Solubility Measurement and Correlation of Fosfomycin Sodium in Six

Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX-XXX

pubs.acs.org/jced

Solubility Measurement and Correlation of Fosfomycin Sodium in Six Organic Solvents and Different Binary Solvents at Temperatures between 283.15 and 323.15 K Zhe Ding,†,‡ Huihui Zhang,†,‡ Dandan Han,†,‡ Peipei Zhu,†,‡ Peng Yang,†,‡ Shasha Jin,†,‡ Mingchen Li,†,‡ 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 University, Tianjin 300072, People’s Republic of China S Supporting Information *

ABSTRACT: The solubility data of fosfomycin sodium (FOM-Na) in six pure solvents (methanol, ethanol, propanol, cyclohexane, acetone, N,N-dimethylformamide) and two binary solvents (methanol + ethanol, methanol + acetone) at temperatures ranging from 283.15 to 323.15 K were measured by a laser monitoring dynamic method at atmospheric pressure. It turned out that the solubility data decreased with increasing temperature, and also varies with the composition of the solvents. Moreover, the experimental data in pure solvents have been correlated with two thermodynamic models (i.e., modified Apelblat and van’t Hoff), and the data in binary solvents have been correlated with CNIBS/R-K equation and two modified versions of Jouyban−Acree models (Van’t-JA equation and Apel-JA equation), respectively. All the results showed a good agreement with the experimental data. Intermolecular interaction force and dielectric constants are introduced to explain the relationship between solubility and temperature. In addition, the analysis of the solubilities implies that higher temperature may destroy the forces between the solvent and solute molecules, leading to lower solubility. And this can give a guide to the design and optimization of the crystallization process of FOM-Na in the industry.

1. INTRODUCTION The compound fosfomycin sodium (FOM-Na) (C3H5Na2O4P; CAS Registry No. 26016-99-9. Figure 1), is a novel broadspectrum antibacterial agent which has been widely applied in the treatment of bacterial infection. As shown in Figure 1, the molecular structure of FOM-Na is similar to that of phosphoenolpyruvate, which can compete with the bacteria

for the same transferase, and inhibits the synthesis of bacteria cell walls and leads to bacteria death.1 FOM-Na has a very wide range of applications, that not only can effect the gram positive and negative bacteria, but also can reduce the occurrence of anaphylactic shock, so it is mainly used for treatment of urinary tract, skin, soft tissue, intestinal infection, and etc.2−4 During the manufacturing process of FOM-Na, crystallization is the key step. The quality of product, such as purity, size distribution, and mobility, will be directly determined by the design and operation of crystallization process.5 The major crystallization method in industry is solvent-out crystallization. Received: July 13, 2017 Accepted: October 12, 2017

Figure 1. Chemical structure of FOM-Na. © XXXX American Chemical Society

A

DOI: 10.1021/acs.jced.7b00638 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Sources and Mass Fraction Purity of the Materials chemical name

CAS RN

FOM-Na methanol ethanol propanol acetone cyclohexane N,N-dimethylformamide

26016-99-9 170082-17-4 64-17-5 71-23-8 67-64-1 110-82-7 68-12-2

source Northeast Pharmaceutical General Factory Jiangtian Chemical Technology Co.,Ltd., Tianjin, Jiangtian Chemical Technology Co.,Ltd., Tianjin, Jiangtian Chemical Technology Co.,Ltd., Tianjin, Jiangtian Chemical Technology Co.,Ltd., Tianjin, Jiangtian Chemical Technology Co.,Ltd., Tianjin, Jiangtian Chemical Technology Co.,Ltd., Tianjin,

