Measurement and Correlation of the Solubilities of Sulfur S8

Feb 16, 2018 - Engineering, Shihezi University, Shihezi, Xinjiang 832003, People,s Republic of China. ABSTRACT: The solubility of sulfur S8 in toluene...
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Measurement and Correlation of the Solubilities of Sulfur S8 in 10 Solvents Rongjie Wang,†,‡ Benxian Shen,*,† Hui Sun,† and Jigang Zhao*,† †

Research Institute of Petroleum Processing, East China University of Science and Technology, Shanghai 200237, People’s Republic of China ‡ Key Laboratory for Green Processing of Chemical Engineering of Xinjiang Bingtuan, School of Chemistry and Chemical Engineering, Shihezi University, Shihezi, Xinjiang 832003, People’s Republic of China ABSTRACT: The solubility of sulfur S8 in toluene, ethylbenzene, styrene, chlorobenzene, 1,2,3,4-tetrahydronaphthalene, HAS, benzene, cyclohexene, cyclohexane, and hexane was measured by using a gravimetric method in the temperature range between 298.15 and 363.15 K under atmospheric pressure. The solubility data of sulfur S8 in these solvents were correlated by using the van’t Hoff equation, modified Apelblat equation, and λh equation. Furthermore, the dissolution of S8 in each tested solvent is endothermic and nonspontaneous.

1. INTRODUCTION Insoluble sulfur (IS), known as polymeric sulfur,1,2 is insoluble in carbon disulfide and rubber. It is widely used in rubber production as an indispensable radial tire additive. In order to prepare the insoluble sulfur product with high insoluble sulfur content, high thermal stability, and high dispersion, various processes including a low-temperature melting synthesis method and gas-phase transition method were developed.3,4 In general, synthesized IS products contain different contents of elemental sulfur S8, which is soluble in carbon disulfide. Therefore, an extraction process involving various solvents has been employed to achieve the efficient separation of the nonreacted S8 from the IS product. In view of the excellent ability to dissolve S8, carbon disulfide has benefitted from extensive research and applications in the industrial process to remove the soluble S8 and to update the product quality.5,6 However, carbon disulfide is flammable, explosive, and harmful to human health. Replacing the carbon disulfide in IS production is considered to be another crucial problem that needs to be addressed urgently. As a result, the development of green and safe solvents has received increasing research and industrial interest. In this work, the solubility of sulfur S8 in 10 solvents was determined for temperatures ranging from 298.15 to 363.15 K under atmospheric pressure by using a gravimetric method. The van’t Hoff equation,7 modified Apelblat equation,8 and λh equation9 were applied to correlate the solubility data. The corresponding thermodynamic parameters including the Gibbs free energy, the changes in enthalpy, and the changes in entropy were derived. The present results provide insight into © XXXX American Chemical Society

the development of a promising extraction process in IS production.

2. EXPERIMENTAL SECTION 2.1. Materials. Sulfur S8, toluene, ethylbenzene, styrene, chlorobenzene, 1,2-dichlorobenzene, 1,2,3,4-tetrahydronaphthalene, benzene, cyclohexene, cyclohexane, and hexane were obtained from Shanghai Lingfeng Chemical Reagent Co., Ltd. (Shanghai, China). HAS solvent is a mixture of chlorobenzene and 1,2-dichlorobenzene with chlorobenzene to 1,2-dichlorobenzene in a molar ratio of 4:6. All chemicals were used without further purification in the present work. Deionized water prepared in our laboratory was used for each experiment. The major information is listed in Table 1. 2.2. Solubility Measurement. The solubilities of sulfur S8 in different solvents were measured by the cloud-point method using laser beam scattering in the temperature range of 298.15 to 363.15 K under atmospheric pressure.10 The schematic diagram for the setup of the solubility measurement is presented in Figure 1. A 100 mL jacked glass vessel was heated, and the temperature was controlled to an uncertainty of ±0.01 K by using a DC-2006 smart thermostatic bath (Ningbo Scientific Biotechnology Co., Ltd., China). A glass tube condenser was fixed in the vessel to cool the solvent. A laser monitoring observation technique was employed to monitor the disappearance of the last crystal particles in the mixtures. The light signal transmitted through the vessel was collected Received: July 30, 2017 Accepted: February 9, 2018

