Determination and Correlation of Solubility of N-tert-Butylacrylamide in

Jul 6, 2015 - In addition, the standard enthalpy, standard entropy and Gibbs free energy change for the solution process were calculated from the solu...
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Determination and Correlation of Solubility of N-tert-Butylacrylamide in Seven Different Solvents at Temperatures between (279.15 and 353.15) K Xu Gao, Wei-Lan Xue,* Zuo-Xiang Zeng, and Xin-ran Fan Institute of Chemical Engineering, East China University of Science and Technology, Shanghai 200237, China ABSTRACT: The solubility data of N-tert-butylacrylamide (TBA) in the ethyl acetate, ethanol,dichloromethane, water, formamide, N,N-dimethylformamide (DMF), and N,N-dimethylacetamide (DMAC) at temperatures ranging from (279.15 to 353.15) K were measured by synthetic method. The experimental data were correlated by the van’t Hoff plot, modified Apelblat equation, and two local composition models (NRTL and UNIQUAC), respectively. It was found that modified Apelblat equation could obtain the better correlation results than the other three models. In addition, the standard enthalpy, standard entropy and Gibbs free energy change for the solution process were calculated from the solubility data by the van’t Hoff analysis. Furthermore, on the basis of the NRTL model and experimental data, the thermodynamic excess functions (GE,SE,HE) of TBA + solvents (ethyl acetate, ethanol, dichloromethane, water, formamide, DMF, DMAC) systems were determined.

1. INTRODUCTION

2. EXPERIMENTAL SECTION 2.1. Materials. The N-tert-butylacrylamide was produced in our laboratory.4 A short description of synthesis of TBA is given as follows: Portions of 29.6 g of tert-butanol, 10.6 g of acrylonitrile, and 12.1 g of diphosphorus pentoxide were put into a 250 mL three-mouth flask, respectively. The system was stirred for 2 h at the temperature of 353.15 K. After reaction finished, the mixture was cooled to room temperature. Then, 150 mL of deionized water was joined into the mixture. The product was obtained by filtration and purified by recrystallization from ethanol. Its mass fraction purity determined by HPLC is better than 99.3%. All of the solvents, ethyl acetate, ethanol, dichloromethane, formamide, DMF, and DMAC (purchased from Shanghai Chemistry Reagent Co. China) used for experiments were analytical reagent grade, and their mass fraction purity were higher than 99.8%. Detailed information about the materials used in this work was listed in Table 1. 2.2. Apparatus and Procedure. The solubility of a solid in a solvent is generally determined by two static methods:5 analytical method6,7 and synthetic method.8,9The solubility of TBA in seven pure solvents was measured by the synthetic method, the program was similar to the method that was described in the literature.10,11 A laser monitoring system (HJ-1B He−Ne Laser, NanJing Laser Instruments Factory), which consisted of a laser generator, a photoelectric transformer, and a light intensity display, was used to determine the disappearance of the solid in the mixtures. The solubility apparatus was composed of a specially designed jacketed glass

N-tert-Butylacrylamide (TBA,C7H13NO, CAS Registry No. 107-58-4) is a type of white, powdery crystal with a molar mass of 127.18 g/mol. TBA is useful in the chemical industry. For example, as a useful additive in copolymer, TBA can enhance the rigidity of molecular chain and then to improve the temperature resistance and salt resistance of copolymer.1It is also of great importance in the preparation of temperature sensitive superabsorbent hydrogels.2 TBA is mainly synthesized by means of Ritter reaction with tert-butanol and acrylonitrile as raw materials, and the pure product is always obtained by extraction and recrystallization.3 In order to choose the proper solvent and improve the effects of purification, it is necessary to know the solubility of TBA in different solvent. Moreover, the solubility of a solid in liquids is one of scientific interest for the development of the solution theory. However, the solubility of TBA has not been reported in the literature as far as we know. In this article, solubility measurement of TBA in pure ethyl acetate, ethanol,dichloromethane, water, formamide, N,N-dimethylformamide (DMF), and N,N-dimethylacetamide (DMAC) at the temperatures ranging from (279.15 to 353.15) K were performed at atmospheric pressure by the synthetic method. The van’t Hoff plot, the modified Apelblat equation, NRTL model, and UNIQUAC model were used to correlate and predict the solubility of TBA in pure solvents. The standard enthalpy, standard entropy, and Gibbs energy change for the solution process (ΔHOsoln, ΔGOsoln, ΔSOsoln) were calculated from the solubility data. In addition, for the nonideal system, thermodynamic excess functions(GE, SE, HE)were calculated. © XXXX American Chemical Society