China China China China China China

mass fraction purity

purification method

analysis method

≥0.99 ≥0.995 ≥0.995 ≥0.995 ≥0.995 ≥0.995 ≥0.995

none none none none none none none

HPLCa GCb GCb GCb GCb GCb GCb

a

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

maintained at a constant temperature in the water circulating through the outer jacket from a thermostatic water bath (type CF41, German), and the temperature of the solution was determined with a standard uncertainty of 0.1 K. A mechanical agitation device was applied to promote the dissolution process at a desired temperature. At the beginning of the experiment, the intensity of the laser beam dropped due to a large number of undissolved FOM-Na particles suspended in the solution. And the intensity of the laser beam increased to a maximum level until the solid particles dissolved completely, and the solution became clear. Then an additional solid solute of known mass (about 5 mg) was added into the vessel. The process of addition was repeated several times until the intensity of the laser beam started to decline below the maximum level after the final addition of solute. The interval time of addition, dependent on the dissolution speed of FOM-Na, was usually greater than 30 min. When the intensity of the laser beam could not reach 90% of the maximum, it was determined that the solid and liquid phases was reached an equilibrium.10 The total amount of the solute added into the vessel was recorded. In order to ensure the accuracy of the experimental values, same experiment was repeated three times, and the arithmetic average was taken as the final experimental value. The X-ray diffraction (XRD) analysis was performed to determine the crystalline structure of the sample during the measurement.11 The consistent PXRD patterns indicated that there was no phase transition during the experiment. The mole fraction solubility (xA) of FOM-Na in monosolvents and mixed solvents is defined as follows:

For example, FOM-Na crystal can be obtained by adding antisolvent, ethanol, into FOM-Na methanol solution.6 So in order to make a reliable and robust crystallization process, it is crucial to know the solubility data. These data are valuable in theoretical study, such as the selection of crystallization method and solvents, the calculation of yield, and annual output. From literature review, Zhang and his co-worker investigated the solubility of FOM-Na in water at 293.15 K.7 However, there is no more systematic research focused on the solubility data of FOM-Na in organic solvents in different temperatures. In this work, the solubility data of FOM-Na in six pure solvents (i.e., methanol, ethanol, propanol, cyclohexane, acetone, N,N-dimethylformamide) and two groups of binary mixed solvents (methanol + ethanol, methanol + acetone) were experimentally determined at temperatures ranging from 283.15 to 323.15 K by using a laser monitoring dynamic method. The monosolvents’ solubility data have been correlated by modified Apelblat and the Van’t Hoff equation. While in binary mixed solvents, the CNIBS/R-K equation and two modified versions of JA equation were applied.

2. EXPERIMENTAL SECTION 2.1. Materials. Fosfomycin sodium (FOM-Na) was supplied by Northeast Pharmaceutical General Factory with mass fraction purity higher than 0.99. All solvents used in this work, including methanol, ethanol, propanol, cyclohexane, acetone, and N,N-dimethylformamide (DMF), are of analytical grade (mass fraction purity > 0.995). All of them were purchased from Jiangtian Chemical Co., Ltd., China and used without purification. Deionized water used was of HPLC grade. The materials used in this article are listed in Table 1. 2.2. Characterization of FOM-Na. Powder X-ray diffraction (PXRD) was performed to identify the crystal form of samples used in this work. The PXRD patterns were obtained by using a D/MAX 2500 diffractometer (Cu Kα radiation, λKα1 = 1.5406 Å) at 100 mA and 40 kV. The measurements were carried out at 2θ degrees from 2° to 40° with a scanning rate of 8°/min. 2.3. Solubility Measurements. The solubility of FOM-Na in six pure solvents and two binary mixed solvents from 283.15 to 323.15 K was determined by a laser monitoring dynamic method. The experimental instrument and procedure are similar to those described in the previous literature.8 A predetermined excess mass of solvent (50 mL) and an accurate mass of solute were added into a jacketed glass vessel (100 mL) with the laser light adjusted accordingly.9 The mass of the solute and solvents were measured with an analytical balance (type AB204, Mettler-Toledo, Switzerland) with a standard uncertainty of 0.0001 g. The solution in the vessel was

xA =

mA /MA mA /MA + ∑ m i /M i

(1)

Where mA and mi represent the mass of the solute and the solvent, respectively; MA and Mi are the corresponding molar mass. In mixed solvents, the initial mole fraction (x0B) of methanol is defined as follows: x B0 =

mB /MB mB /MB + mC /MC

(2)

Where mB represents the mass of methanol and mC represents the corresponding mass of ethanol or acetone in the solvent mixtures, respectively; MB and MC are the corresponding molar mass.

