Solubility and Mixing Thermodynamics Properties of p

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Solubility and Mixing Thermodynamics Properties of p‑Toluenesulfonamide and o‑Toluenesulfonamide in Seven Monosolvents at Different Temperatures Yüfang Wu,* Xiaolu Zhang, Yanchao Di, Yu Kang, and Li Bai Department of Biological Sciences, XinZhou Teachers University, Xinzhou, Shanxi 034000, P. R. China ABSTRACT: The solubility of p-toluenesulfonamide and o-toluenesulfonamide in seven monosolvents of methanol, ethanol, n-propanol, isopropanol, n-butanol, acetonitrile, and ethyl acetate were measured by using the isothermal saturation method at temperatures ranging from 283.15 to 318.15 K under 101.3 kPa. The mole fraction solubility of p-toluenesulfonamide and o-toluenesulfonamide in those selected monosolvents increased with the increase in temperature. The maximum mole fraction solubility of o-toluenesulfonamide was observed in ethyl acetate (0.07748 at 318.15 K), followed by that in acetonitrile (0.07368 at 318.15K), methanol (0.05790 at 318.15 K), ethanol (0.04564 at 318.15 K), n-propanol (0.04271 at 318.15 K), isopropanol (0.04142 at 318.15 K), and n-butanol (0.03879 at 318.15 K). For p-toluenesulfonamide + solvents systems, the maximum mole fraction solubility was observed in acetonitrile (0.1588 at 318.15 K), followed by that in ethyl acetate (0.1329 at 318.15K), methanol (0.1043 at 318.15 K), ethanol (0.09142 at 318.15 K), n-propanol (0.06888 at 318.15 K), isopropanol (0.05092 at 318.15 K) and n-butanol (0.05645 at 318.15 K). The measured solubility data were correlated and calculated by using the modified Apelblat equation, Buchowski− Ksiazaczak λh equation, Wilson model, and NRTL model. The largest values of relative average deviations (RAD) and the rootmean-square deviations (RMSD) between the experimental and calculated solubility were 0.87 × 10−2 and 8.46 × 10−4, respectively. On the basis of the obtained solubility, the standard enthalpy of solution (ΔHosol), the standard Gibbs energy (ΔGosol) of solution, and the standard entropy of solution (ΔSosol) of p-toluenesulfonamide and o-toluenesulfonamide dissolved in monosolvents were calculated. The results show that the dissolution of p-toluenesulfonamide and o-toluenesulfonamide in these monosolvents is a spontaneous process. The correlation and curve fitting results indicated good correlation of the experimental solubility data of p-toluenesulfonamide and o-toluenesulfonamide with the modified Apelblat model. Therefore, the experimental solubility and correlation equations established in this study can be useful in the crystallization, purification in laboratories, and related industries.

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INTRODUCTION Sulfonamides constitute an important class of drugs, with several types of pharmacological agents possessing antibacterial, anticarbonic anhydrase, diuretic, hypoglycemic, and antithyroid activity among others. They are employed to synthesize β-secretase inhibitors for Alzheimer’s disease,1 dipeptidyl peptidase IV inhibitors for diabetes,2 insulin-like growth factor receptor (IGF-IR), inhibitors for cancer,3 HCV-NS5B polymerase inhibitors for acute hepatitis and chronic liver disease,4 and antibacterial agents.5 p-Toluenesulfonamide (CAS Registry No. 70-55-3) and o-toluenesulfonamide (CAS Registry No. 88-19-7) are all key precursors for the preparation of pharmaceutical products (such as Chlorsulfuron, Thiamphenicol, and Chloramphenicol).6 They are usually considered the important raw that synthesize artificial fibers, and coloring and plastic additives.7 Because of their significance, a number of advancements in these two compounds synthesis have been developed. The old industrial processes known for producing o-toluenesulfonamide include chlorosulfonation of toluene and chlorosulfonic acid at low temperature, and then hydrolysis, freeze crystallization, filtration, ammoniation, alkali solution, acid precipitation, oxidation decolorization, refining purification. However, the reaction has © XXXX American Chemical Society

an isomerization equilibrium with an isomer (p-toluenesulfonamide) produced as a byproduct. The purity of o-toluenesulfonamide obtained by changing the temperature in the alkaline solution is only 90%, and further purification is required for its use. The cumbersome operation makes the method face out. In order to more efficiently and quickly separate and purify byproducts, we try to use green solvents on the basis of the old process to separate. In previous publication, Li and co-workers reported the solubility of p-toluenesulfonamide and sulfanilamide in pure and modified supercritical carbon dioxide.8,9 With the purpose of acquiring high purity o-toluenesulfonamide and p-toluenesulfonamide, it remains a challenge to get the pure o-toluenesulfonamide and p-toluenesulfonamide in monosolvents. In order to provide the comprehensive basic data for engineering application and more systematic and useful thermodynamic information on the crystallization and separation of o-toluenesulfonamide and p-toluenesulfonamide from some mixed systems. The aims of Received: August 7, 2017 Accepted: October 12, 2017

A

DOI: 10.1021/acs.jced.7b00714 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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liquid phase, respectively. Generally, the term containing ΔCp in eq 3 is less important than the first term on the right side,16 therefore it can be neglected. For a solid−liquid equilibrium, a little change of pressure does not affect critically on equilibrium unless the pressure change is very large (10−100 MPa).16 Generally, it is very difficult to acquire the triple point temperature Ttp and corresponding enthalpy ΔHtp for many substances. However, the triple point temperature Ttp is almost equal to the melting temperature Tm. Substituting the Ttp and ΔHtp with Tm and melting enthalpy ΔfusH, respectively, eq 4 can be derived.

this work are to (1) determine the solubility of o-toluenesulfonamide and p-toluenesulfonamide in seven monosolvents studied systematically by using the isothermal saturation method at the temperature range of 283.15 to 318.15 K; (2) correlate solubility data by modified Apelblat equation, Buchowski− Ksiazaczak λh equation, Wilson model, and NRTL model; and (3) evaluate the mixing properties for the solution process of o-toluenesulfonamide and p-toluenesulfonamide in those monosolvents. In a word, the solubility data of o-toluenesulfonamide and p-toluenesulfonamide obtained would be very useful in crystallization and separation development of o-toluenesulfonamide and p-toluenesulfonamide.