Received: February 12, 2015 Accepted: June 26, 2015

A

DOI: 10.1021/acs.jced.5b00135 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 1. Materials Used in This Work chemical name N-tert-butylacrylamide(TBA) ethyl acetate ethanol dichloromethane water formamide N,N-dimethylformamide (DMF) N,N-dimethylacetamide (DMAC) a

source synthesized by us Shanghai Chemistry Shanghai Chemistry Shanghai Chemistry prepared by us Shanghai Chemistry Shanghai Chemistry Shanghai Chemistry

Reagent Co. China Reagent Co. China Reagent Co. China Reagent Co. China Reagent Co. China Reagent Co. China

mass purity

analysis method

purification method

>0.993 >0.998 >0.998 >0.998 >0.999 >0.998 >0.998 >0.998

HPLCa HPLCa HPLCa HPLCa HPLCa HPLCa HPLCa HPLCa

recrystallized none none none three times distillation none none none

High-performance liquid chromatography.

3.2. Correlation of the Solubility Data. 3.2.1. van’t Hoff Plot. The temperature dependence of the solubility of TBA in the selected solvents can be correlated by the van’t Hoff plot12

vessel that was maintained at the desired temperature by circulating water. The water temperature was controlled with a super thermostatic water bath (DC-3005A, NingBo TianHeng Instruments Factory)connecting with a preprogrammed automatic temperature controller (uncertainty of ± 0.05 K). The jacket temperature could be maintained within ± 0.05 K of the required temperature. A magnetic stirrer was used to mix the solvent with the solute, and a condenser was connected to the vessel to prevent solvents from evaporating. A mercuryin-glass thermometer (WNG-0150 + 100, Changzhou Ruiming Instruments Factory) was inserted into the inner chamber of the vessel for the measurement of temperature with an uncertainty of ± 0.05 K. The thermometer is calibrated by Shanghai Institute of Measurement and Testing Technology before experimental measurement. The mass of solute and solvent were prepared using a Mettler H542 balance that has a range of measurement up to 160 g with an uncertainty of ± 0.0001 g. Predetermined mass of solvent (about 100 g ± 0.0001 g) was added into the vessel and the system was controlled at a desired temperature, and then a known mass of TBA determined by the balance was added into the system in portions. When the solid was completely dissolved, the intensity of the transmitted laser light maintained its maximum. The above process was repeated until the intensity was suddenly declined and the last introduced portion of TBA was less than 0.001 g. To make it attain equilibrium, the solution should constantly have been stirred for 2 h. Three parallel experiments were performed at the same solvent for each temperature, and the average value was used to calculate the mole fraction solubility. Because of uncertainties in the temperature, weighting measurement procedure and instabilities of the water bath, the estimated uncertainty of the solubility values was within 2%. By repeating the above procedure at different temperatures, the solubilities of TBA were obtained. The saturated mole fraction solubility of TBA can be determined from eq 1 x1 =

m1/M1 m1/M1 + m2 /M 2

ln x1 = −

ΔHsoln ΔSsoln + RT R

(2)

where ΔHOsoln and ΔSOsoln are the van’t Hoff enthalpy and entropy of solution,13 respectively. 3.2.2. Modified Apelblat Equation. The relationship between solubility of TBA and temperature is correlated with the modified Apelblat equation14 ln x1 = a +

b + c ln T T

(3)

where a, b, and c are the empirical constants. The values of a and b represent the variation in the solution activity coefficient and provide an indication of the influence of nonideal solution on the solubility of solute. The value of c reflect the effect of temperature on the fusion enthalpy, as a deviation of heat capacity.15 3.2.3. Local Composition Models. Another commonly used method to model the solubility of solid solute in liquid solvent is to use the activity coefficient models. In order to calculate the activity coefficient, a universal equation for (solid + liquid) equilibrium is written16 ln x1γ1 =

ΔfusHm ⎛ 1 1⎞ − ⎟ ⎜ R ⎝ Tm T⎠

(4)

where ΔfusHm is the enthalpy of fusion of solute at the melting point and Tm is melting temperature of TBA. The values of ΔfusHm and Tm can be determined by the differential scanning calorimetry (DSC).17 Figure 3 shows the heating DSC curves of TBA at the heating rate of 10 K/min. From Figure 3, the enthalpy of fusion and the melting temperature are determined to be 21.57 kJ·mol−1 and 401.65 K for TBA. The standard uncertainties of ΔfusHm and Tm are 0.50 kJ·mol−1 and 0.30 K, respectively. To estimate the activity coefficient, two commonly used expressions for strongly nonideal binary mixtures were chosen, namely the NRTL and UNIQUAC models. The expressions of the models for binary systems are explained as below: (1). NRTL Model. Renon and Prausnitz18proposed the NRTL model, which has been quite successful in correlating a wide variety of systems. The activity coefficient of this model which contains three parameters can be expressed as

(1)

where m1 and m2 represent the mass of TBA and seven solvents, respectively, and M1 and M2 are the molar mass.