3. THERMODYNAMIC MODELS One main purpose of determination of solubility is to provide necessary data for industrial application, so the simplicity of the B



Article

models are of great importance.12 To extend the application range of the solubility, it is necessary to correlate the data with various thermodynamic models. In this work, the modified Apelblat equation and van’t Hoff equation were employed to correlate the solubility of FOM-Na in six pure solvents, which embody the effect of temperature on the solubility of FOM-Na. While in methanol + ethanol and methanol + acetone binary solvent mixtures, the CNIBS/R-K model and Jouyban−Acree models were applied in which both temperature and solvent composition were considered. 3.1. Modified Apelblat Equation. The modified Apelblat equation is a semiempirical expression for the solubility of a solid in a solution based on Clausius−Clapeyron equation.13 The relationship between solubility of FOM-Na and temperature is correlated with the modified Apelblat equation as follows: ln xA = A +

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

temperature effects on the solubility of solute in binary solvents, which was proposed by Jouyban-Gharamaleki and his coworkers.18 The model can be written as follows: N

ln xA, T = x B0 ln(xA )B, T + xC0 ln(xA )C, T + x B0xC0 ∑ i

C

T (8)

(3)

ΔHsoln ΔSsoln + RT (K) R

B

Where Ji is the model parameter and the other symbols represent the same meanings as eq 6. The solubility of the solute in pure solvents, (xA)B and (xA)C, can be obtained from the modified Apelblat19,20 and van’t Hoff equation.21 Modified Apelblat Equation. The corresponding values from modified Apelblat equation as eq 3, when combining eq 3 with eq 8 and substituting x0C with (1 − x0B), a new equation (called Apel-JA equation) can be obtained and further simplified by introducing a set of constants as follows: x0 (x 0)2 V2 + V3 ln T + V4x B0 + V5 B + V6 B T T T 0 3 0 4 (x ) (x ) + V7 B + V8 B + V9x B0 ln T (9) T T

ln xA = V1 +

Where xA refers to the mole fraction solubility of the FOM-Na; T is the experimental temperature; A, B, and C are the model parameters. The values of A and B represent the effect of solution on the solubility and the value of C reflects the effect of temperature on the fusion enthalpy.14 3.2. Van’t Hoff Equation. The van’t Hoff equation reveals the relationship between the mole fraction solubility of a solute and the absolute temperature in real solution.15 The relationship between solubility of FOM-Na and temperature is correlated with the van’t Hoff equation as follows: ln xA = −

Ji(x 0− x 0)i

This is Apel-JA equation and V1, V2, V3, V4, V5, V6, V7, V7, V8, V9 are the model parameters. Van’t Hoff Equation. The corresponding values from van’t Hoff equation as eq 5, substituting eq 5 into eq 8 and substituting x0C with (1 − x0B), a new simplified equation (called VF-JA) referred can be shown as follows x0 (x 0)2 (x 0)3 V2 + V3x B0 + V4 B + V5 B + V6 B T T T T 0 4 (x ) + V7 B (10) T

ln xA = V1 +

(4)

where xA is the mole fraction solubility of FOM-Na and ΔHsoln and ΔSsoln are the van’t Hoff enthalpy and entropy of solution, respectively. T is the experimental temperature, and R is the gas constant. Because the van’t Hoff equation deviates from the real solution, so there are some deviations in the results of thermodynamic parameter. In order to make it clear, van’t Hoff equation can be further simplified as follows: a ln xA = +b T (K) (5)

This is VF-JA equation and V1, V2, V3, V4, V5, V6, V7 are the model parameters.

4. RESULTS AND DISCUSSION 4.1. Characterization and Identification of FOM-Na. In order to verify the identity and determine the crystal form of the sample during the measurement, the powder X-ray diffraction (PXRD) analysis was performed. The typical

where parameters a and b are the model constants, but do not have exact significance. 3.3. CNIBS/R-K Equation. The CNIBS/R-K model is usually applied in the binary solvents, which was suggested by Acree and his co-workers.16,17 It is wildly used to describe the relationships between the solubility and the temperature, which was shown as follows: N

ln xA = x B0 ln(xA )B + xC0 ln(xA )C + x B0xC0 ∑ Si(x B0 − xC0)i i=1

(6)

x0B

x0C

where and refer to the initial mole fraction of the mixtures on the absence of the solute. (xA)B and (xA)C are the solubility of the solute in pure solvents B and C, respectively. In this article, N = 2, and eq 6 can be further simplified as eq 7. 0 4 ln xA = B0 + B1x B0 + B2 (x B0)2 + B3(x B0)3 + B4 (x B4 )

(7)

Where B0, B1, B2, B3, and B4 are the model constants. 3.4. Jouyban−Acree Equation. The basic Jouyban−Acree model is widely used to describe both composition and

