Solubility Determination and Thermodynamic Modeling of Sodium

Article pubs.acs.org/jced

Solubility Determination and Thermodynamic Modeling of Sodium Thioglycolate in Pure and Binary Solvent Mixtures from T = (293.15 to 333.15) K Jingyu Wu, Lianzheng Zhang, Dongmei Xu,* Jun Gao,* Kai Zhang, and Meng Kong College of Chemical and Environmental Engineering, Shandong University of Science and Technology, Qingdao, 266590, China S Supporting Information *

ABSTRACT: The solubility of sodium thioglycolate in five pure solvents of water, methanol, ethanol and isopropyl alcohol, n-propanol and four binary solvent mixtures (water + methanol, water + ethanol, water + isopropyl alcohol, water + n-propanol) was determined within the temperature range from (293.15 to 333.15) K by using the gravimetrical method under atmospheric pressure (p = 0.1 MPa). The solubility of sodium thioglycolate in water, ethanol, isopropyl alcohol, and n-propanol increases with a rise of temperature, but the solubility decreases in methanol with increasing temperature. Meanwhile, in the binary solvent mixtures (water + methanol, water + ethanol, water + isopropyl alcohol, water + n-propanol), the solubility of sodium thioglycolate increases with increasing the mole fraction of water and with temperature. The modified Apelblat equation and van’t Hoff equation were applied to correlate the solubility of sodium thioglycolate in the five pure solvents, while in the binary solvent mixtures, the solubility was correlated by the modified Apelblat equation, CNIBS/R-K model, and Jouyban−Acree model. It was shown that the correlated results were in better agreement with the experimental data. Also, the mixing thermodynamic properties for sodium thioglycolate in the binary solvent mixtures were calculated.

1. INTRODUCTION Sodium thioglycolate (CAS No. 367-51-1) is an important industrial chemical, which is applied in the pharmaceutical and cosmetic industries. Also, it can be applied in the flotation separation process of minerals as a kind of mineral inhibitor.1−4 Generally, sodium thioglycolate can be extracted from the byproducts of thiourethane synthesis. However, the crude product of sodium thioglycolate generally contains some impurities which are difficult to separate. The presence of impurities may significantly influence the properties of the sodium thioglycolate and limit its application. Usually, to purify sodium thioglycolate from the crude product, a crystallization process is applied in industry. Therefore, the solubility of sodium thioglycolate can provide basic information and is necessary to the development and optimization of the crystallization process.5−7 However, to our knowledge, no solubility data of sodium thioglycolate have been reported in previous works. To understand better and design an optimized crystallization process for sodium thioglycolate, it is essential to obtain the accurate (solid + liquid) equilibrium relationship of sodium thioglycolate in the different solvents at various temperatures and the thermodynamic properties of the solutions. The purposes of the work are to (1) determine the solubility of sodium thioglycolate in the five pure solvents of water, methanol, ethanol, isopropyl alcohol, n-propanol, and four binary solvent mixtures of (water + methanol), (water + ethanol), (water + isopropyl alcohol) and (water + n-propanol) at temperatures © 2017 American Chemical Society

ranging from (293.15 to 333.15) K by using the gravimetric method; (2) correlate the solubility data using the modified Apelblat equation, the van’t Hoff equation in the five pure solvents, and using the modified Apelblat equation, CNIBS/R-K model and Jouyban-Acree models in the four binary solvent mixtures of (water + methanol, water + ethanol, water + isopropyl alcohol, water + n-propanol); and (3) calculate the mixing thermodynamics properties for the dissolution process of sodium thioglycolate in the four binary solvent mixtures.

2. EXPERIMENTAL SECTION 2.1. Chemicals. Sodium thioglycolate with a mass fraction of 0.97 was purchased from Aladdin Industrial Corporation. Methanol, ethanol, isopropyl alcohol, n-propanol, and triphenylphosphine were of analytical-reagent grade and were provided by Chengdu KeLong Reagent Co. Ltd., China. All the chemicals were used without further purification. Deionized water (conductivities < 1.0 μs·cm−1) was made in our laboratory by a NANOPURE system from BARNSTEAD (Thermo Scientific Co., China). The detailed information on sodium thioglycolate and the solvents is presented in Table 1. Received: March 9, 2017 Accepted: August 9, 2017 Published: August 21, 2017 3105

DOI: 10.1021/acs.jced.7b00245 J. Chem. Eng. Data 2017, 62, 3105−3123

Journal of Chemical & Engineering Data

Article

Table 1. Sources and Mass Fraction Purity of Chemicals

a

chemicals

CASRN

molar mass g·mol−1

mass fraction purity

purification method

analysis method

source

sodium thioglycolate triphenylphosphine methanol ethanol isopropyl alcohol n-propanol water

367-51-1 603-35-0 67-56-1 64-17-5 67-63-0 71-23-8 7732-18-5

114.09 262.29 32.04 46.07 60.06 60.1 18.01

0.97 ≥0.99 ≥0.997 ≥0.997 ≥0.997 ≥0.997

none none none none none none distilled

HPLCa HPLCa GCb GCb GCb GCb

Aladdin industrial Corporation Chengdu Kelong Reagent Co. Ltd. Chengdu Kelong Reagent Co. Ltd. Chengdu Kelong Reagent Co. Ltd. Chengdu Kelong Reagent Co. Ltd. Chengdu Kelong Reagent Co. Ltd. Lab made

High-performance liquid chromatography. bGas−liquid chromatography.

2.2. Characterization of Sodium Thioglycolate. The crystalline form before and after the solubility measurement of sodium thioglycolate was verified by powder X-ray diffractometer (RigakuD/max-2500, Japan). The experiment was carried out using the XRD by Cu Kα radiation (0.15405 nm) over a diffraction angle (2θ) range of 2−50° with a scanning rate of 8° per minute. 2.3. Melting Properties Determination. The melting temperature Tm and the enthalpy of fusion ΔfusH were determined by the differential scanning calorimetry (DSC 1/500, Mettler-Toledo, Switzerland) under the protection of nitrogen gas flow. The DSC instrument was precalibrated with indium before the experiment. A pinch of sodium thioglycolate (about 5 mg) was placed in a standard DSC aluminum pan and heated from (293.15 to 645.15) K at the rate of 10 K·min−1. The uncertainty for the melting temperature measurement was ±0.5 K and 400 J·mol−1 for the melting enthalpy. 2.4. Preparation of Solvent Mixtures. In the preparation process of the solvent mixtures, an analytical balance (model AR1140) was employed. The mass fractions of methanol, ethanol, isopropyl alcohol, and n-propanol in the binary mixtures varied from 0.0 to 1.0. An amount of the mixed solvent, about 50 g, was used for each experiment and the standard uncertainty was estimated to be 0.0001 g. The jacketed glass vessel was covered with a stopper to prevent the solvent from escaping when the mixed solvent was added. 2.5. Solubility Measurement. The solubility of sodium thioglycolate was determined by using a gravimetric method which was similar to that described in the references.8−10 To verify the experimental method, the solubility data of triphenylphosphine in ethanol was measured and compared with those in the literature,10 which are presented in Table 2 and Figure 1. As shown in Table 2 and Figure 1, the solubility data of triphenylphosphine in ethanol measured in this work are in good

Figure 1. Validation of the solubility measurement method: ○, the solubility data of triphenylphosphine in methanol in this work; ▲, the solubility data from the literature.10

Table 2. Experimental Mole Fraction Solubility (x) of Triphenylphosphine in Ethanol at the Temperature Range from T = (303.5 to 333.0) K under 0.1 MPaa T/K

this work (10x)

ref 10 (10x)

RD

303.5 308.3 313.3 318.6 323.2 327.9 333.0

0.090 0.117 0.162 0.225 0.279 0.385 0.494

0.095 0.120 0.160 0.220 0.280 0.380 0.500

0.005 0.003 −0.002 −0.005 0.001 −0.005 0.006

Figure 2. Powder X-ray diffraction pattern of sodium thioglycolate.

agreement with those from the literature, which indicate the method applied in this work is reliable. To measure the solubility of sodium thioglycolate, first, the excess amount of solid of sodium thioglycolate was added into a 100 mL jacketed glass vessel which contained the binary solvent mixture of 50 g. The solution in the vessel was maintained at a constant temperature in a thermostat water bath. The temperature of the solution was determined by a mercury glass thermometer with a standard uncertainty of 0.1 K. The solid of sodium thioglycolate and solvent were mixed sufficiently by stirring continuously about 8 h so that the system reached equilibrium.

a

Relative standard uncertainties ur are ur(xA) = 0.05 and xr(x) = 0.05. The standard uncertainty of temperature is u(T) = 0.1 K. The standard uncertainty of pressure is u(p) = 10 kPa. x denotes the mole fraction solubility of triphenylphosphine. RD is the relative deviation. 3106



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Table 3. Experimental mole fraction solubility (x) of sodium thioglycolate in different pure solvents at the temperature range from T = (293.15 to 333.15) K under 0.1 MPaa 100RD T/K

Figure 3. DSC scan of sodium thioglycolate.

