Measurement and Correlation for Solubilities of Adipic Acid, Glutaric

Article pubs.acs.org/jced

Measurement and Correlation for Solubilities of Adipic Acid, Glutaric Acid and Succinic Acid in Acetic Acid + Cyclohexanone Mixtures Weiping Luo,*,† Xiuqing Li,† Dong Ruan,† Dawei Liu,† Kaili Xie,† Jing Wang,† Wei Deng,† Qiang Liu,† and Zhaoke Chen*,‡ †

College of Chemistry and Chemical Engineering, Hunan University, Changsha, 410082, P. R. China State Key Laboratory of Powder Metallurgy, Central South University, Changsha, 410083, P. R. China

‡

S Supporting Information *

ABSTRACT: Under atmospheric pressure, the solubilities of adipic acid, glutaric acid, and succinic acid in acetic acid + cyclohexanone mixtures were measured respectively by using the laser dynamic method in which the temperature ranged from 298.55 to 340.85 K and the mass fraction of cyclohexanone in the binary solvent mixtures ranged from 0.0 to 1.0. The results showed that the solubilities of adipic acid, glutaric acid, and succinic acid in acetic acid + cyclohexanone solvent mixtures all increased with decreasing of the mass fraction of cyclohexanone in the solvent mixtures at the constant temperature, and with the gradually increasing of temperature the measured solubilities of adipic acid, glutaric acid and succinic acid in acetic acid + cyclohexanone solvent mixtures would increase at the constant proportion solvent mixtures. The λh equation and the nonrandom two liquid (NRTL) activity coefficient model were used to correlate the experimental solubilities, and the average relative deviation was lesser than 2% respectively. It was found that the solubilities calculated by these models showed a good agreement with the experimental observations. In addition, the λh equation with a small number of adjustable parameters is very suitable for engineers so that they could use directly. Compared with the λh equation, the NRTL equation has a wider range of applications due to the stronger theory.

1. INTRODUCTION

Recently, most related solubilities of dibasic acid (AA, GA, SA) in different solvents had been reported in the literature.10−28 The solubilities of AA in HAc + ε-caprolactone and cyclohexanone + ε-caprolactone mixtures were measured by Luo with the dynamic method.10 The solubilities of AA and GA in cyclohexanone + cyclohexanol, cyclohexane + cyclohexanone, and cyclohexane + cyclohexanol solvent mixtures were determined respectively by Sheng11,12 at different temperature range, and Yu13 also measured the solubilities of AA in cyclohexanone + cyclohexanol and cyclohexane + cyclohexanone solvent mixtures. Li researched the solubilities of AA and SA in GA + acetone mixtures and GA + n-butanol mixtures.14 Shen investigated the solubilities of AA in HAc + water mixtures and HAc + cyclohexane mixtures using static method.15 Suren also measured the solubilities of AA in several solvents, for instance, water, HAc, HAc + water, cyclohexanol, and cyclohexanone at high temperature.16 In addition, the solubilities of AA was studied in some pure solvents, such as ethanol, chloroform, n-butanol, acetone, toluene, HAc, cyclohexanone, cyclohexanol, methanol, N,N-dimethylformamide, propanol, isopropanol, N,N-dimethylacetamide, dimethyl sulfoxide, ethyl acetate, tert-butanol, and 1,4-dioxane.17−21 Zhang measured the solubilities of GA and SA in HAc, ethanol, acetone,

As an important intermediate, adipic acid (AA) is widely used in the fields of chemical production, organic synthesis industry, pharmaceutical industry, and lubricant manufacturing, etc.1−3 Commercially, AA was usually obtained by a two-step method.4 In the first step, the cyclohexane was used to produce the mixtures of cyclohexanone and cyclohexanol (KA oil) with air, and then the KA oil would be oxidized further to become the AA with the oxidant nitric acid.5,6 It was a complex process discharging massive pollutant such as NOx gas, which resulted in serious environmental pollution.1,4,7 Therefore, an environmentally friendly process for production of AA with high productivity was urgently desirable. Recently, it was reported that AA could be obtained from oxidation of cyclohexanone by air or oxygen without producing NOX;8,9 in these techniques, acetic acid (HAc) was usually used as the solvent, AA was main product, and glutaric acid (GA) and succinic acid (SA) were also appeared simultaneously as the side products. Sequentially, dibasic acids (AA, GA, SA) must be purified from the mixture of HAc + cyclohexanone. Usually, crystallization is used to obtain products with a high purity. Therefore, solid−liquid equilibrium (SLE) data measurement for dibasic acid (AA, GA, SA) in HAc + cyclohexanone become the crucial factor in designing the separation equipment as well as in controlling the relevant operating conditions. © XXXX American Chemical Society

Received: September 13, 2016 Accepted: February 22, 2017

A

DOI: 10.1021/acs.jced.6b00800 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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Figure 1. Devices for measuring the solubility of SLE: 1, computer monitoring center; 2, temperature display panel; 3, a photoelectric transformer; 4, Pt100 temperature sensor; 5, reflux condenser; 6, magnetic stirring system; 7, a jacketed equilibrium glass bottle; 8, semiconductor laser emitter; 9, thermostatic water-circulator bath; 10, temperature-programmed controller.