Figure 2. Powder X-ray diffraction patterns for FOM-Na and sample. C



Article

Table 2. Experimental and Correlated Mole Solubility of FOM-Na in Six Pure Solvents at Different Temperature (p = 0.1 MPa)a,b Apelblat equation T/K methanol 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 ethanol 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 propanol 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 acetone 283.15 288.15

10000xexp A

10000xcal A

100RD

Apelblat equation

van’s Hoff equation 10000xcal A

T/K

100RD

177.422 165.159 151.615 137.656 128.641 120.913 110.520 104.755 98.449

178.680 163.670 150.540 139.000 128.810 119.780 111.750 104.590 98.170

−0.710 0.900 0.710 −0.130 0.935 −1.118 0.157 0.279 0.215

178.063 163.668 150.870 139.453 129.235 120.062 111.802 104.345 975.93

−0.36 0.90 0.49 −1.31 −0.46 0.70 −1.16 0.39 0.87

10.895 9.342 7.693 6.428 5.483 4.633 3.832 3.159 2.662

10.920 9.220 7.760 6.520 5.460 4.570 3.820 3.190 2.660

−0.27 1.34 −0.85 −1.38 0.36 1.33 0.31 −0.93 0.17

11.098 9.169 7.625 6.381 5.371 4.546 3.868 3.309 2.844

−1.86 1.85 0.88 0.73 2.04 1.88 −0.95 −4.74 −6.83

1.080 0.801 0.619 0.452 0.309 0.195 0.134 0.104 0.071

1.041 0.819 0.607 0.438 0.309 0.203 0.141 0.099 0.069

0.51 −2.33 1.94 2.96 −0.09 0.22 5.22 4.82 2.82

1.109 0.790 0.570 0.415 0.306 0.228 0.171 0.129 0.099

0.010 −0.036 0.042 −0.074 0.034 0.195 0.066 −0.380 0.033

1.862 1.599

1.872 1.593

−0.53 0.42

1.890 1.588

−1.49 0.72

293.15 298.15 303.15 308.15 313.15 318.15 323.15 cyclohexane 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 DMF 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

10000xexp A

van’s Hoff equation

10000xcal A

100RD

10000xcal A

100RD

1.377 1.154 0.972 0.830 0.709 0.607 0.547

1.356 1.155 0.984 0.840 0.717 0.614 0.524

1.52 −0.07 −1.31 −1.19 −1.23 −1.09 4.06

1.342 1.140 0.974 0.837 0.722 0.626 0.545

2.53 1.19 −0.25 −0.79 −1.89 −3.06 0.29

4.034 3.530 2.996 2.522 2.255 1.958 1.751 1.513 1.276

4.040 3.485 3.005 2.604 2.251 1.958 1.707 1.489 1.302

−0.05 1.52 −0.18 −3.02 0.06 −0.03 2.52 1.56 −2.12

4.067 3.476 2.987 2.580 2.239 1.952 1.710 1.503 1.327

−0.80 1.54 0.31 −2.30 0.71 0.31 2.35 0.66 −4.02

6.060 5.319 4.810 4.429 3.963 3.582 3.391 3.116 2.912

6.032 5.371 4.818 4.359 3.973 3.638 3.357 3.121 2.910

0.42 −0.97 −0.17 1.63 −0.12 −1.59 0.97 −0.09 −0.01

5.966 5.376 4.861 4.411 4.015 3.666 3.357 3.082 2.838

1.55 −1.07 −1.06 0.41 −1.31 −2.35 1.01 1.07 2.55

a exp xA

is the experimental solubility; xcal A represents the calculated solubility by the modified Apelblat equation or van’t Hoff equation. b The standard uncertainty of temperature is uc(T) = 0.1 K. The relative standard uncertainty of the solubility measurement is ur(x) = 0.05; The relative uncertainty of pressure is ur (p) = 0.05.

Figure 4. Mole fraction solubility, xexp of FOM-Na in methanol A solvents.

Figure 3. Mole fraction solubility, xexp A of FOM-Na in pure solvents. ▼, ethanol; ◆, N,N-dimethylformamide; ■,cyclohexane; ●, acetone; ▲, propanol.

4.2. Pure Solvents. The mole fraction solubility (xA) data of FOM-Na in methanol, ethanol, propanol, cyclohexane, acetone, and N,N-dimethylformamide at temperatures ranging from 283.15 to 323.15 K at atmospheric pressure was recorded in Table 2, and graphically plotted in Figures 3 and 4.

