Determination and Correlation of Solubility and Thermodynamic

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

pubs.acs.org/jced

Determination and Correlation of Solubility and Thermodynamic Properties of trans-Cinnamyl Alcohol in Pure and Binary Solvents from 253.15 K to 293.15 K Si Li,†,‡ Lingyu Wang,†,‡ Minghe Zhu,†,‡ Dandan Han,†,‡ Ya Liu,†,‡ Mingyang Chen,†,‡ Jie Hou,†,‡ and Junbo Gong*,†,‡,§ †

School of Chemical Engineering and Technology, State Key Laboratory of Chemical Engineering, Tianjin University, Tianjin, 300072, China ‡ Collaborative Innovation Center of Chemistry Science and Engineering, Tianjin, 300072, China § Key Laboratory for Modern Drug Delivery and High Efficiency, Tianjin University, Tianjin, 300072, China ABSTRACT: The solubility of cinnamyl alcohol in 11 pure solvents (methanol, ethanol, n-propanol, isopropyl alcohol, n-butyl alcohol, isobutyl alcohol, sec-butyl alcohol, acetone, methyl acetate, ethyl acetate and n-hexane) and two binary solvents of n-hexane + (n-propanol, n-butyl alcohol) was measured by a gravimetric method over temperatures from 253.15 K to 293.15 K at atmosphere pressure. From the experimental results, it was found that the solubility increased with the increasing temperature in all these solvents. The Apelblat model, the λh model, and the nonrandom two-liquid (NRTL) model were used to correlate the solubility data of cinnamyl alcohol in pure and mixed solvents. The thermodynamic properties of the mixing process in binary solvents were calculated by the NRTL model. The result indicates that the mixing process of cinnamyl alcohol is endothermic and spontaneous. The experimental solubility provides good guidance for the subsequent study of crystallization design and crystal morphology of cinnamyl alcohol.

1. INTRODUCTION Cinnamyl alcohol (3-phenyl-2-propene-1-ol, C9H10O, CAS registry No: 4407-36-7, Figure 1) is a new efficient fixative

alcohol, isobutyl alcohol, sec-butyl alcohol, acetone, methyl acetate, ethyl acetate, and n-hexane) and two kinds of binary solvents (n-propanol + n-hexane, n-butyl alcohol + n-hexane) under atmospheric pressure at temperatures ranging from 253.15 K to 293.15 K.9,10 The experimental data were then correlated by the Apelblat model, the λh model and the nonrandom two-liquid (NRTL) model to calculate the solubility of CA under different conditions. In addition, the mixing thermodynamic properties (ΔmixH, ΔmixG, and ΔmixS) of the two kinds of binary solvents were modeled by the NRTL function, which provided us a better understanding about the mixing behaviors of cinnamyl alcohol and the selected solvent.

Figure 1. Chemical structure of cinnamyl alcohol.

agent1−4 which is being widely applied as an additive in foods and beverages because of its innocuousness. Furthermore, cinnamyl alcohol is also a common pharmaceutical intermediate in the synthesis of cardiovascular or cerebrovascular drugs such as cinnarizine and flunarizine dihydrochloride. However, industrial production cinnamyl alcohol suffers from several yet to be solved problems, such as low yield, low purity and unfavorable crystal morphologies, which are critical for the quality of cinnamyl alcohol product.5−8 Therefore, it is important to optimize the crystallization process of cinnamyl alcohol to increase yield and improve product quality. As the driving force for the crystallization process, the supersaturation degree of cinnamyl alcohol is dependent on its solubility in different solvents, which is unfortunately not reported. We herein tested the solubility profiles of cinnamyl alcohol in 11 commonly applied solvents (methanol, ethanol, n-propanol, isopropyl alcohol, n-butyl © XXXX American Chemical Society