3. RESULTS AND DISCUSSION 3.1. Solubility Data. The measured mole fraction solubilities of TBA in ethyl acetate, ethanol, dichloromethane, water, formamide, DMF, DMAC in the temperature range of 279.15 K to 353.15 K are obtained by eq 1, and the data are listed in Tables 2 and 3 and shown in Figures 1 and 2.

2 ⎤ ⎡ τ21G21 τ12G12 ⎥ ln γ1 = x 22⎢ + 2 2 (x 2 + x1G12) ⎦ ⎣ (x1 + x 2G12)

B

(5)

DOI: 10.1021/acs.jced.5b00135 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 2. Experimentally Determined Solubility Data and Excess Function Values of TBA in Ethyl Acetate, Ethanol, Dichloromethane, and Water at Temperature T and Pressure p = 0.1 MPaa T

100(xc1 − xe1)/xe1

100x1

K

van’t Hoff

Apelblat

287.15 290.15 293.15 296.15 299.15 302.15 305.15 310.15 315.15 320.15 325.15 330.15 335.15 340.15 100RAD

1.504 1.554 1.660 1.779 1.876 2.037 2.245 2.557 2.889 3.269 3.626 4.064 4.502 5.061 1.58

6.12 1.25 0.33 1.43 4.05 3.48 1.28 0.50 0.13 0.74 0.03 0.56 0.34 1.85 1.45

3.60 −0.32 −0.99 −1.32 −3.30 −2.24 0.28 1.33 1.64 2.12 0.71 0.36 −1.08 −1.01 1.30

284.95 287.95 291.15 294.15 297.15 300.15 304.15 307.15 310.15 313.15 316.15 319.15 324.15 330.15 335.15 100RAD

0.1359 0.1519 0.1704 0.2097 0.2404 0.2829 0.3441 0.3920 0.4631 0.5219 0.5976 0.6771 0.8637 1.126 1.417 1.86

6.36 1.23 4.57 0.48 1.34 0.23 0.38 1.84 0.67 1.32 1.43 2.35 0.23 1.50 4.05 1.21

3.31 −0.71 −5.44 0.50 −0.64 0.97 1.23 −0.09 2.34 0.22 −0.21 −1.58 −0.05 −0.47 0.39 2.17

279.15 283.15 285.15 287.15 289.15 291.15 293.15 296.15 298.15 301.15 304.15 100RAD

0.5408 0.6499 0.7199 0.7980 0.8885 0.9618 1.057 1.169 1.278 1.416 1.604 1.35

1.61 1.92 0.82 0.47 2.30 1.48 2.21 0.40 0.17 1.91 1.57 2.84

−7.27 −3.91 −1.43 0.91 3.49 3.18 4.16 1.54 1.77 −1.22 −2.33 1.54

294.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

0.08948 0.09937 0.1107 0.1219 0.1358 0.1527 0.1721 0.1915 0.2150 0.2398 0.2671

2.82 2.77 0.85 1.95 3.11 2.94 2.22 2.43 1.39 0.72 0.12

−0.82 0.95 0.82 −0.61 −0.85 −0.21 0.57 0.08 0.45 0.15 −0.29

GE

NRTL ethyl acetate 5.02 0.62 −0.51 −1.22 −3.51 −2.70 −0.36 0.54 0.85 1.46 0.31 0.31 −0.65 −0.11 1.30 ethanol −2.77 −5.97 −9.63 −3.14 −3.39 −1.15 0.03 −0.45 2.14 0.86 0.88 0.07 1.22 0.22 −0.58 1.69 dichloromethane −3.27 −2.58 −1.17 0.34 2.26 1.73 2.52 0.36 0.87 −0.98 −0.90 1.62 water 1.56 2.59 1.71 −0.32 −1.03 −0.72 −0.14 −0.70 −0.26 −0.38 −0.52 C

100SE −1

−1

HE −1

UNIQUAC

(J·mol )

(J·mol ·K )

(J·mol−1)