PXRD pattern is shown in Figure 2. All FOM-Na samples used in this work were found to be same crystal form, and this suggested that there was no polymorphism, solvates, or armorphous during the solubility measurement. D



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cal Table 3. Experimental (xexp A ) and Correlated (xA ) Mole Fraction Solubility Data of FOM-Na in Binary Mixed solvents of Methanol + Ethanol (p = 0.1 MPa)a,b

104xcal A x0B T = 283.15 0.14 0.26 0.38 0.49 0.59 0.68 0.76 0.84 0.91 T = 288.15 0.14 0.26 0.38 0.49 0.59 0.68 0.76 0.84 0.92 T = 293.15 0.14 0.26 0.38 0.49 0.59 0.68 0.77 0.85 0.92 T = 298.15 0.14 0.26 0.38 0.49 0.59 0.68 0.77 0.85 0.92 T = 303.15 0.14 0.26 0.38 0.49 0.59 0.68 0.77

104xexp A K 14.714 18.701 27.867 38.492 55.521 73.684 99.848 120.431 145.801 K 12.214 15.241 22.134 30.115 42.353 59.512 78.595 99.678 131.094 K 9.498 11.505 17.115 23.635 33.714 47.821 65.564 85.597 117.865 K 7.644 9.115 13.532 18.492 26.583 36.421 52.593 69.588 102.015 K 6.345 7.484 10.542 14.021 20.840 29.401 42.684

CNIBS/R-K

Apel-JA

104xcal A x0B

VF-JA

14.642 19.038 27.063 39.115 55.237 75.059 97.460 121.485 145.741

16.689 19.738 26.436 36.241 49.199 66.363 90.399 127.684 190.411

17.237 20.306 27.098 37.026 50.110 67.401 91.573 129.029 191.991

12.160 15.257 21.368 30.583 42.983 58.601 77.734 101.230 130.485

12.999 15.536 20.965 28.925 39.513 53.578 73.470 104.220 155.491

13.083 15.624 21.068 29.048 39.657 53.743 73.658 104.438 155.753

9.465 11.712 16.520 23.955 34.175 47.446 64.473 86.899 117.385

10.135 12.248 16.661 23.143 31.813 43.399 59.823 85.254 127.545

10.024 12.130 16.521 22.975 31.614 43.169 59.560 84.953 127.198

7.567 9.283 13.038 18.786 26.639 37.016 50.989 71.096 101.650

7.911 9.671 13.268 18.564 25.690 35.284 48.914 70.112 105.324

7.749 9.497 13.060 18.312 25.391 34.936 48.515 69.651 104.786

6.301 7.538 10.233 14.480 20.607 29.255 41.603

6.182 7.648 10.588 14.930 20.806 28.760 40.124

6.042 7.496 10.403 14.704 20.537 28.446 39.761

0.85 0.92 T = 308.15 0.14 0.26 0.38 0.49 0.59 0.68 0.77 0.85 0.92 T = 313.15 0.14 0.26 0.38 0.49 0.59 0.68 0.77 0.85 0.92 T = 318.15 0.14 0.27 0.38 0.49 0.59 0.68 0.77 0.85 0.92 T = 323.15 0.14 0.27 0.38 0.49 0.59 0.68 0.77 0.85 0.92

104xexp A 57.896 89.028 K 5.288 6.197 8.901 11.412 15.492 21.492 33.687 45.213 77.035 K 4.215 5.231 6.905 8.891 12.908 17.913 25.392 37.935 68.951 K 3.203 3.893 5.183 7.101 10.489 14.113 20.705 32.690 60.034 K 2.381 3.421 4.303 6.111 8.509 12.415 17.492 28.431 55.044

