Determination, Correlation, and Application of Sodium l-Ascorbate

Article Cite This: J. Chem. Eng. Data 2018, 63, 233−245

pubs.acs.org/jced

Determination, Correlation, and Application of Sodium L‑Ascorbate Solubility in Nine Pure Solvents and Two Binary Solvents at Temperatures from 278.15 to 323.15 K Hui Zhang,*,† Zengkun Liu,‡ Xiping Huang,† and Qi Zhang† †

Institute of Tianjin Seawater Desalination and Multipurpose Utilization, State Oceanic Administration, Tianjin 300192, People’s Republic of China ‡ China Tianchen Engineering Corporation, Tianjin 300400, People’s Republic of China S Supporting Information *

ABSTRACT: The solubility data of sodium L-ascorbate in water, methanol, ethanol, acetone, chloroform, ethyl acetate, isopropyl alcohol, isobutyl alcohol, n-hexane, water−methanol mixture and water−ethanol mixture have been determined in the temperatures range of 278.15−323.15 K by a static analytic method at atmospheric pressure. The experimental data were correlated with the modified Apelblat equation, CNIBS/R-K model, and Jouyban−Acree model. On the basis of the solubility data, a novel model-free design approach (semisupersaturation control, SSSC) for combined cooling and antisolvent crystallization (CCAC) processes has been proposed and evaluated for sodium L-ascorbate in a methanol−water mixture. This approach can be easily implemented without complicated online monitors. Sodium L-ascorbate crystals with large and uniform morphology were obtained using the CCAC process, which was designed by the SSSC approach.

1. INTRODUCTION Sodium L-ascorbate (C6H7NaO6, CAS registry No. 134-03-2, Figure. 1) is a mineral salt of L-ascorbic acid. L-Ascorbic acid is

Therefore, we have to get vitamin C from food and other sources (such as vitamin tablets). It is worth noting that L-ascorbic acid becomes harder to take by mouth with age. Sometimes lesions form at the bottom of the esophagus, thus tissues leading to the stomach are not acid protected. Moreover, it is too acidic to safely use intravenously.7−9 As a form of vitamin C, the basic properties and health benefits of sodium L-ascorbate are virtually identical with L-ascorbic acid. And most of all, the mineral salt lowers the acidity of L-ascorbic acid.10 For people who are experiencing both swallowing discomfort and hypoimmunity, sodium L-ascorbate is an excellent choice. The buffered sodium L-ascorbate can be used by sensitive persons to avoid the acidity of L-ascorbic acid through either intravenous infusions or intramuscular injections. Additionally, as a food additive, it is always used as antioxidant and acidity regulator.11−13 Sodium L-ascorbate can be prepared from the reaction between equivalent amount of L-ascorbic acid and sodium bicarbonate in water. After cessation of effervescence, the sodium L-ascorbate is precipitated by using the method of crystallization.14−16 It is well-known that batch crystallization is the critical step for separation and purification of chemical and pharmaceutical products. The quality of the final product is dependent on the crystal habit, purity, yield, crystal size distribution (CSD), etc. For sodium L-ascorbate, a crystalline product with uniform size

Figure 1. Chemical structure formula (a) and three-dimensional structure (b) of sodium L-ascorbate.

the most powerful and fastest acting form of vitamin C.1 To meet nutritional requirements, 100 mg/day of vitamin C is suggested for healthy individuals. Enough intake of vitamin C can reduce the probability of many diseases.2,3 Vitamin C exists extensively in fresh fruits and vegetables. Most animals and plants synthesize vitamin C from D-glucose or D-galactose.4−6 However, the human body does not produce its own vitamin C due to the absence of the enzyme L-gulonolactone oxidase. © 2017 American Chemical Society

Received: September 24, 2017 Accepted: November 21, 2017 Published: December 7, 2017 233

DOI: 10.1021/acs.jced.7b00846 J. Chem. Eng. Data 2018, 63, 233−245

Journal of Chemical & Engineering Data

Article

Table 1. Purities and Sources of Materials Used in This Worka chemical name L-ascorbic

acid sodium L-ascorbate sodium bicarbonate para-tert-butylbenzoic acid methanol ethanol acetone chloroform ethyl acetate isopropyl alcohol isobutyl alcohol n-hexane a

CASRN

sources

mass fraction purity

purification method

analysis method

50−81−7 134−03−2 144−55−8 98−73−7 67−56−1 64−17−5 67−64−1 67−66−3 141−78−6 67−63−0 78−83−1 110−54−3

Aladdin Chemical Co., Ltd., China Aladdin Chemical Co., Ltd., China Guangfu Chemical Co., Ltd., China Heowns Chemical Co., Ltd., China Tianjin Kewei Chemical Co., Ltd., China Tianjin Kewei Chemical Co., Ltd., China Tianjin Kewei Chemical Co., Ltd., China Tianjin Kewei Chemical Co., Ltd., China Tianjin Kewei Chemical Co., Ltd., China Tianjin Kewei Chemical Co., Ltd., China Tianjin Kewei Chemical Co., Ltd., China Tianjin Kewei Chemical Co., Ltd., China

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

none

titrationb titration ICc GCd GC GC GC GC GC GC GC GC

The purity and analysis methods were provided by the suppliers. bStoichiometry titration method. cIon chromatography. dGas chromatography.

crystal product were analyzed by using SEM and Mastersizer, respectively.

and shape is desired in the market, as the crystal size distribution (CSD) determines the efficiency of the downstream processes. To improve the final crystal properties, the driving force of crystallization, supersaturation, should be controlled by adjusting cooling or antisolvent addition rate. Compare with cooling crystallization or antisolvent addition crystallization, the combined cooling and antisolvent crystallization (CCAC)17−20 is more applicable in industry due to its higher yield. Besides, an integrated control of solvent/antisolvent ratio and temperature can have a significant effect on the crystal properties, including shape, size, and so on. Because of the relatively widespread industrial use of CCAC, the growing interest has been motivated in design and optimizing this process in recent years. Generally, a suitable supersaturation set point is selected to promote growth and avoid undesired nucleation. The supersaturation is maintained during the crystallization process, which is called the supersaturation control (SSC)21−23 approach. There are two SSC methods to optimize the crystallization process: model-based control and “direct” feedback approach. In the former method, a complete model describing the crystallization process is needed, while various robust in situ sensors have to be used to monitor and control the latter process. In short, the above two methods are time-consuming, complicated, and costly. Therefore, a simple and effective approach of design and optimizing the CCAC process is desperately needed. To select suitable solvents and to design an optimal crystallization process, it is essential to know the solubility of sodium L-ascorbate in the single solvent and mixed solvent. Unfortunately, the solubility data of sodium L-ascorbate at different temperatures are not available in the literature. In this work, the solubility of sodium L-ascorbate in nine pure solvents (water, methanol, ethanol, acetone, chloroform, ethyl acetate, isopropyl alcohol, isobutyl alcohol, n-hexane) and two binary solvents (water−methanol and water−ethanol) has been determined by a static analytic method at atmospheric pressure in the temperature range from 278.15 to 323.15 K. The modified Apelblat equation, CNIBS/R-K model, and Jouyban− Acree model were chosen to correlate the measured solubility data. Moreover, based on these solubility data, an efficient control approach for the CCAC process of sodium L-ascorbate has been put forward using neither a complicated model nor expensive online monitoring. Finally, crystal products of sodium L-ascorbate with uniform size and shape were obtained by applying the new approach. The morphology and CSD of the

2. EXPERIMENTAL SECTION 2.1. Materials. L-Ascorbic acid and sodium L-ascorbate with a purity of 99.0% were purchased from Aladdin Chemical Co., Ltd., Shanghai, China. Sodium bicarbonate with purity greater than 99.0% was supplied by Guangfu Chemical Reagents Co., Tianjin, China. Methanol, ethanol, acetone, chloroform, ethyl acetate, isopropyl alcohol, isobutyl alcohol, and n-hexane obtained from Tianjin Kewei Co. of China were of analytic reagent grade. Both organic solvents and deionized water were used without any treatment. The information on the materials used in the experiment was presented in Table 1. 2.2. Apparatus and Procedures. 2.2.1. Thermodynamic Properties Measurements. Thermogravimetric analysis (TGA) was carried out on a thermogravimetric analyzer (Q50, TA Corporation USA). The temperature range was from 298.15 K to 1073.15 K. The melting properties of sodium L-ascorbate were also determined by differential scanning calorimeter (DSC)(Q2000, TA Corporation USA) within the temperature range from 298.15 K to 503.15 K. The DSC instrument was calibrated with indium and zinc standards before analysis. Both TGA and DSC measurements were under a nitrogen atmosphere of 50 mL·min−1. The heating rate was 5 K·min−1. 2.2.2. Solubility Measurements. The solubility of sodium L-ascorbate was measured by a static method, which was described in the literature.24−27 Briefly, excess amounts of sodium L-ascorbate were added to the selected solvents in a jacketed glass vessel. The solution was stirred continuously with a magnetic stir bar for 5 h. A heating and cooling bath (type CF41, Julabo Technology (Beijing) Co., Ltd., China, temperature stability ±0.05 K) was used to control the temperature of the solution. When solid−liquid equilibrium was achieved, the suspension was settled down. The upper clear solution was extracted by a syringe, filtered through a 0.2 μm PTFE filter and dried in a vacuum drying oven. What is more, to guarantee the accuracy of the solubility measurement in insoluble solvents, the quantity of sampling has been increased 10 times. The crystal structure of sodium L-ascorbate was identified by powder X-ray diffraction (PXRD, D/MAX 2500 Japan) pattern. Each sample was weighted every 30 min until the values no longer changed (weighed by an analytical balance, type AB204, Mettler Toledo, Switzerland, with an accuracy of ±0.0001 g). Each of the experiments was repeated three times and the arithmetic average value was used as the final result. To verify the reliability of the 234



