Determination and Correlation of the Solubility of Musk Ketone in Pure

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Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Determination and Correlation of the Solubility of Musk Ketone in Pure and Binary Solvents at 273.15−313.15 K Xin Fang, Huanxin Li, Zongpeng Zou, and Li Xu*

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Collage of Chemical Engineering and Energy, Zhengzhou University, Zhengzhou, Henan 450001, PR China ABSTRACT: The solubility of musk ketone in four pure solvents (methanol, ethanol, n-butanol, and ethyl acetate) and three binary mixed solvents (methanol + ethanol, ethanol + ethyl acetate, and n-butanol + ethyl acetate) at different temperatures (273.15−313.15 K) was determined by the static equilibrium method. The results showed that the solubility of musk ketone in the above solvents increases with the increasing temperature. The musk ketone has different solubilities in four pure solvents under the same environmental conditions (ethyl acetate > n-butanol > ethanol > methanol). In the binary solvent of methanol + ethanol, the solubility of musk ketone was positively correlated with the mass fraction of ethanol. In the binary mixed solvents of ethanol + ethyl acetate and n-butanol + ethyl acetate, the solubility was positively correlated with the mass fraction of ethyl acetate. Seven thermodynamic equations (van’t Hoff equation, modified Apelblat equation, λh equation, nonrandom two-liquid model, Wilson model, Jouyban−Acree model, and Sun model) were used to correlate the experimental solubility data. The deviation between the experimental values and the correlated values was calculated and analyzed. The results showed that these models can predict the experimental results very well. In addition, the Hansen solubility parameters of musk ketone and the solvents were calculated and discussed. The results showed that the non-hydrogen bond interaction has a great influence on the solubility of musk ketone.

1. INTRODUCTION Most spices are used as raw materials for flavoring, and also for medical research.1−4 Musk ketone (C14H18N2O5, 2,6-dimethyl3,5-dinitro-4-t-butylacetophenone, CAS registry no: 84-14-1, molar mass: 294.3 g·mol−1, the structure is presented in Figure 1) is an important synthetic musk, which is prepared by tertbutylation, acetylation, and digestion of m-xylene. The aroma is sweet and soft, closer to the aroma of natural musk, especially suitable for sweet and aromatic flavor.5 With the increasing market demand, the purity of musk ketone is required to be higher, but there are still many problems in the separation and purification of musk ketone. It is well known that musk crude products are of high boiling point and strong thermal sensitivity. It is difficult to separate musk crude products by the conventional distillation method. At present, solution crystallization is the main method of separation and purification in industrial production.6−8 The solvents selected for crystallization will directly affect the quality, output, and production cost of the product. However, the published theoretical study on the separation and purification method of musk ketone system has not been found. As everyone knows, solubility is the basis of crystallization.9 The solubility of musk in different solvents is an important datum. It is a great pity that there are few reports about the solubility of musk ketone in solvents, which leads to the lack of theoretical guidance in industrial production. Therefore, it is important to find several suitable solvents for the purification and crystallization of musk. Several common solvents (methanol, ethanol, n-butanol, ethyl acetate) and mixed solvents (methanol + ethanol, ethyl © XXXX American Chemical Society

acetate + ethanol/n-butanol) were selected to carry out the experiments by the static equilibrium method10 at 273.15− 313.15 K. These solvents are inexpensive and stable and suitable for crystallization and purification of high-boiling-point substances. The experimental solubility data of musk ketone were correlated by seven models: van’t Hoff equation,11,12 modified Apelblat equation,13 λh equation,14 nonrandom two-liquid (NRTL) model,15 Wilson model,16 Sun model,17 and Jouyban− Acree model.18 Furthermore, the Tm (melting point temperature) and ΔfusH (melting enthalpy) of musk ketone at atmospheric pressure were analyzed by a generally accepted method [differential scanning calorimetry (DSC)] according to a set procedure. X-ray diffraction (XRD) was used to measure the crystal morphology of musk ketone. In addition, the Hansen solubility parameters (HSPs) of musk ketone and solvents were calculated and discussed.

2. EXPERIMENTAL SECTION 2.1. Materials. The musk ketone with analytical purity produced by Puyang Maoyuan Chemical Co., Ltd. was purchased, and directly used in experiments. The solvents come from China Chemical Reagent Co., Ltd. The details of the solvents used are shown in Table 1. Received: April 10, 2019 Accepted: June 26, 2019

A

DOI: 10.1021/acs.jced.9b00310 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Figure 1. Chemical structure of musk ketone.

Table 1. Purity and Sources of Solute and Solvents chemicals

CAS reg. no.

musk ketone methanol ethanol n-butanol ethyl acetate

81-14-1 67-56-1 64-17-5 71-36-3 141-78-6

Mr/g·mol

mass fraction purity

294.3 32.04 46.07 74.12 88.11

≥0.995 ≥0.995a ≥0.995a ≥0.995a ≥0.995a

density/g·cm3

a

19

1.2051 0.791920 0.789421 0.809721 0.900520

source Puyang Maoyuan Chemical Co., Ltd. Hebei Siyou Excellent Technology Co., Ltd. Tianjin Fengchuan Chemical Reagent Technology Co., Ltd. Tianjin Fengchuan Chemical Reagent Technology Co., Ltd. Tianjin Fengchuan Chemical Reagent Technology Co., Ltd.

a

Determined by GC.

Table 2. Specification and Sources of the Instruments and Equipment equipment thermostatic waterbath balancing kettle analytical balance magnetic stirrer GC differential scanning calorimetry XRPD apparatus

specification

source

DCW-0506

Shanghai Bilang Instrument Manufacturing Co., Ltd. 50 mLa Zhengzhou Zhongyuan Glass Instrument Co., Ltd. AB-204-N Mettler Toledo 79-1 Shanghai Huayan Medical Devices Co., Ltd. GC-2014C Shimadzu DSC Q2000 Shanghai Sheng Instrument Technology Co., Ltd D8 ADVANCE Brooke Company, Germany

a

The volume is 50 ml of balance kettle.

Figure 2. Thermal analysis (DSC) of musk ketone.

The experimental instruments include gas chromatograph (GC2014C), constant temperature water bath (precision, 0.01 K), balancing kettle, magnetic stirring, analytical balance (precision, 0.1 mg), precision thermometer (precision, 0.1 K), DSC (Q2000), and so forth. Detailed information of the experimental instruments is shown in Table 2. The reliability of the instruments has been verified. 2.2. Differential Scanning Calorimetry. The differential scanning calorimeter (DSC Q2000) has high sensitivity and resolution in the analysis of crystal properties of organic substances. The Tm and ΔfusH of musk ketone were measured by DSC.22−24 The specific operation steps are as follows: take about 6 mg of the sample to be measured and place it in a DSC pot, and heat it from room temperature to 450 K at the speed of 2 K/min. 2.3. X-ray Powder Diffraction. X-ray powder diffraction (XRPD) is usually used to characterize the crystal structure. In this study, the XRD spectra of raw materials and excessive solid crystals in solid−liquid equilibrium experiments were measured by using a D8 ADVANCE diffractometer (Cu Kα radiation, λ = 0.15406 nm) at 40 mA and 40 kV. The diffraction

Figure 3. XRD patterns of musk ketone.

angle (2θ) ranges from 5° to 80° and the scanning rate is 0.02°/s. The crystal morphology of musk ketone in the experimental process was analyzed and compared. B



Article

Table 3. Experimental Mole Fraction Solubility (x) and RDs of Musk Ketone in Pure Solvents at Temperature T and Pressure p = 0.1 MPaa 100xc T/K