2. EXPERIMENT 2.1. Materials. The cinnamyl alcohol (≥0.990 mass fraction) was purchased from Nanjing Shengbicheng Chemical Technology Co., Ltd. The organic solvents used in the experiment including methanol, ethanol, n-propanol, isopropyl alcohol, n-butyl alcohol, isobutyl alcohol, sec-butyl alcohol, acetone, methyl acetate, ethyl acetate, and n-hexane were of analytical grade (≥0.995 mass fraction) and purchased from Tianjin Shiyuan Chemical Co., China. All materials above were used without Received: July 19, 2017 Accepted: November 17, 2017

A

DOI: 10.1021/acs.jced.7b00665 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Details of the Chemicals chemical name

CASRN

source

trans-cinnamyl alcohol

4407-36-7

salicylic acid

69-72-7

methanol

67-56-1

ethanol

64-17-5

n-propanol

71-23-8

isopropyl alcohol n-butyl alcohol

67-63-0

isobutyl alcohol

78-83-1

sec-butyl alcohol

78-92-2

acetone

67-64-1

methyl acetate

79-20-9

ethyl acetate

141-78-6

n-hexane

110-54-3

Nanjing Shengbicheng Chemical Technology Co., Ltd. Tianjin Heowns Biochemical Technology Co., Ltd. Tianjin Shiyuan Chemical Co. Tianjin Shiyuan Chemical Co. Tianjin Shiyuan Chemical Co. Tianjin Shiyuan Chemical Co. Tianjin Shiyuan Chemical Co. Tianjin Shiyuan Chemical Co. Tianjin Shiyuan Chemical Co. Tianjin Shiyuan Chemical Co. Tianjin Shiyuan Chemical Co. Tianjin Shiyuan Chemical Co. Tianjin Shiyuan Chemical Co.

a

71-36-3

mass fraction purity

analysis method

≥0.990

HPLCa

≥0.980

HPLCa

≥0.995

GCb

≥0.995

GCb

≥0.995

GCb

≥0.995

GCb

≥0.995

GCb

≥0.995

GCb

≥0.995

GCb

≥0.995

GCb

≥0.995

GCb

≥0.995

GCb

≥0.995

GCb

Figure 3. X-ray powder diffraction patterns of cinnamyl alcohol in different conditions: (A) raw material; (B) excess solid in solvents; (C) dried crystal from the supernatant.

2.3. Solubility Measurements. The solubility of cinnamyl alcohol in 11 pure solvents (methanol, ethanol, n-propanol, isopropyl alcohol, n-butyl alcohol, isobutyl alcohol, sec-butyl alcohol, acetone, methyl acetate, ethyl acetate, and n-hexane) and two kinds of binary solvent mixtures (n-propanol (1) + n-hexane (2), n-butyl alcohol (1) + n-hexane (2) were measured by a gravimetric analysis method at temperatures ranging from 253.15 K to 293.15 K under atmospheric pressure.11 In a typical experiment, an initial amount of solid cinnamyl alcohol (approximately 4 g, with the remainder being the applied solvents) was added into a glass tube (type, B2702-A15 mL-20EA, Shanghai Aladdin Bio-Chem Technology Co., LTD) containing 4 mL of either single or binary solvent. The mixtures were kept at a predetermined temperature controlled by a refrigeration machine (CF41, Julabo Technology (Beijing) Co. LTD) and were magnetically stirred (2000 rpm) for 10 h until solid−liquid equilibrium was achieved. Because the solubility varied with the changes of solvents and temperatures, a successive amount of cinnamyl alcohol was added as needed into the system to retain the solids excess. After that, the solid−liquid mixtures were kept still for about 4 h to precipitate the undissolved solids, with the saturated supernatant being collected and filtrated with a preheated organic membrane (Φ13 mm, 0.45 μm, Tianjin Jinteng Experimental Equipment Co., Ltd.). The filtrate (about 3 mL) was transferred to a drying Petri dish (m0) and weighed immediately (m1), and then was allowed to evaporate at room temperature in the fume hood for a week. The dried solutes together with petri dish were weighed again (m2) to calculate the mass of dissolved cinnamyl alcohol and the corresponding solvent, respectively. All experiments were repeated three times, and the results were shown as mean ± SD (stand error). The mole-fraction solubility of cinnamyl alcohol (xc) in pure or binary solvents was separately calculated by eqs 1 and 2, respectively.