A

DOI: 10.1021/acs.jced.7b00699 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 2. Mole Fraction Solubilities x of NaCl in Water at Temperature T under 101.2 kPaa,b

Table 1. Mass Fraction, CAS, and Density (ρ) at 293.15 K under 101.3 kPaa chemical name sulfur S8 sodium chloride toluene ethylbenzene styrene chlorobenzene 1,2-dichlorobenzene 1,2,3,4-tetrahydronaphthalene benzene cyclohexene cyclohexane hexane

CAS 10544-50 -0 7647-14-5 108-88-3 100-41-4 100-42-5 108-90-7 95-50-1 119-64-2 71-43-2 110-83-8 110-82-7 110-54-3

mass fraction purity, w

analysis method

0.996

GCb

0.999 0.995 0.985 0.995 0.995 0.990 0.952 0.996 0.994 0.995 0.989

ICc GCb GCb GCb GCb GCb GCb GCb GCb GCb GCb

a Uncertainty for mass fraction purity u(w) = 0.001. chromatography. cIon chromatography.

b

m1/M1 m1/M1 + m2/M 2

xe, mol/mol

xl, mol/mol

RD, %

293.15 303.15 313.15 323.15

0.0998 0.1004 0.1014 0.1024

0.0996 0.1001 0.1009 0.1019

0.200 0.199 0.198 0.196

a e

x , experimental solubility values of NaCl in water; xl, solubilities obtained from the literature;11 RD, the mean relative deviation (calculated from eq 2). bStandard uncertainties u(T) = 0.01 K, u(p) = 1 kPa, and u(x) = 0.0001.

(RD) (calculated from eq 2) of less than 0.20%, indicating its high reliability. RD =

Gas

e

xe − xc × 100% xe

(2)

c

where x and x represent the experimental and estimated solubilities, respectively. 3.2. Solubility. In the tested temperature range, the observed solubilities of sulfur S8 in toluene, ethylbenzene, styrene, chlorobenzene, 1,2,3,4-tetrahydronaphthalene, HAS, benzene, cyclohexene, cyclohexane, and hexane are summarized in Table 3 and Figure 2. As the temperature increases from 298.15 to 333.15 K, our measured solubilities for S8 in toluene change from 0.782 to 2.535%, which is consistent with previously reported values.10,12 The solubilities at higher temperatures show a more significant deviation from the documented data.10 It is clearly indicated that the solubility of S8 in each solvent exhibits a rising trend with increasing temperature. However, the rate of increase varies for different solvents. The solubilities rank in the following order: HAS > chlorobenzene > styrene >1,2,3,4-tetrahydronaphthalene > toluene > cyclohexene > benzene > ethylbenzene > cyclohexane ≈ hexane. S 8 demonstrates high solubility in halogenated aromatics (chlorobenzene) and their mixture (HAS) but has very low solubility in nonpolar solvents including hexane, cyclohexene, and cyclohexane. On the other hand, our results indicate that the polarity of a solvent is not the only factor which determines the solubility of sulfur S8 because the solubility in benzene was observed to be lower than in

with an FGF-3 detector. Under constant stirring, precisely determined sulfur S8 samples were slowly added to the vessel containing approximately 80 mL of solvent until the system was saturated with sulfur. All of the average values were used to calculate the mole fraction solubility, x, according to eq 1

x=

T/K

(1)

where m1 and m2 represent the masses of the solute and the solvent and M1 and M2 are the molar masses of the solute and the solvent, respectively.

3. RESULTS AND DISCUSSION 3.1. Assessment of the Apparatus for Solubility Measurements. To evaluate the feasibility and uncertainties of the measurement, the solubilities of NaCl in water were first determined with the same apparatus (see Figure 1). In comparison with the documented values from the literature (see Table 2), our experimental results are in good agreement with the reported values11 by giving a mean relative deviation

Figure 1. Schematic diagram of the setup for solubility measurements: (1) thermostat, (2) transistor laser generator, (3) feed inlet, (4) precise mercurial thermometer, (5) condenser pipe, (6) jacketed vessel, (7) signal display, (8) laser acceptor, and (9) magnetic stirrer. B