Figure 2. Comparisons between experimental solubility of AA in cyclohexanone with the reported data in literature: ■, experimental solubility data; □, literature data from Sheng;11 ○, literature data from Yu;13 ◇, literature data from Suren;16 △, literature data from Fan.19

Figure 4. Comparisons between experimental solubility of GA in cyclohexanone with the reported data in literature: ■, experimental solubility data; □, literature data from Sheng;12 ○, literature data from Song.23

Figure 3. Comparisons between experimental solubility of AA in HAc with the reported data in literature: ■, experimental solubility data; □, literature data from Luo;10 ▲, literature data from Shen;15 ▼, literature data from Suren;16 ○, literature data from Fan;19 ◇, literature data from Gaivoronskii;20 + , literature data from Zhang.21

Figure 5. Comparisons between experimental solubility of GA in HAc with the reported data in literature: ■, experimental solubility data; □, literature data from Zhang;21 ○, literature data from Song.23

HAc + cyclohexane.28 Meanwhile, there are many models that were used for correlating the experimental solubilities of acid, such as NRTL equation,10,11,15,19,22,23 λh equation,13,14,17,19,22,23,26 Apelblat equation,11,13,14,16−18,26 UNIFAC equation,17 UNIQUAC equation,28 Van’t Hoff equation,26 PC-SAFT equation,29,30 and so on. Among these models, the most commonly used models which were used to correlate the solubilities of AA, GA, and SA in different solvents and mixed solvents were the λh equation, Apelblat equation, and NRTL equation. Due to need, only a small number of adjustable parameters, the λh equation and Apelblat equation are very suitable for engineers so that they

21

and ethyl acetate, respectively. Solubilities of SA and GA in cyclohexanone, cyclohexanol, and their mixed solvents were measured respectively by Fan22 and Song.23 Song measured the SLE data of SA in cyclohexanol, cyclohexanone, N,Ndimethylformamid, N,N-dimethyllacetamide, and acetic acid.24 Yu determined the solubilities of SA in water, ethanol, 1-propanol, 2-propanol, acetone, and HAc at temperatures between 283 and 333 K.25 Of course, there were also other studies on solubilities data of SA in the mixed solution, like methanol + water,26 ethanol + water,26,27 HAc + water,27 and B



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Table 1. Comparisons Between Experimental Solubility of AA, GA, and SA in Pure Cyclohexanone and HAc with the Reported Data in Literaturea10−13,15,16,19−25,28 T (K)

10xb

102 RDc

T (K)

10xb

102 RDc

102 ARD

0.369 0.422 0.478 0.542 0.616

−5.94 −5.56 −4.39 −1.64 −2.12

4.58

0.426 0.479 0.563 0.663 0.760

1.58 0.76 1.19 1.89 −0.15

1.09

3.067 3.278 3.678 4.143 4.692

5.23 5.24 4.99 1.85 0.44

5.38

3.555 3.806 4.005 4.299 4.640

4.00 3.13 1.90 1.98 2.05

4.03

0.279 0.326 0.377 0.422 0.469

0.55 −1.04 −0.42 −2.33 −2.94

1.42

0.270 0.301 0.338 0.375 0.410

0.26 0.19 0.21 −0.46 −0.95

0.77

10

Figure 6. Comparisons between experimental solubility of SA in cyclohexanone with the reported data in literature: ■, experimental solubility data; □, literature data from Fan.22

Figure 7. Comparisons between experimental solubility of SA in HAc with the reported data in literature: ■, experimental solubility data; △, literature data from Zhang;21 ◇, literature data from Song;24 □, literature data from Yu;25 ○, literature data from Lei.28

could be used directly. However, it is hazardous to extrapolate it from the empirical correlations under several given compositions of the mixture. Compared with the λh equation and Apelblat equation, the NRTL model has a wider range of applications due to the stronger theory. Unfortunately, no reports about dibasic acid (AA, GA, SA) in HAc + cyclohexanone mixtures could be available under the particular temperature and composition required in a particular program. It is therefore necessary for measuring and correlating the solubility of dibasic acid (AA, GA, SA) in HAc + cyclohexanone mixtures. When suitable data are lacking, the desired equilibrium data could be estimated from some appropriate correlation by interpolating or extrapolating these SLE data. In this work, the solubilities of AA, GA and SA in HAc + cyclohexanone solvent mixtures were respectively determined at 298.55−340.85 K, and the λh equation and the NRTL activity coefficient model were applied to correlate the experimental values. The interaction parameters of AA and HAc, AA and cyclohexanone, GA and HAc, GA and cyclohexanone, SA and HAc, SA and cyclohexanone, and HAc and cyclohexanone were determined first by the available ternary SLE of AA/GA/SA + HAc + cyclohexanone mixtures.

301.25 305.45 309.95 314.45 318.25

0.147 0.185 0.227 0.274 0.321

301.85 305.25 308.85 311.45 314.65

0.230 0.265 0.300 0.331 0.379

303.55 306.25 309.35 311.55 314.35

2.000 2.213 2.450 2.611 2.801

303.45 307.55 312.85 317.35 321.15

2.107 2.413 2.761 3.098 3.404

298.55 303.95 309.75 316.05 319.35

0.120 0.144 0.174 0.215 0.240

301.35 305.65 309.65 313.75 317.15

0.150 0.167 0.190 0.214 0.239

AA + Cyclohexanone 7.26 321.15 −2.52 324.35 −5.61 327.65 −5.67 331.65 −5.08 334.75 AA + HAc 2.73 318.15 0.13 321.05 1.30 325.65 1.21 330.55 0.00 334.05 GA + Cyclohexanone 11.53 317.95 8.16 320.65 5.89 325.35 5.15 329.15 5.29 334.05 GA + HAc 9.27 323.15 5.41 325.75 4.81 327.45 4.09 330.65 3.65 334.15 SA + Cyclohexanone 1.51 323.85 1.11 328.55 1.60 333.75 1.34 337.15 1.37 340.85 SA + HAc 1.02 321.15 1.92 324.95 0.81 328.95 1.44 332.45 0.44 335.55

a

Standard uncertainties u are u (T) = 0.05 K, ur (p) = 0.05, ur (ω1) = 0.01, ur (x) = 0.10. bx represents the experimental molar fraction of solubility in pure cyclohexanone and HAc, respectively. cRD is the relative deviation between the experimental solubility data and the literature data.10−13,15,16,19−25,28 ARD is the averaged relative deviation.