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SOLUBILITY MODELING In order to find suitable model to describe the solubility behavior of o-toluenesulfonamide and p-toluenesulfonamide in the studied solvents, in this work, four models are used to correlate the solubility data, which correspond to the modified Apelblat equation,10,11 λh equation,12 Wilson model,13 and NRTL model.14 The modified Apelblat equation10,11 expressed in eq 1 is a semiempirical model with three parameters. It has been widely used in describing the solubility of solute in monosolvents for binary solid−liquid phase equilibrium. ln x = A + B /(T /K) + C ln(T /K)

⎤ ⎡ Λ 21 Λ12 ln γ1 = −ln(x1 + Λ12x 2) + x 2⎢ − ⎥ x 2 + Λ 21x1 ⎦ ⎣ x1 + Λ12x 2 (5)

(1)

⎛ λ ij − λjj ⎞ Vj ⎛ Δλ ij ⎞ exp⎜ − ⎟ = exp⎜ − ⎟ Vi ⎝ R(T /K) ⎠ Vi ⎝ R(T /K) ⎠ Vj

Λ ij =

(6)

Here Vi refers to the molar volume, which is obtained via molar mass divided by density of component i. Δλij refers to the adjustable interaction energy parameter (J·mol−1) between the components i and j. The NRTL model is proposed on the basis of the local composition concept.14 It is widely employed in correlating and calculating the fluid phase equilibrium. The NRTL model is described as eqs 7−10 for a component i. N

ln γi =

∑j = 1 τjiGjixj N

∑i = 1 Gijx i

N

+

∑ j=1

N ⎡ ∑ xτG ⎤ ⎢τ − i = 1 i ij ij ⎥ ij N N ∑i = 1 Gijx i ⎢⎣ ∑i = 1 Gijx i ⎥⎦

xjGij

(7)

(2)

Where λ and h are equation parameters; and Tm is the melting temperature of o-toluenesulfonamide or p-toluenesulfonamide in Kelvin under standard pressure. The λ value is regarded as the association number of solute molecules in a binary system, which provides an indication of nonideality for the solution; and h is in relation to excess enthalpy of solution. In terms of the traditional theory of solid−liquid phase equilibrium, as a solid−liquid system reaches equilibrium at a certain temperature and pressure, the solubility of a solute in solvents at different temperatures can be described as eq 3.15 ln(x i·γi) =

(4)

With the intention of correlating the solubility data of o-toluenesulfonamide or p-toluenesulfonamide with Wilson and NRTL models, the activity coefficient should be known in advance. For a binary solid−liquid equilibrium system, the activity coefficient of a solute expressed by the Wilson equation is given as follows.13

In eq 1, x is the mole fraction solubility of o-toluenesulfonamide or p-toluenesulfonamide in seven organic solvents; A, B, and C are adjustable parameters in modified Apelblat equation. The parameters A and B indicate the influence of solution nonideality upon the solute solubility and the variation of solute activity coefficient, respectively. The value of parameter C reflects the influence of temperature upon the fusion enthalpy of a solute. The λh equation is another equation to describe the solid− liquid equilibrium behavior of o-toluenesulfonamide or p-toluenesulfonamide in solvents. It is first proposed by Buchowski and co-workers to study the solvent activity along a saturation line and solubility of hydrogen-bonding solids.12 The equation has an excellent effect on correlating the solubility of a solid solute in solvent. The λh equation is expressed as eq 2. ⎛ 1 ⎡ λ(1 − x) ⎤ 1 ⎞ − ln⎢1 + ⎟ ⎥ = λh⎜ ⎣ ⎦ x Tm/K ⎠ ⎝ T /K

ΔfusH ⎛ 1 1 ⎞ − ⎟ ⎜ R ⎝ Tm/K T /K ⎠

ln(x i·γi) =

Gji = exp( −αjiτji)

(8)

αij = αji = α

(9)

τij =

g ij − g jj RT

=

Δg ij R(T /K)

(10)

Δgij are adjustable model parameters which relate to energy interaction (J·mol−1). α is the parameter relating to the nonrandomness of a solution, which value usually varies in the range from 0.2 to 0.47. Supposing that the cross-interaction parameters in the Wilson and NRTL models have a linear relationship with temperature,17,18 τij in NRTL model and Λij in Wilson model can be described as eqs 11 and 12.

⎞ ΔHtp ⎛ 1 Ttp 1 ⎞ ΔCp ⎛ Ttp ⎜⎜ − ⎟⎟ − − + 1⎟ ⎜ln R ⎝ Ttp T⎠ R ⎝ T T ⎠ ΔV − (p − ptp ) (3) RT

τij = a ij +

Where R is the universal gas constant having a value of 8.314 J·K−1·mol−1. ΔCp and ΔV denote the difference of heat capacity and volume of solute between in solid phase and in

Λ ij = B

bij T/K

⎡ ⎛ bij ⎞⎤ exp⎢ −⎜a ij + ⎟⎥ ⎢⎣ ⎝ T /K ⎠⎥⎦ Vi

(11)

Vj

(12) DOI: 10.1021/acs.jced.7b00714 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 1. Detailed Information on the Materials Used in the Work chemicals

molar mass g·mol−1

p-toluenesulfonamide o-toluenesulfonamide methanol ethanol n-propanol isopropanol acetonitrile ethyl acetate n-butanol

171.22 171.22 32.04 46.07 60.10 60.10 41.05 88.11 74.12

a

melting point K

melting enthalpy kJ·mol−1

410.42a 482.62a

23.93a 28.26a

source Aladdin Chemical Co. Ltd. (China)

Sinopharm Chemical Reagent Co., Ltd.,China

mass fraction purity 0.994 0.995 0.996 0.998 0.999 0.998 0.996 0.998

analytical method HPLCb GCc GC GC GC GC GC GC

Taken from ref 7. bHigh-performance liquid phase chromatograph. cGas chromatography.

Solubility Measurement. In this work, the solid−liquid equilibrium for the binary systems of o-toluenesulfonamide and p-toluenesulfonamide + solvent were obtained by using the isothermal saturation method in the temperatures ranging from 283.15 to 318.15 K under 101.3 kPa, and the high-performance liquid phase chromatograph was employed to determine the solubility of o-toluenesulfonamide and p-toluenesulfonamide in seven monosolvents. The reliability of experimental apparatus was verified by determining the solubility of benzoic acid in toluene.19 Some excess o-toluenesulfonamide or p-toluenesulfonamide and about 50 mL monosolvent and were added into the 100 mL glass vessel. Magnetic stirrer was employed to mix the solution sufficiently. The temperature was kept at the desired value by circulating water system and the value was shown by a mercury glass micro thermometer (standard uncertainty: 0.02 K) inserted in the inner chamber of the glass vessel. The liquid phase was taken out and tested by HPLC every 2 h using a 2 mL syringe connected with a 0.2 μm pore filter. The solution was assumed to be in equilibrium once the composition of liquid phase became constant. Once the system arrived at equilibrium, the magnetic stirrer was stopped and the solution was permitted to settle for 1 h before sampling. The upper portion was taken out with a 5 mL of preheated syringe connected with a filter (PTFE 0.2 μm), and transferred into a volumetric flask of 25 mL preweighed with the balance with a standard uncertainty of 0.0001 g. The volumetric flask with sample was covered quickly with a rubber stopper. The total amount of the solution and flask was weighed again by using the balance. Then the sample was diluted to 25 mL with methanol, and analyzed with a highperformance liquid chromatography. All the experiments were carried out three times, and the average value was employed to calculate the mole fraction solubility. The atmosphere pressure was about 101.2 kPa during our experiment. The mole fraction solubility (x) of o-toluenesulfonamide and p-toluenesulfonamide in monosolvents was calculated with eq 13.

