Article pubs.acs.org/jced
Determination and Correlation for the Solubility of Glutaric Acid in Cyclohexane + Cyclohexanol + Cyclohexanone Solvent Mixtures Xiaoxiao Sheng,† Qinbo Wang,*,† Linhui Chen,‡ Zhipeng Shen,† and Yinchuan Pei† †
Department of Chemical Engineering, Hunan University, Changsha, 410082 Hunan, P. R. China Hangzhou Xingyong Multiplex Material Co. Ltd., Hangzhou, 312402 Zhejiang, P. R. China
‡
ABSTRACT: The solubilities of glutaric acid in binary cyclohexane + cyclohexanol solvent mixtures at 298.05− 343.65 K, in binary cyclohexane + cyclohexanone solvent mixtures at 299.10−340.65 K, in binary cyclohexanone + cyclohexanol solvent mixtures at 299.75−343.65 K, and in ternary cyclohexanol + cyclohexanone + cyclohexane solvent mixtures at 298.15−330.95 K were studied by the dynamic method. The results show that the solubility of glutaric acid increases as temperature increases at constant solvent composition in three determined binary solvent systems. For binary cyclohexane + cyclohexanol and cyclohexane + cyclohexanone solvent mixtures, solubilities of glutaric acid decrease monotonically with the increasing mass fraction of cyclohexane in solvent mixtures at constant temperature. However, for binary cyclohexanone + cyclohexanol solvent mixtures, cyclohexanone with a mass fraction at 0.6 in solvent mixtures has the best dissolving capacity for glutaric acid at constant temperature. The experimental solubility data of three determined binary solvent systems were correlated by the Apelblat equation and nonrandom two-liquid (NRTL) activity coefficient model, and the correlated solubilities data were in good accord with the experimental data. The obtained binary interaction parameters for the NRTL model were used to calculate the solubilities of glutaric acid in the ternary cyclohexanol + cyclohexanone + cyclohexane solvent mixtures, which were compared with the experimental solubilities data.
1. INTRODUCTION Adipic acid is an important raw material, which is widely used in chemical production, organic synthesis industry, pharmaceutical industry, and lubricant manufacturing etc. With the development of green chemistry, the direct oxidation of cyclohexane to adipic acid without the use of nitric acid has attracted increasing attention.1,2 For this method, the nonsolvent system is preferred. Its major intermediates are cyclohexanol and cyclohexanone, and the major byproducts are glutaric acid and succinic acid. Usually, crystallization is used to separate adipic acid from the reacted mixture.2,3 However, the byproducts of glutaric acid and succinic acid would crystallize out simultaneously. Glutaric acid is a main raw material for producing glutaric anhydride, and it has an important application worth on industry production. Therefore, for the aim of properly designing operation conditions to improve the purification of adipic acid and recovering glutaric acid to make full use of resources, the solubilities of glutaric acid in binary cyclohexane + cyclohexanol, cyclohexane + cyclohexanone, and cyclohexanone + cyclohexanol solvent mixtures are extremely essential physical property data. Recently, Song et al.4 measured the solubilities of glutaric acid in pure cyclohexanol at 299.75−352.95 K, pure cyclohexanone at 294−353.65 K, and binary cyclohexanol + cyclohexanone solvent mixtures at 292.15−354.60 K. However, there was no such literature published to report the solubilities of glutaric acid © XXXX American Chemical Society
in the other solvent mixtures for the aforementioned system. In this work, the solubilities of glutaric acid were studied at 299.10− 343.65 K in binary cyclohexane + cyclohexanol, cyclohexane + cyclohexanone, and cyclohexanone + cyclohexanol solvent mixtures. The experimental data were correlated by the Apelblat equation and nonrandom two-liquid (NRTL) activity coefficient model.5 The obtained binary interaction parameters for the NRTL Model could be used to calculate the solubilities of glutaric acid in the ternary cyclohexanol + cyclohexanone + cyclohexane solvent mixtures. Then, the solubility of glutaric acid was measured in ternary cyclohexanol + cyclohexanone + cyclohexane solvent mixtures at 298.15−333.65 K and compared with the calculated data.
2. EXPERIMENTAL SECTION 2.1. Materials. Glutaric acid (mass fraction >0.990), cyclohexane (mass fraction >0.990), cyclohexanol (mass fraction >0.970), and cyclohexanone (mass fraction >0.995) were supplied by Aladdin Chemistry Co. The mass purity of glutaric acid was verified by high-performance liquid chromatography, and the mass purities of cyclohexanone, cyclohexanol, and Received: April 20, 2016 Accepted: October 11, 2016
A
DOI: 10.1021/acs.jced.6b00325 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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3. RESULTS AND DISCUSSION 3.1. Verification of the Experimental Technique. In hope of verifying the reliability of the experimental device, the solubilities of glutaric acid in pure water were measured and compared with the literature data from Apelblat,8 Lin,9 and Deng.10 The results are listed in Table 2 and depicted in Figure 1,
cyclohexane were verified by gas chromatography. Purified water was obtained from supermarket (596 mL each bottle), produced by Hangzhou Wahaha Group Co., and had the measured resistivity of 18.2 MΩ·cm. All of the materials were used as received. The mass purity and suppliers of the materials are listed in Table 1. Table 1. Mass Fraction Purity and Suppliers of the Materials
a
component
mass fraction
suppliers
glutaric acid cyclohexane cyclohexanol cyclohexanone water
>0.990 >0.990 >0.970 >0.995 >0.999
Aladdin Chemistry Co. Aladdin Chemistry Co. Aladdin Chemistry Co. Aladdin Chemistry Co. Hangzhou Wahaha Group Co.