The Supporting Information lists a table containing molecular formulas, mass fractions, analysis methods, and suppliers of materials. 2.2. Apparatus and Procedure. The laser dynamic method was widely applied for the measurement of solubility.10−12,14 The experimental apparatus are shown in Figure 1, whose core components were a SLE cell, a laser-detecting system, a temperature-controlling and measurement system, and a magnetic stirring system, and it was introduced in detail in our previous work.10 Briefly, the experiment was conducted in a 100 mL glass bottle with a jacket which was connected with the thermostatic water-circulator bath. The temperature of the solution was determined by a thermoelectric controlling system with a precision of ±0.1 K. To prevent effectively the evaporation of HAc, cyclohexanone, and the rest of species, the bottle was sealed by a rubber stopper at the top of the reflux condenser.

2. EXPERIMENTAL SECTION 2.1. Materials. AA, GA, and SA were purchased from Shanghai Fine Chemical Reagent Company, whose mass fraction could reach 99.0%. Cyclohexanone and HAc were bought from Changsha Chemical Reagent Company. C



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Table 2. Solubility of AA (1) in HAc (4) + Cyclohexanone (5) Solvent Mixtures at Temperature (301.25−336.75 K) and Pressure p = 0.1 MPaa λh T (K)

10x

301.25 305.45 309.95 314.45 318.25 321.15 324.35 327.65 331.65 334.75

0.147 0.185 0.227 0.274 0.321 0.369 0.422 0.478 0.542 0.616

301.85 305.35 308.85 313.35 317.45 321.85 324.75 327.65 330.05 333.55

0.202 0.239 0.276 0.328 0.385 0.465 0.524 0.579 0.635 0.723

303.95 307.05 311.55 315.35 318.85 323.45 327.55 330.15 333.55 336.95

0.239 0.273 0.326 0.380 0.440 0.520 0.597 0.666 0.754 0.856

303.25 305.15 308.35 311.05 314.85

0.232 0.254 0.291 0.321 0.372

10xc

λh

NRTL 102 RDb

ω1 = 1.0 10 0.154 4.82 0.186 0.54 0.227 0.07 0.275 0.62 0.323 0.69 0.364 −1.46 0.414 −1.98 0.471 −1.35 0.550 1.52 0.619 0.39 ω1 = 0.9 0.202 0.21 0.236 −1.52 0.274 −0.85 0.331 0.90 0.391 1.36 0.465 −0.08 0.520 −0.75 0.581 0.36 0.635 −0.05 0.722 −0.07 ω1 = 0.7 0.237 −0.50 0.271 −0.93 0.326 −0.05 0.380 0.07 0.436 −0.76 0.521 0.02 0.607 1.56 0.667 0.24 0.754 0.04 0.850 −0.64 ω1 = 0.5 0.233 0.33 0.252 −0.69 0.288 −0.92 0.322 0.25 0.374 0.51

10xc

102 RDb

T (K)

10x

0.154 0.186 0.227 0.275 0.323 0.364 0.415 0.473 0.553 0.623

5.20 0.77 0.18 0.65 0.73 −1.31 −1.72 −0.97 2.00 1.12

319.85 324.15 327.25 331.85 336.75

0.454 0.533 0.601 0.701 0.842

0.203 0.236 0.272 0.326 0.383 0.454 0.506 0.563 0.614 0.696

0.82 −1.55 −1.43 −0.36 −0.48 −2.48 −3.50 −2.73 −3.38 −3.75

302.75 305.85 308.85 311.45 313.95 319.35 324.45 329.05 333.15 336.25

0.233 0.262 0.291 0.321 0.356 0.440 0.537 0.625 0.729 0.820

0.245 0.278 0.333 0.385 0.440 0.522 0.605 0.662 0.744 0.835

2.58 1.66 1.90 1.46 0.08 0.20 1.20 −0.56 −1.26 −2.45

301.55 304.05 307.15 310.25 314.25 317.45 320.35 324.75 328.25 332.65

0.220 0.243 0.272 0.306 0.357 0.405 0.455 0.533 0.606 0.704

0.237 0.256 0.292 0.325 0.377

1.95 0.76 0.30 1.31 1.29

301.85 305.25 308.85 311.45 314.65 318.15 321.05 325.65 330.55 334.05

0.230 0.265 0.300 0.331 0.379 0.426 0.479 0.563 0.663 0.760

10xc

NRTL 102 RDb

ω1 = 0.5 −0.04 0.16 −0.32 0.73 −0.38 ω1 = 0.3 0.227 −2.75 0.258 −1.37 0.292 0.43 0.324 1.08 0.358 0.45 0.441 0.34 0.534 −0.45 0.632 1.15 0.731 0.31 0.814 −0.77 ω1 = 0.1 0.213 −3.17 0.237 −2.74 0.269 −1.22 0.305 −0.35 0.358 0.35 0.406 0.30 0.453 −0.40 0.535 0.26 0.607 0.30 0.711 0.96 ω1 = 0.0 0.228 −0.83 0.261 −1.46 0.301 0.58 0.333 0.68 0.377 −0.56 0.430 0.78 0.478 −0.22 0.564 0.05 0.669 0.91 0.754 −0.74 0.454 0.534 0.599 0.706 0.839