Where aij and bij designate the parameters used in correlating the solubility data with the Wilson and NRTL models, respectively. The two parameters are independent of temperature and composition.

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EXPERIMENTAL SECTION Materials. o-Toluenesulfonamide and p-toluenesulfonamide were provided by Aladdin Chemical Co., Ltd., with the mass fraction of 0.995 and 0.994, respectively, which were determined by high-performance liquid phase chromatograph (HPLC). The selected solvents (methanol, ethanol, n-propanol, isopropanol, n-butanol, ethyl acetate, and acetonitrile) were all purchased from Sinopharm Chemical Reagent Co., Ltd., China. The purities of these solvents with analytical grade were all no less than 0.994 in mass fraction, which were determined by gas chromatography (GC). The detailed information on these experimental materials was collected and presented in Table 1. Apparatus. The experimental apparatus is shown graphically in Figure 1. It included a 100 mL jacketed glass vessel with

Figure 1. Schematic diagram of experimental apparatus: (I) smart thermostatic water bath; (II) mercury-in-glass thermometer; (III) magnetic stirrer; (IV) stirrer controller; (V) jacketed glass vessel; (VI) sampling port; (VII) condenser.

x=

m1/M1 m1/M1 + m2 /M 2

(13)

Where m1 and m2 are the mass of o-toluenesulfonamide and p-toluenesulfonamide and corresponding solvent, respectively, and M1 and M2, the molar mass of o-toluenesulfonamide and p-toluenesulfonamide and the solvent. Analysis Method. The analysis method was the same in previous work. The concentration of o-toluenesulfonamide and p-toluenesulfonamide in seven monosolvents was analyzed by Agilent-1260 high-performance liquid-phase chromatograph

circulating water system and magnetic stirrer. The system temperature was controlled by the circulating water. A condenser was connected with the jacketed glass vessel to prevent the solvent from escaping. A mercury thermometer with a standard uncertainty of 0.02 K inserted in the vessel was used to display the true temperature of solutions. The mass of the solute, solvent, and saturated solution were determined by using an analytical balance. C

DOI: 10.1021/acs.jced.7b00714 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 2. Experimental Mole Fraction Solubility (x) of p-Toluenesulfonamide in Different Solvents at the Temperature Range T = 283.15 to 318.15 K under 101.1 kPaa modified Apelblat equation