CNIBS/R-K

Apel-JA

VF-JA

59.928 87.822

57.828 87.258

57.406 86.764

5.269 6.371 8.480 11.550 15.800 21.895 31.303 47.302 76.072

4.837 6.059 8.466 12.035 16.901 23.530 33.032 47.920 72.591

4.749 5.962 8.348 11.889 16.725 23.324 32.792 47.640 72.263

4.222 5.124 6.851 9.301 12.622 17.426 25.218 39.434 67.663

3.789 4.808 6.784 9.726 13.762 19.296 27.290 39.782 60.521

3.761 4.776 6.746 9.678 13.704 19.227 27.210 39.688 60.412

3.215 3.832 5.243 7.310 10.107 14.128 20.716 33.166 59.523

2.972 3.821 5.448 7.879 11.238 15.876 22.602 33.127 50.709

3.001 3.853 5.488 7.929 11.299 15.948 22.687 33.227 50.829

2.427 3.243 4.487 6.154 8.424 11.851 17.766 29.289 53.980

2.335 3.042 4.383 6.397 9.202 13.096 18.775 27.681 42.563

2.411 3.129 4.493 6.535 9.371 13.298 19.014 27.964 42.902

a exp xA

is the experimental solubility; xcal A represents the calculated solubility by the CNIBS/R-K, Apel-JA and VF-JA equation. bThe standard uncertainty of temperature is uc(T) = 0.1 K. The relative standard uncertainty of the solubility measurement is ur(x) = 0.05. The relative uncertainty of pressure is ur(p) = 0.05.

acetone (5.40) > ethanol (4.3) > propanol (4.00) > cyclohexane (0.10).23 It seems that the order of solubility is not strictly consistent with the order of polarity of pure solvents, according to the principle of “like dissolves like”.24 It means that the polarity of solvents might not be the only factor to affect the solubility in the selected solvents. In addition, it can be found from Table S5 and Figure S1 of the Supporting Information that the dielectric constants of solvents, methanol, ethanol, and acetone, decrease with increasing temperature,25

It can be seen that the solubility of FOM-Na in six pure solvents are in the following order: methanol > ethanol > N,Ndimethylformamide > cyclohexane > acetone > propanol after a cursory glance in Figures 3 and 4. Therefore, methanol is often used as the good solvent for solution crystallization of FOMNa. From Figure 1, the molecule is proved as high polarity judged by the structure of FOM-Na. At a certain temperature, according to the polarity parameter,22 the polarity order of the solvents is methanol (6.60) > N,N-dimethylformamide (6.40) > E



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cal Table 4. Experimental (xexp A ) and Correlated (xA ) Mole Fraction Solubility Data of FOM-Na in Binary Mixed solvents of Methanol + Acetone (p = 0.1 MPa)a,b

104xcal A x0B T = 283.15 0.14 0.26 0.38 0.49 0.59 0.68 0.77 0.85 0.92 T = 288.15 0.14 0.26 0.38 0.49 0.59 0.68 0.77 0.85 0.92 T = 293.15 0.14 0.26 0.38 0.49 0.59 0.68 0.77 0.85 0.92 T = 298.15 0.14 0.26 0.38 0.49 0.59 0.68 0.77 0.85 0.92 T = 303.15 0.14 0.26 0.38 0.49 0.59 0.68 0.77

104xexp A K 5.795 11.482 17.511 23.121 30.154 40.095 57.984 81.843 125.300 K 4.631 8.921 13.542 18.621 24.095 32.832 46.912 68.011 100.914 K 3.585 7.186 10.786 14.499 19.301 26.522 38.386 55.355 95.448 K 2.913 5.834 8.521 11.802 15.689 21.468 30.514 45.051 85.462 K 2.512 4.776 6.978 9.911 13.122 17.915 25.473

CNIBS/R-K

Apel-JA

104xcal A x0B

VF-JA

5.797 11.533 17.396 23.226 30.095 39.868 55.423 81.393 125.461

6.213 11.479 17.111 22.762 29.209 38.280 53.374 81.050 135.452

6.100 11.259 16.769 22.290 28.583 37.435 52.163 79.164 132.216

4.591 8.954 13.491 18.318 24.368 33.08 46.519 67.765 101.209

4.774 8.918 13.467 18.159 23.611 31.317 44.124 67.742 113.505

4.757 8.884 13.413 18.083 23.509 31.177 43.922 67.420 112.942

3.602 7.122 10.84 14.675 19.335 26.173 37.486 57.572 93.874

3.717 7.019 10.736 14.668 19.312 25.920 36.886 57.083 96.079

3.741 7.066 10.810 14.773 19.455 26.118 37.175 57.540 96.854

2.924 5.616 8.717 11.951 15.659 20.911 29.901 47.366 83.424

2.931 5.593 8.662 11.987 15.978 21.685 31.171 48.636 82.328

2.966 5.663 8.774 12.149 16.200 21.997 31.631 49.370 83.590

2.516 4.663 7.147 9.815 13.003 17.664 25.812

2.339 4.509 7.069 9.907 13.363 18.332 26.597

2.370 4.572 7.171 10.055 13.571 18.626 27.035

0.85 0.92 T = 308.15 0.14 0.27 0.38 0.49 0.59 0.68 0.77 0.85 0.92 T = 313.15 0.14 0.27 0.38 0.49 0.59 0.68 0.77 0.85 0.92 T = 318.15 0.14 0.27 0.38 0.49 0.59 0.68 0.77 0.85 0.92 T = 323.15 0.14 0.27 0.38 0.49 0.59 0.68 0.77 0.85 0.92

