Measurement and Correlation of Solubility of Cefathiamidine in Water

Nov 12, 2015 - Measurement and Correlation of Solubility of Cefathiamidine in Water + (Acetone, Ethanol, or 2-Propanol) from (278.15 to 308.15) K. Lan...
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Measurement and Correlation of Solubility of Cefathiamidine in Water + (Acetone, Ethanol, or 2‑Propanol) from (278.15 to 308.15) K Lanlan Lin,†,‡ Kaifei Zhao,†,‡ Bo Yu,†,‡ Haisheng Wang,†,‡ Mingyang Chen,†,‡ and Junbo Gong*,†,‡ †

School of Chemical Engineering and Technology, State Key Laboratory of Chemical Engineering, Tianjin University, Tianjin 300072, People’s Republic of China ‡ Collaborative Innovation Center of Chemistry Science and Engineering, Tianjin 300072, People’s Republic of China S Supporting Information *

ABSTRACT: In this study, the solubility of cefathiamidine was measured in water + (acetone, ethanol, or 2-propanol) at temperature from (278.15 to 313.15) K by using a gravimeteic method. The solubility of cefathiamidine increased with increasing temperature. Besides, at a given temperature, solubility in different mixtures follows different rules. In water + (acetone or 2-propanol), it decreases with the increase of the initial molar fraction of acetone or 2-propanol; whereas synergistic effect of mixed solvents was observed in water + ethanol mixtures, and solubility reached maximum at the ethanol molar fraction of 0.4. The experimental data were well correlated by the modified Apelblat equation, the CNIBS/R-K model, the combined version of the Jouyban−Acree and van’t Hoff model, and the combined version of the Jouyban−Acree and the modified Apelblat model. Furthermore, the thermodynamic functions of dissolution of cefathiamidine in different mixtures were obtained based on the van’t Hoff equation and the modified Apelblat equation. The results indicate that the dissolution process of cefathiamidine is endothermic.

1. INTRODUCTION Cefathiamidine (CAS Registry No. 33075-00-2, Figure 1) is classified as a semisynthetic first-generation cephalosporin, which works by inhibiting bacterial cell wall biosynthesis. Its antibacterial spectrum is similar to cefalotin. It has a good antimicrobial activity against Gram-negative bacteria, such as Escherichia coli, Proteus mirabilis, Pseudomonas aeruginosa, and Haemophilus influenza, and it is more active against some Gram-positive bacteria, such as Staphylococcus aureus, Viridans streptococci, Streptococcus pneumoniae, and so forth. Crystallization is a key procedure in the purification of cefpiramide sodium and hence its solubility data are especially important.2 According to the Chinese Pharmacopoeia, cefathiamidine is very soluble in water, slightly soluble in ethanol, and practically insoluble in acetone.3 However, no quantitative solubility data of this compound has been reported in previous study. In addition, cooling crystallization was not a desirable method for cefathiamidine due to the amorphous product and the low final yields. Therefore, other solvents are considerable to be employed to reduce the solubility of cefathiamidine © XXXX American Chemical Society

Figure 1. Molecular structure of cefathiamidine.

in the mother liquid.4 To facilitate the effective separation of cefathiamidine from a solution by crystallization, the accurate solid− liquid equilibrium solubility of cefathiamidine in binary solvent systems should be determined. In this paper, the solubility of cefathiamidine in binary acetone + water, ethanol + water, and 2-propanol + water solvent mixtures was determined using a gravimeteic method from 278.15 K to 308.15 K at atmospheric pressure and in the initial mole fraction range of antisolvent (acetone, ethanol, or 2- propanol) about from 0.3 to 0.9. The experimental solubility Received: July 20, 2015 Accepted: October 28, 2015

A

DOI: 10.1021/acs.jced.5b00617 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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data was correlated by the modified Apelblat equation, the CNIBS/R-K model, the combined version of the Jouyban−Acree and van’t Hoff model, and the combined version of the Jouyban− Acree and the modified Apelblat model. Additionally, some of the thermodynamic properties that can help to understand its dissolution behavior, for example the enthalpy was obtained based on the van’t Hoff equation and the modified Apelblat equation. We hope that the solubility model presented in this work will be useful for the reactor design and optimization of the purification of cefathiamidine.

2. EXPERIMENTAL SECTION 2.1. Materials. Cefathiamidine was purchased from Dalian Meilun Biology Technology Co., Ltd., China, as a white crystalline powder. (M w = 472.59, molecular formula C19H28N4O6S2). The organic solvent (acetone, ethanol, and 2-propanol) were of analytical reagent grade and were used without further treatment before use. In addition, distilled− deionized water was made in our laboratory, and the conductivity of distilled−deionized water is 18 MΩ·cm. Relevant information on the material is depicted in Table 1.