High performance liquid chromatography. bGas chromatography.

purification and the detailed information about these chemicals were listed in Table 1. 2.2. Differential Scanning Calorimetry (DSC) and X-ray Powder Diffraction (XPRD). Differential scanning calorimetry (DSC 1/500, Mettler-Toledo, Switzerland) was applied to analyze the melting temperature (Tm) and melting enthalpy (ΔfusHm), for which the calibration material is indium. Approximately 8 mg of raw material was heated by DSC at a rate of 2 K per minute in a nitrogen atmosphere, and the result was shown in Figure 2. The X-ray powder diffraction

xc = Figure 2. DSC pattern of cinnamyl alcohol.

xc =

(m2 − m0)/Mc (m1 − m2)/M p + (m2 − m0)/Mc

(1)

(m2 − m0)/Mc ω10(m1 − m2)/M1 + (1 − ω10)(m1 − m2)/M 2 + (m2 − m0)/Mc

(2)

(Type, R-AXIS-RAPID, Rigaku, Japan) was used to identify the crystal by Cu Ka radiation (1.5405 Å) over the 2-theta range of 2−40° with a scanning rate of 8° per minute, and the result was shown in Figure 3.

ω10 = B

m10 m10 + m20

(3) DOI: 10.1021/acs.jced.7b00665 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


Article

Table 2. Experimental Mole-Fraction Solubility (xexp) and Reported Solubility (xlit) of Salicylic Acid in Methanol, Acetic Acid, Acetone, and Ethyl Acetate Texp

Tlit

a 103xexp 1

a 103xlit 1

a 103xexp 2

a 103xlit 2

a 103xexp 3

a 103xlit 3

a 103xexp 4

a 103xlit 4

298.15 303.15 308.15 313.15 318.15

298.15 303.15 308.15 313.15 318.15

123.24 137.18 150.07 163.33 172.34

128.02 139.37 150.53 163.59 176.81

53.06 61.68 70.89 78.49 90.29

54.93 62.54 71.11 80.54 91.82

175.01 195.89 203.14 218.14 230.71

179.24 191.85 202.38 215.04 228.01

129.98 140.09 154.13 165.18 178.61

135.71 145.17 156.56 167.52 179.88

a exp

x is the experimental solubility; xlit is the reported solubility in the literature; 1, 2, 3, 4 represent methanol, acetic acid, acetone, ethyl acetate, respectively. The standard uncertainty of T is u(T) = 0.1 K. The relative standard uncertainty of the solubility is ur(x) = 0.05. The relative uncertainty of pressure is ur(P) = 0.05.

where ω01, m01, m02 is the mass fraction of alcohols, and the mass of alcohols and n-hexane in the initial binary solvents, respectively. Mc represents the molar mass of cinnamyl alcohol, and in eq 1, Mp, refers to the molar mass of the pure solvents. In eq 2, M1, M2 represent the molar mass of alcohols and n-hexane, respectively.

where xc is the mole-fraction solubility of the solute, T and Tm are the corresponding absolute temperature and melting temperature, respectively, and λ and h are the model constants of the equation. 3.3. The Nonrandom Two-Liquid (NRTL) Model. The NRTL model was developed on the basis of the (solid + liquid) phase equilibrium theory and the solute−solvent interactions, which was commonly applied to solubility correlation and prediction in pure and mixed solvents. Herein a simplified NRTL function developed by Renon and Prausnitz was applied and expressed as15−17