λh equation

xexptl

xcalcd

100RD

xcalcd

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 100RAD

0.04408 0.05047 0.05692 0.06476 0.07298 0.08265 0.09318 0.1043

0.04412 0.05026 0.0571 0.06472 0.07318 0.08257 0.09296 0.1044 0.21

−0.10 0.42 −0.32 0.06 −0.28 0.10 0.24 −0.13

0.0441 0.05027 0.05713 0.06474 0.07319 0.08255 0.09293 0.1044 0.20

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 100RAD

0.03438 0.03918 0.04482 0.05239 0.06082 0.07013 0.08007 0.09142

0.03387 0.03931 0.04551 0.05258 0.0606 0.0697 0.0800 0.09163 0.63

1.50 −0.32 −1.54 −0.36 0.36 0.61 0.09 −0.23

0.03373 0.03931 0.04563 0.05275 0.06077 0.06979 0.07991 0.09125 0.71

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 100RAD

0.02717 0.03129 0.03581 0.04155 0.04696 0.05418 0.06113 0.06888

0.02703 0.03129 0.03607 0.04139 0.04730 0.05384 0.06106 0.06900 0.41

0.51 −0.01 −0.71 0.39 −0.72 0.63 0.12 −0.17

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 100RAD

0.02025 0.02318 0.02671 0.03060 0.03470 0.03919 0.04449 0.05092

0.02033 0.02328 0.02661 0.03037 0.03461 0.03938 0.04473 0.05073 0.44

−0.37 −0.42 0.37 0.74 0.26 −0.48 −0.54 0.36

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 100RAD

0.02421 0.02800 0.03163 0.0358 0.0403 0.04517 0.05011 0.05645

0.02440 0.02783 0.03160 0.03573 0.04024 0.04515 0.05048 0.05624 0.37

−0.8 0.6 0.09 0.19 0.14 0.04 −0.73 0.38

283.15 288.15 293.15 298.15 303.15 308.15 313.15

0.07796 0.08484 0.09552 0.1060 0.1180 0.1301 0.1433

0.07724 0.08594 0.0955 0.1060 0.1175 0.1300 0.1437

0.92 −1.3 0.02 0.02 0.47 0.08 −0.29

T/K

100RD methanol −0.04 0.40 −0.37 0.02 −0.29 0.12 0.27 −0.12

Wilson model

NRTL model

xcalcd

100RD

xcalcd

100RD

0.04392 0.05025 0.05724 0.06495 0.07341 0.08269 0.09285 0.10394 0.38

0.37 0.44 −0.57 −0.29 −0.60 −0.05 0.36 0.35

0.04418 0.05025 0.05705 0.06464 0.07313 0.08261 0.09318 0.1043 0.17

−0.23 0.43 −0.22 0.18 −0.21 0.05 −7.93e-5 4.8e-8

0.03367 0.03933 0.04572 0.05289 0.06091 0.06985 0.07979 0.09082 0.87

2.07 −0.39 −2.00 −0.95 −0.14 0.4 0.35 0.65

0.03382 0.03936 0.04563 0.05272 0.06071 0.06971 0.07983 0.09122 0.73

1.62 −0.46 −1.81 −0.63 0.18 0.60 0.30 0.21

0.02708 0.03132 0.03606 0.04136 0.04725 0.05379 0.06104 0.06907 0.42

0.34 −0.09 −0.71 0.46 −0.61 0.72 0.15 −0.27

0.02712 0.0313 0.036 0.0413 0.04724 0.05389 0.06123 0.06887 0.33

0.18 −0.02 −0.54 0.61 −0.6 0.53 −0.17 0.02

0.02019 0.02326 0.02668 0.0305 0.03475 0.03946 0.04468 0.05048 0.40

0.32 −0.33 0.09 0.32 −0.14 −0.69 −0.44 0.87

0.02033 0.02325 0.02657 0.03033 0.03459 0.03938 0.04479 0.05087 0.46

−0.39 −0.32 0.51 0.87 0.33 −0.49 −0.67 0.10

0.02446 0.02783 0.03154 0.03564 0.04014 0.04509 0.05052 0.05649 0.48

−1.03 0.61 0.27 0.45 0.39 0.18 −0.82 −0.07

0.02424 0.02789 0.03175 0.03585 0.04024 0.04501 0.05032 0.05638 0.26

−0.12 0.41 −0.37 −0.13 0.15 0.35 −0.42 0.12

0.07672 0.08591 0.09584 0.1065 0.1180 0.1303 0.1435

1.59 −1.27 −0.33 −0.49 2.53e-3 −0.16 −0.12

0.07725 0.08600 0.09554 0.1060 0.1174 0.1299 0.1437

0.91 −1.37 −0.02 0.03 0.53 0.17 −0.24

ethanol 1.88 −0.34 −1.80 −0.69 0.08 0.49 0.20 0.18

n-propanol 0.02718 −0.04 0.03133 −0.14 0.036 −0.53 0.04124 0.75 0.04711 −0.33 0.0537 0.89 0.06108 0.08 0.06936 −0.7 0.43 isopropanol 0.02027 −0.09 0.02327 −0.37 0.02663 0.29 0.03041 0.63 0.03464 0.17 0.03939 −0.51 0.04472 −0.52 0.05071 0.4 0.37 n-butanol 0.02458 −1.53 0.02785 0.54 0.03148 0.48 0.03551 0.8 0.04000 0.74 0.04500 0.38 0.05057 −0.91 0.05678 −0.59 0.75 acetonitrile 0.07706 1.15 0.08593 −1.29 0.0956 −0.08 0.1061 −0.12 0.1176 0.35 0.1301 0.02 0.1437 −0.25 D

DOI: 10.1021/acs.jced.7b00714 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 2. continued λh equation

modified Apelblat equation T/K

a

x

exptl

calcd

x

100RD

318.15 100RAD

0.1588

0.1587 0.40

0.07

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 100RAD

0.07279 0.07862 0.08586 0.09462 0.1042 0.1141 0.1235 0.1329

0.07184 0.07909 0.08684 0.0951 0.1039 0.113 0.1231 0.1335 0.68

1.30 −0.6 −1.14 −0.5 0.31 0.78 0.33 −0.48

calcd

x

Wilson model x

100RD

0.1585 0.44

0.22

ethyl acetate 0.0723 0.68 0.07917 −0.70 0.08661 −0.87 0.09466 −0.05 0.1034 0.77 0.1129 1.06 0.1232 0.24 0.1345 −1.17 0.69

calcd

100RD

NRTL model calcd

x

100RD

0.1576 0.59

0.77

0.1588 0.41

−0.02

0.07191 0.07915 0.08687 0.09508 0.1038 0.1131 0.1230 0.1336 0.71

1.20 −0.68 −1.17 −0.48 0.37 0.86 0.39 −0.5

0.07224 0.07915 0.08665 0.09477 0.1035 0.1130 0.1232 0.1341 0.66

0.75 −0.68 −0.92 −0.16 0.63 0.97 0.28 −0.89

Standard uncertainties u are u(T) = 0.02 K, u(P) = 400 Pa; Relative standard uncertainty ur is ur(x) = 0.024.

These H-bonds with the solvent molecules have a direct effect on the solubility behavior. However, it is failure to explain the phenomenon shown in Figure 2 that the solubility in ethyl acetate and acetonitrile is larger than those in alcohols. The case may be due to a lot of factors, e.g., the rule of “like dissolves like”, hydrogen bond, and van der Waals force so on. The major reason is still unclear and needs further study. Solubility Correlation and Calculation. The solubility of o-toluenesulfonamide and p-toluenesulfonamide in these solvents is correlated with the eqs 1−12 by using the nonliner regression method.21 The objective function is described as eq 14 for Wilson and NRTL models.

(HPLC). It was equipped with a reverse phase column with a type of LP-C18 (250 mm × 4.6 mm). The temperature of reverse phase column was 303.15 K. The wavelength of the UV detector was set to 268 nm. Pure methanol was used as mobile phase with a flow rate of 1 mL·min−1. Each analysis was repeated three times to check the repeatability and three samples were taken for each equilibrium solution at a given temperature. The average value was regarded as the final solubility data. The relative standard uncertainty in mass fraction solubility is 2.4%, and in mole fraction solubility, 3.1%.

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RESULTS AND DISCUSSION Solubility Data. The measured mole fraction solubility of o-toluenesulfonamide and p-toluenesulfonamide in methanol, ethanol, n-propanol, isopropanol, n-butanol, acetonitrile, and ethyl acetate within the temperature range of 283.15 to 318.15 K are presented in Tables 2 and 3, graphically shown in Figure 2. Figure 3 is the van’t Hoff plots of ln(x) versus 1/T in different solvents. Figure 2 shows that the solubility of o-toluenesulfonamide and p-toluenesulfonamide in different solvents increase with increasing in temperature. Figure 2a further demonstrates that the solubility of p-toluenesulfonamide decreases according to the following order: acetonitrile > ethyl acetate > methanol > ethanol > n-propanol > n-butanol > isopropanol. Figure 2b further demonstrates that the solubility of o-toluenesulfonamide decreases according to the following order: ethyl acetate > acetonitrile > methanol > ethanol > n-propanol > n-butanol > isopropanol. It is interesting that, for the systems of o-toluenesulfonamide + solvent and p-toluenesulfonamide + solvent, the solubility of p-toluenesulfonamide in seven solvents is larger than o-toluenesulfonamide. This phenomenon may be caused by the greater steric hindrance effect of o-toluenesulfonamide groups. The presence of steric hindrance increases the difficulty of binding sulfonamide groups to solvent molecule groups. In light of Tables 2 and 3, for the systems of o-toluenesulfonamide or p-toluenesulfonamide + alcohols, the order of the solubility values from high to low is consistent with the Hildebrand solubility parameters, dielectric constants, and polarity except for isopropanol.20 But the same tendency cannot be found for the systems of o-toluenesulfonamide or p-toluenesulfonamide + ethyl acetate/acetonitrile. When the electron-withdrawing group and the electron-donating group replace the benzene ring on the ortho and para, the dipole moment of p-toluenesulfonamide increases, the polarity becomes stronger. So, the solubility of p-toluenesulfonamide in acetonitrile is larger than it in ethyl acetate.

F=

∑ (lnγie − lnγic)2 i=1

(14)

For modified Apelblat equation and λh equation, the objective function is defined as F=

∑ (xie − xic)2 i=1

(15)

In eqs 14 and 15, lnγei is the logarithm of activity coefficient which can be calculated from eq 4; and lnγci is the logarithm of activity coefficient computed with solubility models. In addition, the relative deviation (RD), relative average deviation (RAD), and root-mean-square deviation (RMSD) are used to evaluate the thermodynamic models. They are described as eqs 16, 17, and 18, respectively. RD =

xe − xc xe

RAD =

1 N

N

∑ i=1

(16)

x ie − x ic x ie

⎡ ∑N (x c − x e)2 ⎤1/2 i i ⎥ RMSD = ⎢ i = 1 ⎢⎣ ⎥⎦ N

(17)

(18)

Where N denotes the number of experimental data points; xci and xei denotes the calculated and experimental solubility of o-toluenesulfonamide and p-toluenesulfonamide, respectively. During the regression process, the densities of the solvents are taken from the ref 20. The density of o-toluenesulfonamide and p-toluenesulfonamide are calculated using Advanced Chemistry Development (ACD/Laboratories) Software V11.02 E