Figure 2. X-ray powder diffraction patterns of cefathiamidine.

constant. The same experiment was repeated three times to minimize the experiment errors. The mean values were used to calculate the saturated mole fraction solubility as follows:

Table 1. Sources and Mass Fraction Purity of Materials Used in the Experiments chemical cefathiamidine acetone ethanol 2-propanol

source Dalian Meilun Biology Technology Co., Ltd., China Tianjin Kewei Chemical Co, China Tianjin Kewei Chemical Co, China Tianjin Kewei Chemical Co, China

mass fraction purity

xA =

analysis method

≥ 0.991

HPLC

≥ 0.995 ≥ 0.995 ≥ 0.995

GCb GCb GCb

(mA /MA ) (mA /MA ) + (mB /MB) + (mC /MC)

(1)

where mA, mB, and mC represent the mass of the solute, organic solvent, and water, respectively, and MA, MB, and MC are the molecular weights of the solute, organic solvent, and water, respectively.

a

3. RESULTS AND DISCUSSION 3.1. Solubility Data. Solubility data of cefathiamidine in binary acetone + water, ethanol + water, and 2-propanol + water solvent mixtures at temperature ranged from 278.15 K to 308.15 K are listed in Tables 2 to 4 and graphically plotted in Figures 3 to 6. From Figures 3 to 5, it can be seen that the solubility of cefathiamidine increases with increasing temperature in binary solvent mixtures at constant solvent compositions. Besides, at a given temperature, the solubility of cefathiamidine in binary acetone + water and 2-propanol + water solvent mixtures decreases with the increase of the initial molar fraction of acetone or 2-propanol. However, the solubility in ethanol−water system shows different rules. As shown in Figure 6, the solubility of cefathiamidine in ethanol−water first increased with the increase of ethanol molar fraction and reached maximum when the molar fraction of ethanol is about 0.4. After that, the solubility of cefathiamidine started to decrease with the increase of ethanol molar fraction. The results for the X-ray diffraction spectrum of the residual solids showed that there is no crystal transformation in the different proportion ethanol−water mixtures. It is worth noting that the maximum point did not change with temperature. This information is useful for the design of cefathiamidine crystallization process. The influencing factors are comparatively complex, including the polarity of the selected solvent, intermolecular interactions between the solute and solvent, hydrogen bonding interaction, and so on.6 In this work, cefathiamidine is a polar compound. Based on the general rule of “like dissolves like”, it should be more soluble in water than that in other solvents like acetone (ethanol, or 2-propanol). Cefathiamidine contains CONH, which is the hydrogen-bond donor, and COO, which is the hydrogen-bond acceptor. Because of the existence of hydrogen

a

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

2.2. X-ray Diffraction Analysis. To confirm that no physicochemical changes occurred during the entire experiment, the X-ray diffraction spectrum of the residual solids was measured. The patterns were obtained by using Cu Kα (1.54) radiation on a D/MAX 2500 X-ray diffractometer. The samples were recorded between 2θ = 2° and 2θ = 50° with a step size of 0.02° and a scan rate of 1 step/s at ambient conditions. The result of powder X-ray diffraction is shown in Figure 2, which revealed that there was no degradation or crystal transformation in the entire experiment. 2.3. Solubility Measurements. A gravimetric method described in detail in literature5 was used to determine the solubility of cefathiamidine. An excess amount of cefathiamidine was added into the solvent mixture of known molar fraction composition. The solution was stirred for at least 9 h to reach the equilibrium using an air bath shaker with standard uncertainty u(T) = 0.1 K (type HNY-200R, Tianjin Ounuo Instrument Co. Ltd., China). After that, the agitation was stopped and the solution was kept still for 4 h to ensure solid phase to precipitate to the bottom before sampling. The upper saturated solution was filtered with a preheated organic membrane filter (0.45 μm) and transferred into a preweighed Petri dish. The Petri dish with saturated solution was weighed quickly and then put into a vacuum drying oven at 308.15 K for 10 h. The Petri dish with solutes was reweighed several times using an electronic balance (type ML204/02, Mettler Toledo, Switzerland) with standard uncertainty uB(m) = 0.0001 g until the weight of Petri dish was B

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Table 2. Molar Fraction Solubility xA of Cefathiamidine in the Binary Acetone + Water Solvent Mixtures at p = 0.1 MPaa x0B

103xexp A

103xcal A (eq 2)

