE, and HE) were calculated.9

transformer, and a light intensity display. During the experiments, predetermined amounts of solute and solvent were placed in the inner chamber of the crystallizer. In the early stage of the experiment, the intensity of the laser beam penetrating the vessel reached the maximum because the solute was completely dissolved and the solution was clear. Then a certain amount of solute was added into the crystallizer. If the solute dissolved completely, another amount of solute was added. This procedure was repeated until the last addition could not be dissolved completely. The total amount of solute consumed was recorded. The mass of the solute and solvents was weighed by an analytical balance (Mettler Toledo AB204-N of Switzerland) with a standard uncertainty of 1.000·10−7 kg. The final results were used to calculate the mole fraction solubility (x1) based on the following equation

2. EXPERIMENTAL SECTION Materials. Table 1 shows the description of materials used in the paper, including azithromycin monohydrate, ethanol, Table 1. Sources and Mass Fraction Purity of Materials materials

mass fraction purity

purification method

azithromycin

> 0.998

none

ethanol

> 0.997

none

propan-2-ol

> 0.998

none

butan-1-ol

> 0.995

none

ethyl ethanoate

> 0.996

none

2-propanone

> 0.997

none

source Zhejiang Huahai Pharmaceutical Co. Ltd., 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

analysis method HPLCa GCb

x1 =

GCb GC

m1 M1

+

m2 M2

(1)

b

where m1 and m2 represent the mass of the solute and the solvent, respectively; M1 and M2 are the molecular masses of solute and solvent, respectively. The same solubility experiment was conducted three times.

GCb

a High-performance liquid chromatography. bGas−liquid chromatography.

3. THERMODYNAMIC MODELS Van’t Hoff Equation. The van’t Hoff Equation reveals the logarithm of mole fraction of a solute as a linear function of the reciprocal of the absolute temperature for real solutions11−13

propan-2-ol, butan-1-ol, ethyl ethanoate, and 2-propanone. Deionized water was prepared in our laboratory by Thermo Scientific Barnstead Pacific TII (Wuzhou Technology, Beijing) and used throughout. Melting Properties Measurements. The melting temperature (Tm) and enthalpy of fusion (ΔfusH) of azithromycin monohydrate were determined by differential scanning calorimetry (DSC) (Mettler-Toledo, model DSC 1/500, Switzerland) under a nitrogen atmosphere. The mole volume of azithromycin monohydrate was calculated by its density, 1.180 g·cm−3, which was measured using a pycnometer method, and the mole volume of solvents were from the literature10 listed in Table 2.

ln x1 =

−ΔHd ΔSd + (RT ) R

(2)

where x1 is mole fraction solubility, ΔHd and ΔSd are the solution enthalpy and entropy, respectively, T is the corresponding absolute temperature, and R is the gas constant. λh (Buchowski) Equation. Solubility data can also be correlated by λh equation, which was first proposed by Buchowski et al.14, and is given as

Table 2. Mole Volume of Pure Components (293.15 K)

⎛ 1 − x1 ⎞ ⎛ 1 1 ⎞ ln⎜1 + λ ⎟ ⎟ = ⎜λ h − x1 ⎠ ⎝ T Tm ⎠ ⎝

Vm/(10−4 m3/mol) azithromycin ethanol propan-2-ol butan-1-ol ethyl ethanoate 2-propanone

m1 M1

GCb

6.4999 0.5852 0.7678 0.9194 0.9859 0.7393

(3)

where λ and h are two model parameters, the value of λ reflects the nonideality of the solution system, and h represents the excess mixing enthalpy of solution. Tm is melting point of azithromycin monohydrate. Modified Apelblat Equation. The modified Apelblat equation is a semiempirical model, which can be expressed as follows:15