Article

Table 2. Solubility of Sodium L-Ascorbate in Nine Pure Solutions at Temperatures from 278.15 to 323.15 K at Atmospheric Pressure (P = 0.1 MPa)a

T/K

x0expb

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

4.77 5.15 5.53 5.95 6.34 7.23 7.78 8.26 8.77 9.29

× × × × × × × × × ×

10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

3.13 3.41 3.68 3.96 4.25 4.54 4.80 5.09 5.37 5.66

× × × × × × × × × ×

10−04 10−04 10−04 10−04 10−04 10−04 10−04 10−04 10−04 10−04

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

1.90 2.34 2.39 3.84 3.86 4.41 6.28 7.29 9.76 1.27

× × × × × × × × × ×

10−05 10−05 10−05 10−05 10−05 10−05 10−05 10−05 10−05 10−04

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

1.23 1.60 1.97 2.47 3.30 4.29 5.44 7.02 8.83 1.14

× × × × × × × × × ×

10−05 10−05 10−05 10−05 10−05 10−05 10−05 10−05 10−05 10−04

278.15 283.15 288.15 293.15 298.15

9.51 1.17 1.43 1.81 2.38

× × × × ×

10−06 10−05 10−05 10−05 10−05

x0cal,1c Water 4.67 × 5.12 × 5.58 × 6.06 × 6.57 × 7.09 × 7.64 × 8.20 × 8.78 × 9.37 × Methanol 3.13 × 3.41 × 3.68 × 3.96 × 4.25 × 4.53 × 4.81 × 5.10 × 5.38 × 5.65 × Ethanol 2.02 × 2.30 × 2.69 × 3.20 × 3.87 × 4.77 × 5.96 × 7.56 × 9.72 × 1.27 × Acetone 1.14 × 1.50 × 1.96 × 2.55 × 3.31 × 4.27 × 5.48 × 7.01 × 8.93 × 1.13 × Chloroform 9.23 × 1.17 × 1.49 × 1.88 × 2.38 ×

x0exp − x0cal,1 x0exp

10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02

2.07 1.85 8.94 1.55 8.40 3.75 1.29 9.00 3.58 1.16

× × × × × × × × × ×

10−02 10−02 10−03 10−02 10−04 10−04 10−02 10−05 10−03 10−03

10−04 10−04 10−04 10−04 10−04 10−04 10−04 10−04 10−04 10−04

2.40 2.16 9.02 6.52 1.40 1.76 2.18 1.45 3.78 1.17

× × × × × × × × × ×

10−03 10−03 10−04 10−04 10−03 10−03 10−03 10−03 10−04 10−03

10−05 10−05 10−05 10−05 10−05 10−05 10−05 10−05 10−05 10−04

6.34 1.63 1.25 1.68 3.69 8.18 5.02 3.80 3.96 3.14

× × × × × × × × × ×

10−02 10−02 10−01 10−01 10−03 10−02 10−02 10−02 10−03 10−03

10−05 10−05 10−05 10−05 10−05 10−05 10−05 10−05 10−05 10−04

7.21 6.50 3.29 3.32 2.46 5.89 8.49 1.36 1.08 6.84

× × × × × × × × × ×

10−02 10−02 10−03 10−02 10−03 10−03 10−03 10−03 10−02 10−03

10−06 10−05 10−05 10−05 10−05

2.93 1.93 3.94 3.88 8.72

× × × × ×

10−02 10−03 10−02 10−02 10−05

T/K

x0expb

303.15 308.15 313.15 318.15 323.15

3.06 3.80 5.01 6.16 7.51

× × × × ×

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

5.07 5.99 7.95 1.03 1.37 1.93 2.50 3.20 4.30 5.64

× × × × × × × × × ×

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

2.89 3.69 4.53 5.93 7.71 1.01 1.31 1.74 2.47 3.33

× × × × × × × × × ×

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

1.85 2.47 3.21 4.07 4.98 6.06 7.19 8.73 1.04 1.32

× × × × × × × × × ×

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

1.45 1.95 2.41 3.04 3.75 4.72 5.79 7.04 8.39 9.74

× × × × × × × × × ×

x0cal,1c

Chloroform 3.01 × 10−05 3.80 × 10−05 4.79 × 10−05 6.02 × 10−05 7.57 × 10−05 Ethyl Acetate 10−06 4.66 × 10−06 −06 10 6.25 × 10−06 −06 10 8.36 × 10−06 10−05 1.11 × 10−05 −05 10 1.47 × 10−05 −05 10 1.93 × 10−05 10−05 2.53 × 10−05 10−05 3.29 × 10−05 −05 10 4.27 × 10−05 −05 10 5.52 × 10−05 Isopropyl Alcohol 10−06 2.10 × 10−06 −06 10 2.92 × 10−06 −06 10 4.03 × 10−06 10−06 5.53 × 10−06 10−06 7.54 × 10−06 −05 10 1.02 × 10−05 −05 10 1.38 × 10−05 10−05 1.85 × 10−05 −05 10 2.46 × 10−05 −05 10 3.27 × 10−05 Isobutyl Alcohol 10−06 2.05 × 10−06 −06 10 2.55 × 10−06 −06 10 3.17 × 10−06 10−06 3.91 × 10−06 10−06 4.82 × 10−06 −06 10 5.91 × 10−06 −06 10 7.22 × 10−06 10−06 8.80 × 10−06 10−05 1.07 × 10−05 −05 10 1.29 × 10−05 n-Hexane 10−06 1.64 × 10−06 10−06 2.03 × 10−06 −06 10 2.51 × 10−06 −06 10 3.09 × 10−06 10−06 3.78 × 10−06 −06 10 4.62 × 10−06 −06 10 5.63 × 10−06 10−06 6.84 × 10−06 10−06 8.28 × 10−06 −06 10 9.99 × 10−06 10−05 10−05 10−05 10−05 10−05

x0exp − x0cal,1 x0exp 1.74 1.82 4.57 2.27 7.98

× × × × ×

10−02 10−03 10−02 10−02 10−03

8.14 4.39 5.05 8.15 7.48 2.54 1.12 2.99 6.42 2.04

× × × × × × × × × ×

10−02 10−02 10−02 10−02 10−02 10−03 10−02 10−02 10−03 10−02

2.74 2.08 1.10 6.66 2.12 1.19 5.54 5.92 1.82 1.80

× × × × × × × × × ×

10−01 10−01 10−01 10−02 10−02 10−02 10−02 10−02 10−03 10−02

1.08 3.41 1.40 3.83 3.30 2.43 4.85 8.43 3.01 1.84

× × × × × × × × × ×

10−01 10−02 10−02 10−02 10−02 10−02 10−03 10−03 10−02 10−02

1.33 4.01 4.11 1.59 8.59 1.98 2.72 2.82 1.27 2.63

× × × × × × × × × ×

10−01 10−02 10−02 10−02 10−03 10−02 10−02 10−02 10−02 10−02

a

Standard uncertainty of T is u(T) = 0.05 K. The relative standard uncertainty of the solubility is ur(x0) = 0.3. The relative uncertainty of pressure is ur(P) = 0.05. The relative standard uncertainty of the initial mole fraction of organic solvent in the binary solvent mixtures is ur(x1) = 0.02. bx0exp is molar fraction of experimental solubility. cx0cal,1 is molar fraction of calculated solubility by modified Apelblat equation.