Table 2. Solubilities of Glutaric Acid in Pure Water, Pure Cyclohexanol, and Pure Cyclohexanone at Different Temperatures and Pressures p = 101.3 KPaa
analysis method HPLCa GCb GCb GCb
T/K 298.65 302.75 306.15 310.35 313.75
High-performance liquid chromatography. bGas chromatography.
2.2. Apparatus and Procedures. The dynamic method, also called synthetic method, was applied to measure the solubilities of glutaric acid in the solvent mixtures in this work. The method and the apparatus for the experiment were introduced in detail by Wang et al.6,7 Briefly, the experimental apparatus mainly contained a 125 cm3 solid−liquid equilibrium cell with a reflux condenser, a magnetic stirring system, a temperature controlling and monitoring system, and a laser transmitting and receiving system. The thermocouple was applied to monitor the solution temperature with an uncertainty of ±0.05 K. In each experiment, a certain amounts of glutaric acid and solvents were weighed carefully by a type AL204 electronic analytical balance with an mass uncertainty of ±0.0001 g, which was manufactured by Mettler Toledo Instrument Co. Ltd. Then all of the chemicals were put into the equilibrium cell. Afterward, the equilibrium cell was heated in thermostatic water bath, and the solid−liquid mixture was stirred continuously by the magnetic agitator. The water bath was heated slowly to rise the solution temperature at the rate of 2.5 K/h in a stepwise fashion. The solute glutaric acid dissolved gradually with the rising of temperature. Near the point of glutaric acid dissolved completely, the rate of the rising the solution temperature was controlled in less than 0.2 K/h. The point of solid−liquid equilibrium was monitored by the laser transmitting and receiving system. A steady laser beam passed through the solvent−solute mixture and then was received and recorded by a laser power meter. The glutaric acid particles would scatter the laser beam and reduce the received laser beam intensity. With the glutaric acid dissolving gradually, the received laser beam intensity would increase. The temperature corresponding to the maximum value of the received laser beam intensity is solid−liquid equilibrium temperature at the given composition. In this work, the mole fraction of the glutaric acid in solution was used to express the solubility data, and the mole fraction of the glutaric acid was defined as x=
mGA MGA
+
mcyclohexane Mcyclohexane
+
mGA MGA mcyclohexanol Mcyclohexanol
+
306.25 310.85 314.55 317.85 322.85 299.75 303.95 307.75 312.55 316.85
RDi%
T/K
x
Glutaric Acid + Water 0.1789 −7.40 317.85 0.2954 0.2000 −6.02 322.05 0.3276 0.2206 −5.62 326.55 0.3663 0.2439 −3.54 331.05 0.4092 0.2665 −2.83 335.35 0.4515 Glutaric Acid + Cyclohexanol 0.2456 −4.01 327.55 0.3970 0.2704 −2.45 331.05 0.4309 0.2943 −2.07 336.75 0.4839 0.3174 −1.82 340.65 0.5275 0.3586 −2.38 343.65 0.5646 Glutaric Acid + Cyclohexanone 0.2130 −10.67 321.95 0.3687 0.2379 −9.78 326.85 0.4077 0.2618 −8.88 332.25 0.4605 0.2946 −7.78 336.55 0.5048 0.3244 −6.22 340.65 0.5512
RDi%
ARD 2.96
−1.89 −1.08 −0.65 −0.51 −0.01 2.03 −1.82 −2.13 −1.06 −1.13 −1.39 6.19 −6.04 −4.12 −3.45 −2.71 −2.28
a Standard uncertainties u are u(T) = 0.05 K, ur(p) = 0.05, and ur(x) = 0.05. The solubility x is defined as the mole fraction of glutaric acid in pure water, pure cyclohexanol, and pure cyclohexanone, respectively. RDi% is the relative deviation of the experimental solubility data with the literature data.4,8 ARD is the averaged relative deviation.
Figure 1. Comparisons between experimental solutility of glutaric acid in pure water with that reported in literature: ■, experimental data; □, literature data from Apelblat;8 ○, literature data from Lin;9 △, literature data from Deng.10
where RDi is the relative deviation and ARD is the averaged relative deviation between the experimental solubility data and the literature data. It can be seen that the experimental data are generally consistent with literature data, which proves that the experimental device is reliable. For the aim of further checking the accuracy of the experimental results, the solubilities of glutaric acid in pure cyclohexanol and pure cyclohexanone were measured. The results were listed in Table 2 and depicted in Figures 2 and 3. It can be
mcyclohexanone Mcyclohexanone
x
(1)
where mGA, mcyclohexane, mcyclohexanol, and mcyclohexanone are the masses of glutaric acid, cyclohexane, cyclohexanol and cyclohexanone, respectively; MGA, Mcyclohexane, Mcyclohexanol, and Mcyclohexanone are the molecular weights of glutaric acid, cyclohexane, cyclohexanol, and cyclohexanone, respectively. B
