Thermodynamic Models for Determination of the Solubility of

Article pubs.acs.org/jced

Thermodynamic Models for Determination of the Solubility of Dibenzothiophene in Different Solvents at Temperatures from (278.15 to 328.15) K Qi Zhang,† Yonghong Hu,*,† Ying Shi,‡ Yang Yang,† Limin Cheng,† Cuicui Cao,† and Wenge Yang† †

State Key Laboratory of Materials-Oriented Chemical Engineering, Nanjing Tech University, Nanjing 210009, China Taiyuan Qiaoyou Chemical Industrial Co. Ltd., Taiyuan 030025, China

‡

ABSTRACT: Data on corresponding solid−liquid equilibrium of dibenzothiophene (DBT) in different solvents are essential for a preliminary study of industrial applications. In this study, the solubility behavior of DBT in different solvents, such as methanol, ethanol, isopropyl alcohol, butan1-ol, formic acid, and acetonitrile at temperatures ranging from (278.15 to 328.15) K was investigated. An analytical stirred-flask method was employed to measure the dissolubility of DBT. For the temperature range investigated, the solubility of dibenzothiophene in the solvents increased with increasing temperature. The thermodynamic models, such as the Van ‘t Hoff model, the modified Apelblat model and the Buchowski−Ksiazaczak λh model were investigated to describe the experimental data. It was found that the modified Apelblat model was the most suitable for predicting the solubility behavior of DBT with a temperature increment. The calculated thermodynamic parameters indicated that in each studied solvent the dissolution process of DBT is endothermic.

1. INTRODUCTION At the present time, very stringent environmental regulations and the increasing demand of clean fuel bring new challenges to the development of deep desulfurization technologies.1,2 Thus, the ultradeep desulfurization methods of oil have become hot point in research. Desulfurization via extraction is a common way of deep desulfurization in oil refinery streams. The efficiency of extractive desulfurization is mainly limited by the solubility of the organic sulfur compounds in the solvent.3 DBT and its derivatives are regarded as the sulfides that are the most difficult to desulfurate. Meanwhile, realizing desulfurization in the industrial production generates the necessity to have data about the physicochemical properties of these materials. Dibenzothiophene (C12H8S, CAS RN: 132-65-0, shown in Figure 1), or DBT for short, is a colorless or white needle-like

equilibria (SLE) or phase equilibria in the development of a crystallization process, or liquid−liquid equilibria in extraction and extractive or azeotropic distillation processes.4−6 More particularly, knowledge of an accurate solubility of DBT is needed for the design of separation processes such as extractive crystallization and the safety of operating different processing units such as distillation columns, absorption units, and extraction plants. The solubility of DBT can also supply experimental data for industrial production. To determine proper solvents and to design an optimized production process, it is necessary to know the solubilities of DBT in different solvents.4−6,18 The present work is focused on the study of the solubilities of DBT in six solvents, that is, methanol, ethanol, isopropyl alcohol, butan-1-ol, formic acid, and acetonitrile in the temperature range from (278.15 to 328.15) K. The temperature range is commonly used for the water baths in industry.5 The modified Apelblat equation and the Buchowski−Ksiazaczak λh equation were used to correlate and predict the solubilities of DBT in pure solvents. Thermodynamic models of C12H8S solubility corresponding to mathematic expressions were developed and employed to correlate and predict the measured solubility data. For the thermodynamic parameters of dissolution, the standard enthalpy (ΔH0Diss), standard entropy (ΔS0Diss), and Gibbs free energy (ΔG0Diss) of solution of DBT were determined from the solubility data by the Van ‘t Hoff equation.

Figure 1. Chemical structure of dibenzothiophene.

crystal that is widely used as an important intermediate in the production of cosmetics and pharmaceuticals. DBT can be used as additives in rose-scented perfume. More important, it is also an important model compound in the study of hydrodesulfurization reaction for diesel oil. DBT is the organosulfur compound consisting of two benzene rings fused to a central thiophene ring, which can be obtained by the reaction of biphenyl with sulfur dichloride in the presence of aluminum trichloride.1,2 The solubilities of organic compounds in different solvents play an important role for understanding the solid−liquid © 2014 American Chemical Society