100x

van’t Hoff

Apelblat

λh

273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15

0.1081 0.1275 0.1568 0.1872 0.2249 0.2719 0.3257 0.3869 0.4576

0.1031 0.1271 0.1555 0.1889 0.2280 0.2735 0.3261 0.3866 0.4558

0.1058 0.1285 0.1556 0.1877 0.2257 0.2705 0.3231 0.3848 0.4569

0.1049 0.1283 0.1560 0.1887 0.2271 0.2720 0.3246 0.3861 0.4577

273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15

0.1598 0.1985 0.2409 0.2950 0.3545 0.4259 0.5118 0.6190 0.7400

0.1560 0.1941 0.2395 0.2934 0.3570 0.4316 0.5184 0.6190 0.7350

0.1619 0.1978 0.2408 0.2923 0.3539 0.4272 0.5144 0.6177 0.7399

0.1586 0.1958 0.2403 0.2931 0.3556 0.4293 0.5160 0.6178 0.7373

273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15

0.2197 0.2856 0.3680 0.4491 0.5330 0.6663 0.8115 0.9717 1.1990

0.2235 0.2826 0.3545 0.4412 0.5451 0.6686 0.8145 0.9860 1.186

0.2296 0.2862 0.3552 0.4388 0.5399 0.6614 0.8071 0.9812 1.188

0.2266 0.2849 0.3556 0.4410 0.5434 0.6658 0.8115 0.9845 1.189

273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15

5.504 6.409 7.425 8.522 9.543 11.05 12.18 13.93 15.60

5.544 6.412 7.377 8.446 9.626 10.92 12.34 13.89 15.57

5.549 6.416 7.381 8.450 9.629 10.93 12.34 13.89 15.58

5.572 6.428 7.382 8.441 9.614 10.91 12.33 13.89 15.60

100RD NRTL

Wilson

Methanol 0.1019 0.1046 0.1257 0.1282 0.1540 0.1562 0.1873 0.1892 0.2265 0.2279 0.2722 0.2733 0.3254 0.3262 0.3870 0.3877 0.4580 0.4592 Ethanol 0.1589 0.1600 0.1962 0.1971 0.2407 0.2413 0.2935 0.2938 0.3557 0.3559 0.4288 0.4291 0.5143 0.5153 0.6138 0.6165 0.7293 0.7353 n-Butanol 0.2258 0.2275 0.2843 0.2850 0.3554 0.3547 0.4410 0.4391 0.5437 0.5410 0.6664 0.6635 0.8122 0.8108 0.9850 0.9877 1.189 1.200 Ethyl acetate 5.5070 5.542 6.4110 6.411 7.4100 7.377 8.5070 8.447 9.7040 9.627 11.0020 10.93 12.4020 12.35 13.9040 13.90 15.509 15.59

van’t Hoff

Apelblat

λh

NRTL

Wilson

4.66 0.37 0.84 −0.95 −1.40 −0.60 −0.14 0.08 0.39

2.15 −0.78 0.76 −0.30 −0.36 0.53 0.79 0.55 0.16

2.95 −0.62 0.49 −0.82 −0.97 −0.05 0.32 0.22 −0.02

5.74 1.44 1.81 −0.09 −0.71 −0.12 0.08 −0.02 −0.09

3.25 −0.52 0.38 −1.09 −1.34 −0.51 −0.16 −0.20 −0.34

2.39 2.25 0.58 0.53 −0.71 −1.33 −1.29 0.00 0.68

−1.31 0.38 0.04 0.90 0.17 −0.31 −0.51 0.21 0.01

0.79 1.36 0.27 0.66 −0.30 −0.79 −0.82 0.19 0.37

0.59 1.17 0.08 0.51 −0.34 −0.68 −0.49 0.84 1.45

−0.10 0.72 −0.17 0.41 −0.39 −0.75 −0.68 0.40 0.64

−1.69 1.03 3.67 1.75 −2.26 −0.34 −0.37 −1.47 1.05

−4.48 −0.23 3.48 2.28 −1.28 0.73 0.55 −0.97 0.88

−3.10 0.24 3.36 1.81 −1.95 0.07 0.00 −1.31 0.81

−2.76 0.45 3.43 1.80 −2.00 −0.02 −0.08 −1.37 0.81

−3.53 0.20 3.62 2.23 −1.49 0.42 0.09 −1.64 −0.10

−0.73 −0.05 0.65 0.90 −0.86 1.19 −1.34 0.33 0.19

−0.81 −0.11 0.60 0.85 −0.90 1.16 −1.37 0.29 0.16

−1.23 −0.30 0.58 0.95 −0.74 1.32 −1.26 0.30 −0.01

−0.05 −0.04 0.21 0.18 −1.69 0.46 −1.84 0.22 0.61

−0.69 −0.03 0.66 0.89 −0.88 1.16 −1.39 0.25 0.08

a

The standard uncertainties u are u(T) = 0.1 K, ur(p) = 0.05, and ur(x) = 0.05.

2.4. Measurement of the Solubility. A certain amount of solvent (about 15−20 mL) was added to the special balance kettle (working volume of 50 mL). Then, excessive musk ketone was gradually added, stirred continuously for more than 12 h at a certain temperature, the stirring was stopped, and the mixture was left to stand for more than 12 h to achieve solid−liquid equilibrium as far as possible.24,25 The temperature rise or decrease of solid−liquid equilibrium system can be controlled by a constant temperature circulating bath. The solid−liquid equilibrium temperature is measured by a precision thermometer (precision 0.1 K). The upper transparent liquid was weighed on the analytical balance and diluted with corresponding solvents. The composition of the upper clear liquid was analyzed by gas chromatography (GC; GC-2014C). The GC method system configuration is as follows: carrier gas is N2; gasification chamber

temperature is 523.15 K; capillary column (InertCap WAX, ID = 0.25 mm, L = 30 m, DF = 0.25 μm), the temperature of the column box is maintained for 5 min at 323.15 K, then increased to 523.15 K at a rate of 50 K/min, and maintained for 15 min at this temperature; the hydrogen flame ionization detector (FID) temperature is constant at 523.15 K. Each experimental condition was analyzed three times, and the molar fraction of the musk ketone was calculated by average. In addition, binary mixed solvents are prepared by analytical balance (precision 0.1 mg). During the experiment, the atmospheric pressure was near to 0.1 MPa. The molar fraction of musk ketone (x) in saturated solutions can be calculated by eq 1. x= C

m/M m /M + m1/M1

(1) DOI: 10.1021/acs.jced.9b00310 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


Article

Table 5. Model Parameters (NRTL Equation, Wilson Model) of Musk Ketone in Different Pure Solvents NRTL Δg12

Δg21

α

Δλ12

Δλ21

methanol ethanol n-butanol ethyl acetate

2404.67 1364.30 4680.00 3949.76

624.55 385.49 687.02 −229.50

0.2353 0.2348 0.2947 0.3037

162.64 161.29 264.33 −672.49

5364.81 1190.29 574.31 925.71

ln x = A +

where m and m1 represent the masses of musk ketone and solvents, respectively. M and M1 represent the molar mass of the corresponding substance, respectively. The mass fraction (ω2) interval of ethyl acetate or ethanol in binary mixed solvents is 0.2. ω2 can be calculated by eq 2. m2 ω2 = m1 + m2 (2)

ij Λ 21 Λ12 zyz ln γ1 = −ln(x1 + Λ12x 2) + x 2jjj − z jx + Λ x Λ 21x1 + x 2 zz{ 12 2 k 1

(3)

ij yz Λ12 Λ 21 zz ln γ2 = −ln(x 2 + Λ 21x1) + x1jjj − jx + Λ x Λ12x 2 + x1 zz{ 21 1 k 2

in which m represents the mass of musk ketone; m1 and m2 represent the quality of methanol and ethanol or ethanol and ethyl acetate or n-butanol and ethyl acetate, respectively; M, M1, and M2 represent the molar mass of the corresponding substance, respectively.