DOI: 10.1021/acs.jced.6b00325 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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acid increases as temperature increases at constant solvent composition. However, the solvent composition has a different effect on the solubilities of glutaric acid. In order to clearly express the effect of solvent composition on the solubilities, the solubilities of glutaric acid in binary cyclohexanone + cyclohexanol solvent mixtures at (303.15 to 343.15) K was calculated by both eq 2 and the data-fitted Apelblat model parameters given in Table 6. The result was scattered in Figure 7. It shows that the solubility of glutaric acid increases as the valve of w2 is getting bigger at constant temperature, and then the maximum solubility appears when the valve of w2 is 0.6. When the valve of w2 is bigger than 0.6, the solubility of glutaric acid decreases as the valve of w2 is getting bigger. The solid−liquid equilibrium system of glutaric acid + cyclohexanone + cyclohexanol exists a maximum-solubility effect, which was also been noted by Chen and Ma for the solid−liquid equilibrium of terephthalic acid + acetic acid + water,11 and Wang et al. for the solid−liquid equilibrium of Phthalic Acid + Acetic Acid + Water,12 succinic acid + acetic acid + water,1 adipic + acetic acid + water2 and benzoic acid + methylbenzene + benzylalcohol,6 and so forth. 3.3. Correlation of Experimental Data. Apelblat Correlation. The empirical Apelblat equation proposed by Apelblat et al.13,14 was introduced to correlate the experimental solubility data. The mole fraction x1 of solute glutaric acid and absolute temperature T can be correlated by eq 2
Figure 2. Comparisons between experimental solutility of glutaric acid in pure cyclohexanol with that reported in literature: ■, experimental data; □, literature data from Song.4
ln x1 = A +
B + C ln T T
(2)
where A, B, and C are the empirical parameters. In order to correlate the solubilities of glutaric acid at diverse solvent compositions by eq 2, the following empirical polynomial were adopted to discribe the effect of solvent composition on the solubilities.15
Figure 3. Comparisons between experimental solutility of glutaric acid in pure cyclohexanone with that reported in literature: ■, experimental data; □, literature data from Song.4
known that the experimental data have no significant deviations with the related literature from Song,4 which further proves that the experimental results are reliable. 3.2. Experimental Results. Solubilities of Glutaric Acid in Cyclohexane + Cyclohexanol Mixtures. The experimental solubilities of glutaric acid in cyclohexane + cyclohexanol mixtures at 298.05−343.65 K are listed in Table 3 and scattered in Figure 4, where w2 is defined as the mass fraction of cyclohexane in binary cyclohexane + cyclohexanol solvent mixtures. From the results, it can be known that the solubility of glutaric acid increases as temperature increases at constant solvent composition and decreases as the valve of w2 is getting bigger at constant temperature. Solubilities of Glutaric Acid in Cyclohexane + Cyclohexanone Mixtures. The experimental solubilities of glutaric acid in cyclohexane + cyclohexanone mixtures at 299.10−340.65 K are listed in Table 4 and scattered in Figure 5, where w2 is defined as the mass fraction of cyclohexane in binary cyclohexane + cyclohexanone solvent mixtures. The result shows that the solubility of glutaric acid increases as temperature increases at constant solvent composition and decreases as the valve of w2 is getting bigger at constant temperature, which is similar to the results of cyclohexane + cyclohexanol solvent mixture. Solubilities of Glutaric Acid in Cyclohexanone + Cyclohexanol Mixtures. The experimental solubility of glutaric acid in cyclohexanone + cyclohexanol mixtures at 299.75−343.65 K are listed in Table 5 and scattered in Figure 6, where w2 is defined as the mass fraction of cyclohexanone in binary cyclohexanone + cyclohexanol solvent mixtures. Again, the solubility of glutaric
A = A 0 + A1x 2 + A 2 x 22 + A3x 23 B = B0 + B1x 2 + B2 x 22 + B3x 23 C = C0 + C1x 2 + C2x 22 + C3x 23
(3)
where Ai, Bi, and Ci are model parameters. For binary cyclohexane + cyclohexanol and cyclohexane + cyclohexanone solvent mixtures, x2 is the mole fraction of cyclohexane in solvent mixtures. For binary cyclohexanone + cyclohexanol solvent mixtures, x2 is the mole fraction of cyclohexanone in solvent mixtures. The solubilities of glutaric acid were calculated by eqs 2 to 3, and the model parameters was optimized by Nelder−Mead Simplex method.16 Function f minsearch in Matlab (Mathwork, MA) is a standard programmed algorithm using the Nelder− Mead Simplex method for the minimization of the objective function, which had been introduced in detail by Wang et al.12 In this work, we adopted it for the parameters optimization. The objective function was defined as the averaged relative deviation (ARD) between the experimental solubility xi and the calculated solubility xci, and the expression is ARD =