In independent observation numbered k, the molality solubility of sodium L-ascorbate in solutions (x0,k), the solute-free mole fraction of alcohols solvent (x1,k) and water (x2,k) in the solvent mixtures could be expressed as eqs 1, 2, 3, and 4), respectively:

above method, the solubility data of para-tert-butylbenzoic acid in methanol have been determined from 293.15 K to 333.15 K.28 The experimental data were compared with the reported data, as listed in Table S1 and Figure S1. 235



Article

Table 3. Solubility of Sodium L-Ascorbate in Methanol(1) + Water(2) Mixture at Temperatures from 278.15 to 323.15 K at Atmospheric Pressure (P = 0.1 MPa)a

T/K

x0expb

x0cal,1c

x0cal,2d

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

4.77 5.15 5.53 5.95 6.34 7.23 7.78 8.26 8.77 9.29

× × × × × × × × × ×

10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02

4.67 5.12 5.58 6.06 6.57 7.09 7.64 8.20 8.78 9.37

× × × × × × × × × ×

10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

3.70 4.40 4.81 5.46 5.88 6.33 6.65 7.09 7.40 7.60

× × × × × × × × × ×

10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02

3.77 4.32 4.85 5.38 5.88 6.33 6.74 7.09 7.37 7.59

× × × × × × × × × ×

10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02

4.03 4.63 5.07 5.67 6.12 6.68 7.10 7.63 8.14 8.53

× × × × × × × × × ×

10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

3.23 3.56 3.79 4.09 4.40 4.71 5.06 5.45 5.91 6.29

× × × × × × × × × ×

10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02

3.27 3.52 3.79 4.08 4.39 4.73 5.08 5.46 5.87 6.31

× × × × × × × × × ×

10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02

2.67 3.06 3.31 3.68 4.01 4.31 4.62 5.00 5.38 5.72

× × × × × × × × × ×

10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

1.36 1.50 1.59 1.74 1.92 2.10 2.31 2.55 2.82 3.11

× × × × × × × × × ×

10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02

1.36 1.48 1.60 1.75 1.91 2.10 2.31 2.55 2.81 3.12

× × × × × × × × × ×

10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02

1.54 1.72 1.83 1.99 2.19 2.36 2.58 2.82 3.09 3.35

× × × × × × × × × ×

10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

8.31 9.23 1.01 1.09 1.22 1.35 1.50 1.67 1.87 2.08

× × × × × × × × × ×

10−03 10−03 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02

8.36 9.13 1.00 1.10 1.22 1.35 1.50 1.67 1.86 2.08

× × × × × × × × × ×

10−03 10−03 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02

8.48 9.25 9.79 1.05 1.17 1.29 1.44 1.60 1.79 2.01

× × × × × × × × × ×

10−03 10−03 10−03 10−02 10−02 10−02 10−02 10−02 10−02 10−02

278.15 283.15

4.56 × 10−03 5.12 × 10−03

4.62 × 10−03 5.07 × 10−03

x0cal,3e x1f=0

4.71 × 10−03 5.13 × 10−03

x1 =

x1 =

x1 =

x1 =

x1 =

4.56 5.04 5.54 6.04 6.55 7.07 7.58 8.08 8.58 9.07 0.10 4.03 4.43 4.86 5.29 5.75 6.22 6.70 7.19 7.69 8.20 0.20 2.61 2.87 3.15 3.45 3.77 4.11 4.47 4.85 5.25 5.67 0.30 1.46 1.61 1.78 1.96 2.16 2.37 2.61 2.87 3.15 3.46 0.40 7.95 8.80 9.76 1.08 1.20 1.34 1.49 1.66 1.85 2.06 0.50 4.54 5.04

236




× × × × × × × × × ×

10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02

2.07 1.85 8.94 1.55 8.40 3.75 1.29 9.00 3.58 1.16

× × × × × × × × × ×

10−02 10−02 10−03 10−02 10−04 10−04 10−02 10−05 10−03 10−03

8.88 5.30 5.38 3.80 4.03 5.52 6.78 7.63 9.93 1.23

× × × × × × × × × ×

10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−01

4.45 2.10 1.48 1.58 3.39 2.25 2.59 2.12 2.13 2.38

× × × × × × × × × ×

10−02 10−02 10−03 10−02 10−02 10−02 10−02 10−02 10−02 10−02

× × × × × × × × × ×

10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02

2.07 1.85 8.94 1.55 8.40 3.75 1.29 9.00 3.58 1.16

× × × × × × × × × ×

10−02 10−02 10−03 10−02 10−04 10−04 10−02 10−05 10−03 10−03

8.88 5.30 5.38 3.80 4.03 5.52 6.78 7.63 9.93 1.23

× × × × × × × × × ×

10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−01

8.91 7.76 9.62 3.02 2.23 1.79 7.16 1.41 3.95 7.94

× × × × × × × × × ×

10−02 10−03 10−03 10−02 10−02 10−02 10−03 10−02 10−02 10−02

× × × × × × × × × ×

10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02

1.09 1.27 1.18 3.16 8.53 3.88 3.61 2.71 7.49 2.48

× × × × × × × × × ×

10−02 10−02 10−03 10−03 10−04 10−03 10−03 10−03 10−03 10−03

1.74 1.43 1.25 1.02 8.88 8.53 8.85 8.23 8.97 9.08

× × × × × × × × × ×

10−01 10−01 10−01 10−01 10−02 10−02 10−02 10−02 10−02 10−02

1.93 1.94 1.69 1.56 1.43 1.28 1.17 1.11 1.12 9.82

× × × × × × × × × ×

10−01 10−01 10−01 10−01 10−01 10−01 10−01 10−01 10−01 10−02

× × × × × × × × × ×

10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02

1.75 1.32 9.68 7.75 4.50 1.66 1.25 1.71 1.56 1.82

× × × × × × × × × ×

10−03 10−02 10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−03

1.34 1.49 1.54 1.47 1.40 1.27 1.15 1.06 9.50 7.85

× × × × × × × × × ×

10−01 10−01 10−01 10−01 10−01 10−01 10−01 10−01 10−02 10−02

7.26 7.34 1.17 1.25 1.23 1.30 1.30 1.25 1.18 1.12

× × × × × × × × × ×

10−02 10−02 10−01 10−01 10−01 10−01 10−01 10−01 10−01 10−01

× × × × × × × × × ×

10−03 10−03 10−03 10−02 10−02 10−02 10−02 10−02 10−02 10−02

5.61 1.15 4.76 1.36 1.36 8.27 7.31 6.05 4.68 2.84

× × × × × × × × × ×

10−03 10−02 10−03 10−02 10−04 10−04 10−04 10−04 10−03 10−03

2.07 1.37 2.60 2.93 3.62 4.61 3.94 4.03 4.11 3.33

× × × × × × × × × ×

10−02 10−03 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02

4.35 4.64 3.36 5.96 1.31 8.04 6.30 5.88 1.06 8.23

× × × × × × × × × ×

10−02 10−02 10−02 10−03 10−02 10−03 10−03 10−03 10−02 10−03

× 10−03 × 10−03

1.12 × 10−02 1.11 × 10−02

3.18 × 10−02 4.02 × 10−04

4.30 × 10−03 1.55 × 10−02



Article

Table 3. continued

T/K

x0expb

x0cal,1c

x0cal,2d

288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

5.61 6.21 7.06 7.88 8.90 1.03 1.16 1.35

× × × × × × × ×

10−03 10−03 10−03 10−03 10−03 10−02 10−02 10−02

5.60 6.24 7.00 7.89 8.95 1.02 1.17 1.35

× × × × × × × ×

10−03 10−03 10−03 10−03 10−03 10−02 10−02 10−02

5.49 5.99 6.74 7.60 8.69 9.94 1.15 1.33

× × × × × × × ×

10−03 10−03 10−03 10−03 10−03 10−03 10−02 10−02

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

2.96 3.25 3.57 4.07 4.69 5.51 6.70 8.02 1.01 1.25

× × × × × × × × × ×

10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−02 10−02

2.98 3.23 3.58 4.06 4.70 5.54 6.64 8.09 1.00 1.26

× × × × × × × × × ×

10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−02 10−02

2.72 3.03 3.35 3.78 4.30 4.99 5.81 6.86 8.20 9.76

× × × × × × × × × ×

10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−03

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

1.67 1.91 2.11 2.41 2.67 3.08 3.43 4.03 4.61 5.23

× × × × × × × × × ×

10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−03

1.68 1.88 2.11 2.38 2.70 3.07 3.49 3.99 4.57 5.25

× × × × × × × × × ×

10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−03

1.64 1.90 2.18 2.58 2.96 3.51 4.12 4.99 6.12 7.41

× × × × × × × × × ×

10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−03

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

9.65 1.11 1.29 1.58 1.75 2.10 2.51 2.99 3.81 4.51

× × × × × × × × × ×

10−04 10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−03

9.80 1.12 1.29 1.51 1.78 2.11 2.53 3.05 3.71 4.54

× × × × × × × × × ×

10−04 10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−03

1.00 1.20 1.43 1.75 2.01 2.39 2.78 3.39 4.17 5.03

× × × × × × × × × ×

10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−03

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

5.84 7.41 9.42 1.17 1.40 1.66 1.88 2.33 2.76 3.41

× × × × × × × × × ×

10−04 10−04 10−04 10−03 10−03 10−03 10−03 10−03 10−03 10−03

6.35 7.67 9.26 1.12 1.35 1.62 1.95 2.34 2.81 3.37

× × × × × × × × × ×

10−04 10−04 10−04 10−03 10−03 10−03 10−03 10−03 10−03 10−03

5.92 7.10 8.42 1.02 1.15 1.34 1.51 1.78 2.11 2.45

× × × × × × × × × ×

10−04 10−04 10−04 10−03 10−03 10−03 10−03 10−03 10−03 10−03

278.15 283.15 288.15 293.15 298.15

3.13 3.41 3.68 3.96 4.25

× × × × ×

10−04 10−04 10−04 10−04 10−04

3.13 3.41 3.68 3.96 4.25

× × × × ×

10−04 10−04 10−04 10−04 10−04

x0cal,3e x1 = 0.50 5.61 6.27 7.03 7.89 8.88 1.00 1.13 1.28 x1 = 0.60 2.79 3.11 3.47 3.90 4.40 4.98 5.66 6.46 7.39 8.48 x1 = 0.70 1.82 2.02 2.26 2.55 2.90 3.30 3.79 4.37 5.07 5.89 x1 = 0.80 1.17 1.30 1.46 1.66 1.89 2.17 2.52 2.94 3.44 4.06 x1 = 0.90 6.69 7.46 8.41 9.58 1.10 1.28 1.50 1.77 2.11 2.52 x1 = 1 2.89 3.25 3.69 4.25 4.96 237