(7)

3. THERMODYNAMIC MODELS 3.1. van’t Hoff Equation. The van’t hoff equation25,26 (formula 4) is considered to be a general equation that can be used to correlate experimental solubility data. It can be expressed as follows b ln x = a + T /K

(5)

where λ and h are the parameters of the λh equation. Tm represent the melting temperature of musk ketone. 3.4. Wilson Model. The Wilson equation (eq 7 to formula 10)25,32 is based on the activity coefficient equation of local composition, which is used to correlate the relationship between the activity coefficient and the molar fraction at different temperatures.

in which m2 represents the mass of solvents with higher molar mass in binary mixed solvents; m1 is the mass of another component in this binary solvent. The mole fraction solubility of musk ketone (x) in the above binary mixed solvents can be calculated by eq 3. m/M m1/M1 + m2 /M 2 + m/M

B + C ln(T /K ) T /K

In the formula, T is the experimental temperature in Kelvin; x is the molar fraction solubility; A, B, and C are the parameters of the Apelblat model, which can be obtained by fitting the experimental data. 3.3. λh Equation. The λh equation was first proposed by Buchowski.30,31 Its derivation process takes into account the influence of activities and is widely used in data fitting. Its form can be described by formula 6. É ÅÄÅ ij 1 λ(1 − x) ÑÑÑÑ 1 yzz Å lnÅÅÅ1 + ÑÑ = λhjjj − z jT ÅÅÇ ÑÑÖ x Tm zz{ (6) k

Figure 4. Mole fraction solubility (x) of musk ketone in different pure solvents; ■, methanol; ●, ethanol; ▲, n-butanol; ▼, ethyl acetate; , calculated values from the modified Apelblat equation.

x=

Wilson

solvents

Λ12 =

Λ 21 =

V21 ij λ12 − λ11 yz i Δλ y j z − = exp expjjj− 12 zzz j z 1 1 RT { V1 V1 k k RT {

(8)

V21

(9)

V11 ij λ 21 − λ 22 yz i Δλ y j z − = exp expjjj− 21 zzz j z 1 1 RT { V2 V2 k k RT { V11

(10)

In the above formula, γ1 and γ2 stand for the activity coefficients; Δλ12 and Δλ21 are the Wilson parameters, which can be obtained by fitting the experimental data; the molar volumes (V11, V21) of the solute and solvent are obtained by the ratio of molar mass to density. 3.5. NRTL Equation. NRTL equation is a very valuable equation.33,34 It is often used to fit the experimental data of phase equilibrium. It is usually described by eqs 11−14.

(4)

where a and b are the parameters of the van’t Hoff model. 3.2. Modified Apelblat Equation. The modified Apelblat equation27−29 (eq 5) is derived from the Clausius equation. It is considered to be a convenient model for fitting dissolution equilibrium data. The relationship between x and T can be described and predicted by eq 5.

Table 4. Model Parameters (van’t Hoff, Modified Apelblat, λh Equation) of Musk Ketone in Different Pure Solvents van’t Hoff

λh

Apelblat

solvents

a

b

A

B

C

λ

h

methanol ethanol n-butanol ethyl acetate

4.761 5.670 6.966 5.193

−3179.04 −3314.09 −3569.99 −2208.52

−63.53 −79.74 −59.35 4.666

−147.68 478.79 −621.99 −2184.65

10.201 12.756 9.902 0.0785

0.03833 0.07074 0.1464 0.7279

77564.84 44282.64 23431.76 2919.52

D



Article

Table 6. ARD and the rmsd of Musk Ketone in Different Pure Solvents 100ARD

1000rmsd

solvents

van’t Hoff

Apelblat

λh

NRTL

Wilson

van’t Hoff

Apelblat

λh

NRTL

Wilson

methanol ethanol n-butanol ethyl acetate average ARDa

1.05 1.08 1.51 0.69 1.08

0.71 0.43 1.65 0.70 0.87

0.72 0.62 1.41 0.74 0.87

1.12 0.68 1.41 0.59 0.95

0.87 0.47 1.48 0.67 0.87

0.023 0.040 0.094 0.840 0.249

0.016 0.016 0.086 0.839 0.239

0.015 0.024 0.084 0.848 0.243

0.024 0.043 0.085 0.996 0.287

0.019 0.025 0.086 0.837 0.242

a

Average value of ARD representing the solubility model in different solution systems.

Table 7. Experimental Mole Fraction Solubility (x) and RDs of Musk Ketone in Methanol (1) + Ethanol (2) Mixtures at Temperature T and Pressure p = 0.1 MPaa 100xc

100RD

T/K

100x

van’t Hoff

Apelblat

λh

Sun

273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15

0.1145 0.1354 0.1649 0.1997 0.2385 0.2894 0.3416 0.4105 0.4855

0.1092 0.1346 0.1647 0.2002 0.2416 0.2898 0.3456 0.4097 0.4831

0.1127 0.1367 0.1653 0.1993 0.2395 0.2870 0.3429 0.4087 0.4857

0.1111 0.1359 0.1653 0.1999 0.2406 0.2882 0.3439 0.4090 0.4850

0.1111 0.1365 0.1664 0.2015 0.2424 0.2898 0.3444 0.4070 0.4785

273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15

0.1256 0.1511 0.1840 0.2217 0.2630 0.3205 0.3781 0.4571 0.5475

0.1196 0.1480 0.1816 0.2213 0.2679 0.3223 0.3853 0.4579 0.5413

0.1247 0.1511 0.1828 0.2205 0.2655 0.3189 0.3823 0.4573 0.5458

0.1218 0.1495 0.1824 0.2212 0.2669 0.3207 0.3837 0.4574 0.5435

0.1228 0.1510 0.1844 0.2236 0.2694 0.3225 0.3838 0.4542 0.5347

273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15

0.1349 0.1676 0.2000 0.2440 0.2906 0.3460 0.4152 0.4995 0.6056

0.1300 0.1611 0.1981 0.2419 0.2933 0.3533 0.4231 0.5036 0.5961

0.1371 0.1657 0.2001 0.2412 0.2905 0.3494 0.4198 0.5036 0.6034

0.1323 0.1627 0.1988 0.2416 0.2921 0.3514 0.4211 0.5027 0.5982

0.1334 0.1644 0.2011 0.2443 0.2948 0.3535 0.4214 0.4995 0.5888

273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15

0.1443 0.1802 0.2163 0.2609 0.3158 0.3785 0.4551 0.5496 0.6607

0.1395 0.1734 0.2139 0.2618 0.3183 0.3845 0.4616 0.5508 0.6536

0.1471 0.1783 0.2158 0.2610 0.3151 0.3800 0.4576 0.5503 0.6609

0.1420 0.1751 0.2147 0.2616 0.3172 0.3827 0.4597 0.5500 0.6560

0.1436 0.1774 0.2174 0.2646 0.3200 0.3844 0.4591 0.5451 0.6436

273.15 278.15 283.15 288.15 293.15 298.15

0.1545 0.1929 0.2319 0.2829 0.3441 0.4055

0.1497 0.1863 0.2300 0.2819 0.3431 0.4148

0.1582 0.1919 0.2324 0.2812 0.3399 0.4102

0.1524 0.1882 0.2310 0.2819 0.3421 0.4131

0.1534 0.1899 0.2333 0.2846 0.3448 0.4150

Jouyban−Acree ω2 = 0.0997 0.1140 0.1351 0.1659 0.1985 0.2385 0.2881 0.3451 0.4106 0.4860 ω2 = 0.2999 0.1254 0.1501 0.1838 0.2210 0.2653 0.3200 0.3835 0.4579 0.5431 ω2 = 0.5039 0.1357 0.1641 0.2004 0.2421 0.2908 0.3503 0.4200 0.5032 0.5980 ω2 = 0.6998 0.1455 0.1779 0.2166 0.2632 0.3161 0.3803 0.4564 0.5489 0.6539 ω2 = 0.8995 0.1548 0.1913 0.2324 0.2839 0.3411 0.4100 E