10xc

102 RDb

0.456 0.534 0.597 0.702 0.829

0.32 0.16 −0.61 0.05 −1.58

0.230 0.261 0.295 0.327 0.361 0.444 0.536 0.632 0.728 0.809

−1.47 −0.18 1.55 2.10 1.34 0.93 −0.20 1.15 −0.03 −1.39

0.218 0.242 0.275 0.312 0.365 0.412 0.460 0.541 0.613 0.714

−0.74 −0.43 0.99 1.72 2.21 1.95 1.02 1.39 1.16 1.47

0.221 0.255 0.295 0.327 0.371 0.424 0.472 0.559 0.664 0.749

−3.55 −3.84 −1.48 −1.15 −2.16 −0.55 −1.38 −0.87 0.20 −1.40

a Standard uncertainties u are u (T) = 0.05 K, ur (p) = 0.05, ur (ω1) = 0.01, ur (x) = 0.10. bRD = (xc − x)/x. x and xc represent the experimental and calculated molar fraction of solubility, respectively. ω1 is the mass fraction of cyclohexanone (5) in binary (HAc + cyclohexanone) solvent mixtures.

solute blocked the laser beam. When the solute disappeared exactly and the intensities of transmitted laser reached the maximum, the SLE would be achieved. Just then, the corresponding solution temperature was the SLE temperature. 2.3. Verfication of the Experimental Methods. In our previous report,10 the reliability and accuracy of the experimental apparatus and method had been verified by comparison of the experimental data with the published data for the solubility of AA in HAc and cyclohexanone, respectively. To further verify the reliability and accuracy of the experimental apparatus and method, the solubilities of AA, GA, and SA in cyclohexanone and HAc were measured respectively in this work. The experimental measured solubilities of AA, GA, and SA in cyclohexanone are plotted in Figures 2, 4, and 6, which is consistent with the data reported.11−13,16,19,22,23 Meanwhile, Figures 3, 5, and 7 plotted the solubilities of AA, GA, and SA in HAc between the experimental

The laser-detecting system mainly consists of a semiconductor laser emitter of 25 mW, a photoelectric transformer, and a computer in which the real-time temperature and laser intensity value could be displayed and recorded through the Kingview software. For each experiment, excessive amounts of solute and 50 g of solvent were separately added into the equilibrium bottle carried on stirring continuously at the same time, in which the solid particle still presented in the solution after fully mixing. Next, the thermostatic water-circulator bath was set to heat the equilibrium bottle in a stepwise fashion (1.5 K/h) until the solute was going to dissolve. When the temperature of the solution closed to the SLE temperature (more than 1 K below), the heating rate was kept at 0.2 K/h. Meanwhile, a steady laser beam went through the mixture of solute and solvent continuously, it would be scattered and the transmitted intensities would weak because the unsolved D



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data and the data from the literature.10,15,16,19−21,23−25,28 From Table 1, our results also agree well with the available literature reported data, which indicates the accuracy and reliability of our experimental technique.

cyclohexanone mixtures decreased at constant temperature or temperature increased under the same concentration, the solubility of SA both would increase. Hence, the dissolution process of SA in HAc + cyclohexanone mixtures was also endothermic as AA and GA,21 and the SA was more soluble in solvents with large polarity.21 Furthermore, the solubility of GA in the binary solvents was much greater than the solubilities of AA and SA under the same conditions, which could be explained as follows. Compared with the AA and SA, there were looser interlayers for the chains of GA with odd number of carbon atoms so that the solvent molecules were easier to reside between the GA molecular planes in the dissolution process.21 3.2. Correlation of Experimental Data. λh Equation. Commercially, correlating AA, GA, and SA SLE data with a small number of adjustable parameters is necessary for engineers so that they could use directly. In this work, we correlate the experimental solubility with the λh equation, and the form is described by eq 1:31

3. RESULTS AND DISCUSSION 3.1. Solubility Data. Solubility of AA in HAc + Cyclohexanone Mixtures. The solubility of AA in HAc + cyclohexanone mixtures is presented in Table 2, where x represents the mole fraction of AA in saturated solutions and ω1 is defined as the mass fraction of cyclohexanone in the solvent mixtures. As shown in the Figure 8, comparing all of the solubility of AA in

⎡ ⎛1 λ(1 − xi) ⎤ 1 ⎞ ln⎢1 + ⎥ = λh⎜ − ⎟ xi Tm ⎠ ⎣ ⎦ ⎝T xi = Figure 8. Solubility of AA (1) in HAc (4) + cyclohexanone (5) solvent mixtures; ω1 is the mass fraction of cyclohexanone (4) in binary (HAc + cyclohexanone) solvent mixtures; ■, ω1 = 1.0; □, ω1 = 0.9; ●, ω1 = 0.7; ○, ω1 = 0.5; ▲, ω1 = 0.3; ◇, ω1 = 0.1; ▼, ω1 = 0.0; solid line, NRTL equation calculated solubility curve; ⧳, RD of solubility between experimental data and the calculated; S is defined as the mass of solute (g) in 100 g of solvent.