When the system was at equilibrium, the stirring was stopped and the solution was set for at least 3 h before sampling. Then, 3 mL of the supernatant was extracted out rapidly with a 5 mL preheated syringe with a filter (PTFE 0.2 μm), and was transferred into a preweighed glass vessel. The glass vessel was weighed immediately by an analytical balance (AR1140, Ohaus Corporation, America) with an accuracy of ±0.0001 g. Second, the glass vessel was placed into an electric blast drying oven at T = 333.15 K until the weight of the glass vessel remained constant. The measurement was repeated three times, and the average value was used to calculate the mole fraction solubility. The mole fraction solubility of sodium thioglycolate (x) was calculated according to eq 1 and the initial mole fraction (xA) of water in the solvent mixture was calculated by eq 2: x= xA =

m/M m /M + mA /MA + mi /Mi mA /MA mA /MA + mi /Mi

100x

modified Apelblat equation

Van’t Hoff equation

−0.44 −0.88 −0.82 0.09 0.07 −0.08 −0.37 −0.23 −0.14

0.20 −0.76 −1.04 −0.30 −0.33 −0.35 −0.37 0.17 0.78

1.99 2.81 2.95 2.76 −0.28 −4.98 −5.06 −1.25 5.25

6.55 3.41 0.78 −1.05 −4.72 −9.01 −7.40 −0.94 8.69

−0.39 −0.36 0.79 1.35 0.91 0.04 −2.93 0.87 2.43

3.53 0.31 −0.85 −1.65 −2.59 −3.12 −4.99 0.75 4.78

2.31 1.23 −1.07 −2.46 0.44 1.48 1.64 0.24 −0.35

5.52 1.19 −3.38 −5.99 −3.09 −1.15 0.77 1.93 4.64

−1.51 −2.86 1.05 3.55 −0.85 −1.47 −3.66 −2.25 3.45

1.37 −2.11 0.50 2.53 −1.67 −1.32 −1.87 1.73 9.77

Water 293.15 14.710 298.15 16.085 303.15 17.650 308.15 19.505 313.15 21.327 318.15 23.257 323.15 25.294 328.15 27.590 333.15 30.047 Methanol 293.15 0.1886 298.15 0.1650 303.15 0.1457 308.15 0.1302 313.15 0.1147 318.15 0.1008 323.15 0.0940 328.15 0.0920 333.15 0.0938 Ethanol 293.15 0.1424 298.15 0.1482 303.15 0.1573 308.15 0.1671 313.15 0.1769 318.15 0.1877 323.15 0.1962 328.15 0.2205 333.15 0.2436 Isopropyl Alcohol 293.15 0.0104 298.15 0.0110 303.15 0.0115 308.15 0.0123 313.15 0.0139 318.15 0.0154 323.15 0.0171 328.15 0.0188 333.15 0.0209 n-Propanol 293.15 0.0439 298.15 0.0493 303.15 0.0587 308.15 0.0690 313.15 0.0760 318.15 0.0871 323.15 0.0986 328.15 0.1159 333.15 0.1426

(1)

(2)

where m and M represent the mass and the molar mass of the solute, respectively. The mA and MA represent the mass and the molar mass of the water, respectively. The mi and Mi represent the mass and the molar mass of the other solvents (methanol, ethanol, isopropyl alcohol, and n-propanol).

3. SOLUBILITY MODELS On the basis of the thermodynamic theory, many equations are generally used to study the solid−liquid equilibrium.11,12 In this work, the modified Apelblat equation13,14 and the van’t Hoff equation15,16 were used to correlate the sodium thioglycolate solubility in the five pure solvents of water, methanol, ethanol, isopropyl alcohol, and n-propanol. The modified Apelblat equation, CNIBS/R-K model,17,18 and the Jouyban−Acree model19−21 were used to correlate the sodium thioglycolate solubility in the binary solvent mixtures of (water + methanol, water + ethanol, water + isopropyl alcohol, and water + n-propanol) at different temperatures. 3.1. Modified Apelblat Equation. The modified Apelblat equation is a semiempirical model, which is extensively applied to express the relation between the solubility and the absolute temperature in the pure and mixed solvents.22 It is based on the

a Relative standard uncertainties ur are ur(xA) = 0.05 and xr(x) = 0.05. The standard uncertainty of temperature is u(T) = 0.1 K. The standard uncertainty of pressure is u(p) = 10 kPa. x denotes the mole fraction solubility of sodium thioglycolate. RD is the relative deviation.

solid−liquid equilibrium theory and can be described as follows:13,14 ln x c = A + 3107

B + C ln T T

(3) DOI: 10.1021/acs.jced.7b00245 J. Chem. Eng. Data 2017, 62, 3105−3123


Article

Table 4. Experimental Mole Fraction Solubility (x) of Sodium Thioglycolate in (Water + Methanol) Binary Solvent Mixtures at the Temperature Range from T = (293.15 to 333.15) K under 0.1 MPaa 100RD xA

100x

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

0.2249 0.3298 0.4308 0.8406 1.840 4.000 8.058 14.19

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

0.1987 0.3047 0.4784 0.9041 1.947 4.126 8.549 15.17

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

0.1833 0.2917 0.5089 0.9664 2.080 4.416 9.130 16.16

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

0.1705 0.2809 0.5373 1.015 2.260 4.722 9.797 17.48

0.102 0.201 0.301 0.402

0.1613 0.2707 0.5972 1.111

modified Apelblat equation T= 1.77 1.44 −1.57 −1.23 −0.71 1.43 0.17 −0.18 T= −1.15 −1.30 1.95 1.21 −0.43 −1.14 0.04 0.01 T= −0.96 −0.88 0.81 1.67 0.09 −0.77 −0.20 −0.69 T= −1.11 −0.33 −1.41 −0.84 1.61 −1.19 −0.66 −0.24 T= −0.53 −0.07 1.23 −0.46

100RD

CNIBS/R-K model

Jouyban-Acree model

−8.39 15.09 −2.76 −2.11 −0.09 0.25 −0.06 0.00

17.91 18.71 −3.89 −1.78 1.62 0.61 −2.33 −0.41

−1.12 4.07 −1.83 −2.04 1.45 −0.36 0.05 0.00

2.65 7.29 1.16 −0.07 1.77 −1.66 −1.70 0.74

1.34 0.27 −0.15 −1.80 1.22 −0.32 0.04 0.00

−11.36 −2.75 1.07 0.23 2.08 −1.04 −1.26 0.61

5.59 −2.36 0.88 −3.64 2.28 −0.61 0.08 −0.01

−19.77 −14.01 −0.44 −1.93 3.30 −1.26 −1.13 1.26

10.54 −10.59 2.84 −3.18

−43.73 −27.17 2.52 −0.65

xA

100x

293.15 K

298.15 K

303.15 K

308.15 K

313.15 K

0.500 0.601 0.702 0.801

2.444 5.100 10.68 18.86

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

0.1530 0.2617 0.6249 1.198 2.514 5.622 11.71 20.54

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

0.1466 0.2525 0.70989 1.358 2.822 6.231 12.86 22.53

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

0.1419 0.2450 0.7515 1.508 3.071 6.700 14.25 24.60

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

0.1388 0.2377 0.8453 1.793 3.466 7.508 15.80 27.01

modified Apelblat equation T= 2.08 −1.27 −0.21 −0.45 T= −0.73 0.11 −2.46 −2.65 −3.01 0.09 0.17 −0.13 T= −0.89 −0.23 1.71 −0.80 0.11 1.41 0.20 0.54 T= −0.85 −0.36 −1.15 −2.00 −0.37 −0.82 0.55 0.43 T= −0.63 −0.83 1.69 2.76 2.33 0.59 0.53 0.57