× × × × × × × ×

10−03 10−03 10−03 10−03 10−03 10−02 10−02 10−02

1.67 4.64 8.16 2.26 6.09 5.16 3.93 1.64

× × × × × × × ×

10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−03

2.15 3.53 4.52 3.55 2.41 3.16 1.35 1.40

× × × × × × × ×

10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02

7.49 9.97 4.84 1.27 2.17 2.75 2.43 5.10

× × × × × × × ×

10−04 10−03 10−03 10−03 10−03 10−02 10−02 10−02

× × × × × × × × × ×

10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−03

4.36 7.74 3.66 2.89 1.33 4.63 8.06 8.65 4.95 1.06

× × × × × × × × × ×

10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−03

8.16 6.88 6.26 7.14 8.40 9.46 1.32 1.45 1.85 2.22

× × × × × × × × × ×

10−02 10−02 10−02 10−02 10−02 10−02 10−01 10−01 10−01 10−01

5.59 4.44 2.79 4.26 6.29 9.66 1.55 1.95 2.68 3.21

× × × × × × × × × ×

10−02 10−02 10−02 10−02 10−02 10−02 10−01 10−01 10−01 10−01

× × × × × × × × × ×

10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−03

1.07 1.44 3.13 9.32 9.81 6.37 1.94 8.91 7.28 4.22

× × × × × × × × × ×

10−02 10−02 10−03 10−03 10−03 10−03 10−02 10−03 10−03 10−03

1.59 6.69 3.51 7.34 1.07 1.39 2.03 2.39 3.29 4.16

× × × × × × × × × ×

10−02 10−03 10−02 10−02 10−01 10−01 10−01 10−01 10−01 10−01

8.87 5.82 7.27 5.89 8.45 7.30 1.06 8.51 9.89 1.27

× × × × × × × × × ×

10−02 10−02 10−02 10−02 10−02 10−02 10−01 10−02 10−02 10−01

× × × × × × × × × ×

10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−03

1.56 6.89 2.51 4.73 1.19 3.33 8.60 2.22 2.58 6.93

× × × × × × × × × ×

10−02 10−03 10−03 10−02 10−02 10−03 10−03 10−02 10−02 10−03

4.08 8.34 1.10 1.07 1.44 1.37 1.10 1.36 9.53 1.16

× × × × × × × × × ×

10−02 10−02 10−01 10−01 10−01 10−01 10−01 10−01 10−02 10−01

2.14 1.74 1.34 4.82 8.04 3.56 3.56 1.79 9.62 9.97

× × × × × × × × × ×

10−01 10−01 10−01 10−02 10−02 10−02 10−03 10−02 10−02 10−02

× × × × × × × × × ×

10−04 10−04 10−04 10−04 10−03 10−03 10−03 10−03 10−03 10−03

8.72 3.54 1.72 4.22 4.14 2.24 3.85 4.90 1.81 1.32

× × × × × × × × × ×

10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−03 10−02 10−02

1.29 4.18 1.06 1.26 1.78 1.93 1.96 2.34 2.36 2.81

× × × × × × × × × ×

10−02 10−02 10−01 10−01 10−01 10−01 10−01 10−01 10−01 10−01

1.45 6.27 1.07 1.81 2.12 2.29 2.02 2.40 2.37 2.61

× × × × × × × × × ×

10−01 10−03 10−01 10−01 10−01 10−01 10−01 10−01 10−01 10−01

× × × × ×

10−04 10−04 10−04 10−04 10−04

2.40 2.16 9.02 6.52 1.40

× × × × ×

10−03 10−03 10−04 10−04 10−03

7.68 4.84 3.52 7.44 1.67

× × × × ×

10−02 10−02 10−03 10−02 10−01



Article

Table 3. continued

x0expb

T/K 303.15 308.15 313.15 318.15 323.15

4.54 4.80 5.09 5.37 5.66

× × × × ×

x0cal,1c

10−04 10−04 10−04 10−04 10−04

4.53 4.81 5.10 5.38 5.65

× × × × ×

x0cal,2d

x0cal,3e x1 = 1 5.84 6.94 8.33 1.01 1.23

10−04 10−04 10−04 10−04 10−04

× × × × ×

10−04 10−04 10−04 10−03 10−03

x0exp − x0cal,1 x0exp 1.76 2.18 1.45 3.78 1.17

× × × × ×


10−03 10−03 10−03 10−04 10−03

x0exp − x0cal,3 x0exp 2.86 4.47 6.38 8.79 1.17

× × × × ×

10−01 10−01 10−01 10−01 1000

a

Standard uncertainty of T is u(T) = 0.05 K. The relative standard uncertainty of the solubility is ur(x0) = 0.3. The relative uncertainty of pressure is ur(P) = 0.05. The relative standard uncertainty of the initial mole fraction of organic solvent in the binary solvent mixtures is ur(x1) = 0.05. bx0exp is molar fraction of experimental solubility. cx0cal,1 is molar fraction of calculated solubility by modified Apelblat equation. dx0cal,2 is molar fraction of calculated solubility by CNIBS/R-K model. ex0cal,3 is molar fraction of calculated solubility by Jouyban−Acree model; fx1 is the initial mole fraction of organic solvent in the binary solvent mixtures.

3. RESULTS AND DISCUSSION

In pure solvents,

3.1. Thermodynamic Properties. Experimental TGA and DSC measurements were listed in Figure S2. Figure S2(a) showed that the sample of sodium L-ascorbate started to decompose at about 493.15 K. However, Figure S2(b) indicated that the heat flow did not change before 493.15 K. That is, the sample decomposed before melting. Therefore, sodium L-ascorbate had no certain melting point. 3.2. Solubility Data. Solid−liquid equilibrium experimental data in pure solvents (water, methanol, ethanol, acetone, chloroform, ethyl acetate, isopropyl alcohol, isobutyl alcohol, n-hexane) and solvent mixtures (water + methanol, water + ethanol) were summarized in Tables 2−4 and plotted in Figure 2 and 3. The PXRD patterns of sodium L-ascorbate obtained from the above solvents were shown in Figure S3. It can be seen that the crystal structures of sodium L-ascorbate in different systems are the same. In pure solvents, it can be seen that the solubility of sodium L-ascorbate increased with the increasing temperature. At the same temperature, the order of solubility was water > methanol > ethanol > acetone > chloroform > ethyl acetate > isopropyl alcohol > isobutyl alcohol > n-hexane. This could be ascribed to the physicochemical property of the solvent: the larger the polarity of solvent, the higher the solubility of solute. It is of particular note that the solubility of sodium L-ascorbate in organic solvents was much less than that in water. Thus, the organic solvent which is mutually soluble with water could be used as antisolvent, such as methanol and ethanol. While in binary solvents, the solubility was controlled by temperature and the composition of solvent simultaneously. Within the temperature range of the measurements, the solubility of sodium L-ascorbate increased with the temperature and decreased with the addition of methanol (or ethanol) monotonously. As it is shown in Figure 4, the distance between solubility contours was smaller vertically than horizontally. That is to say, compared with temperature, the influence of the antisolvent on solubility was greater. So the addition of antisolvent was the key step in the process of dilution crystallization. Furthermore, the variation trends of solubility were different in different regions. In methanol + water mixture, solubility difference was small and irregular in (x1 > 0.70) with the variation of temperature. Obvious solubility difference existed in other ranges of x1, especially in (0.10 < x1 < 0.30). Analogously, in the ethanol + water mixture, the variation of the solubility was relatively greater in (0 < x1 < 0.55) than that in (x1 > 0.55). These irregularities

m0, k /M 0

x0, k =

m0, k /M 0 + ms, k /Ms

(1)

where k is the serial number of the observation, m0,k, ms,k represent the mass (g) of sodium L-ascorbate and pure solvent, respectively; M0, Ms are the molecular mass (g mol−1) of sodium L-ascorbate, pure solvent, respectively. In binary solvents, m0, k /M 0

x0, k =

m0, k /M 0 + m1, k /M1 + m2, k /M 2

(2)

m1, k /M1

x1, k =

m1, k /M1 + m2, k /M 2

x 2, k =

(3)

m2, k /M 2 m1, k /M1 + m2, k /M 2

(4)

where m0,k, m1,k and m2,k represent the mass (g) of sodium L-ascorbate, alcohols solvent, and water, respectively; M0, M1, and M2 are the molecular mass (g mol−1) of sodium L-ascorbate, alcohols solvent, and water, respectively. The arithmetic average value was used as the final solubility result x0. x0 =