0.3 0.4 0.5 0.6 0.7 0.8 0.9

13.0454 4.2114 2.6437 1.1338 0.3156 0.0621 0.0104

12.7350 4.2356 2.6925 1.1350 0.3080 0.0608 0.0101

0.3 0.4 0.5 0.6 0.7 0.8 0.9

14.8148 5.9907 3.4699 1.3503 0.3556 0.0710 0.0117

14.8262 6.0467 3.3274 1.3167 0.3612 0.0711 0.0117

0.3 0.4 0.5 0.6 0.7 0.8 0.9

17.1665 9.0300 4.2582 1.5390 0.4153 0.0831 0.0133

18.2072 8.7080 4.2921 1.5882 0.4422 0.0872 0.0142

0.3 0.4 0.5 0.6

23.3266 12.5893 5.6711 1.9580

23.4972 12.6404 5.7614 1.9860

103xcal A (eq 5) T = 278.15 K 12.8972 4.3987 2.4625 1.1510 0.3280 0.0597 0.0105 T = 283.15 K 14.6688 6.2214 3.2727 1.3631 0.3690 0.0685 0.0118 T = 288.15 K 17.1544 9.0588 4.2348 1.5450 0.4151 0.0830 0.0133 T = 293.15 K 23.4128 12.4561 5.6522 2.0403

103xcal A (eq 10)

103·xcal A (eq 14)

9.4152 5.0503 2.4650 0.9485 0.2674 0.0550 0.0089

10.4087 5.6005 2.7421 1.0584 0.2993 0.0618 0.0100

13.4415 7.0511 3.3713 1.2761 0.3558 0.0729 0.0117

13.3756 7.0154 3.3538 1.2693 0.3539 0.0724 0.0116

18.9539 9.7312 4.5611 1.6993 0.4689 0.0955 0.0153

17.7765 9.1086 4.2608 1.5843 0.4363 0.0887 0.0142

26.4155 13.2832 6.1074 2.2409

24.3748 12.2265 5.6076 2.0524

x0B

103xexp A

103xcal A (eq 2)

0.7 0.8 0.9

0.5993 0.1099 0.0173

0.5634 0.1119 0.0180

0.3 0.4 0.5 0.6 0.7 0.8 0.9

33.6033 18.3471 7.9224 2.5893 0.7800 0.1591 0.0258

31.7582 18.4810 8.0255 2.5682 0.7449 0.1497 0.0236

0.3 0.4 0.5 0.6 0.7 0.8 0.9

46.7503 26.4535 11.8430 3.5919 0.9807 0.2161 0.0343

44.8098 27.1967 11.5705 3.4266 1.0193 0.2081 0.0323

0.3 0.4 0.5 0.6 0.7 0.8 0.9

63.2230 41.1463 17.1254 4.5827 1.4444 0.2889 0.0433

65.8094 40.2588 17.2241 4.7068 1.4403 0.3000 0.0457

103xcal A (eq 5) T = 293.15 K 0.5593 0.1138 0.0172 T = 298.15 K 33.6285 18.3602 7.8031 2.6822 0.7467 0.1625 0.0257 T = 303.15 K 46.4481 27.1818 11.2826 3.6827 0.9868 0.2134 0.0345 T = 308.15 K 63.0876 41.8262 16.1844 4.9338 1.3319 0.2980 0.0431

103xcal A (eq 10)

103·xcal A (eq 14)

0.6120 0.1241 0.0199

0.5592 0.1131 0.0181

36.4069 17.9435 8.0983 2.9278 0.7918 0.1597 0.0256

34.4043 16.9269 7.6261 2.7522 0.7430 0.1496 0.0239

49.6492 23.9996 10.6388 3.7916 1.0157 0.2039 0.0326

49.8835 24.1164 10.6921 3.8111 1.0211 0.2050 0.0328

67.0300 31.7982 13.8529 4.8692 1.2924 0.2583 0.0413

74.1542 35.2880 15.4214 5.4375 1.4478 0.2903 0.0465

a 0 xB

cal cal cal is the initial mole fraction of acetone in the binary solvent mixture; xexp A is the experimentally determined solubility. xA (eq 2), xA (eq 5), xA (eq 10), and xcal A (eq 14) are the calculated solubility according to eq 2, eq 5, eq 10, and eq 14, respectively. The standard uncertainty of T is u(T) = 0.01 K. The relative standard uncertainty of the solubility measurement is ur(x) = 0.08. The relative uncertainty of pressure is ur(P) = 0.05.