Solubility Measurements. The solubility of azithromycin monohydrate in ethanol, propan-2-ol, butan-1-ol, ethyl ethanoate, and 2-propanone from 278.15 K to 323.15 K were measured by a synthetic method. The experiments were carried out in a jacketed crystallizer of about 100 mL and the temperature was controlled by circulating water from a thermostatically controlled water bath (Sunny Instrument CH1015, China). The equilibrium temperature was measured by a mercury thermometer with an accuracy of ± 0.05 K that was inserted into the inner chamber of the crystallizer. Continuous agitation was achieved by a magnetic stir bar. The dissolution of solute was examined by a laser monitoring system, which includes a laser generator, a photoelectric

ln x1 = A +

B T + C ln T

(4)

where A, B, and C are empirical constants. The values of A and B indicate the effect of solution nonidealities on the solubility of solute. The value of C reflects the effect of temperature on the fusion enthalpy.16 The Local Composition Models. Based on thermodynamic principles, a universal equation for the solid−liquid equilibrium can be described as follows:17 785

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Journal of Chemical & Engineering Data ln x1 = ln x1id − ln γ1 = −

Article

⎞ ΔfusH ⎛ T − 1⎟ ⎜ RT ⎝ Tm ⎠

ΔCp ⎛ Tm ⎞ T ⎜ln − m + 1⎟ − ln γ1 ⎝ ⎠ R T T

4. RESULTS AND DISCUSSION Property Evaluation of Pure Components. The melting temperature Tm and enthalpy of fusion ΔfusH of azithromycin monohydrate can be identified from Figure 2. The corresponding data are listed in Table 3 with their uncertainties.

(5)

where x1, x1id, γ1, Tm, ΔfusH, ΔCp, R, and T represent the mole fraction solubility of the solute, the ideal mole fraction solubility of the solute, the melting point of the solute, the solute enthalpy of fusion at its melting point, difference of heat capacities between subcooled liquid and solid, the gas constant and the absolute temperature of the solution, respectively. On the right-hand side of the equation containing ΔCp, the three terms almost cancel each other.18 Equation 4 simplifies to ln x1 = ln x1id − ln γ1 =

⎞ ΔfusH ⎛ T − 1⎟ − ln γ1 ⎜ RT ⎝ Tm ⎠

(6)

In this study, two well-established activity coefficient models, namely, the Wilson model and the NRTL model are used to derive the solute activity coefficient γ1. Wilson Model. The activity coefficient of this equation can be expressed in the following binary form9

Figure 2. DSC curve of azithromycin monohydrate.

Table 3. Thermodynamic Properties of Azithromycin Monohydrate (0.1 MPa)a

ln γ1 = −ln(x1 + Λ12x 2) ⎞ ⎛Λ Λ 21 + x 2⎜ 12 + Λ12x 2 − ⎟ x 2 + Λ 21x1 ⎠ ⎝ x1

azithromycin monohydrate

(7)

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

17.10

(8)

Solubility Data. The measured mole fraction solubility data of azithromycin monohydrate in the five pure solvents from 278.15 K to 323.15 K are available in Table 4 and plotted in Figure 3. The van’t Hoff equation, the λh (Buchowski) equation, the modified Apelblat equation, the Wilson model, and the NRTL model were used to correlate the solubility data by Matlab software. The nonlinear least-squares method is applied in this program to minimize the objective function f = (x1cal − x1exp). The calculated mole fraction solubility data x1cal are also presented in Table 4 and the model parameters during the optimization procedure are listed in Table 5. As observed in Table 4 and Figure 3, the solubility of azithromycin monohydrate increases with temperature. At constant temperature, the solubility order of azithromycin in the five solvents is ethyl ethanoate > 2-propanone > ethanol > propan-2-ol > butan-1-ol. However, the polarity order of these solvents is ethanol > 2-propanone > propan-2-ol > butan-1-ol > ethyl ethanoate.21,22 This indicates that the polarity is not the only factor to determine the solubility of azithromycin monohydrate. It can be explained by the fact that intermolecular interaction and the ability of a solvent to form a hydrogen bond with the drug molecules can influence the dissolution of drugs in pure solvents. In addition, the steric structure of solvent molecules may also influence the solubility of azithromycin monohydrate. Compared with propan-2-ol and butan-1-ol, solvent molecules of ethyl ethanoate, 2-propanone, and ethanol are more compact in size, so they have more success in facilitating solute−solvent interactions and improving solute dissolution. To evaluate the applicability and accuracy of the models used in this paper, the average relative deviation percentage (ARD

(9)

Here, Δλ12 and Δλ21 are the cross interaction energy parameters, and V1 and V2 are the mole volumes of solute and solvent, respectively.19 NRTL Model. In the binary system, the activity coefficient of this model is calculated by8 ⎡ τ G 2 τ12G12 2 ⎤ 21 21 ⎥ ln γ1 = x 2 2⎢ + 2 (x 2 + G12x1)2 ⎦ ⎣ (x1 + G21x 2)

(10)

Here, G12 = exp( −α12τ12) G21 = exp( −α12τ21)

τ21 =

386.15

The standard uncertainty u is u(Tm) = 0.5 K; relative standard uncertainties u are ur(ΔfusH) = 0.05 (0.95 level of confidence).