van’t Hoff

Apelblat

λh

Sun

Jouyban−Acree

4.60 0.61 0.08 −0.26 −1.30 −0.15 −1.16 0.19 0.49

1.53 −0.95 −0.27 0.19 −0.41 0.83 −0.39 0.44 −0.05

2.91 −0.36 −0.25 −0.12 −0.85 0.42 −0.68 0.36 0.11

2.94 −0.78 −0.93 −0.92 −1.62 −0.13 −0.81 0.85 1.44

0.41 0.25 −0.62 0.58 0.01 0.45 −1.02 −0.03 −0.11

4.75 2.11 1.28 0.18 −1.86 −0.56 −1.89 −0.19 1.14

0.75 0.01 0.65 0.54 −0.94 0.48 −1.10 −0.04 0.32

3.01 1.08 0.87 0.24 −1.49 −0.06 −1.47 −0.06 0.74

2.23 0.09 −0.24 −0.84 −2.42 −0.63 −1.50 0.63 2.34

0.16 0.69 0.09 0.33 −0.86 0.15 −1.42 −0.18 0.81

3.61 3.88 0.95 0.87 −0.93 −2.13 −1.89 −0.82 1.57

−1.61 1.15 −0.01 1.13 0.02 −1.01 −1.10 −0.82 0.37

1.91 2.93 0.59 0.97 −0.52 −1.58 −1.41 −0.64 1.23

1.12 1.93 −0.54 −0.13 −1.45 −2.18 −1.49 0.00 2.78

−0.59 2.11 −0.19 0.77 −0.07 −1.25 −1.15 −0.74 1.26

3.28 3.78 1.11 −0.35 −0.81 −1.59 −1.43 −0.23 1.07

−1.95 1.07 0.20 −0.02 0.21 −0.39 −0.55 −0.14 −0.04

1.61 2.82 0.73 −0.28 −0.45 −1.10 −1.00 −0.09 0.71

0.47 1.56 −0.53 −1.41 −1.34 −1.56 −0.88 0.81 2.59

−0.85 1.29 −0.16 −0.88 −0.10 −0.47 −0.29 0.12 1.03

3.06 3.44 0.83 0.35 0.31 −2.29

−2.41 0.56 −0.21 0.58 1.24 −1.16

1.34 2.43 0.39 0.35 0.60 −1.87

0.69 1.57 −0.60 −0.61 −0.20 −2.34

−0.22 0.84 −0.21 −0.37 0.88 −1.11



Article

Table 7. continued 100xc T/K

100x

303.15 308.15 313.15

van’t Hoff

0.4900 0.5953 0.7152

λh

Apelblat

0.4984 0.5953 0.7070

100RD

0.4945 0.5954 0.7159

0.4967 0.5948 0.7100

Sun

Jouyban−Acree

0.4966 0.5907 0.6987

ω2 = 0.8995 0.4925 0.5945 0.7099

van’t Hoff

Apelblat

λh

Sun

Jouyban−Acree

−1.71 −0.01 1.14

−0.92 −0.02 −0.09

−1.35 0.08 0.73

−1.34 0.77 2.31

−0.50 0.13 0.74

The uncertainties u are u(T) = 0.1 K, ur(p) = 0.05, and ur(x) = 0.05. ω2 is the mass fraction of ethanol in mixed solvents with uncertainty ur(w2) = 0.0002. a

N

ln γi =

∑ j = 1 τjiGjixi N

∑i = 1 Gijxi

N

+

∑ j=1

ÄÅ ÉÑ N ÅÅ ∑i = 1 xiτijGij ÑÑÑÑ ÅÅ ÅÅτji − ÑÑ N N Å Ñ ∑i = 1 Gijxi ÅÅÅÅ ∑i = 1 xiGij ÑÑÑÑ Ç Ö xjGij

(11)

Gij = exp( −αijτij)

(12)

αij = αji = α

(13)

τij =

gij − gjj RT

=

Δgij (14)

RT

Among these equations, Δgij is a parameter of the interaction energy equation between molecules. α is a measure of the nonrandomness of solutions. R is the gas constant (8.314 J·mol−1·K−1). 3.6. Jouyban−Acree Model. It is generally known that the solubility of solutes in binary solvents is complex. It is also related to temperature and solvent composition. The Jouyban− Acree model (eq 15) can well correlate solubility with temperature and solvent composition.35,36 Its form is as follows

Figure 5. Mole fraction solubility (x) of musk ketone in methanol (1) + ethanol (2) binary solvents with various mass fractions at different temperatures: ω2, mass fraction of ethanol; ●, ω2 = 0; ■, ω2 = 0.0997; ▲, ω2 = 0.2999; ▼, ω2 = 0.5039; ◆, ω2 = 0.6998; ◀, ω2 = 0.8995; ▶, ω2 = 1; , calculated values from the Jouyban−Acree model.

Among them, N is the number of experimental points, xi is the solubility data measured by experiments, and xic are the corresponding solubility data obtained by equation-fitting.

2

ln x = ω1 ln x1 + ω2 ln x 2 +

ω1ω2 · ∑ J (ω1 − ω2)i T i=0 i

(15)

4. RESULTS AND DISCUSSION 4.1. Physical Properties. Thermal analysis (DSC) data of musk ketone are described and analyzed through Figure 2. When the phase state of a substance changes, it will be reflected by a specific thermal effect. The peak in Figure 2 is the result of the phase transition of musk ketone. From Figure 2, the melting point (Tm) of the musk ketone is 409.50 K (the uncertainty is u(Tm) = 0.08 K), which is very close to the research of He and Sun5 (407.65−409.65 K) and Qu et al.38 (407.49−409.35 K). The fusion enthalpy (ΔfusH) of musk ketone is 23 820.64 J·mol−1 (the uncertainty is u(ΔfusH) = 2.53 kJ·mol−1), which is very close to the report of Qu et al.38 (23814.1 J·mol−1). DSC spectra of excess solid crystals in solid−liquid equilibrium experiments were measured with the same instrument and program and are plotted in Figure 2. It is well known that the polymorphism of pure substances or the solvate formation can lead to different thermal effects. As can be seen from Figure 2, all the test results did not show any different characteristics, which indicated that there was no solvation formation or polymorphism. The results showed that these solvents can be used to purify musk ketone. The XRD patterns of raw materials and excessive solid crystals in solid−liquid equilibrium experiments are furnished in Figure 3. By comparison, it can be seen that the crystal morphology of musk ketone in all pure solvents in the experiment has not been detected to change. This result again showed that there are no polymorphic forms in the experimental solid−liquid equilibrium process. 4.2. Solubility Data and Model Correlation. 4.2.1. Solubility in Pure Solvents. The experimental data of the solubility

in which x is the solubility of musk ketone in the mixed solvent; x1 and x2 are the solubility of musk ketone in the corresponding pure solvent; ω1 and ω2 are the mass fraction of each component in the mixed solvent; Ji is a parameter of the model. 3.7. Sun Model. The Sun model is relatively simple in form and can be used to correlate solubility data of solutes in mixed solutions35,37 in the following eq 16 Dω Dω2 Dω3 D2 + D3ω1 + 4 1 + 5 1 + 6 1 T T T T D7ω14 + T

ln x = D1 +

(16)

in which D1 to D7 are the parameters of this model. 3.8. Data Correlation. In order to evaluate the fitting results of experimental data and model, the relative deviation (RD), the average RD (ARD), and the root-mean-square deviation (rmsd) were also obtained by the equations RD =

xi − xic xi

(17)