CNIBS/R-K model

Jouyban-Acree model

2.39 −0.75 0.11 0.00

3.42 −1.19 −0.14 0.95

1.94 −14.42 6.49 0.90 −1.30 0.31 −0.03 0.01

−62.96 −42.25 −1.10 −1.45 −2.04 0.26 0.69 0.84

6.36 −24.50 8.01 1.03 −1.41 0.30 −0.03 0.00

−83.95 −60.28 2.74 2.17 0.57 1.62 1.12 0.81

11.60 −37.73 4.01 3.11 0.02 −0.48 0.11 0.00

−66.48 −80.53 −0.64 3.18 −0.46 −0.59 1.80 −0.29

13.20 −55.04 2.12 6.08 −0.79 −0.52 0.14 0.00

−70.54 −44.35 1.37 10.09 1.63 0.77 2.06 −1.41

313.15 K

318.15 K

323.15 K

328.15 K

333.15 K

a Relative standard uncertainties ur are ur(xA) = 0.05 and xr(x) = 0.05. The standard uncertainty of temperature is u(T) = 0.1 K. The standard uncertainty of pressure is u(p) = 10 kPa. xA denotes the mole fraction of water in the binary solvent mixture. x denotes the mole fraction solubility of sodium thioglycolate. RD is the relative deviation.

where xc is the mole fraction solubility of sodium thioglycolate, and T represents the absolute temperature. A, B, and C are semiempirical constants of the model, which can be obtained from fitting the experimental solubility values with eq 3. 3.2. van’t Hoff Equation. For real solutions, the van’t Hoff model that is based on the thermodynamic principles of the (liquid−solid) equilibrium15,16 is expressed as ln x c = A +

B T /K

3.3. CNIBS/R-K Model. The combined nearly ideal binary solvent/Redlich−Kister (CNIBS/R-K) model, suggested by Acree and co-workers23 indicates a connection between the isothermal mole fraction solubility and the solvent composition of binary solvent mixtures. It can be shown as eq 5: N

ln x c = xA ln XA + xi ln Xi + xAxi ∑ Sn(xA − xi)n n=0

(4)

(5)

where xc refers to the mole fraction of sodium thioglycolate, xA and xi are the initial mole fractions of (water, methanol, ethanol, isopropyl alcohol, and n-propanol) in the absence of sodium thioglycolate. Sn is the model constant, and N refers to the number of the fit-curve parameter. XA and Xi are the mole

where xc is the calculated mole fraction solubility of sodium thioglycolate at the temperature T; A and B are the model parameters. The values of A and B are related to the dissolution entropy and enthalpy. 3108



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Table 5. Experimental Mole Fraction Solubility (x) of Sodium Thioglycolate in (Water + Ethanol) Binary Solvent Mixtures at the Temperature Range from T = (293.15 to 333.15) K under 0.1 MPaa 100RD

100RD xA

100x

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

0.1832 0.2667 0.4553 0.8775 1.818 3.894 8.293 14.40

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

0.1955 0.2787 0.4815 0.9189 1.936 4.177 8.741 15.37

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

0.2044 0.2961 0.5064 0.9607 2.064 4.492 9.211 16.36

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

0.2145 0.3186 0.5396 1.018 2.201 4.791 9.811 17.32

0.102 0.201 0.301 0.402

0.2348 0.3408 0.5857 1.114

modified Apelblat equation T= 0.24 0.40 −0.85 0.38 −0.44 −0.69 −0.13 −0.44 T= 0.89 −0.93 −0.15 0.81 0.78 0.27 0.27 0.12 T= −0.60 −1.04 −0.84 −0.29 1.13 0.74 −0.21 0.25 T= −1.87 −0.26 −0.97 −1.31 0.44 −0.28 −0.44 −0.36 T= 1.07 −0.43 0.04 −0.24

CNIBS/R-K model

Jouyban-Acree model

8.57 −5.18 −4.00 0.56 1.61 −0.62 0.09 −0.01

2.94 2.42 2.08 0.65 −2.16 −3.68 1.03 2.59

4.14 −3.36 −1.01 −0.16 0.79 −0.27 0.04 0.00

3.77 0.86 1.57 −0.73 −1.64 −2.04 1.05 3.69

−1.99 1.06 1.96 −0.95 −0.07 0.08 −0.01 0.00

2.14 0.39 −0.05 −2.91 −1.57 −0.88 0.31 3.81

−3.14 2.33 2.22 −1.35 −0.01 0.09 −0.02 0.00

0.36 0.70 −0.88 −4.31 −2.16 −1.22 −0.06 2.71

−1.01 −0.17 1.47 −0.20

2.36 −0.03 −0.34 −2.87

xA

100x

0.500 0.601 0.702 0.801

2.358 5.149 10.57 18.57

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

0.2485 0.3709 0.6359 1.222 2.546 5.618 11.54 19.81

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

0.2621 0.4010 0.6852 1.345 2.807 6.178 12.56 21.23

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

0.2758 0.4279 0.7613 1.530 3.210 6.929 13.72 22.82

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

0.3021 0.4680 0.8400 1.718 3.628 7.713 15.19 24.50

293.15 K

298.15 K

303.15 K

308.15 K

313.15 K

modified Apelblat equation T= −0.67 −1.17 −0.23 0.13 T= 0.58 0.81 0.41 −0.12 −1.92 −1.13 0.48 −0.06 T= −0.34 1.07 −0.60 −0.66 −1.87 −0.84 0.32 0.03 T= −1.65 −0.26 0.87 1.14 1.10 0.90 −0.11 0.31 T= 1.20 0.60 1.12 0.71 2.14 1.42 0.25 0.34

CNIBS/R-K model

Jouyban-Acree model

−0.28 0.11 −0.02 0.00

−2.79 −1.40 0.11 2.18

−1.06 −0.36 0.93 0.79 −0.78 0.21 −0.03 0.00

0.67 0.57 −0.21 −1.78 −3.21 −0.61 0.88 0.51

−1.45 0.53 0.13 1.06 −0.81 0.21 −0.03 0.00

−1.79 0.12 −1.28 −0.76 −1.96 0.43 0.89 −1.34

−0.78 −0.08 0.03 0.96 −0.64 0.16 −0.02 0.00

−5.00 −2.03 0.35 3.08 2.46 2.91 0.71 −3.45

3.53 −1.59 −2.13 0.73 0.23 −0.13 0.02 0.00

−4.20 −2.03 0.93 5.17 5.17 4.18 1.41 −6.28

313.15 K

318.15 K

323.15 K

328.15 K

333.15 K

a

Relative standard uncertainties ur are ur(xA) = 0.05 and xr(x) = 0.05. The standard uncertainty of temperature is u(T) = 0.1 K. The standard uncertainty of pressure is u(p) = 10 kPa. x denotes the mole fraction solubility of sodium thioglycolate. RD is the relative deviation.

3.4. Jouyban−Acree Model. The Jouyban−Acree model19−21 is applied to correlate the solubility of drugs in the mixed solvent systems25 which embodied both the effect of temperature and solvent composition. The original function by modifying the CNIBS/R-K model is shown as26

fraction solubility of sodium thioglycolate in pure water, methanol, ethanol, isopropyl alcohol, and n-propanol, respectively. For the binary solvent mixtures, the value of N is 2 and xi can be represented as (1 − xA). Equation 5 can be expressed as ln x c = (ln XA − ln Xi + S0 − S1 + S2)xA + (− S0 + 3S1 − 5S2) xA2 + (− 2S1 + 8S2)xA3 + (− 4S2)xA4 + ln Xi

N

(6)

ln x c = xA ln XA + xi ln Xi + xAxi ∑

By replacing constants in eq 6 with a constant term A (containing A0, A1, A2, A3, A4), the CNIBS/R-K model can be as follows:24 lnx c = A 0 + A1xA + A 2 (xA )2 + A3(xA )3 + A4 (xA )4

n=0

Jn T

(xA − xi)n

(8)

where Jn is a constant of the function. The meaning of the other parameters is the same as that in the CNIBS/R-K model. To extend the applicability of solution behavior of nonideal systems, the modified Apelblat equation can be applied into

(7)

where A0, A1, A2, A3 and A4 are empirical parameters. 3109



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Table 6. Experimental Mole Fraction Solubility (x) of Sodium Thioglycolate in (Water + Isopropyl Alcohol) Binary Solvent Mixtures at the Temperature Range from T = (293.15 to 333.15) K under 0.1 MPaa 100RD

100RD xA

100x

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

0.0253 0.2238 0.4822 0.7094 1.250 3.119 7.084 12.32

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

0.0310 0.2647 0.5533 0.7925 1.378 3.368 7.782 12.62

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

0.0382 0.3069 0.6363 0.9037 1.543 3.667 8.253 13.30

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

0.0471 0.3622 0.7371 1.038 1.750 4.114 9.104 14.58

0.102 0.201 0.301 0.402

0.0586 0.4280 0.8670 1.252

modified Apelblat equation T= −0.53 −0.41 −0.49 −1.23 0.10 0.75 −0.42 1.58 T= −0.92 0.67 −0.39 −1.83 0.30 0.75 2.09 0.36 T= −0.57 −0.75 −0.83 −1.62 0.22 −0.47 −0.77 −0.82 T= −0.24 −0.84 −1.31 −1.86 −0.24 −0.55 −1.51 −0.63 T= −0.39 −1.19 −0.91 1.74