2. EXPERIMENTAL SECTION 2.1. Materials. Dibenzothiophene (98 wt %) was purchased from Aladdin (China). Its purity was measured by high Received: May 16, 2014 Accepted: August 5, 2014 Published: August 14, 2014 2799

dx.doi.org/10.1021/je500437m | J. Chem. Eng. Data 2014, 59, 2799−2804

Journal of Chemical & Engineering Data

Article

Table 1. Properties of Solventsa properties MW

solvents

D −1

methanol ethanol isopropyl alcohol butan-1-ol formic acid acetonitrile dibenzothiophene a

source

purity

−1

g mol

g mL

32.04 46.07 60.10 74.12 46.03 41.05 184.26

0.7915 0.7893 0.7855 0.8098 1.2200 0.786 1.252

analysis method

% Shenbo Chemicals Shenbo Chemicals Shenbo Chemicals Shenbo Chemicals Shenbo Chemicals Shenbo Chemicals Aladdin

99.7 99.9 99.7 99.8 99.5 99.5 98.0 All ≥ 98.0

HPLC HPLC HPLC HPLC HPLC HPLC HPLC

The density values are the standard values (provided by Shanghai Shenbo Chemical Co., Ltd. and Aladdin).

Table 2. Mole Fraction Solubilities, x, of DBT in Different Organic Solvents with the Temperature Range from (278.15 to 328.15) K under 0.1 MPaa 100RD

100RD T

100x

Van ‘t Hoff Modified Apelblat Buchowski−Ksiazaczak model, eq 3 model, eq 5 λh model, eq 9

T

Van ‘t Hoff Modified Apelblat Buchowski−Ksiazaczak model, eq 3 model, eq 5 λh model, eq 9

K

K 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15

0.1262 0.1628 0.1923 0.2424 0.2897 0.3310 0.4064 0.4782 0.5727 0.6685 0.7946

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15

0.3470 0.4331 0.5294 0.6185 0.7498 0.9187 1.0467 1.2713 1.4833 1.7357 2.0572

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15

0.2446 0.3473 0.4361 0.5775 0.7031 0.8739 1.1053 1.3612 1.6243 2.0196 2.4915

a

100x

Methanol 4.5959 −4.5959 6.6953 1.2899 1.5081 −1.3521 3.6716 2.9290 1.6569 2.3127 −3.9879 −2.4169 −1.3780 0.4675 −2.2585 −0.5646 −0.5588 0.4889 −0.6731 −0.6582 1.7241 0.3272 Ethanol 5.8790 −2.4207 5.4260 0.3925 4.0612 1.5489 −0.6952 −1.3743 −0.8402 −0.1600 1.0341 2.4709 −3.5158 −1.7197 −0.7315 0.8417 −1.2472 −0.2629 −0.7202 −0.7317 1.7548 0.4131 Isopropyl alcohol 1.6353 −10.2617 7.5727 0.4895 3.2332 −0.9172 5.2641 3.5671 0.4125 0.3840 −1.3159 −0.2174 −0.1448 1.4657 −0.5877 1.0285 −3.2445 −2.0809 −0.7477 −0.5595 1.7740 0.6261

−12.5198 −3.8698 −4.4722 1.7327 2.5889 −0.9970 2.4852 1.6102 2.1477 −0.2992 −1.5857

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15

0.4847 0.6206 0.7885 0.9994 1.3226 1.6027 1.9204 2.4240 3.0327 3.8105 4.5840

12.8946 8.5885 4.7812 1.9912 4.6499 −0.0562 −4.9573 −3.3911 −1.7080 1.3227 0.9010

−10.2594 −4.7333 −1.3789 −2.4899 0.2267 3.9186 0.4204 3.0127 1.3888 −0.4033 −1.5458

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15

0.0475 0.0578 0.0668 0.0756 0.0881 0.0995 0.1116 0.1264 0.1399 0.1571 0.1768

−1.4737 2.0761 1.3473 −0.6614 0.9081 0.1005 −0.8065 −0.1582 −1.2866 −0.4456 1.1312

−17.9886 −4.6070 −4.2880 1.8701 −0.0284 0.4119 2.77753 2.6153 −0.6957 −0.0990 −0.6422

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15

0.4538 0.6105 0.8453 1.2773 1.5662 1.8913 2.4128 3.2059 4.0161 5.0614 6.3857

4.8039 1.2449 2.1531 12.5891 5.1909 −2.9609 −4.4678 −0.5303 −1.4342 −0.6421 1.2591