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

τ12 =

ΔfusH/kJ·mol−1

a

where Λ12 =

Tm/K

(g12 − g22) (RT ) (g21 − g11) (RT )

(11)

Δg12 (= g12 − g22) and Δg21 (= g21 − g11) are interaction parameters specific to a particular pair of species, independent of temperature and composition. Parameter α12 is a measure of the nonrandomness of the mixture, which generally varies between 0.20 and 0.47.20 In this contribution, α12 = 0.40 was used to correlate the solubility data of azithromycin monohydrate in five pure solvents. 786

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Table 4. Experimental and Calculated Solubility of Azithromycin Monohydrate in Five Pure Solvents (0.1 MPa)a T/K

103x1exp

103x1cal,vf

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

29.9 32.5 34.8 37.1 40.6 45.1 49.1 53.8 57.3 58.8

± ± ± ± ± ± ± ± ± ±

1.7 1.8 2.0 2.1 2.3 2.6 2.8 3.1 3.3 3.4

29.3 32.1 35.1 38.1 41.5 45.0 48.6 52.4 56.3 60.4

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

28.1 30.3 32.7 34.9 38.8 43.3 45.9 50.7 54.2 57.5

± ± ± ± ± ± ± ± ± ±

1.6 1.7 1.9 2.0 2.2 2.5 2.6 2.9 3.1 3.3

27.3 30.0 32.9 36.0 39.2 42.7 46.2 50.0 53.9 58.0

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

24.9 25.4 27.4 28.2 30.1 32.4 35.6 38.6 42.2 46.6

± ± ± ± ± ± ± ± ± ±

1.4 1.4 1.6 1.6 1.7 1.8 2.0 2.2 2.4 2.7

22.7 24.8 26.9 29.2 31.5 33.9 36.5 39.2 41.9 44.8

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

32.4 34.1 36.6 39.6 43.6 52.1 59.3 67.1 74.3 81.0

± ± ± ± ± ± ± ± ± ±

1.8 1.9 2.1 2.3 2.5 3.0 3.4 3.8 4.2 4.6

28.5 32.6 37.0 41.9 47.2 52.9 59.2 65.9 73.2 81.0

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

30.5 32.9 35.3 38.6 42.4 46.4 51.2 56.9 63.0 72.1

± ± ± ± ± ± ± ± ± ±

1.7 1.9 2.0 2.2 2.4 2.6 2.9 3.2 3.6 4.1

28.1 31.5 35.2 39.2 43.4 48.0 52.8 58.0 63.4 69.2

103x1cal,Apel Ethanol 29.2 32.1 35.1 38.3 41.6 45.1 48.7 52.4 56.3 60.2 Propan-2-ol 27.5 30.1 33.0 36.0 39.2 42.5 46.1 49.9 53.9 58.1 Butan-1-ol 24.8 25.7 26.9 28.4 30.3 32.6 35.3 38.5 42.3 46.7 Ethyl Ethanoate 30.6 33.7 37.3 41.5 46.2 51.7 57.9 65.1 73.3 82.8 2-Propanone 30.7 32.8 35.4 38.5 42.1 46.3 51.3 57.0 63.7 71.6