1 n

n

∑ x0,k

(5)

k=1

where k is the serial number of the observation, n is the number of independent observations under the same condition of measurement. The uncertainty was calculated according to the “Type A evaluation of uncertainty” from NIST. The value of the solubility is estimated from n independent observations under the same condition of measurement. The standard uncertainty u(x0) can be determined as follows: ⎡ 1 u(x0) = ⎢ ⎢⎣ n(n − 1)

⎤1/2 2⎥ ( x − x ) ∑ 0,k 0 ⎥⎦ k=1 n

(6)

The relative standard uncertainty ur(x0) of x0 is defined by ur (x0) = u(x0)/|x0|

(7) 238



Article

Table 4. Solubility of Sodium L-Ascorbate in Ethanol (1) + Water (2) Mixture at Temperatures from 278.15 to 323.15 K at Atmospheric Pressure (P = 0.1 MPa)a

T/K

x0expb

x0cal,1c

x0cal,2d

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

4.77 5.15 5.53 5.95 6.34 7.23 7.78 8.26 8.77 9.29

× × × × × × × × × ×

10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02

4.67 5.12 5.58 6.06 6.57 7.09 7.64 8.20 8.78 9.37

× × × × × × × × × ×

10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

1.53 2.18 3.10 3.84 4.48 4.98 5.43 5.82 6.26 6.67

× × × × × × × × × ×

10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02

1.75 2.32 2.96 3.64 4.32 4.97 5.55 6.01 6.33 6.49

× × × × × × × × × ×

10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02

1.38 2.00 2.88 3.51 4.20 4.89 5.43 5.90 6.40 6.95

× × × × × × × × × ×

10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

6.46 9.98 1.50 1.97 2.39 2.81 3.20 3.57 3.90 4.16

× × × × × × × × × ×

10−03 10−03 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02

7.44 1.06 1.44 1.88 2.34 2.81 3.25 3.63 3.92 4.11

× × × × × × × × × ×

10−03 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02

6.98 1.07 1.62 2.07 2.51 2.89 3.28 3.63 3.99 4.35

× × × × × × × × × ×

10−03 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

3.64 5.41 7.99 1.02 1.28 1.49 1.73 2.00 2.26 2.52

× × × × × × × × × ×

10−03 10−03 10−03 10−02 10−02 10−02 10−02 10−02 10−02 10−02

4.17 5.74 7.65 9.85 1.23 1.49 1.76 2.03 2.28 2.50

× × × × × × × × × ×

10−03 10−03 10−03 10−03 10−02 10−02 10−02 10−02 10−02 10−02

4.30 6.18 8.79 1.13 1.35 1.53 1.75 2.00 2.24 2.46

× × × × × × × × × ×

10−03 10−03 10−03 10−02 10−02 10−02 10−02 10−02 10−02 10−02

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

2.39 3.21 4.17 5.13 6.22 7.28 8.45 1.00 1.21 1.42

× × × × × × × × × ×

10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−02 10−02 10−02

2.64 3.28 4.05 4.95 6.00 7.22 8.63 1.02 1.21 1.41

× × × × × × × × × ×

10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−02 10−02 10−02

2.49 3.28 4.30 5.44 6.48 7.48 8.65 1.03 1.20 1.35

× × × × × × × × × ×

10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−02 10−02 10−02

278.15 283.15

1.70 × 10−03 1.90 × 10−03

1.69 × 10−03 1.95 × 10−03

x0cal,3e x1f

1.18 × 10−03 1.47 × 10−03

x1

x1

x1

x1

x1

=0 4.43 4.94 5.47 6.01 6.56 7.10 7.64 8.17 8.69 9.19 = 0.10 2.24 2.72 3.23 3.77 4.31 4.86 5.38 5.88 6.32 6.72 = 0.20 9.67 1.28 1.64 2.03 2.45 2.87 3.28 3.67 4.00 4.28 = 0.30 3.80 5.48 7.57 1.00 1.27 1.56 1.84 2.10 2.33 2.51 = 0.40 1.42 2.24 3.33 4.70 6.31 8.06 9.86 1.16 1.30 1.42 = 0.50 5.16 8.90