CNIBS/R-K model

Jouyban-Acree model

−385.37 −3.57 21.44 6.98 −7.27 0.54 0.06 0.00

−2.12 0.14 0.52 1.92 2.72 3.84 −12.86 5.93

−307.48 −7.12 17.29 5.87 −5.40 0.07 0.12 0.02

−1.83 1.58 1.24 1.66 3.09 4.70 −7.06 5.91

−345.20 −4.56 21.32 8.29 −5.48 −0.74 0.31 −0.04

−1.06 0.38 1.14 1.97 3.13 4.11 −8.10 5.60

−309.32 −4.59 19.72 7.24 −5.75 −0.36 0.24 −0.02

−0.57 0.32 0.75 1.63 2.75 4.36 −7.64 6.24

−289.46 −5.86 17.85 8.49

−0.80 −0.14 0.97 4.82

xA

100x

0.500 0.601 0.702 0.801

2.033 4.647 10.13 16.40

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

0.0703 0.5111 1.035 1.464 2.388 5.468 11.64 18.73

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

0.0873 0.6146 1.236 1.716 2.783 6.504 14.18 22.01

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

0.1064 0.7476 1.470 2.069 3.430 7.811 16.90 26.39

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

0.1301 0.8941 1.770 2.532 4.280 9.536 20.22 32.09

293.15 K

298.15 K

303.15 K

308.15 K

313.15 K

modified Apelblat equation T= 0.09 −1.71 −3.06 −0.25 T= −0.64 −0.87 0.28 1.25 0.07 −0.41 −2.91 −0.58 T= 0.82 −0.18 1.04 0.01 −2.18 0.44 1.68 −0.19 T= 0.64 1.33 0.76 0.74 −0.05 0.83 2.62 0.24 T= 0.86 0.89 1.22 2.14 2.08 1.51 2.75 0.25

CNIBS/R-K model

Jouyban-Acree model

313.15 K −5.84 −0.57 0.30 −0.02

3.10 3.34 −8.82 6.76

−185.61 −4.19 12.95 3.13 −6.82 1.24 −0.07 0.01

−1.36 −0.08 1.75 3.89 3.08 4.43 −8.93 6.33

−169.87 −5.76 12.84 3.52 −6.79 1.07 −0.04 0.00

−0.40 0.21 1.90 2.05 0.85 4.88 −5.00 6.30

−138.88 −2.87 10.05 1.48 −5.40 1.18 −0.10 0.01

−1.28 1.19 0.82 1.97 2.84 4.70 −5.55 6.06

−276.73 −1.31 19.22 6.58 −4.97 −0.62 0.33 −0.02

−1.96 0.11 0.29 2.43 4.79 4.62 −7.60 5.18

318.15 K

323.15 K

328.15 K

333.15 K

a


express ln (xc)i as follows: ln(x c)i = ai +

bi + ci ln T T

4. RESULTS AND DISCUSSION 4.1. Characterization and Identification of Sodium Thioglycolate. The powder X-ray diffraction (XRD) analysis was performed to determine the crystal form of the sample before and after solubility measurement. The typical XRD pattern is shown in Figure 2. It can be seen that sodium thioglycolate shows the high crystallinity, and the polymorphic transformation did not occur. The fusion enthalpy ΔfusH and the melting point Tm of the specific substance offers information on molecular packing in crystal lattices and are essential thermodynamic parameters for predicting solid−liquid equilibria (SLE). The endothermic peak in the DSC curve is shown in Figure. 3. It shows that the melting

(9)

Substituting eq 9 into eq 8 and xi instead of (1 − xA), a new simplified model referred as hybrid model can be shown as eq 10: B2 x (x )2 + B3 ln T + B4 xA + B5 A + B6 A T T T 3 4 (x ) (x ) + B7 A + B8 A + B9xA ln T (10) T T

ln x c = B1 +

where B1, B2, B3, B4, B5, B6, B7, B8 and B9 are model constants. 3110



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Table 7. Experimental Mole Fraction Solubility (x) of Sodium Thioglycolate in (Water + n-Propanol) Binary Solvent Mixtures at the Temperature Range from T = (293.15 to 333.15) K under 0.1 MPaa 100RD

100RD xA

100x

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

0.1271 0.2828 0.5254 0.9112 1.643 3.287 6.068 8.277

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

0.1456 0.3119 0.5492 0.9865 1.768 3.509 6.421 8.838

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

0.1543 0.3407 0.5964 1.021 1.913 3.668 6.706 9.389

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

0.1680 0.3759 0.6527 1.099 2.049 4.006 7.038 10.17

0.102 0.201 0.301 0.402

0.1851 0.4021 0.7123 1.254

modified Apelblat equation T= −1.92 −1.03 1.79 −0.06 0.62 −0.82 −0.55 −0.39 T= 2.44 0.41 −1.43 1.61 0.46 0.56 1.21 0.46 T= −1.09 0.48 −1.31 −2.02 0.21 −0.97 0.41 0.13 T= −2.02 1.15 −0.86 −2.52 −1.53 1.13 −1.06 1.08 T= −1.89 −1.63 −1.10 2.05

CNIBS/R-K model

Jouyban-Acree model

−4.78 −3.75 1.69 2.08 −1.17 0.11 0.02 0.00

−1.23 −1.11 2.26 1.41 −1.63 0.92 1.62 −0.73

−2.59 −1.34 −0.80 2.63 −1.14 0.12 0.01 0.00

3.02 0.35 −1.05 2.14 −0.79 1.65 2.09 0.83

−1.19 1.03 0.09 −0.97 0.70 −0.19 0.04 0.01

−0.74 0.43 −1.05 −2.19 −0.18 −0.51 0.38 0.90

−15.18 4.94 4.45 −1.31 −1.78 0.92 −0.20 0.02

−2.09 1.14 −0.74 −3.18 −1.19 0.94 −1.70 1.98

0.91 0.97 −1.27 −0.50

−2.53 −1.58 −1.13 1.14

xA

100x

0.500 0.601 0.702 0.801

2.299 4.218 7.528 10.95

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

0.2084 0.4484 0.7872 1.359 2.529 4.562 8.312 11.53

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

0.2309 0.5021 0.8616 1.514 2.799 5.016 9.082 12.90

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

0.2570 0.5621 0.9772 1.675 3.079 5.609 10.32 14.38

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

0.2894 0.6171 1.070 1.858 3.359 6.381 11.43 15.91

293.15 K

298.15 K

303.15 K

308.15 K

313.15 K

modified Apelblat equation T= 0.92 −1.10 −1.74 0.86 T= 0.39 −0.54 −0.46 0.86 0.92 −1.31 −0.24 −2.22 T= 0.93 0.64 −1.15 1.84 1.13 −0.47 −0.75 0.32 T= 1.87 1.50 1.41 1.44 0.35 1.49 1.70 2.03 T= 3.91 0.17 0.11 0.86 −1.63 4.56 0.86 2.48

CNIBS/R-K model

Jouyban-Acree model

1.01 −0.42 0.08 −0.01

1.85 −1.93 −2.68 1.65

5.11 −0.96 −2.54 −0.95 2.93 −1.39 0.28 −0.03

−0.95 −0.43 −0.66 −0.15 2.33 −2.79 −1.15 −1.77

4.13 0.85 −3.55 −0.70 2.72 −1.29 0.25 −0.03

−1.24 0.83 −1.54 0.94 2.90 −2.58 −1.37 0.19

3.99 −0.96 −2.48 −0.46 2.61 −1.29 0.26 −0.03

−1.24 1.78 0.83 0.81 2.41 −1.22 1.63 1.12

−0.02 0.48 −0.75 0.42 −0.07 −0.01 0.01 0.00

−0.21 0.55 −0.69 0.65 0.65 1.32 1.58 0.60

313.15 K

318.15 K

323.15 K

328.15 K

333.15 K

a


temperature Tfus (onset temperature) is 596.03 K and the melting enthalpy (ΔfusH) of sodium thioglycolate was 21.98 kJ·mol−1. 4.2. Solubility data. The solubility of sodium thioglycolate in the five pure solvents of water, methanol, ethanol, isopropyl alcohol, n-propanol and four binary solvent mixtures of (water + methanol, water + ethanol, water + isopropyl alcohol, water + n-propanol) was determined over the temperature range from (293.15 to 333.15) K and are listed in Tables 3−7 and graphically shown in Figures 4−8. As shown in Table 3 and Figure 4, the solubility of sodium thioglycolate in water is larger than those in methanol, ethanol, isopropyl alcohol, and n-propanol. Therefore, water can be selected as a good solvent for the crystallization of

sodium thioglycolate. The solubility of sodium thioglycolate increases with increasing temperature in water, ethanol, isopropyl alcohol, and n-propanol. While the solubility of sodium thioglycolate in methanol decreases with increasing the temperature, which is similar to that of C60 in hexane, toluene, and xylene.27,28 The solubility of sodium thioglycolate in methanol was verified by the UV spectroscopic method,29 which was presented in the Supporting Information. As shown in Figure 2, the polarity of sodium thioglycolate is strong according to its structure. Meanwhile, the polarity order of the five solvents is water > methanol > ethanol > isopropyl alcohol > n-propanol.30 However, the solubility is not strictly consistent with the order of polarity of the pure solvents, the other factors may affect it, which 3111