Butan-1-ol −1.4442 −0.9990 −0.8624 −0.5203 4.4685 1.2479 −2.8223 −1.2417 −0.2011 1.6087 −0.5628 Formic acid −3.3684 1.2111 1.0479 −0.5291 1.3621 0.6030 −0.2688 0.2373 −1.0722 −0.5092 0.6787 Acetonitrile −9.8281 −8.6650 −3.6555 10.0681 4.5205 −2.2260 −2.9344 1.1011 −0.1892 −0.3141 0.2145

−4.0231 −3.2227 −2.5872 −1.6410 3.9846 1.3228 −2.2652 −0.4208 0.5836 1.9394 −1.2500 −15.5789 −5.7093 −1.7964 −0.3968 3.5187 4.2211 3.8530 3.9557 1.2866 −0.7002 −3.3937 −13.6183 −11.6790 −5.7849 8.8859 3.9395 −2.2260 −2.4494 1.8279 0.5279 0.0059 −0.3602

The relative standard uncertainty is u(x) = 2 %. The standard uncertainty u are u(T) = ± 0.05 K, u(p) = ± 2 KPa.

performance liquid chromatography (HPLC type DIONEX P680 DIONEX Technologies), and the melting point of dibenzothiophene was measured by digital melting point system

(type WRS-1B, Shanghai Precision & Scientific Instrument Co., Ltd.) at 373.15 K. This melting point falls within the range of (370.15 to 373.15) K values reported in the literatures.7−10 All of 2800



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the organic solvents were supplied by Shanghai Shenbo Chemical Co., Ltd., China. The purities of the solvents were determined in our laboratory by gas chromatography and their mass fraction purities were higher than 0.995. Meanwhile, all chemicals were used without further purification. The properties of these solvents are presented in Table 1. 2.2. Apparatus and Procedures. The solubility of DBT was investigated, in various solvents, by the analytical stirredflask method, and we used the gravimetric method to measure the compositions of the saturated solutions. Saturated solutions of DBT, which were produced by 8 mL of corresponding solvent and some excess DBT, were prepared in a spherical, 10 mL Pyrex glass flask. The flask was maintained in a jacket glass vessel full of water at the desired temperature through circulating water, whose temperature was controlled by a thermostat with an accuracy of ± 0.1 K that was supplied from a constant-temperature water bath (type HWC-52, ShangHai Cany Precision Instrument Co., Ltd.). And the actual temperature was measured by a thermometer (uncertainty of ± 0.05 K) inside the vessel. For each measurement, some excess DBT were added to a known volume of solvent. Continuous stirring was achieved for fully mixing the suspension using a magnetic stirrer at the required temperature. The stirring continued for about 12 h to ensure the solid−liquid equilibrium and the solution was allowed to settle for 3 h or more before sampling to achieve a static state.11−13 The supernatant was taken, filtered (vacuum filtration, pore size of filter membrane is 0.22 μm), and poured into a volumetric flask preweighed by using an analytical balance (Sartorius, BS210s, Germany) with a resolution of ± 0.1 mg. Then 1 mL of solution supernatant was transferred into a 5 mL beaker with a cover and weighted immediatedly. This beaker had been weighted before. All beakers were put into a dryer at room temperature and weighed weekly until reaching constant weight. All determinations were repeated three times to check reproducibility, and then an average value was given. The solubility of DBT represented in terms of mole fraction (x) in the corresponding solvent was obtained from eq 1 x=

m1/M1 m + M2

m1 M1

2

Figure 2. Lower mole fraction solubility (x) of DBT versus temperature T in the selected organic solvents: ■, isopropyl alcohol; ●, ethanol; ▲, methanol; ★, formic acid.

Figure 3. Higher mole fraction solubility (x) of DBT versus temperature T in the selected organic solvents: □, acetonitrile; ○, butan-1-ol.