103x1cal,λh

103x1cal,Wil

103x1cal,NRTL

30.6 32.8 35.2 37.9 40.8 44.1 47.7 51.8 56.4 61.7

30.0 32.5 34.8 37.2 40.7 44.9 48.8 53.5 57.2 59.3

29.7 32.3 34.8 37.5 40.9 44.9 48.8 53.2 57.1 59.8

28.5 30.7 33.0 35.7 38.6 41.8 45.4 49.5 54.0 59.3

28.1 30.3 32.7 35.1 38.8 43.0 45.8 50.5 54.2 57.8

27.9 30.3 32.8 35.4 38.9 42.8 45.9 50.3 54.1 57.9

23.7 25.3 27.0 28.9 30.9 33.3 35.8 38.8 42.0 45.8

24.3 25.2 27.2 28.3 30.3 32.7 35.8 38.7 42.3 46.6

23.8 25.0 27.1 28.5 30.6 33.0 36.0 38.9 42.2 46.2

29.8 33.3 37.3 41.7 46.3 52.1 58.3 65.3 73.2 82.2

32.1 34.1 36.8 39.9 44.0 51.9 59.0 66.7 74.2 81.5

31.4 33.9 37.0 40.4 44.6 51.9 58.8 66.4 74.0 81.7

29.4 32.3 35.4 38.9 42.8 47.1 51.9 57.4 63.5 70.5

30.4 32.9 35.4 38.6 42.4 46.4 51.2 56.9 63.1 72.0

29.9 32.6 35.4 38.8 42.6 46.8 51.5 57.1 63.2 71.6

a cal,vf x1 , x1cal,Apel, x1cal,λh, x1cal,Wil, x1cal,NRTL represent the calculated solubility data by the van ’t Hoff, the modified Apelblat, the λh, the Wilson, and the NRTL models, 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).

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Table 6. ARD % of Five Models in Five Pure Solvents model

ethanol

propan-2-ol

butan-1-ol

ethyl ethanoate

2-propanone

Van’t Hoff Apelblet λh Wilson NRTL

1.8 1.8 2.2 0.38 0.76

1.3 1.2 1.7 0.30 0.52

3.4 0.72 1.7 0.70 1.4

3.6 2.9 3.2 0.55 1.2

2.9 0.44 1.4 0.082 0.65

Figure 3. Experimental and correlated solubility data of azithromycin monohydrate in different solvents: ■, ethanol; ○, propan-2-ol; ▲, butan-1-ol; ●, ethyl ethanoate; ▽, 2-propanone. The solid lines are correlated values by the Wilson model.

%) was used to evaluate the correlation results. The average percent deviation (ARD %) is defined as ARD% =

100 N

N

∑ i=1

x1, i − x1, i cal x1, i

Figure 4. Logarithm of activity coefficient of azithromycin monohydrate as a function of temperature at measured solubility points: ■, ethanol; ○, propan-2-ol; ▲, butan-1-ol; ●, ethyl ethanoate; ▽, 2-propanone. The solid lines are calculated values based on the Wilson model.

(12)

where N refers to the number of experimental points and x1,i and x1,ical represent the experimental and calculated solubility data, respectively. The ARD % of different correlation models are shown in Table 6. As we can see in Table 6, the overall ARDs of the five models are 13 % (van’t Hoff), 10 % (λh), 7.1 % (Apelblat), 2.0 % (Wilson), and 4.5 % (NRTL). This means that the Wilson model can be used to correlate the solubility data with best results under the tested condition. The NRTL model also gives good correlation results for the tested solvents, except for butan-1-ol and ethyl ethanoate. The solute activity coefficients γ1 in a saturated solution can estimate the solute−solvent intermolecular interactions, which are mainly decided by temperature. The logarithms of the activity coefficients of azithromycin monohydrate ln γ1 at measured solubility points are presented in Figure 4. As we can see from Figure 4, the values of ln γ1 are positive, which means that there exist repulsive interactions between azithromycin monohydrate and the solvents molecules. In addition, the solubility of azithromycin monohydrate increases with the decreasing repulsive interactions.

Prediction of Mixing Properties. For a nonideal solution, the mixing Gibbs free energy ΔG, mixing enthalpy ΔH, and mixing entropy ΔS can be predicted by

ΔM = ΔM id + ME

(13)

M can be substituted by G, H, and S, ΔM is the mixing property of an ideal solution, and ME is the excess property. For ideal solution, the mixing Gibbs free energy, mixing enthalpy, and mixing entropy in pure solvent can be denoted by23 id

ΔGid = RT (x1 ln x1 + x 2 ln x 2)

(14)

ΔH id = 0

(15)

ΔS id = −R(x1 ln x1 + x 2 ln x 2)

(16)

where x1 and x2 are the mole fractions of solute and solvent at a measured temperature, respectively. The difference between the