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Figure 4. Experimental and calculated mole fraction solubility (x) of sodium thioglycolate in the five pure solvents at different temperatures. Experimental values: ■, water; ●, methanol; ▲, ethanol; ▼, isopropyl alcohol; ⧫, n-propanol. Calculated values by the modified Apelblat model: solid lines.

Figure 5. Experimental solubility of sodium thioglycolate in binary (water + methanol) mixture for different mole fractions of water at various temperatures under atmospheric pressure (p = 0.1 MPa).

are hydrogen bond, dielectric constant, and surface tension of the different solvents.31 The solvation effect of the solute and solvent

increase with increasing temperature, which may produce a mutual repulsive force between methanol and sodium 3112



Article

Figure 6. Experimental solubility of sodium thioglycolate in binary (water + ethanol) mixture for different mole fractions of water at various temperatures under atmospheric pressure (p = 0.1 MPa).

Figure 7. Experimental solubility of sodium thioglycolate in binary (water + isopropyl alcohol) mixture for different mole fractions of water at various temperatures under atmospheric pressure (p = 0.1 MPa). 3113



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Figure 8. Experimental solubility of sodium thioglycolate in binary (water + n-propanol) mixture for different mole fractions of water at various temperatures under atmospheric pressure (p = 0.1 MPa).

Table 8. Parameters of the Equations for the Solubility of Sodium Thioglycolate in the Different Pure Solvents modified Apelblat equation

van’t Hoff equation

2

solvent

A

B/10

C

10 ARD

10 RMSD

A

B/10

102ARD

104RMSD

water methanol ethanol isopropyl alcohol n-propanol

−35.35 −294.1 −221.7 −259.9 −188.4

8.587 1482 891.3 1012 604.5

5.836 41.76 32.52 38.06 28.18

0.346 3.038 1.118 1.247 2.295

8.203 0.395 0.301 0.019 0.247

3.981 −12.35 −2.225 −3.340 1.334

−173.0 176.2 −128.0 −172.6 −266.2

0.480 0.047 2.510 0.031 2.539

12.06 0.680 0.600 0.050 0.482

thioglycolate molecules, which could lead to the decrease of the solubility of sodium thioglycolate in methanol. Additionally the hydrogen bonds could form between the molecules of sodium thioglycolate and water, which could promote the dissolution of sodium thioglycolate in water. As shown in Figures 5−8, the solubility of sodium thioglycolate in the binary solvent systems (water + ethanol, water + isopropyl alcohol, water + n-propanol) increases with the increase of temperature at certain composition of water. While, in the binary solvent system (water + methanol), the solubility of sodium thioglycolate decreases with increasing the temperature when the mole fraction of water is less than 0.2. In the meantime, the solubility of sodium thioglycolate in all the binary solvent systems increases with the increase of mole fraction of water at the same temperature. 4.3. Data Correlation. Two thermodynamic models, the modified Apelblat model and van’t Hoff equation, were used to correlate the solubility of sodium thioglycolate in the five pure solvents, and the modified Apelblat equation, CNIBS/R-K model and the Jouyban−Acree model were used to correlate the sodium thioglycolate solubility in the binary solvent mixtures.

4

On the basis of the experimental solubility data, the model parameters can be optimized by using the nonlinear least-squares method. The object function is defined as eq 11: N

F=

∑ (ln xnexp − ln xncal)2 n=1

(11)

cal where xexp n and xn represent the experimental and calculated solubility, respectively. To evaluate the applicability and accuracy of the models used in this work, the relative deviation (RD), the average relative deviation (ARD), and the root-mean-square deviation (RMSD) are defined as follows:

RD =

x exp − x cal x exp

ARD = 3114

1 N

N

∑ n=1

x exp − x cal x exp

(12)

(13) DOI: 10.1021/acs.jced.7b00245 J. Chem. Eng. Data 2017, 62, 3105−3123


Article

N

water + isopropyl alcohol, water + n-propanol) were well correlated by the modified Apelblat equation, the CNIBS/R-K equation, and the Jouyban−Acree model. A comparison of the correlation results of the three models shows that the Jouyban− Acree model is more adapt to correlate the solubility of sodium thioglycolate in the mixed solvents since it is a function of the temperature and the composition of the solvent. 4.4. Solution Mixing Thermodynamics. It is necessary to explore the dissolution thermodynamic properties of the solute in the different nonideal solvent mixtures. The mixing properties of solution can be calculated by the Lewis−Randall rule. For the ideal ternary solution systems, the mixing thermodynamic properties can be calculated by the following equations:32

RMSD = (∑ (x exp − x cal)2 /N )1/2 (14)

n=1

where N is the number of experimental data points. The parameters of the modified Apelblat model and van’t Hoff equation for the pure solvents are presented in Table 8, and the parameters of the modified Apelblat equation, CNIBS/R-K model and the Jouyban−Acree model for the binary solvent mixtures are presented in Tables 9−11 with the values of RAD and RMSD. Table 9. Parameters of the Modified Apelblat Equation for the Solubility of Sodium Thioglycolate in Water + (Methanol, Ethanol, Isopropyl Alcohol and n-Propanol) Mixtures (p = 0.1 MPa) xA

A

B/102

Water + Methanol 0.102 −225.1 110.8 0.201 −75.46 38.55 0.301 −140.9 49.52 0.402 −365.0 152.0 0.500 −213.3 84.49 0.601 −227.7 90.80 0.702 −231.3 92.12 0.801 −165.3 62.56 Water + Ethanol 0.102 −72.57 20.59 0.201 −148.5 54.46 0.301 −239.2 96.08 0.402 −363.8 152.4 0.500 −299.9 123.3 0.601 −223.1 88.14 0.702 −247.8 101.1 0.801 −95.91 32.74 Water + Isopropyl Alcohol 0.102 −135.0 25.28 0.201 −238.3 79.27 0.301 −297.9 109.0 0.402 −392.8 154.1 0.500 −515.9 211.9 0.601 −546.4 228.5 0.702 −513.7 215.7 0.801 −694.9 300.8 Water + n-Propanol 0.102 −102.9 28.85 0.201 −167.9 59.21 0.301 −176.8 64.45 0.402 −251.0 99.56 0.500 −193.6 72.56 0.601 −234.5 94.45 0.702 −334.2 140.7 0.801 −211.0 83.70

C

102ARD

104RMSD

31.90 9.960 20.87 54.28 31.77 34.06 34.74 25.00

0.958 0.616 1.553 1.513 1.193 0.968 0.303 0.362

0.19351 0.23703 1.012 2.375 4.286 5.448 4.644 8.977

10.43 21.82 35.40 54.05 44.69 33.40 37.10 14.58

0.863 0.644 0.650 0.627 1.167 0.827 0.272 0.228

0.28185 0.25141 0.49105 0.93640 3.893 5.611 3.316 5.049

20.78 36.11 44.95 59.03 77.33 81.86 77.01 103.9

0.624 0.792 0.802 1.379 0.591 0.824 1.979 0.955

0.05415 0.50249 1.030 2.320 3.595 6.204 30.23 9.757

15.21 24.97 26.33 37.38 29.00 35.00 49.90 31.68

1.830 0.840 1.071 1.474 0.864 1.378 0.947 1.108

0.4736 0.4257 0.8220 2.071 2.640 10.66 9.194 19.22

Δmix Gid = RT (x1 ln x1 + x 2 ln x 2 + x3 ln x3)

(15)

Δmix S id = −R(x1 ln x1 + x 2 ln x 2 + x3 ln x3)