239



× × × × × × × × × ×

10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02

1.49 6.16 4.78 5.43 3.62 8.54 2.27 3.25 1.08 2.73

× × × × × × × × × ×

10−01 10−02 10−02 10−02 10−02 10−04 10−02 10−02 10−02 10−02

× × × × × × × × × ×

10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02

1.49 6.16 4.78 5.43 3.62 8.54 2.27 3.25 1.08 2.73

× × × × × × × × × ×

10−01 10−02 10−02 10−02 10−02 10−04 10−02 10−02 10−02 10−02

9.31 8.22 7.09 8.64 6.27 1.72 1.45 1.34 2.16 4.18

× × × × × × × × × ×

× × × × × × × × × ×

10−03 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02

1.52 6.39 3.88 4.71 1.89 2.24 1.58 1.50 4.97 1.25

× × × × × × × × × ×

10−01 10−02 10−02 10−02 10−02 10−04 10−02 10−02 10−03 10−02

8.13 7.04 7.72 4.70 5.19 2.89 2.37 1.45 2.26 4.55

× × × × × × × × × ×

10−03 10−03 10−03 10−02 10−02 10−02 10−02 10−02 10−02 10−02

1.44 6.14 4.24 3.57 3.71 4.51 1.93 1.14 5.86 1.06

× × × × × × × × × ×

10−01 10−02 10−02 10−02 10−02 10−03 10−02 10−02 10−03 10−02

× × × × × × × × × ×

10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−02 10−02 10−02

1.04 2.46 2.93 3.56 3.52 8.16 2.10 2.35 1.55 7.44

× × × × × × × × × ×

10−01 10−02 10−02 10−02 10−02 10−03 10−02 10−02 10−03 10−03

× 10−04 × 10−04

7.53 × 10−03 2.83 × 10−02

x0exp − x0cal,3 x0exp 7.14 4.00 1.03 1.04 3.41 1.79 1.79 1.07 9.19 1.08

× × × × × × × × × ×

10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−03 10−02

10−02 10−02 10−02 10−02 10−02 10−02 10−03 10−02 10−02 10−02

4.65 2.47 4.26 1.87 3.69 2.46 8.77 9.48 1.01 6.93

× × × × × × × × × ×

10−01 10−01 10−02 10−02 10−02 10−02 10−03 10−03 10−02 10−03

× × × × × × × × × ×

10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02

4.97 2.81 9.10 3.07 2.41 2.18 2.62 2.71 2.65 2.87

× × × × × × × × × ×

10−01 10−01 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02

1.80 1.41 1.01 1.05 5.66 3.21 1.55 9.78 8.30 2.53

× × × × × × × × × ×

10−01 10−01 10−01 10−01 10−02 10−02 10−02 10−04 10−03 10−02

4.35 1.37 5.29 1.90 6.52 4.48 6.37 5.24 3.29 2.20

× × × × × × × × × ×

10−02 10−02 10−02 10−02 10−03 10−02 10−02 10−02 10−02 10−03

4.39 2.36 2.98 6.08 4.18 2.65 2.33 3.34 9.47 4.95

× × × × × × × × × ×

10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−02 10−03 10−02

4.06 3.03 2.01 8.33 1.38 1.07 1.67 1.56 7.67 3.41

× × × × × × × × × ×

10−01 10−01 10−01 10−02 10−02 10−01 10−01 10−01 10−02 10−03

3.05 × 10−01 2.26 × 10−01

6.97 × 10−01 5.32 × 10−01



Article

Table 4. continued

T/K

x0expb

x0cal,1c

x0cal,2d

288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

2.27 2.70 3.16 3.70 4.30 5.33 6.31 7.63

× × × × × × × ×

10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−03

2.27 2.66 3.13 3.70 4.40 5.27 6.32 7.63

× × × × × × × ×

10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−03

1.84 2.29 2.82 3.43 4.03 5.13 6.23 7.50

× × × × × × × ×

10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−03

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

6.55 7.76 9.81 1.18 1.43 1.82 2.19 2.95 3.55 4.47

× × × × × × × × × ×

10−04 10−04 10−04 10−03 10−03 10−03 10−03 10−03 10−03 10−03

6.41 7.82 9.59 1.18 1.46 1.82 2.27 2.84 3.56 4.49

× × × × × × × × × ×

10−04 10−04 10−04 10−03 10−03 10−03 10−03 10−03 10−03 10−03

4.45 5.52 6.99 8.66 1.14 1.51 1.82 2.48 3.20 4.20

× × × × × × × × × ×

10−04 10−04 10−04 10−04 10−03 10−03 10−03 10−03 10−03 10−03

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

5.90 9.55 1.39 2.08 3.32 5.48 6.63 1.04 1.49 2.09

× × × × × × × × × ×

10−05 10−05 10−04 10−04 10−04 10−04 10−04 10−03 10−03 10−03

6.04 9.44 1.45 2.21 3.31 4.90 7.16 1.03 1.48 2.09

× × × × × × × × × ×

10−05 10−05 10−04 10−04 10−04 10−04 10−04 10−03 10−03 10−03

1.43 1.87 2.51 3.15 4.45 6.49 8.09 1.17 1.59 2.30

× × × × × × × × × ×

10−04 10−04 10−04 10−04 10−04 10−04 10−04 10−03 10−03 10−03

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

4.99 6.41 8.24 1.02 1.49 2.02 2.83 3.85 5.78 9.31

× × × × × × × × × ×

10−05 10−05 10−05 10−04 10−04 10−04 10−04 10−04 10−04 10−04

5.85 6.80 8.28 1.05 1.39 1.90 2.70 3.95 5.95 9.22

× × × × × × × × × ×

10−05 10−05 10−05 10−04 10−04 10−04 10−04 10−04 10−04 10−04

4.81 6.70 9.42 1.23 1.80 2.76 3.58 5.26 7.48 1.16

× × × × × × × × × ×

10−05 10−05 10−05 10−04 10−04 10−04 10−04 10−04 10−04 10−03

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

3.76 4.98 6.94 8.96 1.13 1.77 2.28 3.81 4.29 6.62

× × × × × × × × × ×

10−05 10−05 10−05 10−05 10−04 10−04 10−04 10−04 10−04 10−04

4.23 5.31 6.81 8.92 1.19 1.62 2.25 3.71 4.51 6.53

× × × × × × × × × ×

10−05 10−05 10−05 10−05 10−04 10−04 10−04 10−04 10−04 10−04

2.28 3.19 4.28 5.99 8.01 1.17 1.59 2.20 3.13 4.78

× × × × × × × × × ×

10−05 10−05 10−05 10−05 10−05 10−04 10−04 10−04 10−04 10−04

278.15 283.15 288.15 293.15 298.15

1.90 2.34 2.39 3.84 3.86

× × × × ×

10−05 10−05 10−05 10−05 10−05

2.02 2.30 2.69 3.20 3.87

× × × × ×

10−05 10−05 10−05 10−05 10−05

x0cal,3e x1 = 0.50 1.43 2.15 3.05 4.07 5.15 6.19 7.10 7.78 x1 = 0.60 1.83 3.45 5.99 9.62 1.44 2.01 2.63 3.24 3.78 4.18 x1 = 0.70 6.18 1.28 2.40 4.12 6.50 9.50 1.29 1.63 1.94 2.16 x1 = 0.80 1.92 4.34 8.83 1.62 2.71 4.15 5.84 7.60 9.19 1.04 x1 = 0.90 5.13 1.28 2.82 5.55 9.84 1.58 2.31 3.10 3.83 4.38 x1 = 1 1.09 2.98 7.18 1.52 2.87 240




× × × × × × × ×

10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−03

1.22 1.69 1.20 9.96 2.39 1.24 2.80 7.03

× × × × × × × ×

10−03 10−02 10−02 10−04 10−02 10−02 10−03 10−04

1.91 1.52 1.10 7.43 6.24 3.80 1.19 1.73

× × × × × × × ×

10−01 10−01 10−01 10−02 10−02 10−02 10−02 10−02

3.70 2.02 3.54 1.00 1.98 1.62 1.25 1.96

× × × × × × × ×

10−01 10−01 10−02 10−01 10−01 10−01 10−01 10−02

× × × × × × × × × ×

10−04 10−04 10−04 10−04 10−03 10−03 10−03 10−03 10−03 10−03

2.18 6.89 2.24 2.53 2.23 7.97 3.75 3.73 2.91 3.52

× × × × × × × × × ×

10−02 10−03 10−02 10−04 10−02 10−04 10−02 10−02 10−03 10−03

3.22 2.89 2.87 2.67 2.05 1.70 1.67 1.59 1.00 5.98

× × × × × × × × × ×

10−01 10−01 10−01 10−01 10−01 10−01 10−01 10−01 10−01 10−02

7.21 5.56 3.90 1.85 5.77 1.03 2.01 9.98 6.55 6.43

× × × × × × × × × ×

10−01 10−01 10−01 10−01 10−03 10−01 10−01 10−02 10−02 10−02

× × × × × × × × × ×

10−05 10−04 10−04 10−04 10−04 10−04 10−03 10−03 10−03 10−03

2.42 1.16 4.43 6.33 3.29 1.06 7.99 2.41 7.45 1.39

× × × × × × × × × ×

10−02 10−02 10−02 10−02 10−03 10−01 10−02 10−03 10−03 10−03

1.43 9.61 8.02 5.16 3.42 1.84 2.21 1.25 6.98 1.03

× × × × × × × × × ×

1000 10−01 10−01 10−01 10−01 10−01 10−01 10−01 10−02 10−01

4.79 3.37 7.25 9.80 9.59 7.33 9.44 5.69 3.00 3.44

× × × × × × × × × ×

10−02 10−01 10−01 10−01 10−01 10−01 10−01 10−01 10−01 10−02

× × × × × × × × × ×

10−05 10−05 10−05 10−04 10−04 10−04 10−04 10−04 10−04 10−03

1.73 6.09 5.43 3.23 6.69 5.95 4.73 2.60 2.93 9.17

× × × × × × × × × ×

10−01 10−02 10−03 10−02 10−02 10−02 10−02 10−02 10−02 10−03

3.57 4.45 1.44 2.07 2.06 3.63 2.65 3.66 2.94 2.42

× × × × × × × × × ×

10−02 10−02 10−01 10−01 10−01 10−01 10−01 10−01 10−01 10−01

6.16 3.22 7.17 5.91 8.20 1.05 1.06 9.74 5.90 1.14

× × × × × × × × × ×

10−01 10−01 10−02 10−01 10−01 1000 1000 10−01 10−01 10−01

× × × × × × × × × ×

10−06 10−05 10−05 10−05 10−05 10−04 10−04 10−04 10−04 10−04

1.27 6.47 1.94 4.15 5.42 8.23 1.30 2.58 5.14 1.31

× × × × × × × × × ×

10−01 10−02 10−02 10−03 10−02 10−02 10−02 10−02 10−02 10−02

3.94 3.60 3.83 3.31 2.92 3.37 3.02 3.19 2.71 2.78

× × × × × × × × × ×

10−01 10−01 10−01 10−01 10−01 10−01 10−01 10−01 10−01 10−01

8.64 7.44 5.94 3.80 1.29 1.07 1.40 1.87 1.08 3.39

× × × × × × × × × ×

10−01 10−01 10−01 10−01 10−01 10−01 10−02 10−01 10−01 10−01

× × × × ×

10−06 10−06 10−06 10−05 10−05

6.34 1.63 1.25 1.68 3.69

× × × × ×

10−02 10−02 10−01 10−01 10−03

9.43 8.72 7.00 6.03 2.55

× × × × ×

10−01 10−01 10−01 10−01 10−01



Article

Table 4. continued

x0expb

T/K 303.15 308.15 313.15 318.15 323.15

4.41 6.28 7.29 9.76 1.27

× × × × ×

10−05 10−05 10−05 10−05 10−04

x0cal,1c 4.77 5.96 7.56 9.72 1.27

× × × × ×

x0cal,2d


x0cal,3e x1 = 1 4.86 7.42 1.03 1.30 1.51

10−05 10−05 10−05 10−05 10−04

× × × × ×

10−05 10−05 10−04 10−04 10−04

8.18 5.02 3.80 3.96 3.14

× × × × ×



10−02 10−02 10−02 10−03 10−03

1.03 1.82 4.10 3.33 1.90

× × × × ×

10−01 10−01 10−01 10−01 10−01

a

Standard uncertainty of T is u(T) = 0.05 K. The relative standard uncertainty of the solubility is ur(x0) = 0.3. The relative uncertainty of pressure is ur(P) = 0.05. The relative standard uncertainty of the initial mole fraction of organic solvent in the binary solvent mixtures is ur(x1) = 0.05. bx0exp is molar fraction of experimental solubility. cx0cal,1 is molar fraction of calculated solubility by modified Apelblat equation. dx0cal,2 is molar fraction of calculated solubility by CNIBS/R-K model. ex0cal,3 is molar fraction of calculated solubility by Jouyban−Acree model. fx1 is the initial mole fraction of organic solvent in the binary solvent mixtures.