Table 5. Parameters for the van’t Hoff, the λh, the Apelblat, the Wilson, and the NRTL Models for the Solubility of Azithromycin Monohydrate in Five Pure Solvents model Van’t Hoff λh Apelblet

Wilson NRTL

ΔH ΔS λ h A B C Δλ12 Δλ21 Δg12 Δg21

ethanol

propan-2-ol

butan-1-ol

ethyl ethanoate

2-propanone

11983.3 13.7417 0.00909 −596.120 17.0309 −2133.86 −2.29097 2353.19 16866.0 6562.37 6737.79

12503.3 15.0161 0.01301 27594.4 −14.9188 −750.570 2.49156 3140.23 16654.5 6443.03 6842.14

11256.33 9.00407 0.00098 39420.4 −247.567 9833.52 37.0488 471.10 25388.1 11929.6 8099.94

17323.9 32.7145 0.09314 14630.3 −158.606 5260.66 24.2008 3659.93 12904.2 4013.65 6873.75

14951.8 24.0683 0.04473 19809.7 −215.688 8057.91 32.5565 2983.89 14561.2 4832.98 6789.74

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Table 7. Mixing Thermodynamic Properties ΔG, ΔH, and ΔS of Azithromycin Monohydrate Obtained from the Wilson Modela GE

T K

−1

J·mol

SE −1

J·mol ·K

−1

ΔG −1

J·mol

ΔH(HE)