N

ARD =

x − xc 1 ∑ i i N i=1 xi

É ÄÅ N ÅÅ ∑ (x − x c)2 ÑÑÑ1/2 ÑÑ ÅÅ i = 1 i i ÑÑ RMSD = ÅÅÅ ÑÑ ÅÅ N ÑÑÖ ÅÇ

(18)

(19) F



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Table 8. Experimental Mole Fraction Solubility (x) and RDs of Musk Ketone in Ethanol (1) + Ethyl Acetate (2) Mixtures at Temperature T and Pressure p = 0.1 MPaa 100xc T/K

100x

van’t Hoff

Apelblat

λh

273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15

0.2423 0.2981 0.3615 0.4289 0.5139 0.6232 0.7367 0.8877 1.054

0.2354 0.2904 0.3556 0.4323 0.5222 0.6267 0.7477 0.8869 1.046

0.2450 0.2961 0.3571 0.4298 0.5163 0.6189 0.7403 0.8839 1.053

0.2393 0.2930 0.3567 0.4317 0.5200 0.6234 0.7443 0.8854 1.050

273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15

0.6053 0.7431 0.8483 1.048 1.221 1.463 1.751 2.015 2.444

0.5835 0.7122 0.8632 1.039 1.243 1.479 1.748 2.056 2.405

0.6111 0.7280 0.8668 1.031 1.226 1.456 1.728 2.048 2.426

0.5927 0.7184 0.8659 1.038 1.239 1.472 1.741 2.053 2.414

273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15

1.305 1.623 1.889 2.242 2.584 3.033 3.667 4.222 4.834

1.312 1.577 1.883 2.235 2.637 3.095 3.613 4.196 4.850

1.324 1.583 1.884 2.230 2.629 3.084 3.603 4.192 4.859

1.328 1.587 1.887 2.232 2.628 3.082 3.601 4.193 4.868

273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15

2.563 3.061 3.557 4.129 4.736 5.585 6.468 7.572 8.759

2.492 2.970 3.518 4.143 4.851 5.651 6.550 7.555 8.674

2.626 3.061 3.566 4.154 4.838 5.632 6.553 7.621 8.859

2.514 2.984 3.523 4.139 4.840 5.635 6.534 7.548 8.689

273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15

4.237 4.935 5.693 6.769 7.844 9.049 10.33 11.59 13.01

4.267 4.999 5.824 6.748 7.780 8.928 10.20 11.60 13.14

4.153 4.939 5.817 6.789 7.856 9.016 10.27 11.61 13.04

4.283 5.007 5.823 6.740 7.767 8.913 10.19 11.60 13.17

100RD Sun

Jouyban−Acree

ω2 = 0.0952 0.2388 0.2425 0.2943 0.2989 0.3601 0.3607 0.4374 0.4384 0.5279 0.5226 0.6331 0.6248 0.7547 0.7438 0.8945 0.8938 1.0545 1.061 ω2 = 0.2948 0.5958 0.6053 0.7224 0.7339 0.8700 0.8741 1.041 1.045 1.238 1.224 1.464 1.449 1.721 1.690 2.013 2.002 2.343 2.338 ω2 = 0.4942 1.348 1.373 1.611 1.640 1.914 1.932 2.259 2.276 2.651 2.624 3.096 3.076 3.596 3.521 4.156 4.118 4.782 4.740 ω2 = 0.6965 2.579 2.631 3.047 3.105 3.578 3.628 4.178 4.222 4.854 4.804 5.611 5.596 6.454 6.300 7.391 7.293 8.428 8.291 ω2 = 0.9000 4.263 4.353 4.992 5.091 5.812 5.913 6.732 6.817 7.758 7.673 8.899 8.901 10.16 9.878 11.55 11.34 13.08 12.76

van’t Hoff

Apelblat

λh

Sun

Jouyban−Acree

2.87 2.59 1.63 −0.80 −1.62 −0.57 −1.49 0.09 0.70

−1.08 0.68 1.20 −0.21 −0.47 0.69 −0.49 0.42 0.03

1.26 1.70 1.32 −0.66 −1.19 −0.03 −1.02 0.26 0.36

1.46 1.28 0.37 −1.98 −2.73 −1.60 −2.44 −0.77 −0.08

−0.06 −0.27 0.21 −2.21 −1.70 −0.26 −0.96 −0.69 −0.67

3.59 4.15 −1.76 0.84 −1.84 −1.03 0.15 −2.01 1.60

−0.96 2.03 −2.17 1.62 −0.40 0.52 1.33 −1.62 0.77

2.08 3.32 −2.07 0.95 −1.46 −0.55 0.55 −1.88 1.26

1.56 2.78 −2.56 0.68 −1.40 −0.03 1.69 0.10 4.14

−0.01 1.23 −3.04 0.28 −0.29 1.02 3.50 0.69 4.37

−0.53 2.85 0.31 0.30 −2.07 −2.05 1.49 0.61 −0.35

−1.46 2.45 0.27 0.51 −1.73 −1.69 1.76 0.70 −0.52

−1.81 2.20 0.12 0.45 −1.70 −1.62 1.82 0.69 −0.71

−3.34 0.72 −1.30 −0.76 −2.61 −2.07 1.96 1.55 1.06

−5.25 −1.07 −2.28 −1.52 −1.56 −1.44 3.99 2.45 1.94

2.78 2.97 1.10 −0.33 −2.43 −1.18 −1.26 0.23 0.97

−2.47 0.01 −0.25 −0.61 −2.15 −0.83 −1.31 −0.65 −1.14

1.93 2.52 0.95 −0.25 −2.20 −0.89 −1.02 0.32 0.79

−0.62 0.47 −0.58 −1.20 −2.49 −0.46 0.21 2.39 3.78

−2.65 −1.45 −1.98 −2.26 −1.44 −0.20 2.59 3.69 5.34

−0.72 −1.30 −2.29 0.31 0.81 1.34 1.28 −0.08 −0.98

1.99 −0.08 −2.18 −0.30 −0.15 0.36 0.58 −0.19 −0.24

−1.09 −1.45 −2.28 0.42 0.98 1.50 1.38 −0.10 −1.20

−0.62 −1.15 −2.10 0.55 1.09 1.66 1.64 0.33 −0.53

−2.73 −3.15 −3.86 −0.70 2.18 1.64 4.38 2.15 1.91

a The uncertainties u are u(T) = 0.1 K, ur(p) = 0.05, and ur(x) = 0.05. ω2 is the mass fraction of ethyl acetate in mixed solvents with uncertainty ur(w2) = 0.0002.

of musk ketone in methanol, ethanol, n-butanol, and ethyl acetate at different temperatures (273.15−313.15 K) are shown in Table 3 and Figure 4. As shown in Table 3 and Figure 4, the solubility of musk ketone in the above solvents increases with the increase of temperature. The musk ketone has different

solubilities in four pure solvents under the same environmental conditions (ethyl acetate > n-butanol > ethanol > methanol). It is obvious that the solubility of musk ketone in the three alcohol solvents is small, and the solubility in ethyl acetate solution is much higher than that in the above alcohol solvents. G



Article

Table 9. Experimental Mole Fraction Solubility (x) and RD, of Musk Ketone in n-Butanol (1) + Ethyl Acetate (2) Mixtures at Temperature T and Pressure p = 0.1 MPaa 100xc T/K