DOI: 10.1021/acs.jced.7b00699 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 3. Mole Fraction Solubilities x of Sulfur S8 in Different Organic Solvents at Temperature T under 101.2 kPa T/K

x/(×10−2 mol/mol) toluene

298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15

0.782 0.927 1.097 1.298 1.536 1.816 2.146 2.535 2.993 3.529 4.158 4.893 5.751 6.747 HAS

298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15

1.916 2.379 2.947 3.651 4.513 5.567 6.849 8.401 10.267 12.488 15.108 18.166 21.686 25.673 styrene

298.15 303.15 308.15 313.15 318.15

0.772 1.061 1.387 1.749 2.143

T/K

x/(×10−2 mol/mol)

ethylbenzene 298.15 0.405 303.15 0.496 308.15 0.608 313.15 0.745 318.15 0.913 323.15 1.117 328.15 1.367 333.15 1.672 338.15 2.044 343.15 2.497 348.15 3.046 353.15 3.711 358.15 4.515 363.15 5.484 1,2,3,4-tetrahydronaphthalene 298.15 1.175 303.15 1.371 308.15 1.599 313.15 1.864 318.15 2.172 323.15 2.529 328.15 2.943 333.15 3.423 338.15 3.978 343.15 4.619 348.15 5.357 353.15 6.205 358.15 7.178 363.15 8.289 chlorobenzene 298.15 1.369 303.15 1.598 308.15 1.865 313.15 2.175 318.15 2.535

T/K

x/(×10−2 mol/mol)

T/K

323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15

2.569 3.025 3.508 4.018 4.553 5.111 5.691 6.293 6.913

323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15

0.712 0.844 1.001 1.186 1.406 1.665 1.972 2.333 2.759 3.260 cyclohexane 0.583 0.664 0.756 0.861 0.979 1.114 1.268 1.442 1.640 1.864 2.118

298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

benzene 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15

298.15 303.15 308.15 313.15 318.15 323.15 328.15

a

x/(×10−2 mol/mol) 2.953 3.438 3.999 4.647 5.395 6.254 7.241 8.369 9.654 cyclohexene 0.844 0.986 1.152 1.345 1.57 1.833 2.137 2.492 2.903 3.380 hexane 0.0336 0.0403 0.0672 0.0839 0.107 0.128 0.168

a

Standard uncertainties u(T) = 0.01 K, u(p) = 1 kPa, and u(x) = 0.001.

cyclohexene. It seems that the structural similarity between solvent and sulfur S8 can benefit greatly from the solubility. The solubility data for different solvents were explained by using different models. The parameter’s root-mean-square deviation (RMSD) (see eq 3) and the relative average deviation (RAD) (see eq 4) were used to evaluate the correlation results. N

RMSD =

∑i = 1 (xic − xie) N

(3)

where N is the number of temperature points for each solvent, xci and xie represent the estimated and the experimental solubility values, respectively. RAD =

1 N

N

∑ i=1

xe − xc × 100% xe

(4)

The dependence of the solubility x on temperature was first correlated by using the van’t Hoff equation (see eq 5)7,13−15

Figure 2. Solubilities of sulfur S8 in 10 solvents at different temperatures. Points represent experiment values, and lines represent the fitted results: ■, toluene; red ●, ethylbenzene; blue ▲, styrene; pink ▼, chlorobenzene; green ⧫, 1,2,3,4-tetrahydronaphthalene; blue, left-pointing ▲, HAS; purple, right-pointing ▲, benzene; maroon ⬢, cyclohexene; maroon ★, cyclohexane; green solid ⬠, hexane.

ln x = A + B/T

(5)

where x is the mole fraction solubility of S8 in solvents, T is the absolute temperature in K, and A and B are the parameters of C

DOI: 10.1021/acs.jced.7b00699 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 4. Parameters A and B of the van’t Hoff Equation for Different Solventsa

a

solvent

A

B

RAD, %

RMSD, ×10−4

toluene ethylbenzene styrene chlorobenzene 1,2,3,4-tetrahydronaphthalene HAS benzene cyclohexene cyclohexane hexane

7.780 9.951 5.867 7.074 6.938 10.941 6.981 6.066 4.063 8.892

−3810.282 −4673.486 −3087.559 −3423.326 −3429.327 −4467.071 −3574.382 −3247.913 −2761.218 −5015.700

3.48 7.31 8.56 2.77 2.89 1.60 1.73 1.54 1.59 6.27

6.56 11.04 18.09 8.73 7.84 7.42 2.57 2.62 1.83 0.43

Standard uncertainties u(A) = 0.001 and u(B) = 0.001.