DOI: 10.1021/acs.jced.7b00714 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 3. Experimental Mole Fraction Solubility (x) of o-Toluenesulfonamide in Different Solvents at the Temperature Range T = 283.15 to 318.15 K under 101.1 kPaa λh equation

modified Apelblat equation xexptl

xcalcd

100RD

xcalcd

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 100RAD

0.02772 0.03050 0.03415 0.03784 0.04249 0.04729 0.05257 0.05790

0.02748 0.03068 0.03421 0.0381 0.0424 0.04714 0.05236 0.05809 0.44

0.86 −0.58 −0.16 −0.7 0.21 0.32 0.41 −0.33

0.02742 0.03068 0.03425 0.03817 0.04246 0.04716 0.05232 0.05798 0.48

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 100RAD

0.02417 0.02663 0.02928 0.03207 0.03503 0.03840 0.04204 0.04564

0.02418 0.02662 0.02924 0.03207 0.03512 0.0384 0.04192 0.0457 0.12

−0.05 0.05 0.13 −0.02 −0.27 −5e-3 0.28 −0.12

0.02426 0.02663 0.0292 0.032 0.03503 0.03834 0.04194 0.04588 0.22

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 100RAD

0.02257 0.02486 0.02743 0.03013 0.03305 0.03613 0.03937 0.04271

0.02252 0.0249 0.02745 0.03016 0.03304 0.0361 0.03933 0.04275 0.11

0.22 −0.17 −0.07 −0.1 0.02 0.09 0.1 −0.09

0.02269 0.02493 0.02736 0.02999 0.03286 0.03598 0.03938 0.04311 0.44

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 100RAD

0.01982 0.02204 0.02460 0.02758 0.03052 0.03368 0.03740 0.04142

0.01979 0.02211 0.02465 0.02743 0.03047 0.0338 0.03743 0.04138 0.23

0.13 −0.31 −0.2 0.54 0.15 −0.35 −0.07 0.10

0.01981 0.02212 0.02464 0.02741 0.03044 0.03377 0.03743 0.04145 0.23

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 100RAD

0.02094 0.02317 0.02575 0.02865 0.03162 0.03484 0.03822 0.04211

0.02089 0.02324 0.0258 0.02858 0.03158 0.03482 0.03831 0.04207 0.19

0.26 −0.32 −0.21 0.25 0.13 0.06 −0.24 0.09

0.02097 0.02326 0.02576 0.0285 0.03149 0.03475 0.03833 0.04226 0.30

283.15 288.15 293.15 298.15 303.15 308.15 313.15

0.03370 0.03754 0.04226 0.04750 0.05335 0.05970 0.06694

0.03341 0.03771 0.04244 0.04764 0.05336 0.05963 0.06649

0.85 −0.44 −0.42 −0.3 −0.02 0.11 0.67

0.03344 0.03773 0.04244 0.04763 0.05333 0.05959 0.06647

T/K

100RD methanol 1.08 −0.59 −0.3 −0.87 0.07 0.27 0.48 −0.14 ethanol −0.37 −5.58e-3 0.26 0.22 −0.01 0.16 0.24 −0.52 n-propanol −0.54 −0.28 0.27 0.46 0.58 0.42 −0.04 −0.93 isopropanol 0.04 −0.34 −0.17 0.62 0.26 −0.27 −0.08 −0.07 n-butanol −0.13 −0.39 −0.05 0.53 0.43 0.25 −0.3 −0.36 acetonitrile 0.77 −0.50 −0.44 −0.28 0.03 0.18 0.70

F

Wilson model xcalcd

100RD

NRTL model xcalcd

100RD

0.02729 0.03067 0.03434 0.03832 0.04261 0.04725 0.05225 0.05764 0.67

1.54 −0.57 −0.56 −1.26 −0.29 0.08 0.60 0.45

0.02772 0.03054 0.03401 0.03801 0.04246 0.04729 0.05247 0.05796 0.17

8.89e-3 −0.14 0.42 −0.44 0.08 −9.67e-3 0.18 −0.11

0.02411 0.02661 0.02929 0.03214 0.03519 0.03843 0.04189 0.04558 0.19

0.24 0.06 −0.03 −0.22 −0.44 −0.08 0.35 0.13

0.02418 0.02662 0.02925 0.03208 0.03512 0.03839 0.04192 0.04571 0.12

−0.04 0.04 0.11 −0.02 −0.25 0.02 0.30 −0.15

0.02256 0.02491 0.02743 0.03012 0.03300 0.03606 0.03934 0.04283 0.12

0.06 −0.21 −0.01 0.02 0.16 0.18 0.09 −0.28

0.02258 0.02486 0.0274 0.03014 0.03306 0.03614 0.03936 0.04271 0.036

−0.05 2.32e-3 0.11 −0.04 −0.03 −0.02 0.03 −1.38e-3

0.01978 0.02211 0.02466 0.02744 0.03047 0.03379 0.03741 0.04139 0.23

0.21 −0.34 −0.25 0.5 0.15 −0.31 −0.03 0.07

0.01978 0.02211 0.02466 0.02744 0.03047 0.03379 0.03742 0.04138 0.24

0.19 −0.33 −0.23 0.51 0.15 −0.33 −0.05 0.08

0.02085 0.02325 0.02583 0.02862 0.03161 0.03483 0.03829 0.04201 0.21

0.44 −0.33 −0.32 0.12 0.02 0.02 −0.19 0.24

0.02089 0.02325 0.0258 0.02857 0.03157 0.03482 0.03831 0.04208 0.19

0.22 −0.33 −0.2 0.27 0.15 0.07 −0.25 0.06

0.03351 0.03774 0.04242 0.04757 0.05326 0.05954 0.06648

0.56 −0.54 −0.37 −0.15 0.17 0.27 0.69

0.03370 0.03755 0.0422 0.04752 0.05342 0.05981 0.06663

−0.01 −0.02 0.14 −0.05 −0.13 −0.18 0.47

DOI: 10.1021/acs.jced.7b00714 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 3. continued λh equation

modified Apelblat equation T/K

a

exptl

x

calcd

x

100RD

calcd

x

318.15 100RAD

0.07368

0.07398 0.40

−0.41

0.07402 0.42

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 100RAD

0.04973 0.05301 0.05664 0.06043 0.06441 0.06870 0.07291 0.07748

0.04966 0.05308 0.05668 0.06045 0.06442 0.06858 0.07294 0.07751 0.08

0.14 −0.13 −0.06 −0.04 −0.01 0.18 −0.04 −0.03

0.04989 0.05311 0.05655 0.06023 0.06418 0.06843 0.07301 0.07796 0.31

Wilson model

100RD −0.46 ethyl acetate −0.31 −0.18 0.16 0.33 0.35 0.39 −0.14 −0.62

calcd

x

NRTL model x

100RD

calcd

100RD

0.07415 0.42

−0.64

0.07384 0.15

−0.22

0.04973 0.05301 0.05663 0.06045 0.06444 0.06861 0.07295 0.07749 0.04

−2.83e-4 −2.49e-4 0.02 −0.04 −0.05 0.14 −0.05 −0.01

0.04968 0.05308 0.05667 0.06044 0.0644 0.06857 0.07294 0.07753 0.08

0.10 −0.13 −0.04 −0.01 8.27e-3 0.19 −0.05 −0.06

Standard uncertainties u are u(T) = 0.02 K, u(P) = 400 Pa. Relative standard uncertainty ur is ur(x) = 0.024.