(1)

where m1 and m2 denote the mass of DBT and solvents, and M1 and M2 are the molecular weights of these components.

order: acetonitrile > butan-1-ol > isopropyl alcohol > ethanol > methanol > formic acid. Meanwhile, we could find that DBT had high solubility in acetonitrile. Butan-1-ol and isopropyl alcohol showed the strongest positive dependency on temperature. The solubility of DBT depends not only on the temperature but also on the structure of the solvent. Polarity follows the order: formic acid > methanol > acetonitrile > ethanol = isopropyl alcohol > butan-1-ol. As is seen from Figure 2, the solubility of DBT increases with decreasing polarity of the solvent. 3.2. Thermodynamic Models. The correlation between temperature and solubility of DBT in different solvents can be explained by thermodynamic models. The Van ‘t Hoff model presented in eq 2 was normally used to predict the relation of solubility vs reciprocal temperature (1/T) in solid−liquid equilibrium B ln x = A + (2) T where x is the mole fraction solubility of DBT, T is the corresponding temperature in Kelvin, and A and B are constants and are listed in Table 3.

3. RESULTS AND DISCUSSION 3.1. Solubility Data. The measured mole fraction solubilities of DBT in methanol, ethanol, isopropyl alcohol, butan-1-ol, formic acid, and acetonitrile in the temperature range of (278.15 to 328.15) K are presented in Table 2 and graphically shown in Figures 2 and 3. The solubility data are ́ similar to those reported by Ramirez-Verduzco et al.7 The mole fraction solubility of DBT in acetonitrile at 303.7 K is 0.0189, which compares well with the reported value of 0.0199, whereas at 323.1 K, the mole fraction solubility of 0.0506 compares well with the reported value of 0.0522.7 As can be seen from Figures 2 and 3, it could be found that solubility is a function of temperature, where it increased with increasing temperature. At 278.15 K, the mole fraction solubility in these solvents changes from high to low in the order: butan-1-ol > acetonitrile > ethanol > isopropyl alcohol > methanol > formic acid. However, at 307.15 K, the solubility in isopropyl alcohol is higher than in ethanol, and when the temperature is increased to 328.15K, the solubility changes from high to low in the 2801



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Table 3. Parameters of the Van ‘t Hoff model for DBT Solubility in the Different Organic Solvents at Temperature Range from (278.15 to 328.15) K B

102 RAD

104 RMSD

0 1 2

(−5.14 ± 0.19) × 105 (−4.87 ± 0.08) × 105 (−6.37 ± 0.22) × 105

2.610 2.355 2.357

0.855 2.094 2.522

3 −3 4

(−6.53 ± 0.28) × 105 (−3.54 ± 0.08) × 105 (−7.37. ± 0.30) × 105

4.113 0.945 3.389 ∑(102 RAD) = 15.769

5.649 0.105 7.337

solvents

A

methanol ethanol isopropyl alcohol butan-1-ol formic acid acetonitrile

Table 4. Parameters of the Modified Apelblat Model for DBT in the Different Organic Solvents at Temperature Range from (278.15 to 328.15) K


−924.926 −1127.43 −2086.75

−74.104 21.45 −35.04

−332.908 −3257.39 −2563.24


C 7.775 6.86 6.5 12.435 −3.08 6.92 ∑(102 RAD) = 11.084

102 RAD

104 RMSD

1.582 1.122 1.963

0.476 1.135 1.667

1.453 0.990 3.974

3.352 0.095 5.707

λ

h

102 RAD

104 RMSD

0 0.03 0.07

206887.9 80139.44 52336.1

3.119 2.707 3.275

0.9169 2.383 2.189

0.14 0 0.27

26608.61 1237279 16167.83

2.113 4.037 4.664 ∑(102 RAD) = 19.915

3.783 0.403 5.851

mean square deviation (RMSD) along with the R2 as expressed by eqs 7−9 are shown in Tables 3−518−20 x − xci RD = i xi (7)

b (4) T where a and b are empirical constants. Introducing γx from eq 4 into eq 3 and subsequent rearrangement results in eq 5 can be written as15 ln γx = a +

RAD =

⎡Δ H ⎤ ΔCp ln x = ⎢ fus − (1 + ln Tt) − a⎥ R ⎣ RTt ⎦

1 N

N

xi − xci xi

∑ i=1

⎡1 RMSD = ⎢ ⎢⎣ N

N

(8)

∑ (xci − xi) i=1

⎤1/2

2⎥

⎥⎦

(9)

The Buchowski−Ksiazaczak λh model eq 10, which was suggested by Buchowski et al.,21 is another way to describe the solution behavior. The Buchowski−Ksiazaczak λh model could fit the experimental data well for many systems with only two parameters λ and h. In this paper, the solubility data were also correlated with the Buchowski−Ksiazaczak λh model

