Solubility of erythritol in methanol, ethanol and methanol + ethanol: Experimental measurement and thermodynamic modeling

Solubility of erythritol in methanol, ethanol and methanol + ethanol: Experimental measurement and thermodynamic modeling

Fluid Phase Equilibria 360 (2013) 134–138 Contents lists available at ScienceDirect Fluid Phase Equilibria journal homepage: www.elsevier.com/locate...

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Fluid Phase Equilibria 360 (2013) 134–138

Contents lists available at ScienceDirect

Fluid Phase Equilibria journal homepage: www.elsevier.com/locate/fluid

Solubility of erythritol in methanol, ethanol and methanol + ethanol: Experimental measurement and thermodynamic modeling Xiang Liu a , Yonghong Hu a,∗ , Wenge Yang b , Yan Liu a , Mengmeng Liang a a b

College of Biotechnology and Pharmaceutical Engineering, Nanjing University of Technology, Nanjing 211816, China School of Pharmaceutical Sciences, Nanjing University of Technology, Nanjing 211816, China

a r t i c l e

i n f o

Article history: Received 22 April 2013 Received in revised form 31 July 2013 Accepted 11 September 2013 Available online 19 September 2013 Keywords: Erythritol Solubility Gravimetric method Purification

a b s t r a c t Data on corresponding solid–liquid equilibrium of erythritol in methanol, ethanol and methanol + ethanol was measured with temperature range from 283.15 K to 333.15 K under atmospheric pressure by employing the gravimetric method. The experimental results indicated that the solubility of erythritol in the solvents increases with increasing both temperature and mass fraction of organic solvents. The experimental data were well-correlated with the modified Apelblat equation, the h equation and the van’t Hoff equation. In addition, the calculated solubilities showed good agreement with the experimental results. It was found that the modified Apelblat equation could obtain the better correlation results than the other two models. The standard enthalpy, standard entropy, and Gibbs free energy change of solution of erythritol were calculated from the solubility data by using the modified Apelblat model and the van’t Hoff equation. What’s more, the experimental data and model parameters would be useful for optimizing the process of purification of erythritol in industry. © 2013 Elsevier B.V. All rights reserved.

1. Introduction Erythritol (C4 H10 O4 , molecular weight 122.12, CAS No. 149-326) also called 1,2,3,4-butanetetrol or meso-erythritol is a white crystals that is an important industrial chemicals. The molecular structure of erythritol is illustrated in Fig. 1. Erythritol is slightly sweet, cool feeling, and it can be used as food additives. What’s more, erythritol does not participate in the metabolism, and does not change in glucose of blood, it is appropriate for diabetics [1]. As we all know, aqueous solubility is an important parameter in the separation and purification process of erythritol. So far, the crystallization processes of erythritol require a large number of accurate solubility data, but there are few solubility date for erythritol reported. Therefore, obtaining the solubility data of the erythritol is a necessary condition in order to determine the crystallization process properly and improve the purity and yield of erythritol [2]. This paper is mainly aimed to measure the solubility of erythritol in methanol, ethanol and methanol + ethanol and test the capability of the selected solubility correlation models (the van’t Hoff equation, the modified Apelblat equation and the ␭h

∗ Corresponding author at: College of Biotechnology and Pharmaceutical Engineering, Nanjing University of Technology, No. 30, South Puzhu Road, Nanjing 211816, China. Tel.: +86 25 58139208; fax: +86 25 58139208. E-mail addresses: [email protected], [email protected] (Y. Hu). 0378-3812/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.fluid.2013.09.027

equation) to correlate the experimental data. Through the solubility data, we hope to select a better organic solvent to improve the purity and yield of erythritol and reduce cost of production [3]. In this paper, the solubility of erythritol in methanol, ethanol and methanol + ethanol was experimentally measured in a temperature range 283.15-333.15 K under atmospheric pressure by the gravimetric method. The experimental data were correlated using the van’t Hoff equation, the modified Apelblat equation and the h equation. The standard enthalpy, standard entropy and Gibbs energy change of solution of erythritol were calculated from the solubility data.

2. Experimental 2.1. Materials Erythritol (C4 H10 O4 ) with a mass fraction of higher 99.0% was obtained from Aladdin. Its purity was measured by high performance liquid chromatography (HPLC type Agilent 1260 Infinity LC, Agilent Technologies). Its melting point is 390.15 K by a melting point apparatus (model: HCRD-2C) which was supplied by Chengdu Huacheng Instruments Co., Ltd., China. All of the organic solvents (HPLC grade) for dissolving were supplied from Shanghai Shenbo Chemical Co., Ltd., China. All chemicals were used received without further purification.