Figure 2. Mole fraction solubility (x) of o-toluenesulfonamide or p-toluenesulfonamide in selected solvents at different temperatures: (a) for p-toluenesulfonamide: filled-in square, methanol; filled-in circle, ethanol; filled-in upright triangle, n-propanol; filled-in upside down triangle, isopropanol; filled-in right-pointing triangle, n-butanol; filled-in diamond, acetonitrile; filled-in star, ethyl acetate; (b) for o-toluenesulfonamide: open square, methanol; open circle, ethanol; open upright triangle, n-propanol; open upside down triangle, isopropanol; open right-pointing triangle, n-butanol; open diamond, acetonitrile; open star, ethyl acetate. Straight line, calculated values via modified Apelblat equation.

with the RMSD values are presented in Tables 4 and 5. The calculated values of RD and RAD are presented in Tables 2 and 3. Moreover, the computed solubility of o-toluenesulfonamide and p-toluenesulfonamide with the modified Apelblat equation is shown graphically in Figure 2, so as to demonstrate the difference between the experimental solubility and the calculated ones. Tables 4 and 5 show that the maximum value of RMSD is 8.46 × 10−4, which is acquired with λh equation for the solvent of ethyl acetate. The RAD values are all less than 0.87%. Generally, the calculated solubility data with the four models are in accordance with the experimental ones for all solvents, so the four models can all be employed to describe the solubility behavior of o-toluenesulfonamide and p-toluenesulfonamide in these solvents at elevated temperatures. Mixing Properties Calculation. According to the LewisRandall rule in which the standard states are the actual states of the pure components, the mixing properties of solution can be calculated. For an ideal solution, the mixing Gibbs free energy, mixing enthalpy, and mixing entropy in monosolvents are expressed as22

Figure 3. Van’t Hoff plots of ln(x) versus 1/T in different solvents: (a) for p-toluenesulfonamide: filled-in square, methanol; filled-in circle, ethanol; filled-in upright triangle, n-propanol; filled-in upside down triangle, isopropanol; filled-in right-pointing triangle, n-butanol; filled-in diamond, acetonitrile; filled-in star, ethyl acetate; (b) for o-toluenesulfonamide: open square, methanol; open circle, ethanol; open upright triangle, n-propanol; open upside down triangle ,isopropanol; open right-pointing triangle, n-butanol; open diamond, acetonitrile; open star, ethyl acetate.

(© 1994−2016 ACD/Laboratories). The melting temperature (Tm) and melting enthalpy (ΔfusH) of o-toluenesulfonamide and p-toluenesulfonamide were cited in ref 7. The regressed values of parameters A, B, and C in the modified Apelblat equation, λ and h in λh equation, aij and bij in Wilson and NRTL models, together G

Δmix Gid = RT (x1ln x1 + x 2 ln x 2)

(19)

Δmix S id = −R(x1ln x1 + x 2 ln x 2)

(20) DOI: 10.1021/acs.jced.7b00714 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 4. Parameters of the Modified Apelblat Equation and λh Equation for o-Toluenesulfonamide and p-Toluenesulfonamide in Different Solvents λh equation

modified Apelblat equation solvent

A

B

methanol ethanol n-propanol isopropanol acetonitrile ethyl acetate n-butanol

−38.91 −55.66 −5.344 −62.04 −47.96 −9.385 1.95

−266.09 181.31 −1951.01 618.69 470.67 −1041.56 −2062.65

methanol ethanol n-propanol isopropanol acetonitrile ethyl acetate n-butanol

−58.85 −32.19 −1.941 −41.06 −30.93 −26.47 −24.07

849.62 −105.62 −1472.42 63.62 −490.7 85.06 −613.70

λ

h

104 RMSD

0.3514 0.4426 0.2649 0.1720 0.3835 0.1857 0.1507

5596.42 5397.22 8099.38 11841.79 4099.09 5992.82 11772.66

1.65 4.22 2.84 1.55 5.52 8.46 2.96

0.1625 0.07486 0.07126 0.1054 0.2601 0.03314 0.092

9815.97 15480.37 16430.51 14460.24 6871.36 12320.74 15112.39

2.02 1.01 1.89 0.82 2.54 2.32 1.08

104 RMSD

C

p-toluenesulfonamide 6.506 1.57 9.145 3.73 1.529 2.14 9.911 1.63 7.747 5.29 1.847 6.89 0.287 1.79 o-toluenesulfonamide 9.254 1.85 5.109 0.59 0.5926 0.34 6.539 0.78 5.184 2.41 4.103 0.59 3.963 0.60

Table 5. Parameters of the Wilson and NRTL Models for o-Toluenesulfonamide and p-Toluenesulfonamide in Different Solvents Wilson model solvent

a12

b12/K

a21

methanol ethanol n-propanol isopropanol acetonitrile ethyl acetate n-butanl

0.1456 −0.3689 0.7640 1.385 0.8456 2.670 2.073

−675.47 −348.72 −535.92 −619.95 −971.37 −1289.29 −819.29

22.06 4735.39 30.18 64.89 113.68 356.65 85.36

methanol ethanol n-propanol isopropanol acetonitrile ethyl acetate n-butanl

2.557 4.140 4.427 5.307 4.021 5.531 4.163

−1485.20 −1794.74 −1786.76 −1842.15 −1805.37 −2252.85 −1631.53

43.61 1953.08 296.29 −0.3357 −1.986 84.68 163.07

Δmix H id = 0

NRTL model b21/K

4

10 RMSD

p-toluenesulfonamide 5055.76 2.85 2.967 −1093042.81 5.12 2.155 7535.12 2.21 3.328 17779.41 2.03 6.549 −16825.06 7.62 100.76 −49674.79 7.11 9.395 23175.07 2.02 −35.22 o-toluenesulfonamide −729.89 2.88 56.96 −398296.48 0.86 2.843 −56548.49 0.56 1.241 439.33 0.75 1.591 1176.49 2.69 58.71 −22510.84 0.39 12.67 −6756.10 0.68 8.297

Δmix M = M + Δmix M

id

b21/K

α

104 RMSD

−850.14 −535.57 −791.59 −1557.18 −49521.53 −1998.30 13712.26

−771.51 −318.90 −261.15 −167.94 3.350 0.4268 −4.375

252016.63 182960.66 93423.49 80974.62 −1140.21 −702.05 1129.08

0.30 0.20 0.20 0.30 0.20 0.20 0.20

1.18 4.18 1.86 1.74 5.50 7.40 1.16

−14181.82 −636.47 −604.96 −532.69 −14628.61 −2248.10 −1488.23

9.091 4.000 −19.99 3.873 8.439 4.789 2.876

−3220.27 −1385.69 13294.71 −1054.37 −3091.53 −2205.93 −1345.99

0.20 0.20 0.20 0.20 0.20 0.20 0.20

0.89 0.61 0.14 0.76 1.34 0.59 0.60

(25)

(22)

For (23)

HE − GE T

(26)

In light of the regressed parameters in Wilson model and the experimental solubility data, the ΔmixG, ΔmixH, and ΔmixS are computed and tabulated in Tables 6 and 7. The values of mixing Gibbs energy (ΔmixG) for a solution can be used to illustrate the dissolution capacity of a solute. Figure 4 and Tables 6 and 7 show that the values of ΔmixG are all negative and increase with the decrease in temperature, thus, the mixing process of o-toluenesulfonamide or p-toluenesulfonamide are spontaneous and favorable in the studied solvents.