solvents may play an important role in the formation of intermolecular hydrogen bond association. 3.2. Data Correlation. The modified Apelblat equation, the CNIBS/R-K equation, and the modified Jouyban−Acree Models were applied to correlate the solubility of cefathiamidine in acetone + water, ethanol + water, and 2-propanol + water solvent mixtures. The modified Apelblat equation was selected to describe the relationship between solubility and temperature. Also, the CNIBS/R-K model was applied to analyze the correlation between solubility and solvent composition, whereas the modified Jouyban−Acree models describe the relationship of solubility, temperature and solvent composition. Modified Apelblat Equation. The modified Apelblat equation12 is a semiempirical model, which depends on temperature

bond and electrostatic force, the intermolecular forces of cefathiamidine−water are much stronger than the intermolecular forces of cefathiamidine−water−acetone when cefathiamidine is dissolved in solvent, so the solubility of cefathiamidine in water is far higher than that in water + acetone (water + ethanol, or water +2-propanol) mixtures. With the composition of water increasing in the solvent mixtures, the intermolecular forces of cefathiamidine−water are enhanced and the intermolecular forces between acetone (or 2-propanol) molecules are weakened, which finally resulted in the significant increasing solubility of cefathiamidine But in the water + ethanol mixtures, the solubility of cefathiamidine have a maximum, which is called synergistic effect, as reported in the previous experiments.7,8 The properties of solute and solvents result in synergistic effect of mixed solvents on solubility, which is often observed when their polarities are closest to each other.9 So, the maximum solubility effect exhibited in ethanol + water may be attributed to a strong intermolecular association of solute molecules with solvent mixtures.10,11 Ethanol acted as an overall water-structure breaker in the solution systems, disrupting the three-dimensional hydrogen-bonded network. Similar results were also found from the solubility measurements of 2-benzoyl-1-naphthol in hexane + 1-butanol mixtures and intermolecular association was verified with the study of UV−vis absorption spectra.7,8 Synergistic effect was not observed in acetone−water and 2-propanol−water systems, indicating that the property of

ln xA = A +

B + C ln(T /K) T /K

(2)

where xA is the molar fraction solubility, A, B, and C are the semiempirical constants, and T is the absolute temperature. The values of A and B reflect the variation in the solution activity coefficient, whereas the value of C responses to the effect of temperature on the fusion enthalpy. CNIBS/R-K Model. The CNIBS/R-K model which relies on the solvent composition is expressed in eq 313 N

ln xA = x B0 ln(xA )B + xC0 ln(xA )C + x B0xC0 ∑ Si(x B0 − xC0)i i=0

C

(3)

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Table 3. Molar Fraction Solubility xA of Cefathiamidine in the Binary Ethanol + Water Solvent Mixtures at p = 0.1 MPaa x0B

103·xexp A

103·xcal A (eq 2)

0.3 0.4 0.5 0.6 0.7 0.8 0.9

46.1607 46.9607 42.4571 25.4427 11.1374 3.6404 1.2787

45.2215 46.9849 43.0178 25.7519 11.0112 3.4605 1.2433

0.3 0.4 0.5 0.6 0.7 0.8 0.9

52.4525 57.5756 52.8660 34.2019 14.5808 5.2520 1.8319

0.3 0.4 0.5 0.6 0.7 0.8 0.9

69.9137 74.5814 64.7185 41.6484 21.5872 7.1387 2.4088

0.3 0.4 0.5 0.6

91.7908 95.6396 77.6947 55.1791

103·xcal A (eq 5)

T = 278.15 K 46.0904 47.3332 41.7150 25.9207 11.0074 3.6530 1.2782 T = 283.15 K 55.0989 52.3516 58.2952 57.9355 51.7219 52.7257 32.7780 33.7196 15.0129 14.9158 5.1979 5.1740 1.7857 1.8380 T = 288.15 K 68.5653 70.2236 73.4598 73.4746 63.6784 65.1250 42.7235 42.9362 21.0427 20.3474 8.0269 7.3719 2.6107 2.3903 T = 293.15 K 87.0067 92.0628 93.9061 94.4073 80.1101 79.1442 56.9242 54.7183

103·xcal A (eq 10)

103·xcal A (eq 14)