Table 5. Parameters C, D, and E of Apelblat Model Parameters for Different Solventsa

a

solvent

C

D

E

RAD, %

RMSD, ×10−4

toluene ethylbenzene styrene chlorobenzene 1,2,3,4-tetrahydronaphthalene HAS benzene cyclohexene cyclohexane hexane

−121.570 −145.163 143.652 −107.790 −123.260 −19.306 −128.877 −128.258 −136.339 25.644

2632.671 3102.839 −9911.084 2280.593 3036.244 −2952.347 2939.556 3183.319 3605.013 −5799.8685

18.936 22.684 −20.190 16.824 19.070 4.424 20.021 19.800 20.879 −2.479

0.11 0.14 2.55 0.28 0.54 0.93 0.03 0.16 3.48 3.20

0.34 0.25 2.08 1.40 1.65 5.61 0.05 0.27 7.37 0.43

Standard uncertainties u(C) = 0.001, u(D) = 0.001, and u(E) = 0.001.

Table 6. Parameters λ and h of the λh Equation for Different Solventsa

a

solvent

λ

h

RAD, %

RMSD, ×10−4

toluene ethylbenzene styrene chlorobenzene 1,2,3,4-tetrahydronaphthalene HAS benzene cyclohexene cyclohexane hexane

0.0218 0.0325 0.0082 0.0221 0.0178 0.2567 0.0427 0.0335 0.0074 0.0124

70 179.392 80 945.749 68 771.196 48 883.171 58 049.187 12 771.215 58 885.505 61 420.947 137 696.384 375 362.221

7.85 7.88 9.30 7.58 7.70 5.86 1.09 1.32 2.55 6.82

18.96 11.59 49.82 29.93 26.01 43.82 1.89 2.51 3.17 0.46

Standard uncertainties u(λ) = 0.0001 and u(h) = 0.001.

The fitting results using the modified Apelblat model are presented in Figure 3. From Tables 3−5 and Figure 3, the modified Apelblat model shows the excellent correlation results, and the predicted solubilities are in good agreement with the experimental results. The RSD values for 10 solvents are found to be no more than 3.5%, indicating that the modified Apelblat equation can explain the solubility data of sulfur S8 in these solvents very well. The same conclusion can also be drawn after analyzing the fitting parameters obtained from the van’t Hoff equation and the λh equation. However, among the three models, the modified Apelblat equation correlates the experimental data with the smallest RSD. The present results are fundamentally important for process development and optimization of the removal of sulfur S8 from the insoluble sulfur. 3.3. Thermodynamic Properties. The standard molar ° ) can be extracted from eq enthalpy of dissolution (ΔHsoln 8.8,16,17

the van’t Hoff equation. Observed parameters A and B as well as RAD and RMSD are listed in Table 4. The modified Apelblat model16−18 (see Equation 6) was also used to explain the solubility data ln x = C + D/T + ET

(6)

where C, D, and E are the model parameters. The observed values are listed in Table 5. In addition, the semiempirical λh model18,19 (see eq 7) is employed to describe the experimental solubilities presented in Table 6. ⎡1 ⎛ λ(1 − x) ⎞ 1 ⎤ ln⎜1 + ⎟ = λh⎢ − ⎥ ⎝ ⎠ x Tm ⎦ ⎣T

(7)

where Tm is the normal melting point of sulfur S8 in Kelvin and λ and h are the model parameters. The correlation results are given in Table 6. D

DOI: 10.1021/acs.jced.7b00699 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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⎛ ∂ ln x ⎞ ° = −R × ⎜ ΔHsoln ⎟ ⎝ ∂(1/T ) ⎠

(8) −1

−1

where R is the gas constant (8.314 J·mol K ) and T is the temperature, K. The van’t Hoff equation can be plotted as ln x versus 1/T. Then ΔH°soln can be derived from the slope of the plots in Figure 4. The standard molar Gibbs energy of dissolution (ΔGsoln ° ) can be obtained from the intercept of the plots.20 Consequently, the corresponding standard molar entropy (ΔS°soln) can be estimated by using eq 9.21,22 ° = ΔSsoln