Here M denotes the excess property in real solutions. ΔmixH, ΔmixG, and ΔmixS are the mixing enthalpy, mixing Gibbs free energy, and mixing entropy, respectively. The superscript id denotes ideal state. In terms of the Wilson model, the excess mixing properties are described as eqs 24−26.23 E

GE = RT (x1ln γ1 + x 2 ln γ2)

a21

⎛ ∂ln γ1 ∂ln γ2 ⎞ =−T 2R ⎜x1 + x2 ⎟ ⎝ ∂T ∂T ⎠

SE =

M = G , H , and S

b12/K

⎡ ∂(GE /T ) ⎤ H E = − T 2⎢ ⎥ ⎣ ∂T ⎦

(21)

Where x1 denotes the mole fraction of solute; and x2, the corresponding solvent. For nonideal solution, the three thermodynamic mixing properties can be obtained with eqs 22 and 23. E

a12

(24) H

DOI: 10.1021/acs.jced.7b00714 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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E,∞a Table 6. Calculated Values of p-Toluenesulfonamide in Different Solvents for ΔmixG, ΔmixH, ΔmixS, lnγ∞ 1 , and H1

T/K

ΔmixG J·mol−1

ΔmixH J·mol−1

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

−428.81 −477.85 −525.58 −580.62 −635.71 −696.84 −759.63 −822.33

−243.31 −277.68 −312.08 −353.52 −396.48 −446.38 −499.89 −555.62

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

−333.04 −371.76 −415.43 −470.57 −529.04 −590.41 −652.75 −719.75

−98.05 −111.43 −127.04 −147.84 −170.74 −195.72 −222.01 −251.54

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

−264.33 −296.66 −330.77 −371.72 −409.05 −455.69 −498.69 −544.05

−119.12 −136.75 −155.95 −180.12 −202.63 −232.35 −260.50 −291.41

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

−197.02 −219.91 −246.19 −273.87 −301.83 −331.04 −363.62 −400.63

−102.70 −117.20 −134.53 −153.46 −173.18 −194.52 −219.38 −249.05

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

−755.96 −806.94 −881.47 −950.84 −1026.24 −1097.27 −1170.28 −1249.42

−619.17 −672.03 −753.69 −832.69 −922.72 −1011.31 −1106.89 −1216.53

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

−706.57 −746.58 −794.16 −848.80 −904.75 −958.79 −1006.37 −1050.50

−768.08 −827.24 −900.19 −987.65 −1081.68 −1177.38 −1266.43 −1353.55

283.15 288.15 293.15 298.15 303.15 308.15

−236.32 −264.99 −291.40 −320.30 −350.00 −380.55

−162.30 −187.05 −210.53 −237.25 −265.76 −296.20

ΔmixS J· K−1·mol−1

lnγ∞ 1

HE,∞ kJ·mol−1 1

0.6563 0.6929 0.7325 0.7638 0.7963 0.8146 0.8325 0.8437

−0.03950 0.001900 0.04180 0.08040 0.1178 0.1539 0.1888 0.2227

−5.609 −5.609 −5.609 −5.609 −5.609 −5.609 −5.609 −5.609

0.8327 0.9038 0.9848 1.125 1.187 1.285 1.374 1.473

0.2368 0.2582 0.2788 0.2988 0.3181 0.3367 0.3548 0.3723

−2.899 −2.899 −2.899 −2.899 −2.899 −2.899 −2.899 −2.899

0.5146 0.5527 0.5939 0.6418 0.6821 0.7254 0.7642 0.7931

0.4615 0.4944 0.5261 0.5568 0.5864 0.6151 0.6429 0.6698

−4.456 −4.456 −4.456 −4.456 −4.456 −4.456 −4.456 −4.456

0.3331 0.3564 0.3809 0.4039 0.4244 0.443 0.4606 1.352

0.7623 0.8003 0.837 0.8724 0.9067 0.9399 0.9720 1.003

−5.154 −5.154 −5.154 −5.154 −5.154 −5.154 −5.154 −5.154

0.4872 0.4758 0.4339 0.3976 0.3469 0.2853 0.2021 0.1033

−0.6323 −0.5728 −0.5153 −0.4598 −0.4061 −0.3541 −0.3038 −0.255

−8.073 −8.073 −8.073 −8.073 −8.073 −8.073 −8.073 −8.073

−0.2244 −0.2895 −0.3627 −0.4638 −0.5898 −0.7183 −0.8336 −0.9513

−0.5625 −0.4834 −0.4071 −0.3333 −0.2619 −0.1928 −0.126 −0.06130

−10.73 −10.73 −10.73 −10.73 −10.73 −10.73 −10.73 −10.73

0.2614 0.2705 0.2759 0.2785 0.2779 0.2737

0.5659 0.6161 0.6646 0.7115 0.7568 0.8006

−6.812 −6.812 −6.812 −6.812 −6.812 −6.812

methanol

ethanol

n-propanol

isopropanol

acetonitrile

ethyl acetate

n-butanol

I

DOI: 10.1021/acs.jced.7b00714 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 6. continued T/K

ΔmixG J·mol−1

ΔmixH J·mol−1

313.15 318.15

−410.06 −445.56

−326.60 −365.06

ΔmixS J· K−1·mol−1 0.2665 0.253

lnγ∞ 1 0.8431 0.8842

HE,∞ kJ·mol−1 1 −6.812 −6.812

ΔmixG, ΔmixH, and ΔmixS denote the mixing Gibbs free energy, mixing enthalpy, and mixing entropy, respectively; γ∞ 1 denotes the infinitesimal denotes infinitesimal concentration reduced excess enthalpy. concentration activity coefficient, and HE,∞ 1 a

E,∞a Table 7. Calculated Values of o-Toluenesulfonamide in Different Solvents for ΔmixG, ΔmixH, ΔmixS, lnγ∞ 1 , and H1