X. Liu et al. / Fluid Phase Equilibria 360 (2013) 134–138

OH

Table 1 Mole fraction solubilities (xe ) of erythritol in methanol (w) + ethanol (1 − w), where w is the mass fraction.

OH

T (K)

OH OH Fig. 1. Chemical structure of erythritol.

2.2. Apparatus and procedure In the experiments, solubility of erythritol in methanol, ethanol and methanol + ethanol was measured by the gravimetric method under atmospheric pressure in the temperature range from 283.15 K to 333.15 K [4]. The experiments were carried out in a magnetically stirred, jacketed glass vessel (1000 cm3 ). A constant temperature (±0.05 K) was maintained by circulating water through the outer jacket from a super thermostatic watercirculator bath (type HWC-52, Shanghai Cany Precision Instrument Co., Ltd.) at the required temperature. A Sartorius balance was used for weighing the solute and solution. In this paper, the excess solutes were put into the 10 mL glass vessels with stoppers were used to measure the solubility of erythritol in methanol, ethanol and methanol + ethanol [5]. The solution was stirred continuously with a magnetic stirrer at a required temperature to sufficient mixing. To ensure the solid–liquid equilibrium, the solid–liquid mixing was continuously stirred about at least 24 h at the fixed temperature, and then the solution was kept still about 3 h was provided in order to settle the suspension media. For each glass vessel, the sample of approximately 1 mL was extracted from the clear saturated solution [6,7]. Subsequently, the mass of the sample was weighed using an analytical balance with an uncertainty of ±0.0001 g (Sartorius, BS210S). Then the sampling vial was quickly transferred to a dryer oven to dry. The solute sample mass was recorded repeatedly in the drying process to determine the final mass until the mass remained unchanged [8]. The mole fraction solubility (xe ) of erythritol in the solvent system could be obtained as follows: xe =

m1 /M1 m1 /M1 + m2 /M2

135

(1)

where m1 and m2 represent the mass of the solute and solvent (methanol, ethanol and methanol + ethanol), respectively, and M1 and M2 are the molecular weights of the solute and solvent, correspondingly. All the experiments were repeated three times at each temperature in order to obtain a required mean value.

3. Results and discussion 3.1. Solubility data The measured mole fraction solubilities of erythritol in methanol, ethanol and methanol + ethanol solvent mixtures at temperature from 283.15 K to 333.15 K are listed in Tables 1–3 and Fig. 2. From Tables 1–3 and Fig. 2, we can conclude that the solubility of erythritol in all the solvents increases with the increase of both temperature and mass fraction of methanol in the mixtures. Erythritol is similar to other compounds, whose solubility increases with the increasing of the temperature, and polarity of erythritol is close to that of methanol, so the solubility increases with the increasing of mass fraction of methanol in the mixtures.

xe

102 RD Eq. (2)

Eq. (6)

Eq. (7)

w = 15% 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

1.780 × 10−3 2.357 × 10−3 2.843 × 10−3 3.520 × 10−3 4.445 × 10−3 5.520 × 10−3 6.906 × 10−3 8.478 × 10−3 1.037 × 10−2 1.277 × 10−2 1.565 × 10−2

−1.67 3.33 −0.53 −1.52 −0.19 −0.20 0.81 0.25 −0.37 −0.07 0.07

−0.84 3.45 −0.80 −1.95 −0.58 −0.44 0.78 0.42 −0.11 0.11 −0.13

12.94 12.60 5.08 0.91 −0.17 −1.72 −1.44 −2.02 −1.97 −0.35 1.66

w = 30% 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

2.111 × 10−3 2.838 × 10−3 3.369 × 10−3 4.250 × 10−3 5.230 × 10−3 6.458 × 10−3 7.967 × 10−3 9.892 × 10−3 1.203 × 10−2 1.469 × 10−2 1.805 × 10−2

−3.77 3.65 −1.07 0.49 −0.17 −0.26 −0.20 0.74 −0.12 −0.42 0.18

−1.97 4.35 −1.00 0.20 −0.58 −0.62 −0.39 0.75 0.03 −0.26 0.09

11.73 13.23 4.73 2.87 −0.26 −1.97 −2.68 −1.69 −1.82 −0.69 1.91

w = 45% 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

2.360 × 10−3 2.968 × 10−3 3.721 × 10−3 4.630 × 10−3 5.777 × 10−3 7.138 × 10−3 8.788 × 10−3 1.086 × 10−2 1.320 × 10−2 1.616 × 10−2 1.973 × 10−2