° − ΔGsoln ° ΔHsoln Tmean

(9)

where Tmean represents the arithmetic mean temperature for the experimental temperature range. Table 7 summarizes the thermodynamic parameters for the dissolution of S8 in different solvents. In all cases, the standard molar enthalpy is positive, indicating that the dissolution of S8 in each selected solvent is endothermic. A large enthalpy value suggests that high energy is required to overcome the cohesive force of the solute and the solvent during the dissolution process, which is strongly temperature-dependent.23 In addition, the standard molar Gibbs energy is found to be positive, which means that the dissolution is nonspontaneous and the entropy is the driving force for the dissolution process. To compare the relative contributions that enthalpy and entropy make to the standard Gibbs energy in the dissolution process, ξH and ξTS were calculated according to eqs 10 and 11.20,21 The values of ξH and ξTS are also given in Table 7. As we can see from the results, the main contribution to the standard molar Gibbs energy can be attributed to enthalpy.

Figure 3. Solubilities of sulfur S8 in toluene at different temperatures: ■, ref 10; red ●, ref 12; and blue ▲, this work.

ξH = ξTS =

−1

Figure 4. van’t Hoff plots of ln x versus T : ■, toluene; red ●, ethylbenzene; blue ▲, styrene; pink ▼, chlorobenzene; green ⧫, 1,2,3,4-tetrahydronaphthalene; blue, left-pointing▲, HAS; purple, right-pointing ▲, benzene; maroon ⬢, cyclohexene; maroon ★, cyclohexane; green solid ⬠, hexane.

° | |ΔHsoln × 100 ° | + |T ΔSsoln ° | |ΔHsoln

(10)

° | |T ΔSsoln × 100 ° | + |T ΔSsoln ° | |ΔHsoln

(11)

4. CONCLUSIONS The solubility data of sulfur S8 in 10 organic solvents were measured via a gravimetric method within the temperature

Table 7. Thermodynamic Functions (ΔG°soln, ΔH°soln, and ΔS°soln) for the Dissolution of S8 in Different Solvents at Temperature T under Atmospheric Pressurea,b solvent

ΔG°soln, kJ/mol

ΔH°soln, J/mol

ΔS°soln, J/(mol·K)

Tmean, K

ξH, %

ξTS, %

toluene ethylbenzene styrene chlorobenzene 1,2,3,4-tetrahy-dronaphthalene HAS benzene cyclohexene cyclohexane hexane

11.86 13.50 10.72 10.44 10.84 9.27 12.86 12.36 13.00 21.46

31 678.68 38 855.36 25 669.97 28 461.53 28 511.43 37 139.23 29 717.41 27 003.14 22 956.77 41 700.53

64.69 82.73 48.78 58.82 57.68 90.97 58.04 50.43 33.78 73.93

330.65 330.65 330.65 330.65 330.65 330.65 320.65 320.65 330.65 323.15

59.70 58.68 61.41 59.41 59.92 55.25 61.49 62.54 67.27 63.58

40.30 41.32 38.59 40.59 40.08 44.75 38.51 37.46 32.73 36.42

Standard uncertainties u are u(ΔG°soln) = 0.01, u(ΔH°soln) = 0.01, and u(ΔS°soln) = 0.01. bΔG°soln, standard molar Gibbs energy of dissolution; ΔH°soln, ° , corresponding standard molar entropy; Tmean, arithmetic mean temperature for the experimental standard molar enthalpy of dissolution; ΔSsoln temperature range; ξH, calculated according to eq 10; ξTS, calculated according to eq 11. a

E

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range between 298.15 and 363.15 K under atmospheric pressure. It was found that the solubilities of sulfur S8 in all of the solvents increase with increasing temperature. The solubility data could be successfully correlated by using the van’t Hoff equation, the modified Apelblat equation, and the λh equation. The modified Apelblat equation can explain the experimental data with the best accuracy. Furthermore, the dissolution process of S8 in 10 solvents is found to be endothermic and nonspontaneous.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Hui Sun: 0000-0002-8544-756X Jigang Zhao: 0000-0002-2773-7200 Funding

Financial support from SINOPEC (project no. LQJS1109QT0005) is gratefully acknowledged. Notes

The authors declare no competing financial interest.

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REFERENCES

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DOI: 10.1021/acs.jced.7b00699 J. Chem. Eng. Data XXXX, XXX, XXX−XXX