104xexp A 41.613 76.438 K 1.910 3.707 5.813 8.116 10.886 15.768 22.483 36.512 67.434 K 1.515 3.014 4.913 6.855 9.531 13.618 19.216 31.813 58.725 K 1.301 2.507 3.900 6.013 8.104 12.021 17.830 26.441 50.903 K 1.120 2.108 3.326 5.124 7.415 10.203 15.815 24.385 43.108

CNIBS/R-K

Apel-JA

VF-JA

41.852 75.979

41.829 71.247

42.533 72.465

1.904 3.681 5.798 8.152 11.044 15.301 22.678 36.988 66.917

1.887 3.676 5.831 8.274 11.293 15.652 22.915 36.274 62.278

1.907 3.717 5.899 8.373 11.434 15.853 23.217 36.764 63.132

1.502 2.994 4.861 6.971 9.521 13.199 19.529 31.914 58.466

1.539 3.028 4.860 6.980 9.636 13.492 19.917 31.784 54.942

1.545 3.041 4.882 7.013 9.685 13.562 20.024 31.958 55.245

1.308 2.442 4.000 5.917 8.314 11.679 17.237 27.784 49.809

1.267 2.519 4.090 5.943 8.298 11.735 17.463 28.047 48.793

1.260 2.504 4.065 5.907 8.245 11.659 17.347 27.855 48.448

1.124 2.065 3.379 5.068 7.269 10.414 15.5 24.738 42.895

1.054 2.115 3.474 5.107 7.208 10.293 15.437 24.952 43.517

1.035 2.075 3.404 5.001 7.055 10.068 15.090 24.377 42.490

a exp xA

is the experimental solubility; xcal A represents the calculated solubility by the CNIBS/R-K, Apel-JA and VF-JA equation. bThe standard uncertainty of temperature is uc(T) = 0.1 K. The relative standard uncertainty of the solubility measurement is ur(x) = 0.05. The relative uncertainty of pressure is ur(p) = 0.05.

in FOM-Na and the solvent,16 such as hydrogen bond between the solvent and the solution, some of the clathrates may be destroyed at a high temperature, thus, the solubility decreases with the increasing of the temperature.29−31 Meanwhile, it can be concluded that cooling crystallization may not be used in producing FOM-Na. In contrast, antisolvent crystallization is the most popular method to produce FOM-Na. Also, methanol is the frequently used solvent because of its advantage in solubility and feasible to

which can describe the solubility’s evolution to a certain extent. The solubility of FOM-Na may also be affected by some other factors, such as hydrogen bonds, ionization constant, and surface tension of the different solvents and so on.26−28 The results suggest that the solubility of FOM-Na decreases with increasing temperature in selected solvents, indicating that the dissolving processes of FOM-Na are exothermic within the experimental temperature range, which is observed during the experiments. It may be attributed to functional groups existing F



Article

ARD =

N

∑ i=1

xAexp − xAcal xAexp

cal Where xexp A denotes the experimental solubility, xA stands for the calculated solubility, and N is the number of experimental points. The correlation results of these models mentioned above and the corresponding values of the RD and ARD are listed in Supporting Information, Tables S1, S2, S3, S4, and S5, respectively. From Tables S1 and S2, it can be concluded that the van’t Hoff and modified Apelblat equation are shown in good agreement due to small ARDs. Therefore, both the van’t Hoff equation and the modified Apelblat equation can be used for model research. From Tables S3−S4, the calculated data obtained from the CNIBS/R-K and Jouyban-Acree equation are in good agreement with the measured data. For the binary solvents, and the CNIBS/R-K equation were all found to provide a satisfactory correlation.

Figure 5. Equilibrium solubility xexp A of FOM-Na in binary (methanol + ethanol) at different temperatures.