RDi = C
1 n
n
∑ abs(RDi) i=1
xci − xi × 100 xi
(4)
(5) DOI: 10.1021/acs.jced.6b00325 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 3. Solubilities of Glutaric Acid (1) in Cyclohexane (2) + Cyclohexanol (3) Mixtures at Temperatures 298.05−343.65 K and Pressure p = 101.3 KPaa T/K
x
xc,1
RD1%
xc,2
306.25 310.85 314.55 317.85 322.85
0.2456 0.2704 0.2943 0.3174 0.3586
0.2450 0.2719 0.2955 0.3183 0.3560
−0.23 0.55 0.40 0.28 −0.70
0.2449 0.2712 0.2943 0.3166 0.3540
298.05 303.25 307.85 311.55 314.75
0.1581 0.1773 0.1964 0.2147 0.2323
0.1563 0.1757 0.1949 0.2119 0.2278
−1.11 −0.89 −0.75 −1.31 −1.94
0.1586 0.1782 0.1976 0.2151 0.2317
301.15 307.30 312.35 316.55 321.45
0.1149 0.1336 0.1518 0.1694 0.1928
0.1157 0.1363 0.1559 0.1743 0.1987
0.74 1.97 2.67 2.92 3.06
0.1123 0.1313 0.1494 0.1666 0.1896
302.70 306.85 310.35 313.45 318.45
0.0681 0.0755 0.0828 0.0899 0.1024
0.0653 0.0737 0.0816 0.0893 0.1034
−4.15 −2.45 −1.44 −0.66 0.98
0.0693 0.0773 0.0847 0.0920 0.1052
299.75 306.25 311.45 315.65 319.45
0.0237 0.0276 0.0313 0.0350 0.0388
0.0233 0.0277 0.0318 0.0356 0.0394
−1.74 0.32 1.55 1.49 1.60
0.0238 0.0277 0.0314 0.0350 0.0387
T/K
RD2%
w2 = 0.0 −0.29 327.55 0.29 331.05 −0.01 336.75 −0.25 340.65 −1.27 343.65 w2 = 0.2 0.33 319.15 0.52 323.05 0.62 327.95 0.18 332.55 −0.26 336.35 w2 = 0.4 −2.23 325.25 −1.74 329.65 −1.59 333.65 −1.65 337.65 −1.65 w2 = 0.6 1.73 322.15 2.35 326.95 2.32 330.95 2.32 334.45 2.76 337.45 w2 = 0.8 0.33 322.65 0.44 325.45 0.36 328.45 −0.10 331.05 −0.17
x
xc,1
RD1%
xc,2
RD2%
0.3970 0.4309 0.4839 0.5275 0.5646
0.3955 0.4275 0.4852 0.5288 0.5649
−0.38 −0.79 0.26 0.25 0.05
0.3932 0.4256 0.4838 0.5288 0.5667
−0.95 −1.24 −0.02 0.25 0.37
0.2556 0.2773 0.3090 0.3461 0.3794
0.2516 0.2749 0.3071 0.3408 0.3714
−1.53 −0.89 −0.60 −1.51 −2.11
0.2564 0.2807 0.3152 0.3533 0.3889
0.33 1.21 2.01 2.09 2.49
0.2151 0.2445 0.2718 0.3036
0.2199 0.2473 0.2751 0.3060
2.23 1.15 1.22 0.80
0.2104 0.2383 0.2666 0.2997
−2.18 −2.52 −1.91 −1.29
0.1146 0.1323 0.1505 0.1701 0.1886
0.1152 0.1326 0.1491 0.1652 0.1803
0.52 0.25 −0.94 −2.87 −4.38
0.1169 0.1344 0.1519 0.1703 0.1884
2.00 1.62 0.93 0.15 −0.10
0.0425 0.0463 0.0503 0.0546
0.0429 0.0463 0.0503 0.0540
1.02 0.12 −0.13 −1.19
0.0424 0.0460 0.0502 0.0545
−0.27 −0.60 −0.28 −0.20
a
Standard uncertainties u are u(T) = 0.05 K, ur(p) = 0.05, ur(w2) = 0.0004, and ur(x) = 0.05. The solubility is defined as the mole fraction of glutaric acid in solution. w2 is the mass fraction of cyclohexane in binary cyclohexane + cyclohexanol solvent mixtures. xc,1 and RD1 represent the correlated solubility data by Apelblat equation and the relative deviation between the correlated and experimental solubilities, respectively. xc,2 and RD2 represent the correlated solubility data by NRTL model and the relative deviation between the correlated and experimental solubilities, respectively.
where n is the total number of experimental points, and the subscript i denotes each experimental point. The calculated solubilities and the corresponding RDi are given in Tables 3−5. The model parameters and the averaged relative deviation ARD are given in Table 6. The correlated solubility data by Apelblat model are dot-lined in Figures 4−6. The result shows that correlated data coincide with the experimental data, which demonstrates that the empirical Apelblat equation can be applied to correlate the solubilities of glutaric acid in cyclohexane + cyclohexanol mixtures, cyclohexane + cyclohexanone mixtures, and cyclohexanone + cyclohexanol mixtures. NRTL Correlation. For the systems of glutaric acid + cyclohexane + cyclohexanol, glutaric acid + cyclohexane + cyclohexanone, and glutaric acid + cyclohexanone + cyclohexanol, the solid−solid phase transition do not occur. The following equation could be applied to approximated solid− liquid equilibrium and correlate the activity coefficient γ1, the mole fraction x1 of solute glutaric acid, and the absolute temperature T when the system reaching solid−liquid equilibrium.12 ln(γ1x1) = −
ΔfusH ⎛ 1 1 ⎞ ⎟ ⎜ − R ⎝T Tfus ⎠
Figure 4. Solubilities of glutaric acid (1) in cyclohexane (2) + cyclohexanol (3) solvent mixtures: ■, w2 = 0.0; ●, w2 = 0.2; ▲, w2 = 0.4; ▼, w2 = 0.6; ◀, w2 = 0.8; w2 is the mass fraction of cyclohexane in binary cyclohexane + cyclohexanol solvent mixtures; “” (solid line), NRTL equation calculated; “--” (dotted line), Apelblat equation calculated.