−0.34 −0.22 −0.02 −0.19 0.28 0.12 −0.06 0.45 −0.37 −0.12 0.10

−0.39 −0.65 −0.59 −0.71 −0.07 0.01 0.07 0.76 −0.01 0.07 −0.20

12.95 8.57 5.03 1.91 0.20 −1.37 −2.22 −1.68 −1.85 −0.36 1.63

w = 60% 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

2.548 × 10−3 3.222 × 10−3 4.050 × 10−3 4.986 × 10−3 6.195 × 10−3 7.664 × 10−3 9.406 × 10−3 1.148 × 10−2 1.400 × 10−2 1.715 × 10−2 2.073 × 10−2

−0.92 −0.02 0.68 −0.29 0.048 0.30 0.15 −0.21 −0.34 0.31 −0.06

−1.64 −0.86 −0.10 −0.89 −0.28 0.28 0.40 0.22 0.10 0.51 −0.45

11.68 8.20 5.34 1.60 −0.11 −1.16 −1.94 −2.26 −1.74 0.10 1.42

w = 75% 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

2.682 × 10−3 3.477 × 10−3 4.353 × 10−3 5.421 × 10−3 6.717 × 10−3 8.288 × 10−3 1.022 × 10−2 1.253 × 10−2 1.533 × 10−2 1.871 × 10−2 2.292 × 10−2

−3.17 0.25 0.49 0.52 0.39 0.17 0.23 −0.07 −0.18 −0.33 0.21

−2.61 0.21 0.15 0.08 0.03 −0.03 0.25 0.14 0.10 −0.15 −0.01

10.90 9.26 5.65 2.65 0.29 −1.39 −2.01 −2.29 −1.72 −0.57 1.80

w = 90% 283.15 288.15 293.15 298.15 303.15 308.15

2.777 × 10−3 3.593 × 10−3 4.613 × 10−3 5.776 × 10−3 7.195 × 10−3 8.922 × 10−3

−3.992 −1.27 0.95 1.02 0.91 0.66

−2.81 −0.90 0.83 0.68 0.53 0.39

10.85 8.37 6.43 3.36 0.92 −0.84

136

X. Liu et al. / Fluid Phase Equilibria 360 (2013) 134–138

Table 1 (Continued)

Table 4 Parameters of Eq. (2) for erythritol in methanol, ethanol and methanol (w) + ethanol mixed solvents with temperature range from 283.15 K to 333.15 K.

T (K)

xe

102 RD Eq. (2)

Eq. (6)

Eq. (7)

313.15 318.15 323.15 328.15 333.15

1.094 × 10−2 1.357 × 10−2 1.668 × 10−2 2.042 × 10−2 2.520 × 10−2

−0.41 0.05 −0.18 −0.48 0.29

−0.51 0.14 0.02 −0.32 0.15

−2.68 −2.21 −1.76 −0.75 1.88

Table 2 Mole fraction solubilities (xe ) of erythritol in methanol. T (K)

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

xe

3.847 × 10 4.787 × 10−3 5.720 × 10−3 7.293 × 10−3 8.939 × 10−3 1.092 × 10−2 1.329 × 10−2 1.614 × 10−2 1.958 × 10−2 2.373 × 10−2 2.877 × 10−2

A

Methanol + ethanol 15% −91.55 −105.0 30% −80.13 45% −72.71 60% 75% −86.36 90% −89.70

B

C

102 RAD

104 RMSD

472.6 1173 23.70 −261.8 325.1 398.5

14.80 16.78 13.11 11.99 14.05 14.60

0.82 1.01 0.21 0.30 0.55 0.93

0.38 0.52 0.24 0.27 0.39 0.64

669.9

14.55

0.55

0.61

18.94

0.67

0.25

Methanol −90.07

102 RD

−3

w

Ethanol

Eq. (2)

Eq. (6)

Eq. (7)

0.05 0.55 −2.75 0.80 0.66 0.43 0.15 −0.09 −0.23 −0.18 0.15

0.65 0.56 −3.07 0.39 0.31 0.24 0.17 0.10 0.04 −0.02 −0.07

13.18 9.10 2.21 2.63 0.33 −1.29 −2.20 −2.36 −1.76 −0.37 1.83

Table 3 Mole fraction solubilities (xe ) of erythritol in ethanol. T (K)

xe

102 RD Eq. (2)

Eq. (6)

Eq. (7)