(5)

Because the coefficients are constants, the solubility in the above equation may be written as the modified Apelblat model, which was first used by Apelblat and Manzurola.16,17 The model (we used Statistica 6.0 to fit the data) can give a relatively more accurate correlation with another parameter ⎛T ⎞ B + C ln⎜ ⎟ ⎝K⎠ T /K

−47.066 −40.2 −34.98

solvent

⎛ 1 ⎞ Δ H ⎛T ⎞ ΔCp ⎛ Tt ⎞ ⎜ − 1⎟ ln⎜⎜ ⎟⎟ = fus ⎜ t − 1⎟ − ⎝ ⎠ ⎝ ⎠ RTt T R T ⎝ γxx ⎠ ΔCp Tt + ln (3) R T Where γxis the activity coefficient of DBT on a mole fraction basis, x is the mole fraction solubility of DBT, ΔfusH is the enthalpy of fusion of DBT,10 ΔCp is the change of the heat capacity, T is the absolute temperature (K), Tt is the triplepoint temperature of DBT, R is the gas constant. For regular solutions, the activity coefficient is obtain by

ln x = A +

B

Table 5. Parameters of the λh Model for DBT in the Different Organic Solvents

To describe solid−liquid equilibrium, the temperature dependence of the solubilities of DBT in different solvents at different temperatures can be described as14

⎡ ⎛Δ H ΔCp ⎞ ⎤ 1 ΔCp − ⎢b + ⎜ fus − ln T ⎟Tt ⎥ + ⎢⎣ R ⎠ ⎥⎦ T R ⎝ RTt

A

solvent

⎡ 1 ⎡ λ(1 − x) ⎤ 1 ⎤ ln⎢1 + − ⎥ ⎥ = λh⎢ ⎣ ⎦ (Tm/K ) ⎦ x ⎣ (T / K )

(6)

(10)

where x is the mole fraction solubility of DBT and T and Tm are the experimental temperature and the standard melting temperature of DBT in Kelvin, respectively. The λ and h are the model parameters determined by the experimental data in the system together with the corresponding RMSD which are listed in Table 5, respectively. According to the above-mentioned correlations of experimental data obtained at different temperatures in various solvents together with the calculated data (Tables 2−5), it was indicated that the solubility of DBT calculated from the studied models showed good agreement. Taking the solubility data in the selected solvents fitted by the modified Apelblat model as

where T is the absolute temperature and the A, B, and C are parameters obtained by fitting the experimental solubility data and are shown in Table 4. The values of B and C reflect the variation in the solution activity coefficient and provide an indication of the effect of solution nonidealities on the solute. The correlations of experimental data and data calculated using the thermodynamic models obtained from the relative deviation (RD) expressed by eq 3 are listed in Table 2. The parameters of models obtained from linear and nonlinear regressions and their values are listed in Tables 3−5. The relative average deviation (RAD) and the corresponding root2802



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Where the intercept is obtained in plots of ln x as a function of 1/T. The standard molar entropy of dissolution (ΔS0Diss) can be obtained according to the literature24

an illustration, the relative average deviations are 1.582 %, 1.122 %, 1.963 %, 1.453 %, 0.990 %, and 3.974 %, respectively; most of the absolute values of relative deviations among all of the values do not exceed 3.00 %, which indicate that the modified Apelblat equation is suitable for correlating the solubility data of DBT in the selected pure solvents. The same conclusion can be drawn after analyzing the solubility data and the parameters that fitted by the Van ‘t Hoff equation and the λh equation. However, we can see that the 102 RAD values of Van ‘t Hoff equation, the modified Apelblat equation and the Buchowski−Ksiazaczak λh equation are 15.769, 11.084, and 19.915. This result indicates that the modified Apelblat model proved to be more accurate and suitable for the description of dissolution of DBT in the studied solvents at various temperatures. 3.3. Thermodynamic Parameters. Thermodynamic parameters of DBT solute relating to the mole fraction of solubility at the corresponding temperatures were estimated. In previous studies, the Van ‘t Hoff equation expressing the logarithm of the mole fraction of a solute vs reciprocal temperature (1/T) was employed to evaluate the values defined in eq 11. The standard molar enthalpy of dissolution (ΔH0Diss) can be obtained from the slope of this equation in the so-called Van ‘t Hoff plot22 ⎛ ∂ln x ⎞ 0 ΔHDiss = −R·⎜ ⎟ ⎝ ∂(1/T ) ⎠