(16)

Δmix H id = 0

(17)

where x1, x2, and x3 are the mole fraction of sodium thioglycolate, water, and (methanol, ethanol, isopropyl alcohol, water). ΔmixGid, ΔmixSid, and ΔmixHid refer to the mixing Gibbs energy, mixing entropy, and mixing enthalpy of ideal solution, respectively. For the nonideal ternary solution systems, the mixing thermodynamic properties can be calculated by the equations33 as follows: Δmix G = GE + Δmix Gid

(18)

Δmix S = S E + Δmix S id

(19)

Δmix H = HE + Δmix H id

(20)

where ΔmixG, ΔmixS, and ΔmixH refer to the mixing properties of the nonideal system, GE, SE, and HE are the excess properties of nonideal solution system and can be calculated by the following equations:34 N

GE = RT ∑ xi ln γi n=1

N ⎛ ∂ ln γi ⎞ HE = −RT 2 ∑ xi⎜ ⎟ ⎝ ∂T ⎠ p , x n=1

SE =

HE − GE T

(21)

(22)

(23)

where γi is the activity coefficient of sodium thioglycolate, water, and (methanol, ethanol, isopropyl alcohol, n-propanol) in the real ternary solution. The excess mixing properties can be calculated by the NRTL model.35 All the calculated values of the dissolution thermodynamic properties and the activity coefficient data of sodium thioglycolate are listed in Tables 12−15. As shown in Tables 12−15, the negative values of ΔmixG indicate that the mixing process of sodium thioglycolate in the binary solvent mixtures is spontaneous and favorable. The positive values of ΔmixH demonstrate that the mixing process is endothermic. The values of ΔmixS are positive within the investigated conditions, which indicates an entropically favorable process.36 In brief, the calculation and discussion of the mixing thermodynamic properties may be helpful for the understanding of the dissolution process of sodium thioglycolate.

According to the ARD and RMSD values as listed in Table 8, it is shown that the correlated results are in good agreement with the experimental solubility data in the five pure solvents within the experimental temperature range. The modified Apelblat equation presented the better correlation results compared with the van’t Hoff equation, and the maximum values of RMSD and RAD are 8.203 × 10−4, 0.03038, respectively. Also with the ARD and RMSD values as presented in Tables 9−11, the solubility in the binary solvent mixtures (water + methanol, water + ethanol, 3115



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Table 10. Parameters of the CNIBS/R-K Equation for the Solubility of Sodium Thioglycolate in Water + (Methanol, Ethanol, Isopropyl Alcohol, and n-Propanol) Mixtures (p = 0.1 MPa) T/K

A0

Water + Methanol 293.15 −5.710 298.15 −6.463 303.15 −6.746 308.15 −7.036 313.15 −7.477 318.15 −7.323 323.15 −7.665 328.15 −8.162 333.15 −8.456 Water + Ethanol 293.15 −7.039 298.15 −6.672 303.15 −6.291 308.15 −6.236 313.15 −6.241 318.15 −6.272 323.15 −6.220 328.15 −6.167 333.15 −6.250 Water + Isopropyl Alcohol 293.15 −7.804 298.15 −8.325 303.15 −7.587 308.15 −7.575 313.15 −7.469 318.15 −8.186 323.15 −8.209 328.15 −8.307 333.15 −6.408 Water + n-Propanol 293.15 −7.950 298.15 −7.724 303.15 −7.708 308.15 −7.051 313.15 −7.476 318.15 −7.607 323.15 −7.422 328.15 −7.427 333.15 −7.045

A1

A2

A3

A4

102ARD

104RMSD

−5.743 2.027 4.290 6.438 10.99 9.334 12.59 18.35 21.69

29.12 4.253 −1.148 −5.661 −19.70 −14.02 −22.00 −41.53 −50.49

−23.97 8.467 14.15 18.02 36.30 29.54 37.62 64.83 74.84

4.854 −10.01 −12.25 −13.34 −21.88 −19.24 −22.16 −35.48 −39.56

3.594 1.366 0.643 1.931 3.800 3.174 5.206 7.133 9.736

2.066 1.418 1.207 2.519 3.093 2.393 3.409 4.060 6.366

7.737 4.012 −0.016 0.040 1.152 2.474 2.459 2.057 3.890

−16.28 −2.61 12.33 12.08 7.858 2.804 3.544 7.317 1.365

38.26 18.52 −3.075 −2.559 3.595 11.47 10.09 2.710 10.97

−25.04 −15.19 −4.446 −4.810 −7.896 −12.18 −11.55 −7.388 −11.62

2.581 1.222 0.766 1.145 0.407 0.519 0.528 0.336 1.044

1.692 0.7840 0.5092 0.7142 0.4438 0.9172 1.061 0.9870 0.9421

14.73 22.86 16.62 18.20 18.75 27.04 29.92 32.16 14.61

−44.88 −75.66 −54.44 −59.71 −60.53 −85.64 −98.06 −103.68 −44.82

83.04 128.5 98.80 105.4 104.6 135.5 155.8 161.3 81.15

−48.50 −71.80 −57.30 −60.27 −58.96 −72.50 −83.65 −85.46 −47.05

17.31 15.69 16.00 9.567 14.65 17.83 16.70 18.51 15.34

−47.75 −41.90 −41.97 −18.71 −34.24 −47.40 −42.54 −50.53 −39.50

80.07 71.34 69.92 36.02 54.80 75.72 67.57 80.74 65.69

−45.96 −41.43 −40.02 −22.84 −30.77 −42.13 −37.49 −44.73 −37.64

water + methanol

water + ethanol

water + isopropyl alcohol

water + npropanol

B1 B2 B3 B4 B5/102 B6/102 B7/102 B8/102 B9 102ARD 104RMSD

−210.3 8420 30.81 −48.99 10.78 8.500 35.29 −37.07 8.366 12.76 10.38

−157.4 5924 23.00 −89.95 28.90 22.11 12.01 −24.67 14.34 1.774 15.05

−112.0 1.199 17.39 −829.3 586.2 −678.2 1005 −515.7 123.0 2.649 36.44

−126.3 3584 18.68 −187.2 125.8 −128.0 211.8 −120.9 28.33 10.64 7.274

1.698 1.080 0.528 3.599 0.647 1.775 1.689 1.509 0.219

6.253 5.744 7.921 8.594 9.965 9.271 10.76 10.49 20.20 1.099 1.198 0.6625 2.481 1.140 3.674 3.819 4.064 0.4184

5. CONCLUSIONS The solubility of sodium thioglycolate was measured by the gravimetrical method in the five pure solvents of water, methanol, ethanol, isopropyl alcohol, and n-propanol, and four binary solvent mixtures (water + methanol, water + ethanol, water + isopropyl alcohol, water + n-propanol) within the temperature range of (293.15−333.15) K under atmospheric pressure (p = 0.1 MPa). The solubility of sodium thioglycolate increases with a rise of temperature in water, ethanol, isopropyl alcohol, and n-propanol, and decreases in methanol. The solubility of sodium thioglycolate in the binary solvent mixtures (water + methanol, water + ethanol, water + isopropyl alcohol, water + n-propanol) monotonously increases with increasing temperature and mole fraction of water. The modified Apelblat equation and van’t Hoff equations were employed to correlate the solubility data in the five pure solvents. For the solubility of sodium thioglycolate in the binary solvent mixtures, the modified Apelblat equation, the CNIBS/R-K model, and the

Table 11. Parameters of the Jouyban−Acree Model for the Solubility of Sodium Thioglycolate in Water + (Methanol, Ethanol, Isopropyl Alcohol and n-Propanol) Mixtures (p = 0.1 MPa) solvent

53.16 42.92 48.24 43.41 41.05 26.75 24.99 19.99 38.72

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Table 12. Mixing Thermodynamic Properties of Sodium Thioglycolate in (Water + Methanol) Binary Solvent Mixtures (p = 0.1 MPa)a xA

ΔmixG/(kJ·mol−1)