where ΔfusH = 20900 J·mol−1 is the enthalpy of fusion for solute glutaric acid,17 Tfus = 369.15 K is the fusion temperature for glutaric acid,17 and R = 8.314 J·mol−1·K−1 is the universal gas constant. In eq 6, it is assumed that the enthalpy of fusion and temperature are independent. In order to calculate γ1, the activity coefficient model of NRTL was used as
(6) D
DOI: 10.1021/acs.jced.6b00325 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 4. Solubilities of Glutaric Acid (1) in Cyclohexane (2) + Cyclohexanone (3) Mixtures at Temperatures 299.10−340.65 K and Pressure p = 101.3 KPaa T/K
x
xc,1
RD1%
xc,2
299.75 303.95 307.75 312.55 316.85
0.2130 0.2379 0.2618 0.2946 0.3244
0.2127 0.2367 0.2602 0.2924 0.3238
−0.14 −0.49 −0.63 −0.75 −0.16
0.2146 0.2375 0.2604 0.2924 0.3242
302.30 306.20 309.35 313.35 317.65
0.1465 0.1668 0.1865 0.2127 0.2464
0.1498 0.1699 0.1877 0.2126 0.2424
2.25 1.83 0.64 −0.06 −1.65
0.1497 0.1694 0.1877 0.2131 0.2446
301.55 305.45 308.65 311.65 315.25
0.0672 0.0798 0.0917 0.1033 0.1204
0.0666 0.0799 0.0926 0.1060 0.1245
−0.92 0.17 0.91 2.61 3.35
0.0678 0.0800 0.0917 0.1038 0.1212
304.25 307.95 311.45 315.25 318.65
0.0232 0.0275 0.0322 0.0387 0.0457
0.0213 0.0261 0.0315 0.0384 0.0458
−8.03 −5.09 −2.28 −0.80 0.38
0.0230 0.0273 0.0321 0.0387 0.0459
299.10 302.85 306.35 309.55 313.25
0.0026 0.0031 0.0036 0.0041 0.0048
0.0025 0.0030 0.0036 0.0042 0.0050
−3.79 −1.34 0.49 2.82 4.41
0.0026 0.0031 0.0036 0.0041 0.0049
T/K
RD2%
w2 = 0.0 0.73 321.95 −0.16 326.85 −0.55 332.25 −0.75 336.55 −0.05 340.65 w2 = 0.2 2.21 322.55 1.56 326.45 0.65 330.55 0.18 333.80 −0.74 336.95 w2 = 0.4 0.93 318.20 0.30 321.25 −0.03 325.45 0.44 328.55 0.62 331.95 w2 = 0.6 −0.87 322.45 −0.72 325.95 −0.33 328.45 −0.11 331.45 0.54 w2 = 0.8 −1.26 317.05 0.59 320.65 0.59 324.55 0.74 327.95 2.86 331.95
x
xc,1
RD1%
xc,2
RD2%
0.3687 0.4077 0.4605 0.5048 0.5512
0.3645 0.4072 0.4587 0.5031 0.5486
−1.13 −0.11 −0.39 −0.33 −0.47
0.3663 0.4109 0.4656 0.5133 0.5624
−0.64 0.80 1.11 1.68 2.03
0.2903 0.3293 0.3713 0.4089 0.4484
0.2805 0.3144 0.3536 0.3876 0.4230
−3.36 −4.52 −4.77 −5.22 −5.65
0.2857 0.3226 0.3647 0.4018 0.4408
−1.58 −2.02 −1.78 −1.74 −1.68
0.1368 0.1572 0.1865 0.2183 0.2531
0.1417 0.1616 0.1932 0.2199 0.2529
3.53 2.80 3.59 0.72 −0.06
0.1377 0.1579 0.1885 0.2185 0.2534
0.62 0.42 1.06 0.07 0.12
0.0561 0.0666 0.0768 0.0905
0.0556 0.0662 0.0749 0.0868
−0.97 −0.56 −2.37 −4.16
0.0563 0.0676 0.0781 0.0928
0.28 1.48 1.73 2.50
0.0057 0.0068 0.0084 0.0101 0.0124
0.0059 0.0070 0.0083 0.0097 0.0115
4.49 2.95 −0.83 −4.76 −7.25
0.0058 0.0069 0.0083 0.0099 0.0120
2.28 1.79 −0.96 −2.38 −3.22
a
Standard uncertainties u are u(T) = 0.05 K, ur(p) = 0.05, ur(w2) = 0.0004, ur(x) = 0.05. The solubility is defined as the mole fraction of glutaric acid in solution. w2 is the mass fraction of cyclohexane in binary cyclohexane + cyclohexanone solvent mixtures. xc,1 and RD1 represent the correlated solubility data by Apelblat equation and the relative deviation between the correlated and experimental solubilities, respectively. xc,2 and RD2 represent the correlated solubility data by NRTL model and the relative deviation between the correlated and experimental solubilities, respectively. 3
ln γi =
∑ j = 1 τjiGjixj 3 ∑k = 1 Gkixk
3
+
xjGij 3 j = 1 ∑k = 1 Gkjxk
∑
3 ⎛ ∑k = 1 xkτkjGkj ⎞ ⎜ ⎟ × ⎜τij − 3 ∑k = 1 Gkjxk ⎟⎠ ⎝
τij = aij +
bij (8)
T
Gij = exp( −αijτij)
αij = αji ,
(7)
τij ≠ τji ,
(9)
τii = 0
(10)
Figure 5. Solubilities of glutaric acid (1) in cyclohexane (2) + cyclohexanone (3) solvent mixtures: ■, w2 = 0.0; ●, w2 = 0.2; ▲, w2 = 0.4; ▼, w2 = 0.6; ◀, w2 = 0.8; w2 is the mass fraction of cyclohexane in binary cyclohexane + cyclohexanone solvent mixtures; “−” (solid line), NRTL equation calculated; “--” (dotted line), Apelblat equation calculated.
where aij and bij are the NRTL binary interaction parameters obtained by correlating experimental data. The solubilities of glutaric acid in the three studied systems could be calculated by solving eqs 6−10, and the model parameters were optimized by Nelder−Mead Simplex method.16 In the optimization process, as proposed by Renon and Prausnitz, αij in eq 10 was set to be the constant 0.3.18 Once again, function f minsearch in Matlab (Mathwork, MA) was adopted for the parameters optimization, and the objective function was defined as eq 4.