0 ΔSDiss =

(13)

The standard thermodynamic parameters calculated by eqs 11−13 are listed in Table 6. The data shows that the Table 6. Thermodynamic Parameters of Dissolution of DBT in the Different Organic Solvents at the Mean Temperature ΔH0Diss

solvents

ΔS0Diss

ΔG0Diss

kJ mol−1 J mol‑1 K−1 methanol ethanol isopropyl alcohol butan-1-ol formic acid acetonitrile

27.400 26.697 34.254 34.097 19.449 39.619

133.563 137.001 186.628 190.614 70.747 228.585

%ξH

%ξTS

40.360 39.129 37.712 37.110 47.557 36.376

59.640 60.871 62.288 62.890 52.443 63.624

kJ mol−1 −13.089 −14.835 −22.322 −23.687 −1.998 −29.676

standard molar enthalpy of dissolution in the studied solvents is positive. Thus, the dissolution process of DBT in each solvent is endothermic. The high values of the standard molar enthalpy show that more energy is required for overcoming the cohesive forces of the solute and the solvent in the dissolution process. In addition, it also implies that the solubility strongly depends on the temperature. The positive standard molar entropy of dissolution means that in each solvent the entropy is the driving force of the dissolution process. The study of the ξH and ξTS is aimed at the comparing of the relative contribution to the standard Gibbs energy by enthalpy and entropy in the solution process,24,25 respectively

(11) −1

0 0 ΔHDiss − ΔG Diss Tmean

−1

where R represents the gas constant (8.314 J mol K ), x is the mole fraction of DBT at system temperature, and T is the corresponding absolute temperature of solution (K). ΔH0Diss can be obtained from the slope of the solubility curve where ln x is plotted versus 1/T. Figure 4 shows the linear ln x/(1/T) curves of DBT in the selected solvents.

%ξTS =

%ξH =

0 |T ΔSDiss | 0 |ΔHDiss |

0 + |T ΔSDiss |

0 |ΔHDiss | 0 |ΔHDiss |

0 + |T ΔSDiss |

× 100 (14)

× 100 (15)

The values of %ξH and %ξTS are shown in Table 6. The results demonstrate that the main contributor to the standard Gibbs energy of dissolution is the entropy because the value of %ξTS are ≥ 52.443 %.

4. CONCLUSIONS The solubility data of dibenzothiophene in a total of six pure organic solvents within the temperature range (278.15 to 328.15) K were measured. Ultimately, the paper gets the following conclusions: (1) The solubility of DBT in the selected solvents increased with increasing temperature, but the increments with temperature varied for different solvents. (2) The solubility phenomena of DBT were evaluated using the thermodynamic models. The data calculated from the modified Apelblat model was in good agreement with the experiment. This model was the most suitable for the description of the dissolution of DBT. (3) The thermodynamic parameters of dissolution were estimated using Van ‘t Hoff equation. The positive standard molar enthalpy indicated that the dissolution process of DBT was endothermic.

Figure 4. A Van ‘t Hoff plot of the mole fraction solubility (ln x) of DBT in the selected organic solvents against 1/T with a straight line to correlate the data: ■, acetonitrile; ●, butan-1-ol; ▲, isopropyl alcohol; ★, ethanol; □, methanol; ○, formic acid.

In the present work, only the fraction of solubility of DBT in the studied solvents at corresponding temperatures was measured. Thus, the standard molar Gibbs energy (ΔG0Diss) can be calculated from eq 12 without activity coefficients as an apparent value23 0 ΔG Diss = −RTmean·intercept

(12) 2803



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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +86 25 5813 9208. Fax: +86 25 5813 9208. Notes

The authors declare no competing financial interest. Funding

This research work was financially supported by Key topics for State Key Laboratory of Materials-Oriented Chemical Engineering (ZK201304), the university scientific research industry promotion project (JHB2011-16), the science and technology support programpart of agriculture (BE2013442) and the Joint innovation and research funding-prospective joint research projects (SBY201320243).

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ACKNOWLEDGMENTS We thank the editors and the anonymous reviewers. REFERENCES

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