4.95 0.58 −0.54 −1.25 −3.49 −2.69 −0.38 0.52 0.85 1.46 0.35 0.35 −0.61 −0.16

59.78 63.01 68.60 74.88 80.37 88.78 99.45 116.29 134.72 156.04 176.95 202.48 228.82 261.96

−39.62 −40.83 −42.96 −45.28 −47.03 −50.27 −54.30 −60.49 −66.50 −73.22 −79.15 −86.23 −93.11 −102.1

−54.00 −55.45 −57.34 −59.23 −60.33 −63.10 −66.25 −71.31 −74.87 −78.39 −80.39 −82.21 −83.26 −85.30

−0.74 −4.38 −8.52 −2.22 −2.78 −0.72 0.22 −0.46 2.15 0.68 0.63 −0.28 1.02 0.12 −0.43

12.73 14.22 15.94 19.57 22.40 26.30 31.89 36.24 42.67 47.95 54.72 61.78 78.13 100.72 125.18

−0.18 −0.10 −0.23 −0.10 −0.28 −0.36 −0.30 −0.69 −0.47 −0.92 −0.97 −2.24 −2.55 −3.47 3.44

12.23 13.93 15.28 19.27 21.57 25.22 30.97 34.12 41.23 45.08 51.66 54.63 69.87 89.25 136.72

−3.42 −2.63 −1.16 0.39 2.35 1.82 2.63 0.43 0.92 −1.01 −1.01

29.87 35.80 39.59 43.80 48.66 52.58 57.63 63.59 69.36 76.61 86.37

−0.77 −0.17 −0.35 −0.44 −0.34 −0.62 −0.59 −0.75 −0.84 −1.27 0.69

27.72 35.31 38.58 42.54 47.67 50.76 55.89 61.37 66.84 72.79 88.46

7.84 7.39 5.08 1.91 0.22 −0.26 −0.26 −1.17 −0.95 −1.11 −1.17

10.21 11.56 13.17 14.80 16.83 19.30 22.15 25.08 28.64 32.45 36.71

−4.81 −5.29 −5.74 −6.14 −6.66 −7.29 −7.99 −8.66 −9.46 −10.28 −11.16

−3.93 −4.22 −4.23 −4.13 −4.02 −3.88 −3.67 −3.33 −2.88 −2.31 −1.58

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Table 2. continued T K 348.15 353.15 100RAD a

100(xc1 − xe1)/xe1

100x1

0.2967 0.3379 2.06

van’t Hoff

Apelblat

0.94 4.47 0.58

−1.03 0.75 0.94

NRTL water −0.84 1.41 2.29

GE

100SE

HE

UNIQUAC

(J·mol−1)

(J·mol−1·K−1)

(J·mol−1)

−1.29 1.09

41.38 47.80

−12.08 −13.55

−0.69 −0.06

Standard uncertainties u are u(T) = 0.05 K, ur(x1) = 0.02, u(p) = 300 Pa.

Table 3. Experimentally Determined Solubility Data and Excess Function Values of TBA in Formamide, DMF, and DMAC at Temperature T and Pressure p = 0.1 MPaa T K 284.15 288.15 294.15 305.15 308.15 312.15 316.15 320.15 324.15 329.15 334.15 340.15 345.15 350.15 100RAD

a

100(xc1 − xe1)/xe1

100x1

0.07801 0.09289 0.1169 0.1987 0.2287 0.2769 0.3478 0.4295 0.5121 0.6388 0.7761 0.9944 1.223 1.502 3.81

van’t Hoff

Apelblat

9.40 5.02 4.12 6.91 7.38 7.14 2.52 0.64 0.72 1.51 0.34 1.13 2.47 4.11 2.94

5.73 3.75 −2.28 −1.69 −1.75 −1.34 2.87 5.40 4.73 4.16 1.22 −0.71 −2.05 −3.43 4.04

288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 100RAD

2.071 2.365 2.831 3.335 4.033 4.632 5.287 5.987 7.086 8.331 9.869 11.74 13.79 16.56 3.74

6.59 1.05 0.68 0.70 1.12 1.69 4.68 8.06 6.23 4.65 1.88 1.70 4.24 9.13 1.67

−0.68 −2.56 0.21 1.16 4.53 2.77 0.27 −3.19 −2.24 −2.04 −1.13 0.20 0.14 2.27 2.32

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 100RAD

8.144 8.967 9.790 11.00 12.70 14.60 17.19 20.28 23.61 27.38 31.65 36.39 42.98 5.07