5. CONCLUSIONS The solubility data of FOM-Na in six pure solvents, methanol, ethanol, propanol, acetone, cyclohexane, and DMF, and in binary mixed solvents of methanol + ethanol and methanol + acetone were experimentally determined over the temperature ranging from 283.15 to 323.15 K with a laser monitoring dynamic method. It was found that in different monosolvents, the solubility of FOM-Na is temperature dependent obviously and decreases with the increasing temperature. In general, around the working temperature, the solubility in six pure solvents are ranked as follow: methanol > ethanol > N,Ndimethylformamide > cyclohexane > acetone > propanol. This phenomenon may be due to the complex interactions between the solute and the solvents, and dielectric constants are also introduced to explain this point. In two binary solvents, methanol + ethanol and methanol + acetone, the solubility of FOM-Na decreases slightly with increasing temperature at low mole fractions of methanol, then decreases obviously with increasing temperature when the mole fraction of methanol increasing to a certain value at 0.8. Moreover, the methanol + ethanol solvent mixtures, temperature dependence is more remarkable compare to methanol + acetone solvent mixtures. The modified Apelblat equation and van’t Hoff equation were employed to correlate the solubility data in six monosolvents. In binary mixtures (methanol + ethanol, methanol + acetone), the CNIBS/R-K, Van’t-JA, and the Apel-JA equation were applied. It turns out that all the selected thermodynamic models show good agreement with the experimental values, and the CNIBS/R-K equation was found to be best. Most importantly, the solubility of FOM-Na in the selected solvents can give a guide to the design and optimization of the crystallization process of FOM-Na in the industry.

Figure 6. Equilibrium solubility xexp A of FOM-Na in binary (methanol + acetone) at different temperatures.

miscible compared with other organic solvents. Therefore, determining the solubility of FOM-Na in mixed solvent which contains methanol is very important in the industry. 4.3. Binary Solvent. The mole fraction solubility (xA) data of FOM-Na in binary mixed solvents at temperatures ranging from 283.15 to 323.15 K at atmospheric pressure are recorded in Tables 3 and 4, and graphically plotted in Figures 5 and 6. In Tables 3 and 4, more intuitively in Figures 5 and 6, it turned out to be that solubility data of FOM-Na in methanol + ethanol and methanol + acetone binary solvent mixtures is negatively correlated with temperature and positive correlated with the mole fraction of methanol. It can also be found that under some circumstances, the effect of solvent composition might play a more important role than temperature under some circumstances, so this makes dilution crystallization to be a better choice. The results suggest that the solubility of FOM-Na decreases obviously with an increasing temperature at high mole fractions of methanol. Interestingly, when the mole fraction of methanol declined to a certain value 0.8, the solubility decreases slightly with the increasing temperature. It may be caused by the intermolecular interactions and the steric hindrance between binary solvents and solvent.32,33 4.4. Data Correlation. To test the applicability and accuracy of the models used in this article, the relative deviation (RD) and the average relative deviation (ARD) are introduced by the following definitions RD =

1 N

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.7b00638.

xAexp − xAcal xAexp

Calculated parameters and ARD for different models, dielectric constant of pure and binary solvents (PDF) G



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Article

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AUTHOR INFORMATION

Corresponding Author

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

Junbo Gong: 0000-0002-3376-3296 Funding

The authors are grateful to the financial support of National Natural Science Foundation of China (NNSFC 21676179, NNSFC 91634117, and NNSFC 21376164), National 863 Program (2015AA021002), Tianjin Science and Technology Project (15JCZDJC33200 and KJXH2015−01), Major Science and Technology Program for Water Pollution Control and Treatment (NO.2015ZX07202-013). Notes

The authors declare no competing financial interest.

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2,4,6,8,10,12-hexaazaisowurtzitane in Five Organic Solvents at Temperatures between 283.15 and 333.15 K and Different Chloralkane plus Ethyl Acetate Binary Solvents at Temperatures between 283.15 and 323.15 K. J. Chem. Eng. Data 2017, 62, 1204− 1213. (33) Han, D. D.; Li, X. N.; Wang, H. S.; Wang, Y.; Du, S. C.; Yu, B.; Liu, Y. M.; Xu, S. J.; Gong, J. B. Determination and correlation of pyridoxine hydrochloride solubility in different binary mixtures at temperatures from (278.15 to 313.15) K. J. Chem. Thermodyn. 2016, 94, 138−151.

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Solubility Measurement and Correlation of Fosfomycin Sodium in Six

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