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

1.664 × 10−3 1.996 × 10−3 2.370 × 10−3 2.930 × 10−3 3.378 × 10−3 4.007 × 10−3 4.748 × 10−3 5.624 × 10−3 6.710 × 10−3 7.920 × 10−3 9.404 × 10−3

−1.49 −0.68 −0.85 3.01 0.01 −0.11 −0.29 −0.45 0.19 −0.18 0.13

−0.63 −0.56 −1.15 2.57 −0.39 −0.33 −0.29 −0.24 0.49 0.01 −0.11

11.57 7.49 3.36 4.08 −1.08 −2.54 −3.23 −3.11 −1.46 −0.19 2.33

−122.4

2573

3.2. Data correlation 3.2.1. The modified Apelblat model The relationship between mole fraction of the solubility and temperature is generally modeled as follows [9]: ln x = A +

B + C ln T/K

T 

(2)

K

which has already been used to correlate the solute concentration in saturated organic acids by Apelblat and Manzurola and was commonly known as the modified Apelblat equation. Where T is the absolute temperature, A–C are model parameters, x is the mole fraction of the erythritol at the system temperature T. The constants A and B represent the variation in the solution activity coefficient and provide an indication of the influence of non-ideal solution on the solubility of solute; the parameter C reflects the effect of temperature on the fusion enthalpy. In addition, the values of the three parameters of A–C are listed in Table 4. The corresponding root-mean-square deviations (RMSD) and the average absolute deviation (RAD) are also presented in Table 4, which is expressed as [10]:



N  i=1

RMSD =

xic − xie

2 (3)

N

The relative average deviation (RAD) is defined as follows: RAD =

0.028

(4)

i=1

0.026 0.024

The relative deviations (RDs) between the experimental values and the calculated values are listed in Tables 1–3. The RD is calculated according to:

0.022 0.020 0.018

RD =

0.016

X



e c 1  xi − xi xe N i N

0.030

0.014

xe − xc xe

(5)

where N is the number of experimental data points and xe and xc represent the experimental and the calculated solubility values, respectively.

0.012 0.010 0.008 0.006 0.004 0.002 0.000 280

290

300

310

320

330

340

T/K Fig. 2. Mole fraction solubilities of erythritol in methanol (w) + ethanol (1 − w), methanol ethanol, where w is the methanol mass fraction. , ethanol; , methanol; , w = 15%; , w = 30%; , w = 45%; , w = 60%; , w = 75%; , w = 90%. Solid line, calculated from Eq. (2).

3.2.2. h model The Buchowski–Ksiazczak h equation, Eq. (6), is another way to describe the solution behavior, which was suggested firstly by Buchowski et al. [5]. The h equation could fit the experimental data well for many systems with only two parameters,  and h [11]. In this work, the solubility data were also correlated with the h equation:



In 1 +

(1 − x) x



= h

1 T



1 Tm



(6)

X. Liu et al. / Fluid Phase Equilibria 360 (2013) 134–138 Table 5 Parameters of Eq. (6) for erythritol in methanol, ethanol and methanol (w) + ethanol mixed solvents with temperature range from 283.15 K to 333.15 K. w



h

102 RAD

104 RMSD

5.618 × 104 4.988 × 104 4.552 × 104 4.412 × 104 3.909 × 104 3.428 × 104

0.88 0.93 0.32 0.52 0.34 0.66

0.41 0.51 0.31 0.46 0.25 0.45

0.11

3.281 × 104

0.51

0.57

0.0

1.242 × 105

0.62

0.28

Methanol + ethanol 0.07 15% 30% 0.07 0.08 45% 0.08 60% 0.09 75% 0.11 90%

From Tables 4–6, we can draw the conclusion that the experimental solubility data of erythritol in the solvents at temperature ranged from 283.15 K to 333.15 K under atmospheric pressure showed good agreement with the calculated solubility data. Compared with h equation, van’t Hoff model, the Apelblat model correlation is better than two other models. 3.2.4. The standard enthalpy, standard entropy, and Gibbs energy The standard enthalpy, standard entropy, and Gibbs free energy change of solution of erythritol in the solvents can be calculated from Eqs. (8)–(10) which are deduced by using of the modified van’t Hoff equation and the modified Apelblat model [13].