All experimental solubilities data of the three studied systems were correlated simultaneously to ensure the model parameters aij and bij could accurately describe the solid−liquid equilibrium. The calculated solubilities and the corresponding RDi are also given in Tables 3−5. The obtained model parameters and the E
DOI: 10.1021/acs.jced.6b00325 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 5. Solubilities of Glutaric Acid (1) in Cyclohexanone (2) + Cyclohexanol Mixtures (3) at Temperatures 299.75−343.65 K and Pressure p = 101.3 KPaa T/K
x
xc,1
RD1%
xc,2
306.25 310.85 314.55 317.85 322.85
0.2456 0.2704 0.2943 0.3174 0.3586
0.2450 0.2719 0.2955 0.3183 0.3560
−0.23 0.55 0.40 0.28 −0.70
0.2449 0.2712 0.2943 0.3166 0.3540
301.65 307.35 312.15 315.85 321.45
0.2391 0.2676 0.2945 0.3192 0.3585
0.2372 0.2667 0.2948 0.3186 0.3587
−0.79 −0.33 0.11 −0.18 0.07
0.2404 0.2706 0.2991 0.3228 0.3629
302.25 308.00 312.65 316.60 321.65
0.2524 0.2814 0.3080 0.3333 0.3701
0.2510 0.2806 0.3077 0.3333 0.3697
−0.55 −0.28 −0.10 0.00 −0.11
0.2502 0.2808 0.3085 0.3346 0.3713
300.80 306.30 310.90 314.70 319.90
0.2458 0.2739 0.2995 0.3236 0.3614
0.2464 0.2740 0.3000 0.3238 0.3601
0.24 0.03 0.18 0.06 −0.34
0.2441 0.2715 0.2979 0.3220 0.3586
302.55 307.50 311.75 315.25 320.45
0.2484 0.2759 0.3012 0.3255 0.3636
0.2472 0.2745 0.3004 0.3237 0.3619
−0.48 −0.52 −0.27 −0.53 −0.48
0.2460 0.2723 0.2981 0.3213 0.3599
299.75 303.95 307.75 312.55 316.85
0.2130 0.2379 0.2618 0.2946 0.3244
0.2127 0.2367 0.2602 0.2924 0.3238
−0.14 −0.49 −0.63 −0.75 −0.16
0.2146 0.2375 0.2604 0.2924 0.3242
T/K
RD2%
w2 = 0.0 −0.29 327.55 0.29 331.05 −0.01 336.75 −0.25 340.65 −1.27 343.65 w2 = 0.2 0.55 325.95 1.11 330.15 1.57 335.05 1.13 338.75 1.23 342.25 w2 = 0.4 −0.86 325.95 −0.20 330.45 0.15 334.05 0.40 337.15 0.33 340.25 w2 = 0.6 −0.71 324.25 −0.88 328.85 −0.53 332.60 −0.49 336.35 −0.76 340.25 w2 = 0.8 −0.98 324.55 −1.31 329.25 −1.04 332.95 −1.28 336.85 −1.02 341.15 w2 = 1.0 0.73 321.95 −0.16 326.85 −0.55 332.25 −0.75 336.55 −0.05 340.65
x
xc,1
RD1%
xc,2
RD2%
0.3970 0.4309 0.4839 0.5275 0.5646
0.3955 0.4275 0.4852 0.5288 0.5649
−0.38 −0.79 0.26 0.25 0.05
0.3932 0.4256 0.4838 0.5288 0.5667
−0.95 −1.24 −0.02 0.25 0.37
0.3936 0.4331 0.4828 0.5247 0.5658
0.3949 0.4321 0.4803 0.5204 0.5615
0.33 −0.23 −0.51 −0.82 −0.76
0.3990 0.4360 0.4843 0.5247 0.5662
1.38 0.66 0.32 0.00 0.07
0.4034 0.4450 0.4814 0.5131 0.5462
0.4044 0.4447 0.4802 0.5134 0.5491
0.23 −0.06 −0.24 0.06 0.54
0.4065 0.4468 0.4823 0.5154 0.5510
0.76 0.41 0.18 0.45 0.89
0.3954 0.4379 0.4748 0.5130 0.5525
0.3942 0.4344 0.4706 0.5102 0.5554
−0.30 −0.81 −0.89 −0.55 0.53
0.3933 0.4337 0.4703 0.5101 0.5552
−0.53 −0.96 −0.96 −0.57 0.49
0.3983 0.4410 0.4781 0.5172 0.5634
0.3952 0.4374 0.4738 0.5155 0.5659
−0.76 −0.82 −0.91 −0.32 0.44
0.3939 0.4371 0.4744 0.5171 0.5680
−1.09 −0.88 −0.78 −0.01 0.82
0.3687 0.4077 0.4605 0.5048 0.5512
0.3645 0.4072 0.4587 0.5031 0.5486
−1.13 −0.11 −0.39 −0.33 −0.47
0.3663 0.4109 0.4656 0.5133 0.5624
−0.64 0.80 1.11 1.68 2.03
a Standard uncertainties u are u(T) = 0.05 K, ur(p) = 0.05, ur(w2) = 0.0004, ur(x) = 0.05. The solubility is defined as the mole fraction of glutaric acid in solution. w2 is the mass fraction of cyclohexanone in binary cyclohexanone + cyclohexanol solvent mixtures. xc,1 and RD1 represent the correlated solubility data by Apelblat equation and the relative deviation between the correlated and experimental solubilities, respectively. xc,2 and RD2 represent the correlated solubility data by NRTL model and the relative deviation between the correlated and experimental solubilities, respectively.