Si /M1 Si /M1 + 100ω1/M 2 + 100(1 − ω1)/M3

(1)

(2)

In eq 1, λ and h are the coefficient parameters of the λh equation, respectively, and T is defined as the absolute temperature, Tm is the melting temperature of the solute listed in Table 5. In addition, xi represents the mole fraction solubility of solute (AA, GA, SA) in saturate solution, and it could be defined by the solubility as eq 2, where Si represents the solubilities of AA, GA, and SA in HAc + cyclohexanone solution, ω1 is the mass fraction of cyclohexanone in the HAc + cyclohexanone mixtures, and M1, M2, and M3 are the molecular weight of solute, cyclohexanone, and HAc, respectively. Meanwhile, the relative deviation (RD), the experimental and the correlated solubilities are shown in Tables 2 to 4, which is defined as the following form:

HAc + cyclohexanone mixtures, it clearly indicates that the solubility of AA increased with increasing of temperature at the same concentration, which explains the dissolution process was endothermic.21 Moreover, the solubility of AA decreased with increasing of mass fraction of cyclohexanone in the solvent mixtures at constant temperature, indicating solvents with small polarity and large molecular would lead to the decrease for solubility of AA, as mentioned by Zhang.21 And it was pure HAc that had the best dissolving capacity for AA at same temperature. Solubilitiy of GA in HAc + Cyclohexanone Mixtures. The solubility of GA in HAc + cyclohexanone mixtures is displayed in Table 3, where x represents the mole fraction of GA in saturated solutions and ω1 is defined as the mass fraction of cyclohexanone in the solvent mixtures. From Figure 9, the change trend for the solubility of GA in mixed solution was the same as with the solubility of AA. The solubility of GA both would increase with decreasing of mass fraction of cyclohexanone in the solvent mixtures at constant temperature or increasing of temperature at the same concentration of solution. In other words, the dissolution process of GA in HAc + cyclohexanone mixtures was also endothermic,21 and the GA was more soluble in solvents with large polarity.21 Solubility of SA in HAc + Cyclohexanone Mixtures. The solubility of SA in HAc + cyclohexanone mixtures is displayed in Table 4, where x represents the mole fraction of SA in saturated solutions and ω1 is defined as the mass fraction of cyclohexanone in the mixed solvent. As shown in Figure 10, similar to the system of AA + HAc + cyclohexanone and GA + HAc + cyclohexanone, when the mass fraction of cyclohexanone in HAc +

RDi =

xci − xi xi

(3)

In Tables 6−8, the values of the coefficient parameters λ and h and the average relative deviation (ARD) are listed, which are calculated according to the eq 4: ARD =

1 n

n

∑ abs(RDi) i=1

(4)

In eq 4, n represents the total experimental points. As shown in Tables 6−8, the ARD are less than 1.34%, which could draw a conclution that the λh equation can be used to correlate the solubilities of AA, GA, and SA in HAc + cyclohexanone solution within the studied ranged temperature. NTRL Equation. The above λh equations, as a function of T, describe solubilities satisfactorily at a given mixture composition, while it was difficult to correlate the parameters with the composition of the mixture and it is hazardous to extrapolate it from the empirical correlations under several given compositions of the mixture. Therefore, it is preferable in such works to rely on some stronger theoretical correlations. Among these models, the NRTL equation was the most commonly used one. E



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Table 3. Solubility of GA (2) in HAc (4) + Cyclohexanone (5) Solvent Mixtures at Temperature (302.55−334.25 K) and Pressure p = 0.1 MPaa λh T (K)

10x

10xc

303.55 306.25 309.35 311.55 314.35 317.95 320.65 325.35 329.15 334.05

2.000 2.213 2.450 2.611 2.801 3.067 3.278 3.678 4.143 4.692

2.032 2.204 2.416 2.574 2.787 3.079 3.312 3.747 4.126 4.652

303.55 306.65 309.75 312.65 315.55 318.25 321.15 324.75 328.35 332.25

2.099 2.347 2.572 2.797 3.041 3.238 3.498 3.799 4.247 4.647

303.25 306.75 309.45 312.65 315.85 318.45 322.25 325.95 329.15 333.75

2.051 2.327 2.508 2.756 3.011 3.216 3.517 3.941 4.270 4.739

302.95 306.65 309.95 312.85 315.95

2.007 2.299 2.532 2.773 3.012

λh

NRTL 102 RDb

10xc

102 RDb

T (K)