11.91 5.30 2.09 6.34 7.38 8.29 6.11 3.37 1.60 0.15 1.95 3.52 7.91 1.82

2.50 0.97 2.14 3.05 1.84 1.54 0.64 2.50 2.57 1.92 0.55 1.75 1.65 3.31

GE

NRTL formamide −3.61 −5.68 −11.35 −8.24 −7.43 −5.81 −0.74 2.58 2.96 3.52 2.04 1.19 0.25 −1.23 4.69 DMF 6.73 2.62 3.18 2.60 4.62 2.34 −0.25 −3.37 −2.43 −2.04 −1.09 0.07 −0.01 1.18 1.34 DMAC 12.28 7.89 2.86 −0.27 −1.62 −3.15 −2.92 −2.35 −2.30 −2.02 −1.32 −0.34 3.64 4.35

100SE −1

−1

HE −1

(J·mol ·K )

(J·mol−1)

UNIQUAC

(J·mol )

−5.91 −7.57 −12.76 −8.64 −7.62 −5.75 −0.39 3.13 3.59 4.20 2.61 1.54 0.25 −1.74

8.22 9.78 12.30 20.82 23.94 28.92 36.23 44.58 52.98 65.76 79.48 101.02 123.24 149.78

−0.10 −0.05 −0.20 0.07 −0.22 −0.35 −0.37 −0.41 −0.90 −0.90 −1.95 −2.05 −3.22 3.02

7.95 9.63 11.70 21.05 23.26 27.83 35.07 43.26 50.07 62.79 72.97 94.05 112.11 160.34

3.03 −0.27 1.17 1.33 3.98 2.23 0.09 −2.63 −1.55 −1.15 −0.36 0.45 −0.08 0.41

70.37 80.65 96.77 114.16 138.00 158.49 180.78 204.44 240.67 280.93 329.32 386.36 446.13 522.33

−9.92 −10.68 −11.92 −14.14 −15.12 −17.41 −19.03 −22.75 −24.34 −28.57 −32.99 −35.19 −48.05 13.80

41.78 49.35 61.23 71.31 91.42 103.97 120.23 130.92 160.79 185.73 217.76 265.60 278.83 571.07

13.76 8.57 2.79 −1.18 −3.24 −5.20 −4.96 −3.95 −3.22 −2.11 −0.53 1.21 5.87

80.86 93.27 106.16 121.66 139.82 158.64 179.13 198.75 215.84 229.64 238.82 242.31 232.90

−153.79 −160.91 −171.82 −187.23 −201.72 −227.56 −247.88 −270.34 −298.20 −318.82 −336.87 −366.01 −276.00

−369.96 −386.49 −414.71 −455.30 −491.87 −565.34 −621.88 −688.38 −777.62 −848.46 −917.17 −1031.96 −741.80

Standard uncertainties u are u(T) = 0.05 K, ur(x1) = 0.02, u(p) = 300 Pa. D

DOI: 10.1021/acs.jced.5b00135 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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where Δg12 and Δg21 are two cross interaction energy parameters (J·mol−1) and α is the parameter related to the nonrandomness in the mixture with α12 = α21. (2). UNIQUAC Model. Abrams and Prausnitz19proposed the UNIQUAC model to calculate activity coefficient of strongly nonideal binary mixtures. The activity coefficient of this model can be easily obtained as ⎛θ ⎞ ⎛ϕ ⎞ ⎛ r ⎞ z ln γ1 = ln⎜ 1 ⎟ + q1ln⎜⎜ 1 ⎟⎟ + ϕ2⎜l1 − 1 l 2⎟ r2 ⎠ 2 ⎝ x1 ⎠ ⎝ ⎝ ϕ1 ⎠ ⎛ ⎞ τ21 τ12 − q1ln(θ1 + θ2τ21) + θ2q1⎜ − ⎟ θ2 + θ1τ12 ⎠ ⎝ θ1 + θ2τ21 (10)

In eq 10,τ12 and τ21 are the interaction parameters between the solute and the solvent, which can be described as

Figure 1. Mole fraction solubility of TBA in: ethyl acetate, ■; ethanol, ◆; dichloromethane, □; water, ●; solid line, calculated from eq 3.

⎛ Δu12 ⎞ ⎛ u − u 22 ⎞ ⎟ = exp⎜ − ⎟ τ12 = exp⎜ − 12 ⎝ ⎠ ⎝ RT ⎠ RT

(11)

⎛ Δu 21 ⎞ ⎛ u − u11 ⎞ ⎟ = exp⎜ − ⎟ τ21 = exp⎜ − 21 ⎝ ⎝ RT ⎠ RT ⎠

(12)

where Δu12 and Δu21 are two adjustable energy parameters for each compounds, which can be regressed from experimental data. The experimental mole fraction solubility data of TBA shown in Tables 2 and 3 are correlated with van’t Hoff plot, modified Apelblat equation, NRTL model, and UNIQUAC model. The model parameters are listed in Table 4.The relative deviations (RDs) and the relative average deviation (RADs) are list in Tables 2 and 3, which are expressed as Figure 2. Mole fraction solubility of TBA in: formamide, ◇; DMF, △; DMAC, ▲; solid line, calculated from eq 3.