Figure 2. Solubility of sodium L-ascorbate in water (□), methanol (○), ethanol (△), acetone(▽), chloroform (◁), ethyl acetate (▷), isopropyl alcohol (◊), isobutyl alcohol (☆), n-hexane (+).

fraction of alcohols solvent and water in the absence of sodium n is the number of “curve-fit” parameters, Si is the model constant, (x0)i is the saturated mole fraction solubility of sodium L-ascorbate in monosolvent i. For binary solvent systems, n = 2 and x2 = 1 − x1. Thus, the CNIBS/R-K model can be simplified into the general single model:

can be attributed to the complicated electrolyte−electrolyte interactions in low concentration alcohol solution. 3.3. Correlation of Solubility Data. In this paper, three thermodynamic models were used to correlate the experiment data and to predict the solubility under the undetected points in the tested ranges. The experimental data in pure solvents were correlated with the modified Apelblat equation.29 The modified Apelblat equation, CNIBS/R-K model, and Jouyban− Acree model30−34 were used to correlate and analyze the experimental data in the binary solvents. 3.3.1. Thermodynamic Models. 1. Modified Apelblat Equation. The modified Apelblat equation is a widely used semiempirical equation, which can be used to describe the relationship between the solubility and temperature as follows: ln x0 = A +

B + C ln T T

L-ascorbate,

ln x0 = B0 + B1x1 + B2 x12 + B3x13 + B4 x14

where B0, B1, B2, B3, and B4 are empirical constants with no special meaning. 3. Jouyban−Acree Model. The Jouyban−Acree model can be used to correlate the solubility data with both temperature and the initial mole fraction composition of the binary solvent mixtures. The basic Jouyban-Acree model can be described as n

(8)

ln x0 = x1 ln(x0)1 + x 2 ln(x0)2 + x1x 2 ∑ i=0

where x0 is the mole fraction solubility of sodium L-ascorbate in pure and binary solvents; T is the absolute temperature; and A, B, and C are the empirical constants. 2. CNIBS/R-K Model. The combined nearly ideal binary solvent (CNIBS)/Redlich−Kister model can be applied to correlate the solubility data with the initial mole fraction composition of the binary solvent mixtures. It can be shown as

i=0

Ji T

(x1 − x 2)i

(11)

where x0 is the mole fraction solubility of sodium L-ascorbate in binary solvent mixtures, x1 and x2 represent the initial mole fraction of alcohols solvent and water in absence of sodium L-ascorbate, Ji is the model constant, and (x0)i is the saturated mole fraction solubility of sodium L-ascorbate in monosolvent i. For binary solvent systems, n = 2 and x2 =1 − x1. Thus, the basic Jouyban−Acree model can be rearranged as

n

ln x0 = x1 ln(x0)1 + x2 ln(x0)2 + x1x2 ∑ Si(x1 − x2)i

(10)

x1 T x2 x3 x4 + [3J1 − J0 − 5J2 ] 1 + [8J2 − 2J1] 1 + [−4J2 ] 1 T T T

ln x0 = ln(x0)2 + [ln(x0)1 − ln(x0)2 ]x1 + [J0 − J1 + J2 ]

(9)

where x0 is the mole fraction solubility of sodium L-ascorbate in binary solvent mixtures, x1 and x2 represent the initial mole 241

(12)



Article

Figure 3. Solubility of sodium L-ascorbate in water + methanol (a) and water + ethanol (b).

The ln(x0)1 and ln(x0)1 can be replaced with the modified Apelblat equation as ln(x0)1 = a1 +

b1 + c1 ln T T

(13)

b2 + c 2 ln T (14) T By the combination of eqs 8, 9, and 10, the Jouyban−Acree model for binary solvent mixtures system can be obtained ln(x0)2 = a 2 +

Figure 4. The contour plots of solubility of sodium L-ascorbate in water + methanol (a) and water + ethanol (b); the dotted line with arrows is the control profile.

A2 x x2 + A3 ln T + A4 x1 + A5 1 + A 6 1 T T T 3 4 x x + A 7 1 + A8 1 + A 9x1 ln T (15) T T where A1 to A9 are the model parameters obtained by a leastsquares analysis. 3.3.2. Evaluation of Thermodynamic Models. The accuracy of the correlation was evaluated by the average absolute deviation (AAD):35 ln x0 = A1 +

AAD =

1 N

N

∑ i=1

The calculated mole fraction solubility was listed in Tables 2−4. The corresponding model parameters and AAD were listed in Tables S2−S5. It can be found that the AAD values of modified Apelblat equation were 1.45%, 0.14%, 5.53%, 2.09%, 2.05%, 4.03%, 8.27%, 3.13%, 3.53% in water, methanol, ethanol, acetone, chloroform, ethyl acetate, isopropyl alcohol, isobutyl alcohol, and n-hexane, respectively. So the solubility in pure solvents fit well with the modified Apelblat equation. In water + methanol and water + ethanol, values of AAD of the modified Apelblat equation were smaller than those of other models. It means that modified Apelblat equation can give better correlation results and relative accurate calculated values of the solubility in the tested temperature ranges. 3.4. Application of the Solubility Data in Purification and Crystallization Process of Sodium L-Ascorbate. The above determined solubility data provided a reference for designing and optimizing a combined cooling and antisolvent crystallization process to get sodium L-ascorbate meeting the market requirements. We have been working on improving the

x0, i − x0,cali x0, i

(16)

where N is the number of experimental data points, x0,i and x0,ical are the experimental solubility and calculated solubility, respectively. Model parameters were obtained by fitting the experimental data and minimizing AAD. Moreover, the average absolute deviation (AAD) was calculated for characterizing the accuracy and predictability of the correlation model. 242



Article

Figure 5. Different crystallization strategies of sodium L-ascorbate in water + methanol: panel a is designed based on SSSC; (b, c) contrast tests; solid line represents the temperature (T/K), dotted line represents the solute-free mole fraction of alcohols solvent in binary solvent (x1).

The process was shown in Figure 5a: cooling crystallization and antisolvent crystallization were carried out alternately. In particular, the solution was heated during the addition of methanol. For comparing and analyzing the influence of crystallization process on the crystal product, other two commonly used strategies (listed in Figure 5b and Figure 5c) have also been applied. The initial temperature, end temperature, start solvent concentration and final solvent concentration of the above three strategies were all the same. The difference is the control method of supersaturation. The temperature profile can be obtained by using a heating and cooling bath (type CF41, Julabo Technology (Beijing) Co., Ltd., China, temperature stability of ±0.05 K). The temperature was controlled by a controlling program set according to the requirement. The crystal size distribution (CSD) of sodium L-ascorbate product was determined using Mastersizer 3000(Malvern Instruments Ltd.) and plotted in Figure 6. The crystal shape was analyzed by scanning electron microscope (30XL, Royal Dutch Philips Electronics Ltd.) and shown in Figure 7. It can be seen that the crystal size of sodium L-ascorbate product obtained from method a were larger and more uniform than those from other methods. Moreover, the crystal shape obtained from method a was mainly cuboid, which was unbreakable, while a large amount of fragile thick plate crystals appeared in the other two methods. Thus, SSSC was a simple and effective strategy to design the crystallization process by keeping the low level of supersaturation without complicated online monitoring system.

Figure 6. CSD of sodium L-ascorbate obtained from strategy a (red line), strategy b (green line), and strategy c (blue line), respectively.

crystallization process of sodium L-ascorbate in water + alcohols solvents mixtures. Here a semisupersaturation control (SSSC) approach is proposed. SSSC is a model-free approach in which the solubility declines as slowly as possible to keep low supersaturation without online monitoring. Thus, the control profile should be close to the contours of solubility, as it is shown in Figure 4 (the blue dotted line with arrows). For brief reason, the process using methanol as antisolvent was taken as an example to be discussed in detail. 243



Article

were investigated by a static analytic method in the temperature range from 278.15 to 323.15 K at atmospheric pressure. In pure solvents, the solubility increased with temperature. In binary solvents, the solubility increased with temperature and decreased with the addition of alcohols solvent. The experiment data were correlated with the modified Apelblat equation, CNIBS/R-K model and Jouyban−Acree model. The modified Apelblat equation showed the best correlation results. What’s more, SSSC was proposed and applied to design the CCAC process of sodium L-ascorbate according to the solubility data. Crystals of sodium L-ascorbate with uniform shape and large grain size were obtained by using the CCAC process designed by the SSSC approach. Therefore, the solubility presented in this work was useful fundamental data in the crystallization process of the sodium L-ascorbate. The SSSC approach was an efficient and effective method for design and optimization of the CCAC process.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.7b00846. Solubility of para-tert-butylbenzoic acid in methanol in the temperature range from 293.15 K to 333.15 K at atmospheric pressure (P = 0.1 MPa); parameters of the modified Apelblat equation for sodium L-ascorbate in pure and binary solvents; parameters of CNIBS/R-K model for sodium L-ascorbate in binary solvents and of the Jouyban− Acree model for sodium L-ascorbate in binary solvents; Thermodynamic properties of sodium L-ascorbate; X-ray diffraction pattern for sodium L-ascorbate in solution (PDF)

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +86-22-87898172. Fax: +86-22-87897912. ORCID

Hui Zhang: 0000-0002-2193-8933 Funding

This work was supported by the Central Nonprofit Research Institutes Special Funds Project (K-JBYWF-2016-T7), P. R. China. Notes

The authors declare no competing financial interest.