10x

1.980 2.179 2.415 2.587 2.812 3.120 3.364 3.817 4.221 4.756

−0.96 −1.54 −1.45 −0.93 0.38 1.72 2.64 3.78 1.89 1.36

319.25 322.85 325.95 329.15 334.25

3.272 3.552 3.911 4.208 4.721

2.104 2.317 2.538 2.757 2.990 3.213 3.468 3.799 4.158 4.561

0.23 −1.28 −1.32 −1.43 −1.68 −0.79 −0.84 0.01 −2.07 −1.86

303.95 308.85 312.65 315.25 317.75 320.65 323.15 326.15 328.75 332.65

2.085 2.438 2.736 2.933 3.118 3.347 3.553 3.884 4.133 4.505

2.117 2.347 2.531 2.764 3.012 3.224 3.551 3.898 4.212 4.689

3.23 0.85 0.89 0.32 0.06 0.27 0.96 −1.09 −1.38 −1.05

302.55 305.05 308.15 310.85 314.25 316.75 319.55 322.85 326.95 330.95

1.965 2.168 2.395 2.588 2.826 3.011 3.242 3.490 3.899 4.286

2.075 2.315 2.541 2.755 2.995

3.38 0.71 0.38 −0.65 −0.56

303.45 307.55 312.85 317.35 321.15 323.15 325.75 327.45 330.65 334.15

2.107 2.413 2.761 3.098 3.404 3.555 3.806 4.005 4.299 4.640

ω1 = 1.0 1.60 −0.39 −1.41 −1.42 −0.49 0.40 1.05 1.87 −0.40 −0.85 ω1 = 0.9 2.126 1.27 2.335 −0.51 2.559 −0.51 2.781 −0.58 3.017 −0.79 3.248 0.31 3.510 0.36 3.854 1.44 4.218 −0.67 4.636 −0.23 ω1 = 0.7 2.076 1.23 2.309 −0.77 2.501 −0.31 2.743 −0.48 3.000 −0.34 3.222 0.19 3.565 1.36 3.922 −0.48 4.249 −0.49 4.749 0.22 ω1 = 0.5 2.057 2.46 2.296 −0.12 2.526 −0.22 2.742 −1.13 2.987 −0.83

10xc

NRTL 102 RDb

ω1 = 0.5 −0.24 0.96 −0.76 −0.13 0.61 ω1 = 0.3 2.116 1.47 2.437 −0.02 2.711 −0.94 2.910 −0.77 3.112 −0.19 3.358 0.34 3.582 0.81 3.863 −0.53 4.119 −0.32 4.526 0.45 ω1 = 0.1 2.020 2.80 2.172 0.16 2.372 −0.94 2.558 −1.17 2.807 −0.67 3.002 −0.31 3.231 −0.35 3.517 0.78 3.898 −0.04 4.297 0.27 ω1 = 0.0 2.132 1.18 2.388 −1.04 2.753 −0.28 3.094 −0.11 3.407 0.08 3.580 0.71 3.815 0.24 3.975 −0.73 4.290 −0.23 4.654 0.30 3.264 3.587 3.881 4.203 4.750

10xc

102 RDb

3.265 3.578 3.870 4.183 4.716

−0.21 0.72 −1.04 −0.60 −0.11

2.114 2.439 2.715 2.915 3.115 3.360 3.582 3.867 4.123 4.525

1.36 0.03 −0.79 −0.62 −0.09 0.40 0.83 −0.42 −0.25 0.43

2.007 2.167 2.375 2.565 2.818 3.016 3.250 3.539 3.930 4.334

2.15 −0.05 −0.84 −0.90 −0.27 0.17 0.26 1.41 0.77 1.11

2.066 2.335 2.711 3.065 3.388 3.566 3.812 3.980 4.303 4.676

−1.95 −3.23 −1.81 −1.07 −0.46 0.33 0.14 −0.61 0.08 0.78

Standard uncertainties u are u (T) = 0.05 K, ur (p) = 0.05, ur (ω1) = 0.01, ur (x) = 0.10. bRD = (xc − x)/x. x and xc represent the experimental and calculated molar fraction of solubility, respectively. ω1 was the mass fraction of cyclohexanone (5) in binary (HAc + cyclohexanone) solvent mixtures. a

Thermodynamically, the solubility correlation equation was built on the equality of chemical potentials between compositions in all the coexisting phases. For pure solid phase, if the solid−solid phase transition did not occur, the SLE is described by eq 5 that involved the properties of pure solute such as the mole fusion enthalpy ΔmH and melting temperature Tm. ln γixi = −

Δm H ⎡ 1 1 ⎤ ⎥ ⎢ − R ⎣T Tm ⎦

(5)

In eq 5, R is the gas constant that is 8.314 J·mol−1·K−1 and T represents the absolute temperature. ΔmH and Tm are listed in Table 5. According to eq 5, to calculate the solubility xi, the activity coefficient model calculated γi must be adopted as eqs 6 and 7.32,33 In eq 5, the activity coefficient depended on the mole fraction xi and temperature, so eq 5 to 7 must be solved iteratively.

Figure 9. Solubility of GA (2) in HAc (4) + cyclohexanone (5) solvent mixtures; ω1 is the mass fraction of cyclohexanone (4) in binary (HAc + cyclohexanone) solvent mixtures; ■, ω1 = 1.0; □, ω1 = 0.9; ●, ω1 = 0.7; ○, ω1 = 0.5; ▲, ω1 = 0.3; ◊, ω1 = 0.1; ▼, ω1 = 0.0; solid line, NRTL equation calculated solubility curve; ⧳, RD of solubility between experimental data and the calculated; S is defined as the mass of solute (g) in 100g solvent. F



Article

Table 4. Solubility of SA (3) in HAc (4) + Cyclohexanone (5) Solvent Mixtures at Temperature (298.55 to 340.85 K) and Pressure p = 0.1 MPaa λh ω1 = 1.0 298.55 303.95 309.75 316.05 319.35 323.85 328.55 333.75 337.15 340.85 ω1 = 0.9 300.25 303.75 306.35 309.95 314.45 319.05 322.95 328.85 333.75 337.35 ω1 = 0.7 302.45 305.65 308.55 312.75 316.35 320.05 324.55 327.75 331.55 334.65 ω1 = 0.5 305.75 308.45 311.65 315.25 318.55