ΔS

J·mol−1

J·mol−1·K−1

64.71 65.72 67.06 69.23 71.79 74.5 77.65 80.48 82.49 63.31

0.4161 0.4217 0.4287 0.4389 0.4518 0.464 0.477 0.4883 0.4956 0.4087

35.45 35.10 34.79 34.60 34.39 34.26 34.20 34.13 34.00 35.77

48.11 51.03 54.12 57.21 61.6 66.42 69.99 75.22 79.54 84.03

0.3425 0.3564 0.3706 0.3841 0.4041 0.4249 0.4395 0.4601 0.477 0.4936

33.56 33.58 33.63 33.69 33.83 34.02 34.07 34.30 34.39 34.50

104.7 120.9 147.2 172.6 209.2 254.9 315.3 383.7 468.2 573.7

0.5174 0.5714 0.661 0.7435 0.8621 1.008 1.197 1.406 1.659 1.969

42.11 42.77 43.59 44.19 44.87 45.48 46.09 46.57 47.01 47.41

67.33 71.02 76.04 81.61 88.55 100.3 110.9 122.1 133.2 144.3

0.4257 0.4413 0.4628 0.4863 0.5153 0.564 0.6055 0.6484 0.6889 0.7289

36.25 36.24 36.31 36.41 36.56 36.97 37.28 37.55 37.80 37.99

52.62 56.29 60.13 64.83 70.19 75.9 82.54 90.17 98.51 109.6

0.368 0.3848 0.4021 0.4228 0.4455 0.4687 0.4955 0.5253 0.5572 0.5984

33.95 34.06 34.17 34.34 34.57 34.82 35.09 35.41 35.72 36.17

% ζH

Ethanol 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 278.15

284.5 305.9 327.7 359.7 398.1 433.2 473.8 505.5 523 260.2

−0.7762 −0.8335 −0.8891 −0.9742 −1.077 −1.164 −1.265 −1.336 −1.363 −0.7079

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

248.6 269.4 292 313.6 347.9 386.6 411.8 453.5 485.2 515.8

−0.7207 −0.7712 −0.8257 −0.8747 −0.9603 −1.056 −1.109 −1.208 −1.275 −1.336

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

230.5 237.4 257.6 267.6 287.1 310.1 340.5 369.1 403 443.8

−0.4525 −0.4114 −0.3834 −0.3239 −0.2615 −0.1821 −0.08167 0.04656 0.2051 0.4021

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

279.4 295.8 319 344.9 379.5 445.1 501.1 559.6 613.8 664.4

−0.7624 −0.7939 −0.8431 −0.8982 −0.9757 −1.137 −1.266 −1.397 −1.511 −1.61

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

265.6 287.9 310.4 339.2 372.7 407.4 447.7 494.1 543.5 611.9

−0.7655 −0.8178 −0.8686 −0.936 −1.015 −1.093 −1.185 −1.29 −1.399 −1.554

−53.12 −55.78 −58.61 −61.63 −65.18 −68.47 −71.72 −74.86 −77.66 −50.36 Propan-2-ol −47.17 −49.88 −52.67 −55.39 −58.89 −62.39 −65.43 −68.86 −72.21 −75.48 Butan-1-ol −39.27 −40.89 −43.33 −45.34 −47.85 −50.61 −53.49 −56.44 −59.44 −62.67 Ethyl Ethanoate −51.09 −53.94 −57.3 −60.94 −65.07 −70.67 −75.7 −80.95 −85.99 −91.25 2-Propanone −49.73 −52.66 −55.74 −59.13 −62.63 −66.2 −70.16 −74.35 −78.76 −83.77

a

Combined expanded uncertainties U are Uc(GE) = 0.070GE; Uc(SE) = 0.070SE; Uc(ΔG) = 0.070ΔG ; Uc(ΔH) = 0.070ΔH; Uc(ΔS) = 0.070ΔS (0.95 level of confidence). 789

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ethanoate > 2-propanone > ethanol > propan-2-ol > butan-1-ol. It indicates that the solubility of azithromycin monohydrate 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 van’t Hoff equation, modified Apelblat equation, λh equation, Wilson model, and NRTL model were used to correlate the solubility data. It was found that the Wilson model provides the best fitting results with the ARD % less than 2.0 %. To understand the solubility behavior, the mixing properties of azithromycin monohydrate in each solvent were derived based on Wilson model parameters. The results show that the dissolution of azithromycin monohydrate is a spontaneous and endothermic process. The experimental solubility data and equations presented in this study are very useful for optimization of the dissolution and purification of azithromycin.

free Gibbs energies of mixing of ideal and nonideal solutions is called the excess Gibbs energy expressed by24 GE = RT (x1 ln γ1 + x 2 ln γ2)

(17)

⎡ GE ⎢∂ T H E = − T 2⎢ ⎢ ∂T ⎣

(18)

( ) ⎤⎥⎥ ⎥ ⎦

HE − GE (19) T The relative contributions of the enthalpy % ζH to the standard free energy of solution are calculated by eq 20. SE =

%ζH = 100

|ΔH | |ΔH | + |T ΔS|

■

(20)

The Wilson model was substituted into eqs 13 to 20, and the values of ΔG, ΔH, and ΔS for azithromycin monohydrate in five pure solvents were calculated and listed in Table 7. As illustrated by Table 7, ΔH values are positive in all solvents, which indicate that the dissolution process of azithromycin monohydrate in these solvents is endothermic. We can also see from Table 7 that ΔS values increase with the increase of temperature in all solvents, which has the same trend as the solubility curves in these solvents. % ζH values shown in Table 7 indicate that the entropy of solution controlled the dissolution behavior. The ΔG values plotted in Figure 5 are

AUTHOR INFORMATION

Corresponding Author

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

The authors are grateful to the financial support of National Natural Science Foundation of China (No. NNSFC 21176173), Tianjin Municipal Natural Science Foundation (No. 11JCZDJC 20700) and National high technology research and development program (863 Program No.2012AA021202). Notes

The authors declare no competing financial interest.

■

REFERENCES

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Figure 5. Predicted mixing Gibbs free energy at measured solubility points based on the Wilson model: ■, ethanol; ○, propan-2-ol; ▲, butan-1-ol; ●, ethyl ethanoate; ▽, 2-propanone.

negative in all solvents, which illustrates the dissolution process of azithromycin monohydrate in these solvents is spontaneous. With an inspection of Figure 5, we can also see that lower ΔG values correspond to higher solubility and more favorable dissolution. These phenomena are in good agreement with the classical thermodynamics theory.

5. CONCLUSIONS The equilibrium solubility data of azithromycin monohydrate in ethanol, propan-2-ol, butan-1-ol, ethyl ethanoate, and 2propanone from 278.15 K to 323.15 K were measured by a synthetic method. It could be concluded that the solubility of azithromycin monohydrate increases with the increase of temperature in all tested solvents. At the given temperature, the solubility values of azithromycin monohydrate rank as ethyl 790

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