averaged relative deviation ARD are given in Table 7. The correlated solubilities data with the NRTL model were lined in Figures 4−6. It can be seen clearly that the correlated data show a good agreement with the experimental data, which demonstrates that the NRTL equation can be applied to correlate the solubilities of glutaric acid in cyclohexane + cyclohexanol mixtures, cyclohexane + cyclohexanone mixtures, and cyclohexanone + cyclohexanol mixtures. Song et al.4 measured the solubilities of glutaric acid in pure cyclohexanol, pure cyclohexanone, and binary cyclohexanone + cyclohexanol solvent mixtures at 292.15−354.60 K. For binary cyclohexanone + cyclohexanol solvent mixtures, the mass fractions of cyclohexanone are 0.1, 0.3, 0.5, 0.7, and 0.9, respectively. The NRTL model and the obtained model parameters aij and bij were used to calculate the solubilities of glutaric acid in cyclohexanone + cyclohexanol solvent mixtures at the literature reported solvent compositions. The calculated solubility data were compared with the related literature data from Song,4 and the results were shown
Figure 6. Solubilities of glutaric acid (1) in cyclohexanone (2) + cyclohexanol (3) solvent mixtures: ■, w2 = 0.0; ●, w2 = 0.2; ▲, w2 = 0.4; ▼, w2 = 0.6; ◀, w2 = 0.8; ▶, w2 = 1.0; w2 is the mass fraction of cyclohexanone in binary cyclohexanone + cyclohexanol solvent mixtures; “−” (solid line), NRTL equation calculated; “---” (dotted line), Apelblat equation calculated. F
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Table 6. Apelblat Equation Parameters (A, B, and C) for Glutaric Acid + Cyclohexane + Cyclohexanol, Glutaric Acid + Cyclohexane + Cyclohexanone, and Glutaric Acid + Cyclohexanone + Cyclohexanol Systems w2
A
B
C
Glutaric Acid (1) + Cyclohexane (2) + Cyclohexanol (3) 0 −80.074 1776.8 12.729 0.2 −93.8532 2397.4 14.7358 0.4 −109.9175 2790.4 17.2568 0.6 −123.545 3181.7 19.3086 0.8 −131.7239 3718.9 20.2629 Glutaric Acid (1) + Cyclohexane (2) + Cyclohexanone (3) 0 −12.514 −1475.4 2.786 0.2 −21.9649 −1630.3 4.4576 0.4 −31.9813 −2343.8 6.4888 0.6 −47.2139 −2361.7 8.942 0.8 −70.7016 −841.05 11.8467 Glutaric Acid (1) + Cyclohexanone (2) + Cyclohexanol (3) 0 −80.074 1776.8 12.729 0.2 −109.0007 3251.8 16.9517 0.4 −132.2276 4405.6 20.3579 0.6 −133.8517 4478.3 20.6018 0.8 −98.7432 2747.2 15.452 1 −12.514 −1475.4 2.786 ARD/% 1.2505
Figure 8. Solubilities of glutaric acid (1) in cyclohexanone (2) + cyclohexanol (3) solvent mixtures from the literature:4 ■, w2 = 0.0; ●, w2 = 0.1; ▲, w2 = 0.3; ▼, w2 = 0.5; ◀, w2 = 0.7; ▶, w2 = 0.9; ◆, w2 = 1; w2 is the mass fraction of cyclohexanone in binary cyclohexanone + cyclohexanol solvent mixtures; “−” (solid line), NRTL equation calculated.
gradually. A generally satisfactory averaged relative deviation of 6.28% was obtained. In order to further verify the reliability and accuracy of the NRTL model and the NRTL binary interaction parameters aij and bij, the solubilities of glutaric acid in the ternary cyclohexanol + cyclohexanone + cyclohexane solvent mixtures were measured at 298.15−333.65 K. The results are listed in Table 8, where w1, w2 and w3 are defined as the mass fraction of cyclohexanol, cyclohexanone, and cyclohexane in the ternary solvent mixtures, respectively. Meanwhile, the solubilities of glutaric acid in the ternary solvent mixtures were calculated by solving eqs 6−10 with the obtained parameters aij and bij. Likewise, αij in eq 10 was set to be the constant 0.3 in the calculation process.18 The calculated solubilities, the corresponding RDi defined in eq 5 and the averaged relative deviation ARD defined in eq 4 are given in Table 8. The result shows that the averaged relative deviation is 0.74%, and the calculated and the measured solubilities are in good agreement with each other. It further proves that the NRTL model and the obtained model parameters aij and bij are fairly reliable and accurate, and they can be applied for the relate design and optimization process.
Figure 7. Solubilities of glutaric acid (1) in cyclohexanone (2) + cyclohexanol (3) solvent mixtures: ■, 303.15 K; ●, 313.15 K; ▲, 323.15 K; ▼, 333.15 K; ◀, 343.15 K; w2 is the mass fraction of cyclohexanone in binary cyclohexanone + cyclohexanol solvent mixtures; “−” (solid line), Apelblat equation calculated.