■

REFERENCES

(1) Gangolli, S. The Dictionary of Substances and their Effects (DOSE): T-Z and Index (2). Index CAS Reg. No. 1999, 7, 915−956. (2) Frei, B.; Traber, M. The new US dietary reference for vitamins C and E. Redox Rep. 2001, 6, 5−9. (3) Carr, A. C.; Frei, B. Does vitamin C act as pro-oxidant under physiological conditions. FASEB J. 1999, 13, 1007−1024. (4) Frei, B.; Forte, T. M.; Ames, B. N.; Cross, C. E. Gas-phase oxidants of cigarette smoke induces lipid peroxidation and changes in lipoprotein properties in human blood plasma: protective effects of ascorbic acid. Biochem. J. 1981, 277, 133−138. (5) Kallner, A.; Hartmann, D.; Hornig, D. On the requirement of ascorbic acid in man: steady-state turnover and body pool in smokers. Am. J. Clin. Nutr. 1981, 34, 1347−1355. (6) Carr, A. C.; Frei, B. Toward new recommended dietary allowance for vitamin C based on antioxidant and health effects in humans. Am. J. Clin. Nutr. 1999, 69, 1086−1107.

Figure 7. SEM of sodium L-ascorbate obtained from strategy a (a), strategy b (b), and strategy c (c), respectively.

4. CONCLUSION The solubilities of sodium L-ascorbate in water, methanol, ethanol, acetone, chloroform, ethyl acetate, isopropyl alcohol, isobutyl alcohol, and n-hexane, water + methanol, and water + ethanol 244



Article

(7) Wallington, N.; Clark, A. C.; Prenzler, P. D.; Barril, C.; Scollary, G. R. The decay of ascorbic acid in a model wine system at low oxygen concentration. Food Chem. 2013, 14, 3139−3146. (8) Demiray, E.; Tulek, Y.; Yilmaz, Y. Degradation kinetics of lycopene, β-carotene and ascorbic acid in tomatoes during hot air drying. LWT-Food Sci. Technol. 2013, 50, 172−176. (9) Blasco, R.; Esteve, M. J.; Frigola, A.; Rodrigo, M. Ascorbic acid degradation kinetics in mushrooms in a high-temperature short-time process controlled by a thermoresistometer. LWT-Food Sci. Technol. 2004, 37, 171−175. (10) Dhondge, S. S.; Deshmukh, D. W.; Paliwal, L. J.; Dahasahasra, P. N. The study of molecular interactions of ascorbic acid and sodium ascorbate with water at temperatures (278.15, 278.15 and 298.15) K. J. Chem. Thermodyn. 2013, 67, 217−226. (11) UK Food Standards Agency. Current EU approved additives and their E Numbers. Retrieved https://www.food.gov.uk/science/ additives/enumberlist (accessed October 27, 2011). (12) US Food and Drug Administration. Listing of Food Additives Status Part II. https://www.fda.gov/Food/ IngredientsPackagingLabeling/FoodAdditivesIngredients/ucm091048. htm (accessed October 27, 2011). (13) Australia New Zealand Food Standards Code. Standard 1.2.4 Labelling of ingredients. https://www.legislation.gov.au/Details/ F2015C00179 (accessed October 27, 2011). (14) Zhang, G. Z. A preparation method of vitamin c sodium salt. CN 201010223684.3, 2010. (15) Yu, H.; Wei, X. F. A method of preparing vitamin C sodium. CN 201410824738.X, 2014. (16) Li, B. S.; Zhang, L. B. A vitamin c sodium salt purification methodCN 201510025003.5, 2015. (17) Knox, M.; Trifkovic, M.; Rohani, S. Combining anti-solvent and cooling crystallization: effect of solvent composition on yield and metastable zone width. Chem. Eng. Sci. 2009, 64, 3555−3563. (18) Yang, Y.; Nagy, Z. K. Model-Based Systematic Design and Analysis Approach for Unseeded Combined Cooling and Antisolvent Crystallization (CCAC) Systems. Cryst. Growth Des. 2014, 14, 687− 698. (19) Hu, Q.; Rohani, S.; Wang, D. X.; Jutan, A. Optimal control of a batch cooling seeded crystallizer. Powder Technol. 2005, 156, 170−176. (20) Feng, L.; Berglund, K. ATR-FTIR for determining optimal cooling curves for batch crystallization of succinic acid. Cryst. Growth Des. 2002, 2, 449−452. (21) Fujiwara, M.; Chow, P. S.; Ma, D. L.; Braatz, R. D. Paracetamol crystallization using laser backscattering and ATR-FTIR spectroscopy: metastability, agglomeration, and control. Cryst. Growth Des. 2002, 2, 363−370. (22) Liotta, V.; Sabesan, V. Monitoring and feedback control of supersaturation using ATR-FTIR to produce an active pharmaceutical ingredient of a desired crystal size. Org. Process Res. Dev. 2004, 8, 488− 494. (23) Grön, H.; Borissova, A.; Roberts, K. J. In-process ATR-FTIR spectroscopy for closed-loop supersaturation control of a batch crystallizer producing monosodium glutamate crystals of defined size. Ind. Eng. Chem. Res. 2003, 42, 198−206. (24) Guo, H.; Song, L. C.; Zhu, Q.; Wu, D.; Yang, C. Measurement and Correlation of Solubility of Pronamide in Five Organic Solvents at (278.15 to 323.15) K. J. Chem. Thermodyn. 2016, 99, 11−15. (25) Zhang, H.; Xie, C.; Liu, Z. K.; Gong, J. B.; Bao, Y.; Zhang, M. J.; Hao, H. X.; Hou, B. H.; Yin, Q. X. Identification and molecular understanding of the odd−even effect of dicarboxylic acids aqueous solubility. Ind. Eng. Chem. Res. 2013, 52, 18458−18465. (26) Zhang, H.; Yin, Q. X.; Liu, Z. K.; Gong, J. B.; Bao, Y.; Zhang, M. J.; Hao, H. X.; Hou, B. H.; Xie, C. Measurement and correlation of solubility of dodecanedioic acid in different pure solvents from T = (278.15 to 323.15) K. J. Chem. Thermodyn. 2014, 68, 270−274. (27) Zhang, H.; Yin, Q. X.; Liu, Z. K.; Gong, J. B.; Bao, Y.; Zhang, M. J.; Hao, H. X.; Hou, B. H.; Xie, C. An odd-even effect on solubility of dicarboxylic acids in organic solvents. J. Chem. Thermodyn. 2014, 77, 91−97.

(28) Aniya, V.; De, D.; Mohammed, A. M.; Thella, P. K.; Satyavathi, B. Measurement and Modeling of Solubility of para-tert-Butylbenzoic Acid in Pure and Mixed Organic Solvents at Different Temperatures. J. Chem. Eng. Data 2017, 62, 1411−1421. (29) Apelblat, A.; Manzurola, E. Solubilities of o-acetylsalicylic, 4aminosalicylic, 3, 5-dinitrosalicylic, and p-toluic acid, and magnesiumDL-aspartate in water from T= (278 to 348) K. J. Chem. Thermodyn. 1999, 31, 85−91. (30) Acree, W. Mathematical representation of thermodynamic properties: Part 2. Derivation of the combined nearly ideal binary solvent (NIBS)/Redlich-Kister mathematical representation from a two-body and three-body interactional mixing model. Thermochim. Acta 1992, 198, 71−79. (31) Williams, N. A.; Amidon, G. L. Excess free energy approach to the estimation of solubility in mixed solvent systems II: Ethanol-water mixtures. J. Pharm. Sci. 1984, 73, 14−18. (32) Barzegar-Jalali, M.; Jouyban-Gharamaleki, A. A general model from theoretical cosolvency models. Int. J. Pharm. 1997, 152, 247− 250. (33) Zhou, Z.; Qu, Y.; Wang, J.; Wang, S.; Liu, J.; Wu, M. Measurement and Correlation of Solubilities of (Z)-2-(2-Aminothiazol-4-yl)-2-methoxyiminoacetic Acid in Different Pure Solvents and Binary Mixtures of Water + (Ethanol, Methanol, or Glycol). J. Chem. Eng. Data 2011, 56, 1622−1628. (34) Jouyban, A.; Fakhree, M. A. A.; Acree, W. E., Jr Comment on “Measurement and Correlation of Solubilities of (Z)-2-(2-Aminothiazol-4-yl)-2-methoxyiminoacetic Acid in Different Pure Solvents and Binary Mixtures of Water + (Ethanol, Methanol, or Glycol). J. Chem. Eng. Data 2012, 57, 1344−1346. (35) Ellegaard, M. D.; Abildskov, J.; O’Connell, J. P. Molecular thermodynamic modeling of mixed solvent solubility. Ind. Eng. Chem. Res. 2010, 49, 11620−11632.

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Determination, Correlation, and Application of Sodium l-Ascorbate

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