100x

van’t Hoff

Apelblat

λh

273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15

0.4292 0.5303 0.6621 0.7738 0.9458 1.123 1.376 1.705 1.988

0.4138 0.5161 0.6387 0.7845 0.9570 1.160 1.396 1.671 1.988

0.4323 0.5269 0.6410 0.7783 0.9432 1.141 1.378 1.660 1.997

0.4195 0.5201 0.6406 0.7839 0.9539 1.155 1.391 1.668 1.993

273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15

1.106 1.274 1.607 1.889 2.266 2.665 3.238 3.903 4.446

1.057 1.295 1.576 1.904 2.286 2.727 3.235 3.817 4.479

1.079 1.312 1.587 1.910 2.289 2.730 3.241 3.833 4.516

1.069 1.304 1.580 1.903 2.281 2.719 3.228 3.815 4.492

273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15

2.169 2.500 3.118 3.553 4.416 4.960 5.671 7.061 7.788

2.130 2.560 3.057 3.628 4.280 5.022 5.861 6.806 7.866

2.136 2.564 3.059 3.628 4.279 5.020 5.860 6.808 7.873

2.147 2.571 3.062 3.626 4.273 5.011 5.852 6.807 7.888

273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15

3.505 4.087 4.920 5.707 6.702 7.647 8.814 10.50 11.69

3.474 4.124 4.867 5.710 6.663 7.735 8.935 10.27 11.76

3.480 4.123 4.858 5.694 6.641 7.709 8.908 10.25 11.75

3.488 4.134 4.871 5.709 6.658 7.728 8.930 10.28 11.78

273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15

5.098 5.708 6.985 8.032 9.122 10.53 12.07 13.56 15.03

5.109 5.958 6.909 7.972 9.153 10.46 11.90 13.49 15.22

5.019 5.939 6.961 8.087 9.318 10.65 12.08 13.61 15.24

5.118 5.960 6.906 7.963 9.141 10.45 11.89 13.49 15.24

100RD Sun

Jouyban−Acree

ω2 = 0.0932 0.4160 0.4078 0.5186 0.5217 0.6413 0.6619 0.7873 0.7989 0.9598 0.9382 1.162 1.159 1.399 1.392 1.673 1.651 1.990 2.010 ω2 = 0.2933 1.086 1.072 1.323 1.334 1.602 1.648 1.926 1.954 2.302 2.257 2.734 2.731 3.229 3.199 3.793 3.744 4.432 4.450 ω2 = 0.4967 2.143 2.131 2.567 2.592 3.055 3.131 3.614 3.665 4.252 4.180 4.975 4.978 5.790 5.711 6.706 6.619 7.731 7.710 ω2 = 0.6965 3.562 3.570 4.207 4.257 4.940 5.045 5.767 5.846 6.698 6.605 7.741 7.761 8.903 8.745 10.19 10.06 11.62 11.52 ω2 = 0.8907 5.058 5.106 5.906 5.984 6.858 6.977 7.922 8.024 9.107 9.002 10.42 10.46 11.87 11.61 13.46 13.29 15.21 14.97

van’t Hoff

Apelblat

λh

Sun

Jouyban−Acree

3.59 2.68 3.53 −1.39 −1.18 −3.24 −1.47 1.98 0.00

−0.71 0.65 3.19 −0.57 0.27 −1.59 −0.12 2.61 −0.46

2.26 1.92 3.25 −1.31 −0.86 −2.81 −1.09 2.14 −0.25

3.08 2.21 3.13 −1.74 −1.48 −3.50 −1.66 1.84 −0.09

4.99 1.63 0.02 −3.24 0.80 −3.18 −1.13 3.13 −1.11

4.38 −1.65 1.95 −0.81 −0.87 −2.34 0.08 2.23 −0.73

2.39 −2.97 1.25 −1.15 −0.99 −2.41 −0.10 1.80 −1.56

3.32 −2.29 1.72 −0.76 −0.63 −2.03 0.32 2.27 −1.03

1.81 −3.84 0.34 −1.97 −1.56 −2.57 0.29 2.84 0.31

3.02 −4.69 −2.53 −3.46 0.43 −2.46 1.21 4.09 −0.08

1.78 −2.41 1.97 −2.11 3.09 −1.25 −3.35 3.60 −1.01

1.54 −2.56 1.91 −2.12 3.11 −1.22 −3.34 3.58 −1.09

1.00 −2.87 1.81 −2.07 3.25 −1.04 −3.20 3.59 −1.29

1.22 −2.67 2.03 −1.74 3.72 −0.30 −2.10 5.02 0.73

1.73 −3.68 −0.40 −3.16 5.35 −0.36 −0.71 6.25 1.00

0.90 −0.90 1.09 −0.05 0.59 −1.15 −1.38 2.19 −0.60

0.71 −0.88 1.26 0.23 0.91 −0.82 −1.08 2.41 −0.49

0.49 −1.14 1.00 −0.03 0.66 −1.06 −1.32 2.17 −0.76

−1.62 −2.93 −0.39 −1.05 0.06 −1.23 −1.01 2.95 0.59

−1.85 −4.14 −2.55 −2.43 1.46 −1.50 0.77 4.20 1.48

−0.21 −4.37 1.08 0.76 −0.33 0.63 1.38 0.56 −1.27

1.56 −4.04 0.34 −0.69 −2.14 −1.18 −0.12 −0.39 −1.38

−0.38 −4.42 1.13 0.86 −0.21 0.74 1.44 0.53 −1.43

0.79 −3.46 1.81 1.37 0.17 1.01 1.65 0.72 −1.22

−0.14 −4.84 0.10 0.10 1.32 0.60 3.84 2.03 0.37

a The uncertainties u are u(T) = 0.1 K, ur(p) = 0.05, and ur(x) = 0.05. ω2 is the mass fraction of ethyl acetate in mixed solvents with uncertainty ur(w2) = 0.0002.

The reason for this result may be that the interaction between musk ketone and ethyl acetate molecules is greater than that between musk ketone and alcohol molecules. From the molecular structure point of view, the molecule of musk ketone contains carbonyl, benzene ring, nitro, methyl, and tert-butyl. It is well

known that the benzene ring has no polarity and the groups of musk ketone are approximately symmetrical. The polarity of the carbonyl group and nitro group makes musk ketone molecules have a certain polarity. Therefore, musk ketone has a certain solubility in polar solvents. For the selected solvent, the order of H



Article

polarity was ethyl acetate < n-butanol < ethanol < methanol. The molar solubility of musk ketone increases with the decrease of solvent polarity. As we all know, there are many factors affecting the solubility of solutes in solvents. Because of their complex functions, it is urgent to develop more accurate theoretical and in-depth experimental studies to explore the law of dissolution. In addition, the model parameters obtained by data-fitting are shown in Tables 4 and 5, and the values of ARD and rmsd are shown in Table 6. For the four pure solvents, the maximum values of ARD does not exceed 1.65%; the maximum values of rmsd do not exceed 0.0996%; the average values of ARD were 1.08% (van’t-hoff), 0.87% (Apelblat), 0.87% (λh), 0.95% (NRTL), and 0.87% (Wilson), respectively; the average values of rmsd were 0.0249% (van’t Hoff), 0.0239% (Apelblat), 0.0243% (λh), 0.0287% (NRTL), and 0.0242% (Wilson), respectively. The experimental data of the solubility of musk ketone in four pure solvents are well fitted with the calculation of five solubility models. However, the Apelblat equation, the λh equation, and the Wilson model gave better correlation of the solubility data than the van’t hoff equation and the NRTL model. 4.2.2. Solubility in Binary Solvents. The solubility data of ketone musk in methanol + ethanol mixed solvents are shown in Table 7 and Figure 5. From Table 7 and Figure 5, it can be seen that the solubility of ketone musk in mixed solvents is positively correlated with the ethanol mass fraction in solvents and solution temperature. The reason for this phenomenon is that the molar solubility of ketone musk in ethanol is higher than that in methanol at the same temperature. The solubility data of musk ketone in ethyl acetate + ethanol/ n-butanol binary mixed solvents at temperatures ranging from 273.15 to 313.15 K are shown in Tables 8, 9 and Figures 6, 7. From Tables 8, 9 and Figures 6, 7, it can be seen that the