45.4501 44.6120 35.1768 22.0264 10.6983 3.8903 1.0101

48.4003 47.6887 37.7460 23.7252 11.5673 4.2224 1.1005

57.8749 58.5828 47.8208 31.1253 15.7850 6.0241 1.6514

57.6968 58.3915 47.6558 31.0122 15.7247 6.0000 1.6445

73.0809 76.2047 64.3205 43.4583 22.9780 9.1878 2.6541

70.2008 73.0239 61.4861 41.4425 21.8589 8.7191 2.5126

91.5505 98.2422 85.6427 59.9912

87.0501 93.1286 80.9380 56.5231

103·xcal A (eq 2)

x0B

103·xexp A

0.7 0.8 0.9

30.5348 12.5352 3.5759

0.3 0.4 0.5 0.6 0.7 0.8 0.9

109.1586 121.1807 102.2104 80.8706 42.9087 21.5578 7.1318

0.3 0.4 0.5 0.6 0.7 0.8 0.9

145.3043 153.7678 137.3251 106.8191 69.9208 45.7108 9.5842

0.3 0.4 0.5 0.6 0.7 0.8 0.9

199.6853 216.6853 178.0034 150.4257 101.5760 51.7286 12.9414

103·xcal A (eq 5)

T = 293.15 K 30.3324 12.6316 3.5682 T = 298.15 K 112.4255 109.2429 121.6439 120.1209 102.8334 105.3600 77.4049 76.0727 44.5515 45.0325 20.6281 21.0088 5.8534 7.1660 T = 303.15 K 147.7286 143.3851 159.5147 160.8246 134.4973 130.9158 107.2575 102.2032 67.0492 76.7091 34.1987 42.0971 8.9539 9.7460 T = 308.15 K 197.1603 200.4266 211.5532 212.7682 178.9799 183.6734 151.2418 146.0124 102.9745 102.5667 57.8498 51.7629 13.8718 12.9300

103·xcal A (eq 10)

103·xcal A (eq 14)

33.0229 13.8126 4.1970

31.0192 12.9350 3.9184

113.8245 125.5782 112.9434 81.9229 46.8852 20.4832 6.5357

109.8578 120.9423 108.5410 78.5611 44.8650 19.5586 6.2274

140.5047 159.2257 147.5935 110.7286 65.8015 29.9832 10.0301

140.9200 159.7248 148.0825 111.1153 66.0431 30.0986 10.0705

172.2576 200.3395 191.2065 148.2067 91.3395 43.3497 15.1802

183.5187 214.2548 205.2716 159.7188 98.8119 47.0760 16.5482

30.2582 12.7167 3.8799

a 0 xB

cal cal cal is the initial mole fraction of ethanol in the binary solvent mixture; xexp A is the experimentally determined solubility. xA (eq 2), xA (eq 5), xA (eq 10), and xcal A (eq 14) are the calculated solubility according to eq 2, eq 5, eq 10, and eq 14, respectively. The standard uncertainty of T is u(T) = 0.01 K. The relative standard uncertainty of the solubility measurement is ur(x) = 0.08. The relative uncertainty of pressure is ur(P) = 0.05.

where x0B is the initial molar fraction composition of acetone, ethanol, or 2-propanol in the solvent mixture when there is no solute added, and x0C is the initial molar fraction composition of water in the solvent mixture without any solute. xA is the molar fraction solubility of the solute. Si is the model constant and N is the number of “curve-fit” parameters. (xA)i is the saturated molar fraction solubility of the solute in pure solvent i. When N = 2 and replacing x0C with (1 − x0B), eq 3 can be written as eq 4

where Ji is a model constant, T is the absolute temperature, N refers to 0, 1, 2, and 3, and the other symbols denote the same meanings as eq 3. The Jouyban−Acree model has been used in many recent reports by replacing the solute solubility ((xA)i,T) in monosolvent i (i = B, C) with the corresponding values from van’t Hoff equation as follows:17

S2)x B0

ln xA = (ln(xA )B − ln(xA )C + S0 − S1 + + ( −S0 + 3S1 − 5S2)(x B0)2 + ( −2S1 + 8S2)(x B0)3 + ( −4S2)(x B0)4 + ln(xA )C (4)

A equation can be obtained by introducing a constant term to eq 4 ln xA = B1 + B2 x B0 + B3(x B0)2 + B4 (x B0)3 + B5(x B0)4

N i=0

(5)

(7)

ln(xA )C, T = a 2 +

b2 T

(8)

ln(xA )m , T = a 2 +

b2 + (a1 − a 2)x B0 T

x B0 T x B0 ×(b1 + b2 + j0 − j1 + j2 ) T (XB0) + (3J1 − J0 − 5J2 ) T (x B0)3 (x 0)4 + (8J2 − 2J1) − 4J2 B T T + (b1 + b2 + j0 − j1 + j2 )