RD =

x1c − x1e x1e

RAD =

with (6)

G21 = exp( −α21τ21)

(7)

τ12 =

τ21 =

g12 − g22 RT

g21 − g11 RT

=

Δg12

=

Δg21

RT

RT

N

∑ i=1

x1,e i − x1,c i x1,e i

(14)

where N is the number of experimental data points and the xe1 and xc1 represent the experimental and the calculated solubility values, respectively. According to the solubility curves of TBA in Figures 1 and 2, it is obvious that the solubility of TBA increases with increase in temperature and increases in the order DMAC > DMF > ethyl acetate > dichloromethane > ethanol > formamide > water at constant temperature. From Tables 2 and 3, the overall RADs of these four models are 2.78% (van’t Hoff), 1.79% (modifief Apelblat), 2.23% (NRTL), 2.47% (UNIQUAC). Therefore, the correlation goodness order is the modified Apelblat > NRTL > UNIQUAC > van’t Hoff. The results mentioned above suggest that the experimental data and the correlation equations in this work are essential for the experimental optimization process of TBA. 3.3. Standard Enthalpy, Standard Entropy, and Gibbs Energy. Because dissolution is a thermodynamic process and it is necessary to calculate some thermodynamic parameters. From the van’t Hoff analysis, the standard molar enthalpy of solution (ΔHOsoln) can be earned with the help of mean temperature and defined as20

Figure 3. Heating DSC curves of TBA.

G12 = exp( −α12τ12)

1 N

(13)

(8)

⎛ ⎞ ∂ln x1 Ο ΔHsoln = −R × ⎜ ⎟ ⎝ ∂(1/T ‐1/Tmean) ⎠

(9) E

(15)

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Table 4. Model parameters in different solvents van’t Hoff

Apelblat

ΔHOsoln

ΔSOsoln

(kJ·mol−1)

(J·mol−1·K−1)

19.27 37.47 30.68 19.20 37.78 26.70 24.50

31.69 76.07 66.64 6.68 72.64 59.86 61.67

solvent ethyl acetate ethanol dichloromethane water formamide DMF DMAC

NRTL

a

b

c

Δg12/R

Δg21/R

α

Δu12/R

Δu21/R

−83.02 −97.57 −342.42 −105.26 −131.45 −152.81 −253.21

1697.51 376.89 11738.6 2726.75 1943.87 4323.03 9420.2

12.88 15.85 52.42 15.66 20.78 23.65 38.50

2846.06 33.97 37.49 8745.74 36.12 2235.34 −1417.58

−1092.57 1104.87 639.14 −5121.1 1238.75 −1652.21 2170.25

0.06 0.49 0.46 0.01 0.40 0.01 0.07

644.44 46.72 152.65 11201.8 303.16 284.72 210.98

−158.91 210.31 38.19 −47.20 125.37 −93.72 360.38

where x1 is the mole fraction solubility, R represents the universal gas constant (8.314 J·K−1·mol−1), T is the corresponding absolute temperature, and Tmean represents the mean temperature of the experimental temperatures. According to the eq 15,ΔHOsoln can be obtained from the slope of the solubility curve where ln x1 is plotted versus (1/T − 1/Tmean). The linear ln x1/(1/T − 1/Tmean) curves of TBA in the seven solvents are shown in Figure 4.

The results of the standard Gibbs energy, enthalpy, and entropy are shown in Table 5, together with ξH and ξTS. The ξH and ξTS represent the comparison of the relative contribution to the standard Gibbs energy by enthalpy and entropy in the solution process,22 respectively. Two of them can be written as %ξH =

%ξTS =

The standard molar Gibbs energy of solution (ΔGOsoln) can be calculated according to21 (16)

where the intercept is obtained from linear ln x1/ (1/T − 1/Tmean) curves. What’s more, the standard molar entropy of solution (ΔSOsoln) can be obtained by Ο ΔSsoln =

Ο Ο ΔHsoln − ΔGsoln Tmean

Ο |ΔHsoln | Ο Ο |ΔHsoln | + |T ΔSsoln | Ο |T ΔSsoln | Ο |ΔHsoln |

Ο + |T ΔSsoln |

× 100 (18)