T/K

ΔmixG J·mol−1

ΔmixH J·mol−1

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

−329.68 −355.40 −387.94 −419.43 −457.41 −494.63 −533.48 −570.48

−340.10 −373.70 −417.69 −461.91 −517.34 −574.09 −635.96 −697.70

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

−288.22 −309.89 −332.23 −354.63 −377.24 −401.81 −426.91 −450.09

−358.38 −394.27 −432.75 −473.00 −515.41 −563.34 −614.61 −664.65

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

−269.24 −289.46 −311.23 −332.99 −355.41 −377.81 −400.08 −421.66

−333.17 −366.44 −403.59 −442.40 −484.07 −527.65 −573.04 −619.28

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

−236.29 −256.57 −279.07 −304.17 −327.75 −351.96 −379.20 −407.14

−262.91 −290.42 −321.76 −357.77 −392.38 −428.74 −470.70 −514.65

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

−401.54 −437.33 −479.73 −524.95 −573.35 −623.62 −678.36 −727.03

−404.87 −442.01 −486.85 −534.49 −585.22 −637.07 −693.14 −738.78

283.15 288.15 293.15 298.15 303.15 308.15 313.15

−593.29 −616.96 −642.61 −667.95 −692.99 −718.46 −741.19

−997.63 −1004.51 −1056.23 −1120.37 −1190.01 −1265.21 −1338.15

ΔmixS J K−1·mol−1

lnγ∞ 1

HE,∞ kJ·mol−1 1

−0.03679 −0.06352 −0.1015 −0.1425 −0.1977 −0.2578 −0.3273 −0.3999

−0.4882 −0.3972 −0.3092 −0.2243 −0.1421 −0.0626 0.01433 0.08887

−12.35 −12.35 −12.35 −12.35 −12.35 −12.35 −12.35 −12.35

−0.2549 −0.2927 −0.3535 −0.3984 −0.4627 −0.5273 −0.5929 −0.6743

−0.361 −0.251 −0.1448 −0.0421 0.0572 0.1532 0.2462 0.3363

−14.92 −14.92 −14.92 −14.92 −14.92 −14.92 −14.92 −14.92

−0.2287 −0.2756 −0.3172 −0.3754 −0.4221 −0.4744 −0.5598 −0.6223

−0.2927 −0.1832 −0.0775 0.0247 0.1236 0.2192 0.3118 0.4015

−14.85 −14.85 −14.85 −14.85 −14.85 −14.85 −14.85 −14.85

−0.09436 −0.1254 −0.1563 −0.1814 −0.2125 −0.2538 −0.2976 −0.3425

−0.1552 −0.0566 0.0383 0.1297 0.2177 0.3025 0.3843 0.4633

−13.41 −13.35 −13.30 −13.25 −13.20 −13.15 −13.10 −13.05

−0.01206 −0.01678 −0.02435 −0.03262 −0.03979 −0.04432 −0.04715 −0.03723

−0.6985 −0.6100 −0.5261 −0.4466 −0.3713 −0.3000 −0.2325 −0.1687

−12.11 −11.89 −11.67 −11.44 −11.19 −10.95 −10.69 −10.43

−1.433 −1.347 −1.416 −1.523 −1.645 −1.771 −1.913

−1.111 −0.9675 −0.8328 −0.7035 −0.5788 −0.4582 −0.3414

−20.18 −19.09 −18.83 −18.76 −18.74 −18.73 −18.73

methanol

ethanol

n-propanol

isopropanol

acetonitrile

ethyl acetate

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Table 7. continued T/K

ΔmixG J·mol−1

ΔmixH J·mol−1

318.15

−764.38

−1416.40

ΔmixS J K−1·mol−1

lnγ∞ 1

HE,∞ kJ·mol−1 1

−2.052

−0.2284

−18.73

−0.1153 −0.1458 −0.1829 −0.2266 −0.273 −0.325 −0.3811 −0.4473

−0.2122 −0.1122 −0.0157 0.0777 0.1679 0.2552 0.3398 0.4217

−13.56 −13.56 −13.56 −13.56 −13.56 −13.56 −13.56 −13.56

n-butanol 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

−249.61 −269.85 −292.36 −316.57 −340.14 −364.47 −388.67 −415.15

−282.24 −311.86 −345.97 −384.12 −422.90 −464.62 −508.00 −557.46

ΔmixG, ΔmixH, and ΔmixS denote the mixing Gibbs free energy, mixing enthalpy, and mixing entropy, respectively; γ∞ 1 denotes the infinitesimal denotes infinitesimal concentration reduced excess enthalpy. concentration activity coefficient, and HE,∞ 1 a

Figure 4. Evaluated mixing Gibbs free energy at measured solubility points based on the Wilson model: (a) for p-toluenesulfonamide: filled-in square, methanol; filled-in circle, ethanol; filled-in upright triangle, n-propanol; filled-in upside down triangle,isopropanol; filled-in right-pointing triangle, n-butanol; filled-in diamond, acetonitrile; filled-in star, ethyl acetate; (b) for o-toluenesulfonamide: open square, methanol; open circle, ethanol; open upright triangle, n-propanol; open upside down triangle, isopropanol; open right-pointing triangle, n-butanol; open diamond, acetonitrile; open star, ethyl acetate.

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CONCLUSION

and p-toluenesulfonamide is spontaneous and favorable in the studied solvents.

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In this work, the equilibrium solubility was obtained experimentally for o-toluenesulfonamide and p-toluenesulfonamide in a total of seven monosolvents within the temperature range of 283.15 to 318.15 K under 101.3 kPa. The solubility of o-toluenesulfonamide and p-toluenesulfonamide in the selected monosolvents increased with the increase in temperature, but the increments with temperature were different for different solvents. At a given temperature, the solubility of o-toluenesulfonamide decrease according to the following order: ethyl acetate > acetonitrile > methanol > ethanol > n-propanol > n-butanol > isopropanol; and the solubility of p-toluenesulfonamide decrease according to the following order: acetonitrile > ethyl acetate > methanol > ethanol > n-propanol > n-butanol > isopropanol. The experimental solubility data were correlated by using the modified Apelblat equation, λh equation, Wilson model and the NRTL model. The maximum values of RMSD and RAD were 8.46 × 10−4 and 0.87%, respectively. On the whole, the four thermodynamic models were all acceptable for the solubility of o-toluenesulfonamide and p-toluenesulfonamide in the studied solvents. Based on the Wilson model, the mixing Gibbs free energy, mixing enthalpy, mixing entropy, infinitesimal concentration activity coefficient (γ∞ 1 ) and reduced excess enthalpy (HE,∞ 1 ) were calculated according to the solubility data of o-toluenesulfonamide and p-toluenesulfonamide in monosolvent. The ΔmixG values are all negative and increase with decreasing in temperature, so the solution process of o-toluenesulfonamide

AUTHOR INFORMATION

Corresponding Author

*Tel: +86 350 3339210; E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The project was supported by College Students’ Science and Technology Innovation Project of XinZhou Teachers University, China (201621).

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REFERENCES

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DOI: 10.1021/acs.jced.7b00714 J. Chem. Eng. Data XXXX, XXX, XXX−XXX