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

−1.017 −1.599 −1.999 −2.237 −2.324 −2.251 −2.008 −1.628

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

−1.031 −1.620 −2.025 −2.265 −2.353 −2.280 −2.030 −1.645

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

−1.045 −1.641 −2.051 −2.293 −2.382 −2.306 −2.052 −1.663

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

−1.059 −1.662 −2.076 −2.322 −2.410 −2.332 −2.072 −1.677

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

−1.073 −1.683 −2.102 −2.350 −2.438 −2.357 −2.088 −1.691

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

−1.087 −1.704 −2.128 −2.378 −2.468 −2.379 −2.102 −1.702

0.102 0.201 0.301 0.402 0.500 0.601 0.702

−1.101 −1.725 −2.154 −2.406 −2.494 −2.400 −2.114

ΔmixH/(kJ·mol−1) T = 293.15 0.126 0.185 0.236 0.295 0.369 0.486 0.679 0.964 T = 298.15 0.124 0.187 0.246 0.306 0.383 0.501 0.710 1.011 T = 303.15 0.124 0.190 0.254 0.317 0.399 0.524 0.744 1.057 T = 308.15 0.124 0.193 0.262 0.327 0.417 0.548 0.781 1.112 T = 313.15 0.124 0.196 0.273 0.340 0.435 0.575 0.826 1.168 T = 318.15 0.125 0.199 0.281 0.353 0.447 0.609 0.875 1.228 T = 323.15 0.126 0.201 0.294 0.371 0.472 0.646 0.927 3117

ΔmixS/(J·K−1·mol−1)

ln γ

3.898 6.087 7.625 8.635 9.188 9.336 9.166 8.843

6.054 5.207 4.592 4.053 3.522 2.951 2.321 1.712

3.873 6.061 7.616 8.623 9.177 9.327 9.191 8.910

5.997 5.163 4.531 3.998 3.468 2.905 2.254 1.633

3.855 6.040 7.603 8.610 9.171 9.335 9.223 8.973

5.934 5.113 4.477 3.944 3.411 2.841 2.181 1.560

3.838 6.020 7.590 8.595 9.173 9.346 9.259 9.053

5.871 5.063 4.424 3.895 3.348 2.776 2.105 1.471

3.824 6.001 7.586 8.591 9.174 9.363 9.307 9.129

5.806 5.041 4.364 3.873 3.287 2.706 2.016 1.385

3.810 5.982 7.573 8.585 9.161 9.392 9.359 9.210

5.742 4.965 4.314 3.782 3.245 2.623 1.921 1.290

3.797 5.963 7.576 8.593 9.180 9.426 9.412

5.678 4.916 4.250 3.715 3.169 2.535 1.823

K

K

K

K

K

K

K



Article

Table 12. continued xA

a


0.801

−1.709

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

−1.115 −1.747 −2.180 −2.434 −2.522 −2.424 −2.122 −1.715

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

−1.129 −1.768 −2.206 −2.460 −2.547 −2.440 −2.127 −1.718

ΔmixH/(kJ·mol−1) T = 323.15 K 1.294 T = 328.15 K 0.127 0.204 0.304 0.388 0.494 0.677 0.985 1.356 T = 333.15 K 0.129 0.207 0.318 0.415 0.524 0.721 1.045 1.419


ln γ

9.291

1.188

3.786 5.945 7.569 8.600 9.191 9.447 9.468 9.358

5.615 4.868 4.199 3.652 3.105 2.465 1.716 1.091

3.775 5.927 7.575 8.629 9.218 9.490 9.521 9.416

5.551 4.820 4.136 3.566 3.023 2.365 1.606 0.989

The expanded uncertainties are U(ΔmixG) = 0.050ΔmixG, U(ΔmixH) = 0.060ΔmixH, U(ΔmixS) = 0.07ΔmixS.

Table 13. Mixing Thermodynamic Properties of Sodium Thioglycolate in (Water + Ethanol) Binary Solvent Mixtures (p = 0.1 MPa)a xA


0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

−0.975 −1.543 −1.923 −2.155 −2.239 −2.171 −1.932 −1.558

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

−0.989 −1.564 −1.948 −2.183 −2.268 −2.197 −1.956 −1.577

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

−1.003 −1.585 −1.974 −2.212 −2.297 −2.223 −1.980 −1.596

0.102 0.201 0.301 0.402 0.500 0.601 0.702

−1.017 −1.606 −2.000 −2.240 −2.326 −2.250 −2.001

ΔmixH/(kJ·mol−1) T =293.15 K 0.171 0.281 0.386 0.486 0.587 0.713 0.912 1.167 T = 298.15 K 0.175 0.284 0.391 0.492 0.597 0.731 0.936 1.208 T = 303.15 K 0.178 0.288 0.396 0.497 0.607 0.750 0.960 1.250 T = 308.15 K 0.181 0.293 0.401 0.504 0.619 0.769 0.990 3118


ln γ

3.909 6.219 7.877 9.009 9.639 9.838 9.702 9.296

6.069 5.228 4.603 4.071 3.560 2.995 2.307 1.691

3.904 6.198 7.847 8.972 9.608 9.821 9.699 9.343

5.985 5.165 4.545 4.017 3.499 2.922 2.240 1.610

3.896 6.179 7.818 8.937 9.579 9.808 9.698 9.388

5.906 5.100 4.488 3.964 3.438 2.849 2.173 1.533

3.889 6.163 7.792 8.906 9.554 9.795 9.707

5.827 5.034 4.430 3.909 3.377 2.781 2.098 DOI: 10.1021/acs.jced.7b00245 J. Chem. Eng. Data 2017, 62, 3105−3123


Article

Table 13. continued xA 0.801

a

ΔmixG/(kJ·mol−1) −1.616

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

−1.031 −1.627 −2.026 −2.269 −2.354 −2.275 −2.021 −1.633

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

−1.045 −1.649 −2.052 −2.297 −2.383 −2.299 −2.038 −1.651

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

−1.059 −1.670 −2.078 −2.325 −2.410 −2.322 −2.054 −1.668

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

−1.073 −1.691 −2.104 −2.353 −2.436 −2.341 −2.069 −1.684

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

−1.088 −1.713 −2.130 −2.381 −2.461 −2.360 −2.079 −1.699

ΔmixH/(kJ·mol−1) T = 308.15 1.289 T = 313.15 0.187 0.298 0.408 0.514 0.631 0.790 1.024 1.336 T = 318.15 0.191 0.304 0.415 0.524 0.645 0.816 1.065 1.380 T = 323.15 0.195 0.310 0.422 0.536 0.664 0.846 1.106 1.428 T = 328.15 0.200 0.315 0.431 0.552 0.690 0.883 1.150 1.476 T = 333.15 0.207 0.322 0.441 0.568 0.717 0.920 1.201 1.524


ln γ

9.428

1.461

3.890 6.148 7.772 8.885 9.533 9.788 9.725 9.482

5.745 4.970 4.370 3.846 3.315 2.707 2.013 1.378

3.886 6.137 7.753 8.868 9.517 9.792 9.753 9.530

5.668 4.904 4.310 3.783 3.250 2.624 1.916 1.300

3.883 6.126 7.735 8.854 9.512 9.802 9.781 9.580

5.593 4.840 4.252 3.718 3.174 2.534 1.820 1.219

3.880 6.114 7.725 8.852 9.525 9.824 9.810 9.629

5.520 4.779 4.188 3.642 3.080 2.427 1.721 1.135

3.885 6.108 7.716 8.851 9.538 9.845 9.845 9.673

5.442 4.714 4.125 3.569 2.987 2.323 1.607 1.053

K K

K

K

K

K


Table 14. Mixing thermodynamic properties of sodium thioglycolate in(water + isopropyl alcohol) binary solvent mixtures (p = 0.1 MPa)a xA 0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

ΔmixG/(kJ·mol−1) −0.922 −1.477 −1.842 −2.062 −2.158 −2.124 −1.948 −1.561

ΔmixH/(kJ·mol−1) T = 293.15 K 0.215 0.434 0.629 0.797 0.940 1.067 1.187 1.271 3119


ln γ

3.879 6.519 8.432 9.753 10.57 10.89 10.69 9.658

6.006 4.526 3.788 3.368 3.044 2.676 2.254 1.883 DOI: 10.1021/acs.jced.7b00245 J. Chem. Eng. Data 2017, 62, 3105−3123