Ji (x B0 − xC0)i T

b1 T

where a1, b1, a2, and b2 are the model parameters. The substitution of eqs 7 and 8 into eq 6 followed by rearrangement yield eq 9

where B1, B2, B3, B4, and B5 are model constants and could be obtained by least-squares regression. Jouyban−Acree Model. The Jouyban−Acree model,14 is particular popular due to its ability of estimating the solute solubility with respect to both temperature and solvent composition of binary solvent mixtures in a fairly simple way. The model can be expressed in eq 615,16 ln xA = x B0 ln(xA )B + xC0 ln(xA )C + x B0xC0 ∑

ln(xA )B, T = a1 +

(6) D

(9)

DOI: 10.1021/acs.jced.5b00617 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 4. Molar Fraction Solubility xA of Cefathiamidine in the Binary 2-Propanol + Water Solvent Mixtures at p = 0.1 MPaa x0B

103·xexp A

0.3 0.4 0.5 0.6 0.7 0.8 0.9

26.8082 13.6341 4.3406 2.1483 0.6690 0.2206 0.0940

0.3 0.4 0.5 0.6 0.7 0.8 0.9

33.1818 21.5504 8.0834 3.0510 0.9473 0.2707 0.1202

0.3 0.4 0.5 0.6 0.72 0.8 0.9

40.0454 25.6076 11.2656 3.9971 1.1336 0.3550 0.1612

0.3 0.4 0.5 0.6

53.0454 34.9199 17.5443 5.4568

103·xcal A (eq 2) T 26.4946 14.2661 4.5432 2.2031 0.6681 0.2088 0.0948 T 32.9897 19.3126 7.2867 2.9284 0.8901 0.2802 0.1211 T 41.7135 26.1607 11.4679 3.9656 1.2192 0.3836 0.1574 T 53.4982 35.4514 17.7279 5.4628

103·xcal A (eq 5) = 278.15 K 27.4383 11.9764 4.9939 1.8901 0.6592 0.2298 0.0928 = 283.15 K 33.6798 20.0858 8.7425 2.9758 0.895 0.2834 0.1187 = 288.15 K 40.1403 25.3120 11.5019 3.9194 1.1417 0.3550 0.1611 = 293.15 K 52.4636 36.4212 16.3893 5.535

103·xcal A (eq 10)

103·xcal A (eq 14)

20.2737 13.5656 6.2094 2.1521 0.6457 0.1981 0.0758

20.8807 14.0732 6.4884 2.2652 0.6846 0.2115 0.0815

28.8424 19.1704 8.7750 3.0563 0.9239 0.2854 0.1095

28.8007 19.1359 8.7561 3.0487 0.9213 0.2845 0.1091

40.5337 26.7677 12.2526 4.2880 1.3056 0.4061 0.1563

39.7764 26.1465 11.9131 4.1499 1.2578 0.3894 0.1492

56.3068 36.9526 16.9149 5.9468

54.9910 35.8806 16.3293 5.7078

x0B

103·xexp A

0.7 0.8 0.9

1.5923 0.5442 0.2128

0.3 0.4 0.5 0.6 0.7 0.8 0.9

73.1197 47.4479 26.9273 7.4358 2.9114 0.8063 0.2789

0.3 0.4 0.5 0.6 0.7 0.8 0.9

92.1327 64.2429 38.6288 10.7906 3.7033 1.1783 0.3539

0.3 0.4 0.5 0.6 0.7 0.8 0.9

119.3042 90.0937 61.5656 15.8857 5.2316 1.5055 0.5478

103·xcal A (eq 2) T 1.7137 0.5349 0.2078 T 69.5176 48.0514 26.9441 7.6454 2.4667 0.7588 0.2787 T 91.4341 65.131 40.2981 10.8572 3.6299 1.0935 0.3790 T 121.6122 88.2690 59.3574 15.6274 5.4520 1.5990 0.5220

103·xcal A (eq 5) = 293.15 K 1.6532 0.5237 0.2148 = 298.15 K 72.3411 49.9575 23.1565 8.3347 2.6460 0.8264 0.2781 = 303.15 K 90.4635 69.0238 32.5299 11.6689 3.7067 1.1454 0.3571 = 308.15 K 116.9877 97.4389 49.731 17.6078 5.0976 1.4809 0.5516

103·xcal A (eq 10)

103·xcal A (eq 14)