Figure 7. Mole fraction solubility (x) of musk ketone in n-butanol (1) + ethyl acetate (2) binary solvents with various mass fractions at different temperatures: ω2, mass fraction of ethyl acetate; ●, ω2 = 0; ■, ω2 = 0.0932; ▲, ω2 = 0.2933; ▼, ω2 = 0.4967; ◆, ω2 = 0.6965; ◀, ω2 = 0.8907; ▶, ω2 = 1; , calculated values from the modified Apelblat equation.

are less than 0.135%. Besides, the minimum values of ARD (0.0023%) and rmsd (0.42%) can be found in the fitting calculation of the methanol + ethanol system. In general, these models can be used to describe the solubility of musk ketone in binary mixtures of methanol + ethanol, ethanol + ethyl acetate, and n-butanol + ethyl acetate in all measured compositions and temperature conditions, and in the methanol + ethanol system, the Jouyban−Acree equation gives the best correlation results among the selected models. 4.2.3. Deviation Discussion. The solubility data of musk ketone in methanol and ethanol at temperatures of 303.15 and 323.15 K have been reported by Cui et al.39 The experimental results are compared with the reported data and shown in Figures 8 and 9. It can be seen that there are some deviations between the experimental results in this paper and the data in the literature. There are many reasons for these differences. The experimental device and method used by Cui et al. are simple and crude. In their study, a certain amount of solvent was added to the equilibrium kettle, and then the solute was gradually added in batches until saturation. In fact, because of the low solubility of musk ketone in methanol and ethanol, the weighing errors, solvent volatilization, and solute wall-hanging may lead to larger experimental errors. In addition, the determination method of the solid−liquid equilibrium state has a great influence on the experimental results. Cui et al. observed that the final added solute did not dissolve within 1 h, thus judging that the solid−liquid equilibrium state was reached. It is well known that they should use laser generators to judge the state of solid− liquid equilibrium. Unfortunately, they did not do that. These experimental details may lead to larger or smaller experimental results than the true values. In our report, the equilibrium method was used to determine the solubility. Excess solute and a certain amount of solvents are added to the equilibrium kettle and stirred for more than 12 h. Then, they are stationary for more than 12 h to achieve solid− liquid equilibrium as far as possible. More accurate solubility data can be obtained by meteorological chromatographic analysis of the supernatant. Each experimental condition was analyzed three times. These methods will make the experimental error smaller. In conclusion, these experimental details can be used to illustrate the differences shown in Figures 8 and 9, and show that the data in this study are more accurate. 4.3. Hansen Solubility Parameters. HSPs are widely used to correlate and predict the behavior of solvents. Solvents for

Figure 6. Mole fraction solubility (x) of musk ketone in ethanol (1) + ethyl acetate (2) binary solvents with various mass fractions at different temperatures: ω2, mass fraction of ethyl acetate; ●, ω2 = 0; ■, ω2 = 0.0952; ▲, ω2 = 0.2948; ▼, ω2 = 0.4942; ◆, ω2 = 0.6965; ◀, ω2 = 0.9000; ▶, ω2 = 1; , calculated values from the modified Apelblat equation.

solubility of musk ketone in mixed solvents increases with the increase of solution temperature and the mass fraction of ethyl acetate in solvents. The results shown in Table 3 and Figure 4 can be used to explain this phenomenon. The molar solubility of musk ketone in ethyl acetate is much higher than that in ethanol or n-butanol at the same temperature and pressure. The RD is shown in Tables 8 and 9. In addition, the equation and model parameters obtained by fitting are shown in Tables 10 and 11, and the values of ARD and RMSD are shown in Table 12. In comparison, in the selected binary mixtures, all values of rmsd I



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Table 10. Model Parameters (van’t Hoff, Modified Apelblat, λh Equation) of Musk Ketone in Binary Solvents van’t Hoff

λh

Apelblat

solvents

a

b

ω2 = 0.0997 ω2 = 0.2999 ω2 = 0.5039 ω2 = 0.6998 ω2 = 0.8995

4.822 5.089 5.275 5.514 5.648

−3179.94 −3227.94 −3255.96 −3301.99 −3319.34

ω2 = 0.0952 ω2 = 0.2948 ω2 = 0.4942 ω2 = 0.6965 ω2 = 0.9000

5.627 5.944 5.904 6.073 5.649

−3190.03 −3028.64 −2796.47 −2667.35 −2404.58

ω2 = 0.0932 ω2 = 0.2933 ω2 = 0.4967 ω2 = 0.6965 ω2 = 0.8907

6.801 6.752 6.379 6.186 5.571

−3356.61 −3086.99 −2793.49 −2607.46 −2334.10

A

B

λ

h

11.380 14.038 17.343 17.478 17.872

0.04067 0.04775 0.05404 0.06204 0.06835

73136.63 63438.93 56660.70 50229.27 45895.41

14.407 17.293 3.664 16.560 −11.270

0.09032 0.1844 0.3162 0.5511 0.7220

33193.85 15408.25 8297.33 4626.29 3228.16

16.001 5.480 0.793 1.525 −11.000

0.2063 0.3873 0.5605 0.7744 0.8240

15553.60 7639.25 4798.77 3294.75 2777.39

C

Methanol (1) + Ethanol (2) −71.37 201.82 −88.90 944.89 −110.84 1899.22 −111.51 1894.62 −114.01 1994.42 Ethanol (1) + Ethyl acetate (2) −90.83 1091.13 −109.82 2105.49 −18.62 −1709.87 −104.74 2239.41 81.06 −5740.64 n-Butanol (1) + Ethyl acetate (2) −100.34 1402.84 −29.93 −1459.11 1.068 −2558.17 −4.022 −2155.51 79.18 −5589.12

Table 11. Model Parameters (Sun Model, Jouyban−Acree Model) of Musk Ketone in Different Binary Solvents Sun solvents

D1

D2

D3

D4

5.48

−3258.58

−0.95

5.62

−2334.27

−0.04

5.49

−2296.06

1.41

Jouyban−Acree D5

D6

D7

Methanol (1) + Ethanol (2) 163.9 41.51 −90.06 Ethanol (1) + Ethyl acetate (2) −650.98 366.75 −1464.74 n-Butanol (1) + Ethyl acetate (2) −456.31 −1400.29 1542.68

J0

J1

J2 −7.1

32.68

36.42

12.12

793.90

439.98

−65.27

−203.42

733.6

169.17

237.96

−940.63

Table 12. ARD and rmsd of Musk Ketone in Different Binary Solvents 100ARD solvents

van’t Hoff

Apelblat

λh

ω2 = 0.0997 ω2 = 0.2999 ω2 = 0.5039 ω2 = 0.6998 ω2 = 0.8995

0.98 1.55 1.85 1.52 1.46

0.56 0.54 0.80 0.51 0.80

0.67 1.00 1.31 0.98 1.02

ω2 = 0.0952 ω2 = 0.2948 ω2 = 0.4942 ω2 = 0.6965 ω2 = 0.9000

1.37 1.89 1.17 1.47 1.01

0.59 1.27 1.23 1.05 0.68

0.87 1.57 1.23 1.21 1.16

ω2 = 0.0932 ω2 = 0.2933 ω2 = 0.4967 ω2 = 0.6965 ω2 = 0.8907

2.12 1.67 2.29 0.98 1.18

1.13 1.62 2.27 0.98 1.31

1.77 1.60 2.23 0.96 1.24

1000rmsd Sun

Jouyban−Acree

van’t Hoff

Methanol (1) + Ethanol (2) 0.026 0.043 1.16 0.42 0.058 0.049 0.057 Ethanol (1) + Ethyl acetate (2) 0.068 0.250 1.43 1.38 0.379 0.721 0.913 n-Butanol (1) + Ethyl acetate (2) 0.214 0.433 1.65 1.55 1.26 0.984 1.28

dissolving solid organic matter can be quickly selected by HSPs, which follow the principle of similar miscibility.40−42 It was therefore logical to use this approach to correlate the solubility of musk ketone. The HSPs of conventional pure solvents can be found in literature or books. However, the HSPs of musk ketone have not been found in the literature. In order to correlate the solubility of musk ketone in solvents, it is convenient for us to calculate the solubility parameters of musk ketone by using the group-contribution method.43