Article



0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

−0.936 −1.499 −1.869 −2.091 −2.188 −2.152 −1.965 −1.585

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

−0.949 −1.520 −1.895 −2.120 −2.218 −2.181 −1.992 −1.605

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

−0.963 −1.542 −1.922 −2.150 −2.249 −2.209 −2.014 −1.619

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

−0.977 −1.563 −1.948 −2.180 −2.280 −2.236 −2.039 −1.625

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

−0.990 −1.585 −1.975 −2.210 −2.310 −2.260 −2.051 −1.625

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

−1.004 −1.607 −2.002 −2.240 −2.341 −2.282 −2.042 −1.611

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

−1.018 −1.628 −2.028 −2.269 −2.370 −2.299 −2.041 −1.582

ΔmixH/(kJ·mol−1) T = 298.15 0.22 0.44 0.64 0.80 0.95 1.08 1.20 1.28 T = 303.15 0.221 0.445 0.643 0.809 0.953 1.084 1.217 1.301 T = 308.15 0.224 0.452 0.650 0.817 0.961 1.098 1.238 1.337 T = 313.15 0.227 0.460 0.659 0.827 0.972 1.113 1.262 1.386 T = 318.15 0.231 0.469 0.669 0.836 0.984 1.134 1.294 1.443 T = 323.15 0.236 0.479 0.681 0.847 0.997 1.160 1.341 1.514 T = 328.15 0.241 0.491 0.693 0.861 1.017 1.189 1.382 1.596 3120


ln γ

3.868 6.501 8.400 9.705 10.51 10.83 10.63 9.613

5.970 4.492 3.752 3.332 3.003 2.627 2.178 1.846

3.859 6.484 8.371 9.664 10.46 10.77 10.59 9.589

5.932 4.458 3.714 3.292 2.958 2.574 2.124 1.789

3.851 6.471 8.346 9.627 10.42 10.73 10.55 9.593

5.892 4.419 3.672 3.249 2.909 2.508 2.044 1.702

3.844 6.460 8.326 9.602 10.38 10.69 10.54 9.614

5.849 4.375 3.623 3.192 2.851 2.437 1.956 1.591

3.839 6.455 8.312 9.576 10.36 10.67 10.51 9.642

5.805 4.325 3.566 3.137 2.785 2.342 1.842 1.464

3.837 6.454 8.302 9.553 10.33 10.65 10.47 9.672

5.757 4.269 3.503 3.078 2.718 2.233 1.674 1.307

3.836 6.458 8.294 9.540 10.32 10.63 10.43 9.686

5.708 4.203 3.434 3.004 2.623 2.109 1.515 1.125

K

K

K

K

K

K

K



Article

Table 14. continued xA 0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801 a

ΔmixG/(kJ·mol−1) −1.032 −1.649 −2.054 −2.298 −2.396 −2.309 −2.030 −1.534

ΔmixH/(kJ·mol−1) T = 333.15 K 0.247 0.504 0.709 0.878 1.040 1.223 1.418 1.683


ln γ

3.838 6.465 8.292 9.533 10.31 10.60 10.35 9.656

5.655 4.134 3.354 2.916 2.510 1.963 1.342 0.923


Table 15. Mixing Thermodynamic Properties of Sodium Thioglycolate in (Water + n-Propanol) Binary Solvent Mixtures (p = 0.1 MPa)a xA


0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

−0.994 −1.600 −1.997 −2.233 −2.322 −2.248 −1.998 −1.666

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

−1.008 −1.621 −2.023 −2.261 −2.349 −2.273 −2.016 −1.676

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

−1.022 −1.642 −2.048 −2.289 −2.377 −2.300 −2.040 −1.690

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

−1.036 −1.663 −2.074 −2.317 −2.404 −2.323 −2.063 −1.699

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

−1.049 −1.684 −2.099 −2.344 −2.429 −2.351 −2.084 −1.704

0.102 0.201

−1.063 −1.704

ΔmixH/(kJ·mol−1) T = 293.15 0.142 0.254 0.352 0.438 0.523 0.634 0.784 0.902 T = 298.15 0.147 0.259 0.357 0.446 0.534 0.651 0.807 0.938 T = 303.15 0.150 0.265 0.364 0.452 0.546 0.664 0.827 0.973 T = 308.15 0.155 0.272 0.371 0.461 0.558 0.686 0.849 1.020 T = 313.15 0.159 0.277 0.380 0.475 0.577 0.702 0.879 1.066 T = 318.15 0.166 0.285 3121


ln γ

3.877 6.322 8.014 9.112 9.705 9.832 9.487 8.760

6.384 5.497 4.862 4.358 3.882 3.344 2.767 2.402

3.875 6.306 7.981 9.081 9.671 9.806 9.468 8.767

6.288 5.419 4.800 4.288 3.811 3.270 2.691 2.317

3.867 6.290 7.956 9.042 9.643 9.777 9.456 8.784

6.202 5.343 4.731 4.233 3.740 3.210 2.629 2.238

3.862 6.277 7.935 9.013 9.614 9.766 9.451 8.821

6.115 5.267 4.660 4.166 3.673 3.122 2.564 2.141

3.860 6.260 7.915 9.002 9.602 9.750 9.460 8.847

6.027 5.197 4.591 4.081 3.584 3.061 2.484 2.049

3.863 6.253

5.939 5.120

K

K

K

K

K

K



Article


a


0.301 0.402 0.500 0.601 0.702 0.801

−2.124 −2.371 −2.455 −2.376 −2.090 −1.725

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

−1.077 −1.726 −2.149 −2.398 −2.480 −2.397 −2.104 −1.715

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

−1.091 −1.746 −2.174 −2.424 −2.505 −2.416 −2.097 −1.714

0.102 0.201 0.301 0.402 0.500 0.601 0.702 0.801

−1.105 −1.767 −2.200 −2.450 −2.529 −2.430 −2.100 −1.714

ΔmixH/(kJ·mol−1) T = 318.15 0.389 0.486 0.595 0.725 0.923 1.101 T = 323.15 0.172 0.294 0.399 0.501 0.615 0.753 0.964 1.174 T = 328.15 0.179 0.304 0.412 0.516 0.636 0.788 1.026 1.248 T = 333.15 0.187 0.313 0.423 0.532 0.656 0.830 1.081 1.321


ln γ

7.900 8.981 9.589 9.746 9.470 8.882

4.518 4.012 3.503 2.981 2.372 1.981

3.865 6.249 7.884 8.970 9.580 9.750 9.495 8.941

5.853 5.042 4.449 3.934 3.418 2.888 2.271 1.850

3.869 6.248 7.882 8.959 9.572 9.763 9.519 9.027

5.768 4.964 4.368 3.858 3.337 2.781 2.129 1.723

3.878 6.244 7.874 8.952 9.562 9.787 9.548 9.109

5.681 4.890 4.297 3.779 3.261 2.657 2.011 1.604

K

K

K

K


Funding

Jouyban−Acree model were applied to correlate the solubility data, and the correlated results were in good agreement with the experimental data. On the basis of the NRTL model, the mixing thermodynamic properties of enthalpy, entropy, and Gibbs energy in the different binary solvent systems were calculated, and the values of ΔmixS, and ΔmixH were all positive, indicating that the dissolution process of sodium thioglycolate in these solvent mixtures was endothermic and entropy-driven.

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Financial support from National Natural Science Foundation of China (Project 21306093) is gratefully acknowledged. Notes

The authors declare no competing financial interest.

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(1) Burkinshaw, S. M.; Paraskevas, M. The dyeing of silk Part 1: Low temperature application of solubilized sulphur dyes using sodium thioglycolate. Dyes Pigm. 2010, 87, 225−233. (2) Tyl, R. W.; Price, C. J.; Marr, M. C.; Myers, C. B.; van Birgelen, A. P. J. M.; Jahnke, G. D. Developmental Toxicity Evaluation of Sodium Thioglycolate Administered Topically to Sprague−Dawley (CD) Rats and New Zealand White Rabbits. Birth Defects Res., Part B 2003, 68, 144−161. (3) Rhodes, D. G.; Holtz, K.; Robinson, P.; Wang, K. Y.; Mcpherson, C. E. Improved stability of recombinant hemagglutinin using a formulation containing sodium thioglycolate. Vaccine 2015, 33, 6011−6016. (4) Hartley, R.; Aros, P.; Bustos-obregón, E.; Romero, F. Reevaluating the Sperm Nuclear Chromatin Decondensation Test by Sodium Thioglycolate of Stallions Spermatozoa. J. Equine. Vet. Sci. 2016, 36, 10−14. (5) Oliveira, A. C.; Coelho, M. G.; Pires, R. F.; Franco, M. R. Solubility of benzoic acid in mixed solvents. J. Chem. Eng. Data 2007, 52, 298−300. (6) Ding, Z.-W.; Zhang, R.-R.; Long, B.-W.; Liu, L.-Y.; Tu, H.-F. Solubilities of m-Phthalic acid in petroleum ether and its binary solvent

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.7b00245.

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REFERENCES

Solubility of sodium thioglycolate in methanol measured by the UV spectroscopic method (PDF)

AUTHOR INFORMATION

Corresponding Authors

*Tel.: +86 532 86057798. E-mail: [email protected]. *Tel.: +86 532 86057103. E-mail: [email protected]. ORCID

Dongmei Xu: 0000-0002-5770-0513 Jun Gao: 0000-0003-1145-9565 3122



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