× 100 (19)

We can see from Table 5, the enthalpy and the standard Gibbs energy of TBA are positive in the studied seven solvents, indicating the solution process of TBA is endothermic. What’s more, the main contributor to the standard Gibbs energy of solution is the enthalpy during the dissolution, because the values of %ξH are ≥ 55.39 %. 3.4. Excess Gibbs Energy, Entropy, and Enthalpy. In this paper, the NRTL model gives a good fit for the system and the values of α ranges from 0.01 to 0.49. It is necessary to discuss the relatively wide value range while the value of α generally varies between 0.20 and 0.47. In fact, Guggenheim’s theory used to estimate the range of α is not applicable for some mixtures, especially for associated mixtures.18 For example, Marina et al.23obtained the better correlation results when α was searched within a wider range. According to Prausnitz,24 when α is zero, the mixture is completely random and can be deemed to be an ideal solution. Therefore, the relatively high values for parameter α show that the mixtures are nonideal. For nonideal solutions, the different between the Gibbs energies of mixing of perfect and nonideal solution is called the excess Gibbs energy, which we shall denote by25

Figure 4. Ln x1 of TBA in different solvents against 104(1/T − 1/Tmean): ethyl acetate, ■; ethanol, ◆; dichloromethane, □; water, ●;formamide, ◇; DMF, △; and DMAC, ▲.

Ο ΔGsoln = −RTmean × intercept

UNIQUAC

G E = RT (x1ln γ1 + x 2 ln γ2)

(17)

(20)

Table 5. Standard Enthalpy, Entropy, and Gibbs Energy Change in Different Solvents at the Mean Temperature solvent

ΔHOsoln −1

ethyl acetate ethanol dichloromethane water formamide DMF DMAC

ΔGOsoln

ΔSOsoln

−1

−1

(kJ·mol )

(kJ·mol )

(J·mol ·K )

19.26 37.47 30.87 19.21 38.20 26.71 24.50

9.33 13.88 11.25 17.04 15.39 7.51 4.77

31.68 76.08 67.27 6.68 71.94 59.87 61.08 F

%ξH

%ξTS

65.97 61.37 61.14 89.88 62.61 58.18 55.39

34.03 38.63 38.86 10.12 37.39 41.82 44.61

−1

DOI: 10.1021/acs.jced.5b00135 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