4. CONCLUSIONS In this work, the solubilities of glutaric acid in cyclohexane + cyclohexanol solvent mixtures at 298.05−343.65 K, in cyclohexane + cyclohexanone solvent mixtures at 299.10−340.65 K, and in cyclohexanone + cyclohexanol solvent mixtures at 299.75−343.65 K were studied at atmospheric pressure by the dynamic method. The following conclusion might be obtained: (1) At constant solvent composition, the solubility of glutaric acid increases as temperature increases in three determined binary solvent systems.
in Figure 8. In the case of lower temperatures, the experimentally determined solubility of glutaric acid in different solvent systems is small, resulting in large relative deviation (RDi). With the temperature increasing, the experimentally determined solubility of glutaric acid increases, and the relative deviation decreases
Table 7. Optimized Temperature-Independent Binary Interaction Parameters for the NRTL Model for Glutaric Acid + Cyclohexanol + Cyclohexanone + Cyclohexane System i
j
aij
aji
bij
bji
αij = αji
glutaric acid glutaric acid glutaric acid cyclohexanol cyclohexanol cyclohexanone ARD/%
cyclohexanol cyclohexanone cyclohexane cyclohexanone cyclohexane cyclohexane
3.0802 3.5486 5.2093 −0.0014 −9.5094 1.1255
−0.2297 −5.9923 −0.4817 7.1318 1.4439 −2.8718
−851.79 −1409.1 −979.39 619.17 3815.6 −93.583
−9.5513 2311.7 3317.1 −2648.5 −808.43 846.77
0.3
0.9267 G
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Table 8. Solubilities of Glutaric Acid in Ternary Cyclohexanol (1) + Cyclohexanone (2) + Cyclohexane (3) Solvent Mixtures at Temperatures 298.15−333.65 K and Pressure p = 101.3 KPaa T/K
x
xc,1
301.75 306.15 310.35 313.75 317.25
0.1838 0.2040 0.2235 0.2421 0.2636
0.1875 0.2059 0.2259 0.2439 0.2646
298.35 302.95 306.90 310.45 314.35
0.1077 0.1199 0.1318 0.1441 0.1597
0.1073 0.1198 0.1321 0.1447 0.1604
298.15 302.85 306.85 310.95 314.75
0.0834 0.0933 0.1032 0.1145 0.1259
0.0823 0.0925 0.1025 0.1140 0.1261
303.30 306.30 309.40 313.30 317.05 ARD%
0.0596 0.0648 0.0701 0.0779 0.0875
0.0580 0.0632 0.0689 0.0773 0.0870
T/K
RD1%
w1:w2:w3 = 4:4:2 2.01 320.15 0.92 323.55 1.06 327.05 0.73 330.65 0.36 333.65 w1:w2:w3 = 3:3:4 −0.40 317.65 −0.05 321.05 0.20 323.95 0.40 327.35 0.42 330.95 w1:w2:w3 = 35:15:50 −1.36 318.85 −0.87 322.40 −0.68 325.45 −0.43 328.85 0.20 w1:w2:w3 = 2:2:6 −2.66 319.90 −2.43 323.90 −1.65 327.35 −0.76 330.55 −0.54 0.7400
x
xc,1
RD1%
0.2842 0.3103 0.3389 0.3703 0.4030
0.2835 0.3080 0.3359 0.3678 0.3979
−0.26 −0.75 −0.90 −0.67 −1.26
0.1754 0.1939 0.2123 0.2361 0.2663
0.1757 0.1936 0.2111 0.2340 0.2625
0.17 −0.15 −0.57 −0.87 −1.43
0.1406 0.1550 0.1708 0.1905
0.1411 0.1560 0.1711 0.1902
0.34 0.61 0.18 −0.16
0.0962 0.1098 0.1231 0.1379
0.0956 0.1095 0.1234 0.1386
−0.59 −0.30 0.24 0.49
a Standard uncertainties u are u(T) = 0.05 K, ur(p) = 0.05, ur(x) = 0.05. The solubility is defined as the mole fraction of glutaric acid in solution. w1, w2, and w3 is the mass fraction of cyclohexanol, cyclohexanone, and cyclohexane in the ternary solvent mixtures, respectively. xc,1 and RD1 represent the calculated solubility data by NRTL model and the relative deviation between the calculated and experimental solubility, respectively. ARD represents the averaged relative deviation between the calculated and experimental solubilities.
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(2) At constant temperature, for binary cyclohexane + cyclohexanol and cyclohexane + cyclohexanone solvent mixtures, the solubility of glutaric acid decreases gradually with the mass fraction of cyclohexane in solvent mixtures increasing. However, for binary cyclohexanone + cyclohexanol solvent mixtures, the solubility of glutaric acid increases gradually with the increasing mass fraction of cyclohexanone in solvent mixtures and then reaches a maximum when the mass fraction of cyclohexanone is 0.6. Conversely, when the mass fraction of cyclohexanone is bigger than 0.6, the solubility of glutaric acid decreases with the increasing mass fraction of cyclohexanone. Thus, there exists a maximum-solubility effect. (3) The experimental data were correlated by the Apelblat equation and NRTL equation, and the correlated solubilities data show a good agreement with the experimental data, which indicates that the Apelblat equation and NRTL equation are suitable for calculating the solubilities of glutaric acid in cyclohexane + cyclohexanol, cyclohexane + cyclohexanone, and cyclohexanone + cyclohexanol solvent mixtures. The obtained model parameters aij and bij by the NRTL equation could be used to calculate the solubilities of glutaric acid in the ternary cyclohexanol + cyclohexanone + cyclohexane solvent mixtures, which were compared with the experimental solubilities data. The result further proves that the NRTL model and the obtained model parameters aij and bij are fairly reliable and accurate for calculating the solubilities of glutaric acid in cyclohexane + cyclohexanol, cyclohexane + cyclohexanone, and cyclohexanone + cyclohexanol solvent mixtures.
AUTHOR INFORMATION
Corresponding Author
*E-mail address:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The project was supported by Key S&T Special Project of Zhejiang Province (2012C13007-2). We are grateful for the assistance from the company. The project was also partly granted financial support from the Fundamental Research Funds for the Central Universities and the National Nature Science Fund (21302049).
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