λh

NRTL

10x

10xc

102 RDb

10xc

102 RDb

0.120 0.144 0.174 0.215 0.240 0.279 0.326 0.377 0.422 0.469

0.117 0.143 0.175 0.217 0.241 0.279 0.324 0.380 0.420 0.469

−1.88 −0.54 0.57 0.54 0.69 0.19 −0.86 0.71 −0.42 0.00

0.106 0.132 0.166 0.211 0.239 0.281 0.333 0.399 0.449 0.509

−11.09 −7.90 −4.63 −2.08 −0.53 0.94 2.02 5.93 6.39 8.54

0.150 0.167 0.185 0.208 0.238 0.278 0.312 0.375 0.436 0.487

0.152 0.171 0.186 0.210 0.242 0.280 0.315 0.375 0.432 0.479

1.32 2.12 1.01 1.05 1.67 0.41 0.98 0.15 −0.85 −1.75

0.147 0.166 0.183 0.207 0.241 0.281 0.320 0.386 0.449 0.501

−2.03 −0.52 −1.07 −0.26 1.33 1.06 2.51 2.93 2.93 2.73

0.160 0.177 0.195 0.223 0.253 0.283 0.329 0.361 0.406 0.447

0.162 0.180 0.198 0.227 0.255 0.286 0.328 0.361 0.403 0.441

0.88 1.59 1.56 2.14 0.67 0.86 −0.47 −0.19 −0.79 −1.31

0.161 0.180 0.199 0.229 0.257 0.290 0.333 0.368 0.412 0.451

0.18 1.33 1.67 2.78 1.63 2.19 1.16 1.70 1.29 0.89

0.177 0.193 0.213 0.240 0.267

0.177 0.193 0.215 0.241 0.268

−0.22 0.34 0.68 0.37 0.30

0.171 0.188 0.209 0.236 0.262

−3.49 −2.61 −1.93 −1.90 −1.70

T (K)

T (K) ω1 = 0.5 322.25 324.35 327.65 330.75 334.55 ω1 = 0.3 300.05 303.65 306.65 309.65 314.35 319.45 323.55 328.95 332.25 335.65 ω1 = 0.1 300.15 302.65 306.35 310.45 314.45 317.95 321.85 325.95 330.65 336.55 ω1 = 0.0 301.35 305.65 309.65 313.75 317.15 321.15 324.95 328.95 332.45 335.55

NRTL

10x

10xc

102 RDb

10xc

102 RDb

0.300 0.319 0.353 0.390 0.435

0.300 0.320 0.354 0.388 0.433

0.10 0.27 0.15 −0.51 −0.49

0.295 0.315 0.349 0.382 0.427

−1.64 −1.36 −1.32 −1.91 −1.81

0.146 0.160 0.176 0.194 0.225 0.265 0.302 0.356 0.391 0.431

0.140 0.159 0.176 0.194 0.226 0.266 0.302 0.355 0.392 0.432

−4.01 −0.98 0.13 0.40 0.49 0.54 0.10 −0.12 0.14 0.27

0.135 0.154 0.171 0.190 0.223 0.263 0.299 0.353 0.389 0.430

−7.44 −3.92 −2.39 −1.75 −1.14 −0.64 −0.81 −0.80 −0.45 −0.29

0.143 0.152 0.170 0.194 0.217 0.243 0.275 0.313 0.359 0.425

0.140 0.152 0.172 0.196 0.222 0.246 0.277 0.312 0.357 0.421

−1.95 −0.09 0.97 0.81 2.11 1.19 0.68 −0.18 −0.65 −1.10

0.135 0.148 0.169 0.194 0.222 0.249 0.282 0.320 0.369 0.438

−5.61 −3.00 −0.84 0.13 2.50 2.37 2.67 2.52 2.74 2.96

0.150 0.167 0.190 0.214 0.239 0.270 0.301 0.338 0.375 0.410

0.145 0.167 0.190 0.216 0.240 0.270 0.302 0.339 0.374 0.408

−2.98 0.04 0.03 1.20 0.40 0.28 0.24 0.34 −0.17 −0.45

0.142 0.165 0.190 0.218 0.243 0.277 0.311 0.352 0.390 0.426

−5.59 −1.33 −0.25 1.99 1.94 2.65 3.30 4.03 3.93 3.96

Standard uncertainties u are u (T ) =0.05 K, ur (p) = 0.05, ur (ω1) = 0.01, ur (x) = 0.10. bRD = (xc − x)/x. x and xc represent the experimental and calculated molar fraction of solubility, respectively. ω1 was the mass fraction of cyclohexanone (5) in binary (HAc + cyclohexanone) solvent mixtures. a

3

ln γi =

∑ j = 1 τjixjGji 3

∑k = 1 Gkixk

3

+

∑ j=1

3

∑k = 1 Gkjxk

3 ⎛ ∑ xτ G ⎞ ⎜τ − k = 1 k kj kj ⎟ 3 ⎜ ij ∑k = 1 xkGkj ⎟⎠ ⎝

Gij = exp( −ηijτij), τii = 0

τij =

Matlab (Mathwork, MA) used the Nelder−Mead Simplex approach and can be employed for the minimization of the objective function, which is the ARD between the experimental and the calculated solubility defined as eq 4.35 In Tables 2−4, the results of calculated solubility and corresponding RD are listed. Simultaneously, the binary interaction parameters bij and ARD are listed in Table 9. From Figures 8, 9, and 10, well-correlated results show that the NRTL activity coefficient model could be used to simulate the solubility of AA, GA, and SA in HAc + cyclohexanone mixtures. Moreover, the interaction parameters of AA and HAc, AA and cyclohexanone, GA and HAc, GA and cyclohexanone, SA and HAc, SA and cyclohexanone, and HAc and cyclohexanone were measured first by the available ternary SLE of AA/GA/SA + HAc + cyclohexanone mixtures. During the design and optimization of the related process, the experimental solubilities of AA, GA, and SA in HAc + cyclohexanone mixtures and the obtained interaction parameters might exist great reference value.