Apelblat

λh

Sun

Jouyban−Acree

0.014 0.019 0.028 0.015 0.030

0.017 0.030 0.044 0.033 0.042

0.056

0.023

0.030 0.180 0.371 0.641 0.570

0.045 0.211 0.376 0.603 1.023

1.11

1.2

0.179 0.440 1.26 0.998 1.34

0.194 0.426 1.27 0.981 1.35

1.12

1.30

The equations for the estimation of HSPs are the following δd =

∑ NC i id + 17.3231 i

δp =

∑ NC i i p + 7.3548 i

δh =

∑ NC i i h + 7.9793 i

J

(20) (21) (22) DOI: 10.1021/acs.jced.9b00310 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


Article

In order to compare the similarity of solubility parameters of solvent Hansen, formulas 24 and 25 were used to calculate % ζδd+δp and % ζδh. % ζδd + δp =

% ζδ h =

δd + δp δd + δp + δ h

× 100 (24)

δh × 100 δd + δp + δ h

(25)

The values of HSPs of pure and mixed solvents and musk ketone are listed in Table 14; the % ζδd+δp and % ζδh are also shown Table 14. HSPs of Musk Ketone and Solvents Figure 8. Mole fraction solubility (x) of musk ketone in methanol; ■, the data from this work; □, the data from ref 39; , calculated values from the modified Apelblat equation in this work.

solvents a

methanol ethanola n-Butanola ethyl acetatea musk ketoneb ω2 = 0.0997 ω2 = 0.2999 ω2 = 0.5039 ω2 = 0.6998 ω2 = 0.8995 ω2 = 0.0952 ω2 = 0.2948 ω2 = 0.4942 ω2 = 0.6965 ω2 = 0.9000

Figure 9. Mole fraction solubility (x) of musk ketone in ethanol; ●, the data from this work; ○, the data from ref 39; , calculated values from modified Apelblat equation in this work.

ω2 = 0.0932 ω2 = 0.2933 ω2 = 0.4967 ω2 = 0.6965 ω2 = 0.8907

In the above formulas, δd, δp, and δh are the dispersion HSP, polar HSP, and hydrogen-bonding HSP, respectively; Cid, Cip, and Cih means first-order group contribution value for the prediction of the partial solubility parameter, respectively, Ni is the corresponding number of groups, and these data are listed in Table 13.

a

contributions

first-order groups

Ni

Ciδd

Ciδp

Ciδh

−CH3 >C< AC ACCH3 ACNO2 >CO constant, C

4 1 2 2 2 1

−0.9714 1.2686 0.8446 0.2174 1.4195 −0.04343 17.3231

−1.6448 2.0838 0.6187 −0.5705 4.4838 0.7905 7.3548

−0.7813 0.0866 0.0084 −1.1473 −0.7167 1.8147 7.9793

a

The values from ref 43.

The HSPs in a binary solvent (δmix) can be calculated by eq 23 δmix = αδ1 + (1 − δ)δ2

δp/MPa1/2

δh/MPa1/2

%δd+δp

%δh

15.1 12.3 22.3 15.8 8.8 19.4 16.0 5.7 15.8 15.8 5.3 7.2 19.6 12.7 3.0 Methanol (1) + Ethanol (2) 15.2 11.9 22.0 15.3 11.2 21.4 15.5 10.5 20.8 15.6 9.8 20.3 15.7 9.2 19.7 Ethanol (1) + Ethyl acetate (2) 15.8 8.5 18.4 15.8 7.9 16.1 15.8 7.2 13.8 15.8 6.5 11.3 15.8 5.7 8.6 n-Butanol (1) + Ethyl acetate (2) 16.0 5.7 15.1 15.9 5.6 13.5 15.9 5.5 11.8 15.9 5.4 10.0 15.8 5.3 8.2

55.13 55.91 57.87 74.56 91.4

44.87 44.09 42.13 25.44 8.6

55.20 55.35 55.50 55.66 55.82

44.80 44.65 44.50 44.34 44.18

56.95 59.46 62.52 66.42 71.48

43.05 40.54 37.48 33.58 28.52

58.95 61.53 64.56 68.02 72.00

41.05 38.47 35.44 31.98 28.00

The values from ref 40. bThe values from eqs 20−22.

in this table. From Table 14, we can see that the values of % ζδd+δp and % ζδh for musk ketone are 91.4 and 8.6%, respectively. It shows that hydrogen bond interaction contributes little to the solubility parameters of musk ketone, whereas dispersion interaction and polarity interaction contribute a lot. Ethyl acetate also showed a similar pattern. The difference is that the values of % ζδd+δp for the selected three alcohols are 55.13, 55.91, and 57.87%, respectively. The results showed that the contribution of hydrogen bond interaction to solubility parameters in the selected alcoholic solvents is not significantly different from that of non-hydrogen bond interaction. On the other hand, it can be seen that the solubility of musk ketone in all tested pure solvents and binary mixed solvents increases with the increase of % ζδd+δp. Obviously, the smaller the difference of % ζδd+δp and % ζδh values between solvents and solute, the higher the similarity. This is consistent with the well-known rule of chemistry: “like dissolves like”.

Table 13. First-Order Group Approximation for the Prediction of the Partial Solubility Parameters, δd, δp, and δh, for Musk Ketonea occurrences

δd/MPa1/2

(23)

5. CONCLUSIONS In this paper, the solubility data of musk ketone in pure solvents of methanol, ethanol, n-butanol, and ethyl acetate and binary

in which α is the volume fraction in the binary solvent, δ1 and δ2 are HSPs of the corresponding pure solvents. K



Article

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mixtures of methanol + ethanol, ethanol + ethyl acetate, and n-butanol + ethyl acetate at temperature from 273.15 to 313.15 K and atmospheric pressure were studied by using the equilibrium method. The data were correlated with the general solid−liquid equilibrium equation. The results showed that the molar solubility of musk ketone in ethyl acetate was higher than that in methanol, ethanol, and n-butanol at the same temperature and atmospheric pressure. At the same temperature and atmospheric pressure, the molar solubility of musk ketone in binary solvents is between its solubility in the corresponding two pure solvents. The fitting results showed that the van’t Hoff equation, the modified Apelblat equation, and the λh equation can be used to correlate the solubility data of musk ketone in the four pure solvents and three mixed solvents mentioned above; the NRTL model and Wilson model can be used to correlate the solubility data of musk ketone in the pure solvents mentioned above; the Sun model and Jouyban−Acree model can be used to correlate the solubility data of musk ketone in the three mixed solvents mentioned above. In comparison, the modified Apelblat equation gives the best correlation results between the selected models in most systems. HSPs of musk ketone and solvents were calculated and discussed. The results showed that the non-hydrogen bond interaction has a great influence on the solubility of musk ketone.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +86 0371 67781713. ORCID

Li Xu: 0000-0001-9083-4858 Notes

The authors declare no competing financial interest.

■

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Determination and Correlation of the Solubility of Musk Ketone in Pure

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