(6) Pinho, S. P.; Macedo, E. A. Solubility of NaCl, NaBr, and KCl in Water, Methanol, Ethanol, and Their Mixed Solvents. J. Chem. Eng. Data 2005, 50, 29−32. (7) Gao, L.; Wang, J. K.; Hao, H. X. Solubility of Acesulfame Potassium in Ethanol+Water and Methanol + Water Systems from 275.84 to 322.90 K. J. Chem. Eng. Data 2008, 53, 854−856. (8) Domanska, U.; Pobudkowska, A.; Rogalski, M. Solubility of Imidazoles, Benzimidazoles, and Phenylimidazoles in Dichloromethane, 1-Chlorobutane, Toluene, and 2-Nitrotoluene. J. Chem. Eng. Data 2004, 49, 1082−1090. (9) Nyvlt, J.; Sohnel, O.; Matuchova, M.; Broul, M. The Kinetics of Industrial Crystallization; Elsevier: Amsterdam, 1985. (10) Jiang, Q.; Gao, G. H.; Yu, Y. X.; Qin, Y. Solubility of Sodium Diemthyl Isophthalate-5-sulfonate in Water and in Water+Methanol Containing Sodium Sulfate. J. Chem. Eng. Data 2000, 45, 292−294. (11) Chen, J.; Zeng, Z. X.; Xue, W. L.; Wang, D.; Huang, Y. Determination and Correlation of Solubility of Decahydropyrazino(2,3-b)pyrazine in Methanol,Ethanol,and 2-Propanol. Ind. Eng. Chem. Res. 2011, 50, 11755−11762. (12) Song, L.; Gao, Y.; Gong, L. Measurement and Corrlated of Solubility of Clopidogrel Hydrogen Sulfate(Metastable Form) in Lower Alcohols. J. Chem. Eng. Data 2011, 56, 2553−2556. (13) Nordstrom, F. L.; Rasmuson, C. Prediction of Solubility Curves and Melting Properties of Organic and Pharmaceutical Compounds. Eur. J. Pharm. Sci. 2009, 36, 330−344. (14) Apelblat, A.; Manzurola, E. Solubilities ofo-acetylsalicylic, 4aminosalicylic, 3,5-dinitrosalicylic, andp-toluic acid, and magnesiumDL-aspartate in water fromT=(278 to 348) K. J. Chem. Thermodyn. 1999, 31, 85−91. (15) Wei, D. W.; Pei, Y. H. Solubility of Diphenyl Carbonate in Pure Alcohols from 283 to 333 K. J. Chem. Eng. Data 2008, 53, 2710−2711. (16) Walas, S. M. Phase Equilibria in Chemical Engineering; Butterworth Publishers: Boston, MA, 1985. (17) Wei, D. W.; Pei, Y. H. Measurement and Correlated of Solubility of Diphenyl Carbonate in Alkanols. Ind. Eng. Chem. Res. 2008, 47, 8953−8956. (18) Renon, H.; Prausnitz, J. M. Local Compositions in Thermodynamic Excess Functions for Liquid Mixtures. AIChE J. 1968, 14, 135−144. (19) Abrams, D. S.; Prausnitz, J. M. Statistical thermodynamics of liquid-mixtures: New expression for excess Gibbs energy of partly or completely miscible systems. AIChE J. 1975, 21, 116−128. (20) Shakeel, F.; Haq, N.; El-Badry, M.; Alanazi, F. K.; Alsarra, I. A. Thermodynamics and solubility of tadalafil in diethylene glycol monoethyl ether+water co-solvent mixtures at (298.15 to 333.15) K. J. Mol. Liq. 2014, 197, 334−338. (21) Li, T.; Jiang, Z. X.; Chen, F. X.; Ren, B. Z. Solubilities of dxylose in water+(acetic acid or propionic acid) mixtures at atmospheric pressure and different temperatures. Fluid Phase Equilib. 2012, 333, 13−17. (22) Gandhi, P. J.; Murthy, Z.V. P. Solubility and Crystal Size of Sirolimus in Different Organic Solvents. J. Chem. Eng. Data 2010, 55, 5050−5054. (23) Marina, J. M.; Tassios, D. P. Effective Local Compositions in Phase Equilibrium Correlations. Ind. Eng. Chem. Process Des. Dev. 1973, 12, 67−71. (24) Prausnitz, J. M.; Lichtenthaler, R. N.; Azevedo de, E. G. Molecular Thermodynamics of Fluid-Phase Equilibria, 3rd ed.; PrenticeHall PTR: Upper Saddle River, NJ, 1999. (25) Kondepudi, D. K.Introduction to modern Thermodynamics; John Wiley & Sons, Ltd: Chichester, England, 2008.

Other excess function, such as excess entropy and enthalpy, can be obtained from GE. For example ⎛ ∂G E ⎞ S E = −⎜ ⎟ ⎝ ∂T ⎠ ⎛ ∂ln γ1 ∂ln γ2 ⎞ = −RT ⎜x1 + x2 ⎟ − R(x1ln γ1 + x 2 ln γ2) ⎝ ∂T ∂T ⎠ (21) E

Similarly H can be obtained using the relation

⎛ ∂ GE ⎞ H E = − T 2⎜ ⎟ ⎝ ∂T T ⎠

(22)

By substitution of NRTL model into eqs 20 to 22, the values of GE, SE, and HE for TBA + solvents (ethyl acetate, ethanol, dichloromethane, water, formamide, DMF, DMAC) systems can be calculated and also listed in Tables 2 and 3.

4. CONCLUSIONS The solubilities of TBA in ethyl acetate, ethanol, dichloromethane, water, formamide, DMF, and DMAC have been measured at temperatures ranging from 279.15 K to 353.15 K. The solubility of TBA increases with the increase of temperature, and in the order DMAC > DMF > ethyl acetate > dichloromethane > ethanol > formamide > water at constant temperature. DMAC can be deemed to be better solvent for the purification process of TBA. The experimental data were correlated by the van’t Hoff plot, modified Apelblat equation and two local composition models (NRTL and UNIQUAC), and the corresponding parameters were derived. The modified Apelblat equation has the best agreement of these. In addition, the value of ΔGOsoln derived from van’t Hoff plot indicates the solution process of TBA in the selected solvents is endothermic, and the value of %ξH show the main contribution to the standard Gibbs energy of solution is the enthalpy during the dissolution. Moreover, the thermodynamic excess functions (GE, SE, HE) of TBA + solvents(ethyl acetate, ethanol, dichloromethane, water, formamide, DMF, DMAC) systems were determined.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

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DOI: 10.1021/acs.jced.5b00135 J. Chem. Eng. Data XXXX, XXX, XXX−XXX