1.8234 0.5709 0.2204

1.7400 0.5417 0.2079

77.3601 50.4641 23.0999 8.1574 2.5181 0.7935 0.3072

76.0836 49.4295 22.5343 7.9253 2.4365 0.7647 0.2949

105.1775 68.2112 31.2240 11.0737 3.4406 1.0909 0.4236

105.3232 68.3289 31.2885 11.1003 3.4501 1.0943 0.4250

141.5791 91.3023 41.7945 14.8842 4.6538 1.4844 0.5779

145.8478 94.7422 43.6860 15.6715 4.9357 1.5858 0.6219

a 0 xB

cal cal cal is the initial mole fraction of 2-propanol in the binary solvent mixture; xexp A is the experimentally determined solubility. xA (eq 2), xA (eq 5), xA (eq 10), and xcal A (eq 14) are the calculated solubility according to eq 2, eq 5, eq 10, and eq 14, respectively. The standard uncertainty of T is u(T) = 0.01 K. The relative standard uncertainty of the solubility measurement is ur(x) = 0.08. The relative uncertainty of pressure is ur(P) = 0.05.

b1 + c 2 ln T + (a1 − a 2)x B0 T x0 + (b1 − b2 + J0 − J1 + J2 ) B T 0 2 (x ) (x 0)3 + (3J1 − J0 − 5J2 ) B + (8J2 − 2J1) B T T 0 4 (x ) + ( −4J2 ) B + (c1 − c 2)x B0 ln T (13) T

Equation 9 can be simplified as x0 (x 0)2 A2 + A3x B0 + A4 B + A5 B T T T 0 3 0 4 (x ) (x ) + A6 B + A 7 B T T

ln xA = a1 +

ln(xA )m , T = A1 +

(10)

this equation is also referred as a hybrid model (1). A1 to A7 are the model parameters. The other symbols denote the same

When introducing a constant term, eq 13 can be further simplified as eq 14

meanings as in eq 3. Meanwhile, the modified Apelblat equation also express

x0 (x 0)2 A2 + A3 ln T + A4 x B0 + A5 B + A 6 B T T T 0 3 0 4 (x ) (x ) + A 7 B + A8 B + A 9x B0 ln T (14) T T

the solute solubility ((xA),T) in monosolvent i (i = B, C)

ln xA = A1 +

in the Jouyban−Acree model. So (xA)B and (xA)C can be expressed by ln(xA )B = a1 + (b1/T ) + c1ln T

(11)

ln(xA )C = a 2 + (b2 /T ) + c 2 ln T

(12)

this equation is also referred as a hybrid model (2).18 A1 to A9 are the model parameters. The other symbols denote the same meanings as in eq 3. These four models were employed to correlate the solubility data by the Matlab program which gave both the parameters in each model and the calculated solubility of cefathiamidine. exp exp To minimize the objective function f = (xcal A − xA )/xA , a nonlinear least-squares method was applied in this work. The

An equation can be obtained when N = 2 and substituting x0C with (1 − x0B) E

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Figure 3. Solubility of cefathiamidine (xA) depending on temperature T and the molar fraction of acetone (x0B) in water + acetone solvent mixture: ■, x0B = 0.3; red ●, x0B = 0.4; blue ▲, x0B = 0.5; green ▼, x0B = 0.6; fuschia ◀, x0B = 0.7; brown ▶, x0B = 0.8; navy ◆, x0B = 0.9.

Figure 5. Solubility of cefathiamidine (xA) depending on temperature T and the molar fraction of ethanol (x0B) in water + ethanol solvent mixture: ■, x0B = 0.3; red ●, x0B = 0.4; blue ▲, x0B = 0.5; green ▼, x0B = 0.6; fuschia ◀, x0B = 0.7; brown ▶, x0B = 0.8; navy ◆, x0B = 0.9.

Figure 4. Solubility of cefathiamidine (xA) depending on temperature T and the molar fraction of 2-propanol (x0B) in water + 2-propanol solvent mixture: ■, x0B = 0.3; red ●, x0B = 0.4; blue ▲, x0B = 0.5; green ▼, x0B = 0.6; fuschia ◀, x0B = 0.7; brown ▶, x0B = 0.8; navy ◆, x0B = 0.9.

Figure 6. Solubility of cefathiamidine (xA) depending on the molar fraction of ethanol (x0B) in water + ethanol solvent mixture and temperature T: ■, 278.15 K; red ●, 283.15 K; blue ▲, 288.15 K; green ▼, 293.15 K; fuschia ◀, 298.15 K; brown ▶, 303.15 K; navy ◆, 308.15 K.

calculated molar fraction solubility data xcal A are also presented in Tables 2 to 4. The average relative deviation (ARD%) was evaluated and shown in Supporting Information to assess the applicability and accuracy of the models used in this paper. The ARD% is defined as ARD% =