Methanol Ethanol

sol H o = RT

Table 6 Parameters of Eq. (7) for erythritol in methanol, ethanol and methanol (w) + ethanol mixed solvents with temperature range from 283.15 K to 333.15 K. w

137



C−



B T

(8)

sol S o = R(A + C + C ln T )



B + C ln T T

(9)



b

102 RAD

104 RMSD

sol Go = −RT

−6.629 × 105 −6.502 × 105 −6.484 × 105 −6.371 × 105 −6.477 × 105 −6.646 × 105

3.71 3.96 3.43 3.23 3.50 3.64

1.71 2.15 2.02 2.06 2.45 2.74

2.00

−6.165 × 105

3.398

3.24

where sol Ho , sol So , sol Go are the standard enthalpy, standard entropy, and Gibbs energy change of solubility of erythritol respectively, A–C are the parameters from the Apelblat model, T is 298.15 K. The calculated standard enthalpy, standard entropy, and Gibbs energy change are presented in Table 7. From Table 7, it can be found that the sol Ho , sol So , sol Go of solubility of erythritol in solvent mixtures are all positive.

0.00

−5.288 × 105

3.68

1.36

a

Methanol + ethanol 15% 2.00 2.00 30% 2.00 45% 2.00 60% 75% 2.00 90% 2.00 Methanol

A+

(10)

Ethanol

4. Conclusions

where T is the absolute temperature,  and h are the model parameters, x is the mole fraction solubility of erythritol and Tm is the melting temperature of erythritol. The values of the two parameters  and h together with the corresponding root-mean-square deviations (RMSD) and the relative average deviation (RAD) which are listed in Table 5, respectively. 3.2.3. van’t Hoff model The temperature dependence of the solubility of erythritol in the selected solvents can be correlated by the van’t Hoff equation [12]. The van’t Hoff equation is defined as follows: In xi = a +

b T/K

(7)

where x is the mole fraction of the solubility at the system temperature T. The parameters of a and b are the model parameters which are presented in Table 6. The corresponding root-mean-square deviations (RMSD) and the relative average deviation (RAD) are listed in Table 6.

The solubility data of erythritol in selected solution of methanol, ethanol and methanol + ethanol were measured at temperatures from 283.15 K to 333.15 K at about 5 K intervals by the gravimetric method. We can draw the following conclusions: (1) the solubilities of erythritol in all solutions increase with increasing temperature, but the increments with temperature varied for different solutions; (2) the solubilities of erythritol in methanol and methanol +ethanol mixtures increase with increasing the mass fraction of methanol in the solutions at constant temperature; (3) the solubility of erythritol in methanol is far greater than that in ethanol; (4) the temperature dependence of solubilities of erythritol in different solutions can be well-correlated by the modified Apelblat equation, the h equation and the van’t Hoff model, and the calculated solubilities show good agreement with the experimental solubility data, and the modified Apelblat equation was more accurate than the other two models for this system; (5) the sol Ho , sol So , sol Go of solubility of erythritol in methanol, ethanol and methanol + ethanol solvents are all positive; and (6) the experimental solubility measured and the parameters in this experiment could be used for erythritol purification in industry.

Table 7 The standard enthalpy, entropy and Gibbs energy change of erythritol in methanol, ethanol and methanol (w) + ethanol mixed solvents. Methanol + ethanol

w = 15%

w = 30%

w = 45%

w = 60%

w = 75%

w = 90%

sol Ho (kJ mol−1 ) sol So (J mol−1 K−1 ) sol Go (kJ mol−1 ) Methanol sol Ho (kJ mol−1 ) sol So (J mol−1 K−1 ) sol Go (kJ mol−1 )

3.275 × 104 63.01 1.396 × 104

3.183 × 104 61.33 1.354 × 104

3.228 × 104 63.6 1.331 × 104

3.187 × 104 62.87 1.313 × 104

3.211 × 104 64.29 1.294 × 104

3.287 × 104 67.33 1.280 × 104

Ethanol sol Ho (kJ mol−1 ) sol So (J mol−1 K−1 ) sol Go (kJ mol−1 )

3.048 × 104 61.28 1.221 × 104 2.554 × 104 36.91 1.453 × 104

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X. Liu et al. / Fluid Phase Equilibria 360 (2013) 134–138

Acknowledgements This research work was financially supported by Doctoral Fund Class topics (20113221110005) and National High Technology Research and Development Program (2011AA100901). This research work was also supported by the grant from the Scientific Achievements in Jiangsu Province (Major projects) in China (No. 12KJA180002) and the project of Scientific Research and Industry Advance (No. JHB2011-16). We thank the editors and the anonymous reviewers. References [1] M.C. Rodriguez, C. Viadas, A. Seoane, J. PLoS ONE 7 (12) (2013) e50876.

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