xjGij

(6)

bij RT

,

ηij = ηji ,

τij ≠ τji , (7)

To obtain the interaction parameter bij, the experimental solubilities of AA, GA, and SA in solvent mixtures are correlated by a equation together, where ηij is 0.3 as proposed by Remon and Prausnitz.34 The optimum algorithm applied in the parameter estimation program was the Nelder−Mead Simplex approach. Function f iminsearch in the optimization toolbox of G



Article

Table 9. Binary Interaction Parameters of the Modified NRTL Equation for AA(1) + GA (2) + SA (3) + HAc (4) + Cyclohexanone (5)

Table 5. Melting Temperature and the Mole Fusion Enthalpy of the Solute AA

GA

SA

426.1510 3485010

371.1523 2090023

460.1522 3295022

Table 6. Regression Results of λh Equation Parameters for AA (1) in HAc (4) + Cyclohexanone (5) Solvent Mixtures system

λ

h (K)

102 ARD

ω1 = 1.0 ω1 = 0.9 ω1 = 0.7 ω1 = 0.5 ω1 = 0.3 ω1 = 0.1 ω1 = 0.0

0.8923 1.0076 0.9935 0.9439 0.9160 0.9082 0.8848

4680.9 4014.5 3984.1 4125.4 4224.9 4264.9 4304.9

1.34 0.61 0.48 0.43 0.91 1.01 0.68

■

λ

h (K)

102 ARD

ω1 = 1.0 ω1 = 0.9 ω1 = 0.7 ω1 = 0.5 ω1 = 0.3 ω1 = 0.1 ω1 = 0.0

1.2122 1.3610 1.3197 1.2263 1.1487 1.0866 1.0598

2406.1 2202.6 2258.2 2348.6 2431.8 2510.5 2452.5

0.99 0.67 0.59 0.75 0.58 0.75 0.49

bji

ηij

102 ARD

1−4 1−5 2−4 2−5 3−4 3−5 4−5

5737.4 −2741.9 −2428.0 −3065.8 18065 −3998.8 −2812.4

−3531.2 4081.1 3916.5 6160.0 −2738.3 6355.9 4537.5

0.3

1.63

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.6b00800. Molecular formulas, mass fractions, analysis methods, and suppliers of experimental materials (PDF)

Table 7. Regression Results of λh Equation Parameters for GA (2) in HAc (4) + Cyclohexanone (5) Solvent Mixture system

bij

4. CONCLUSIONS Under atmospheric pressure, the solubilities of AA, GA, and SA in HAc + cyclohexanone mixtures were measured respectively by using the laser dynamic method, in which the temperature ranged from 298.55 to 340.85 K. The following conclusions would be obtained: (1) At constant solvent composition, the solubilities of AA, GA, and SA increase as temperature increase in HAc + cyclohexanone solvent systems, respectively. (2) At constant temperature, for binary HAc + cyclohexanone solvent mixtures, the solubilities of AA, GA, and SA decrease gradually with the mass fraction of cyclohexanone in solvent mixtures increasing, respectively. (3) At a given temperature, for HAc + cyclohexanone solvent mixtures, the solubilities of GA are greater than AA and SA at constant solvent composition (4) The experimental data were correlated by the λh equation and the NRTL equation, and the correlated solubilities data show a good agreement with the experimental data, which indicates that both the λh equation and the NRTL equation are suitable for calculating the solubilities of AA, GA, and SA in HAc + cyclohexanone mixtures, respectively.

Figure 10. Solubility of SA (3) in HAc (4) + cyclohexanone (5) solvent mixtures; ω1 is the mass fraction of cyclohexanone (4) in binary (HAc + cyclohexanone) solvent mixtures; ■, ω1 = 1.0; □, ω1 = 0.9; ●, ω1 = 0.7; ○, ω1 = 0.5; ▲, ω1 = 0.3; ◇, ω1 = 0.1; ▼, ω1 = 0.0; solid line, NRTL equation calculated solubility curve; ⧳, RD of solubility between experimental data and the calculated; S is defined as the mass of solute (g) in 100 g of solvent.

Tm (K) ΔmH (J·mol−1)

i−j

■

AUTHOR INFORMATION

Corresponding Authors

*For W.L.: phone, +86-731-88821314; fax, +86 731 88821448; E-mail, [email protected],. *For Z.C.: E-mail, [email protected]. ORCID

Weiping Luo: 0000-0001-8472-6375 Funding

Table 8. Regression Results of λh Equation Parameters for SA (3) in HAc (4) + Cyclohexanone (5) Solvent Mixture system

λ

h (K)

102 ARD

ω1 = 1.0 ω1 = 0.9 ω1 = 0.7 ω1 = 0.5 ω1 = 0.3 ω1 = 0.1 ω1 = 0.0

0.5380 0.5134 0.5182 0.5256 0.5066 0.4157 0.4155

6060.7 5950.5 5930.5 5910.5 6129.5 7077.9 7087.9

0.64 1.13 1.05 0.34 0.72 0.97 0.61

We are particularly grateful for the financial support by the Science and Technology Project of Hunan Province (201585) and the Fundamental Research Funds for the Central Universities. Notes

The authors declare no competing financial interest.

■

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Measurement and Correlation for Solubilities of Adipic Acid, Glutaric

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