100 N

N

∑ i=1

solvent mixtures. For ethanol + water solvent mixtures, the overall ARD% for four equations are 3.90, 1.95, 8.69, and 7.26. Besides, in binary 2-propanol + water, the overall ARD% for these equation are 3.56, 4.76, 9.53, and 8.93. These results indicate that the solubility data of cefathiamidine in binary solvent mixtures can be well correlated by these four models. The modified Apelblat equation reprents tempureture effect, and the CNIBS/R-K model presents composition effect. These models only correlates the solubility change with one parameter, so ARD % for these models is smaller. As a function of both temperature and the mole fraction of acetone (ethanol, or 2-propanol), the hybrid models can still give good correlation results with satisfactory accuracy. 3.3. Thermodynamic Properties for the Solution. For a real solution, it is important to study the dissolution behavior of solute in different solvents. In this work, the thermodynamic

xA, i exp − xA, i cal xA, i exp

(15)

xA,iexp

where N refers to the number of experimental points, and xA,ical represent the experimental and calculated solubility data, respectively. As shown in Supporting Information Tables S1, S2, S3, and S4−6, the overall ARD% for the modified Apelblat equation, the CNIBS/R-K model, the hybrid model (1), and the hybrid model (2) are 2.24, 2.30, 9.26, and 6.47 for binary acetone + water F

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Table 5. Thermodynamic Properties of Dissolution Process of Cefathiamidine in Binary Solvent Mixturesa,b x0B

a

0.3

0.4

0.5

0.6

ΔsolH0 in kL/mol

38.81

54.21

44.96

ΔsolH0 in kL/mol

34.81

35.83

33.37

ΔsolH0 in kL/mol

36.51

43.33

61.09

Acetone + Water 35.34 Ethanol + Water 42.96 2-Propanol + Water 47.31

0.7

0.8

0.9

37.62

39.66

36.41

52.86

66.27

57.61

49.80

49.38

40.16

Expanded uncertainties U(ΔsolH0) = 0.060ΔsolH0 (0.95 level of confidence). bCalculated values at 293.15 K

■

properties during the dissolution of cefathiamidine are calculated based on the solubility data in different binary solvent mixtures, and these thermodynamic properties will provide theoretical basis for crystallizer design. Considering the contribution to the control of temperature in the crystallization process, ΔsolH0 is calculated for further understanding of the heat exchange in the dissolution process. Changes of the standard enthalpy during dissolution of cefathiamidine in different solvent mixtures can be calculated by eqs 16, which is obtained by the van’t Hoff equation and the modified Apelblat model19 ⎛ B⎞ Δsol H 0 = RT ⎜C − ⎟ ⎝ T⎠

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.5b00617.

■

Calculated parameters for different models and values of slope and intercept. (PDF)

AUTHOR INFORMATION

Corresponding Author

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

(16)

Funding

where ΔsolH0 is the standard enthalpy change of solution of cefathiamidine, respectively. A, B, and C are parameters of the modified Apelblat equation, which are listed in Supporting Information Table S1. R is the gas constant (8.314 J mol−1 K−1); T is the mean of the experimental temperatures; T = n/∑(1/Ti); n is the number of temperatures investigated (in this study, n = 7); Ti ranges from 278.15 K to 308.15 K and T is 293.15 K. The results are shown in Table 5. According to Table 5, over the temperature range under investigation, it is found that the dissolution process of cefathiamidine in binary solvents is expressed as an endrothermic process, (ΔsolH0 > 0), which partly explains the increasing solubility of cefathiamidine with increasing temperature.

We are grateful for the financial support of the National Natural Science Foundation of China (No. NNSFC 21176173), and the National High Technology Research and Development Program (863 Program No.2012AA021202). Notes

The authors declare no competing financial interest.

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REFERENCES

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4. CONCLUSIONS In this study, the solubility of cefathiamidine in binary water + (acetone, ethanol, or 2-propanol) solvent mixtures was measured from 278.15 K to 308.15 K by using a gravimeteic method. The solubility of cefathiamidine in binary solvents increases with increasing temperature. At a given temperature, the solubility of cefathiamidine increases with the increase of the initial molar fraction of water in binary acetone + water and 2-propanol + water solvent mixtures. However, synergistic effect of mixed solvents was observed in ethanol−water system. The solubility of cefathiamidine first increased with the increase of ethanol molar fraction and reached maximum when the molar fraction of ethanol is about 0.4. After that, the solubility of cefathiamidine started to decrease with the increase of ethanol molar fraction. The calculated solubility of cefathiamidine based on the modified Apelblat equation, the CNIBS/R-K model, and the hybrid models show good agreement with the experimental values. Finally, thermodynamic parameters in binary solvents mixtures were obtained based on the van’t Hoff equation and the modified Apelblat model. The results indicate that the dissolution process of cefathiamidine in these solvent mixtures is endothermic. G

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H

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