3. THERMODYNAMIC MODELS 3.1. The Modified Apelblat Model. The modified Apelblat model is a semiempirical model applied to correlate the measured solubility in the pure and mixed solvents.12,13 The equation describing the relationship between the mole-fraction solubility and temperature is written as

ln xc =

ΔfusH ⎛ 1 1⎞ − ⎟ − ln γc ⎜ R ⎝ Tm T⎠

(6)

where xc is the mole-fraction solubility of the solute, T and Tm are the corresponding absolute temperature and melting temperature, respectively, ΔfusH represents the melting enthalpy, R is the gas constant, and γc is the activity coefficient of the solute in the saturated solution which can be calculated according to the following equation: ln γi = + Figure 4. Mole fraction solubility of salicylic acid (x1) in our experiment and the literature: ▲, literature values of acetone; △, experimental values of acetone; ▼, literature values of ethyl acetate; ▽, experimental values of ethyl acetate; ■, literature values of methanol; □, experimental values of methanol; ●, literature values of acetic acid; ○, experimental values of acetic acid.

ln xc = A +

B + C ln T T

+

(xi + xjGji + xkGki)2

[τijGijxj2 + GijGkjxjxk(τij − τkj)] (xj + xiGij + xkGkj)2 [τikGik xk2 + Gik Gjk xjxk(τik − τjk)] (xk + xiGik + xjGjk )2

(7)

where Gij, Gik, Gji, Gjk, Gki, Gkj, τij, τik, τji, τjk, τki, and τkj are the parameters of the NRTL model. The definition of these terms are further expressed as

(4)

where xc is the mole-fraction solubility of the solute, T is the corresponding absolute temperature, and A, B, and C are the model constants. 3.2. The λh Model. The λh model is also a semiempirical model which is utilized to depict the relationship between the mole-fraction solubility and temperature.14 This model is often applied to solubility correlation and prediction in pure and mixed solvents, and is expressed as ⎛ ⎛1 1 − xc ⎞ 1 ⎞ ln⎜1 + λ ⎟ = λh⎜ − ⎟ xc ⎠ Tm ⎠ ⎝T ⎝

(Gjixj + Gkixk)(τjiGijxj − τkiGkixk)

Gij = exp( −αijτij)

(8)

τij = (gij − gjj)/RT = Δgij /RT

(9)

αji = αij ,

i , j = 1, 2, 3

(10)

where gij − gjj represents the Gibbs energy of intermolecular interaction, αij refers an adjustable empirical constant between 0 and 1, and τ is a criterion of the nonrandomness of the mixtures. The relative deviation (RD) was used as fitting degree between the calculated solubility data and the experimental data. The RD, the average relative deviation (ARD) and the root-mean square deviations (RMSD) between the experimental values (xexp) and the calculated values (xcal) are defined as

(5) C



Article

Table 3. Experimental (xexp) and Calculated (xcal) Mole-Fraction Solubility of Cinnamyl Alcohol in Pure Solvents at Atmosphere Pressure (p = 0.1 MPa) at Temperatures Ranging from 253.15 K to 293.15 Ka solvent

10xexp

methanol ethanol n-propanol isopropyl alcohol n-butyl alcohol isobutyl alcohol sec-butyl alcohol acetone methyl acetate ethyl acetate n-hexaneb

2.22 2.20 1.74 1.95 1.25 0.72 0.89 2.80 1.72 2.08 4.46


2.40 2.56 2.13 2.42 1.62 1.05 1.42 3.22 2.25 2.43 6.64


2.69 2.98 2.66 2.88 2.14 1.65 1.91 3.63 2.70 2.90 10.42

methanol ethanol n-propanol isopropyl alcohol n-butyl alcohol isobutyl alcohol sec-butyl alcohol acetone methyl acetate Ethyl acetate n-hexaneb

3.07 3.42 3.13 3.30 2.69 2.17 2.55 4.14 3.26 3.51 14.25

methanol ethanol n-propanol isopropyl alcohol n-butyl alcohol

3.51 4.04 3.73 3.94 3.42

Apelblat 10xcal T = 253.15 K 2.16 2.17 1.74 1.98 1.19 0.74 0.96 2.75 1.73 1.97 4.70 T = 258.15 K 2.42 2.56 2.15 2.39 1.63 1.11 1.38 3.21 2.20 2.45 7.10 T = 263.15 K 2.73 3.00 2.62 2.85 2.15 1.60 1.91 3.69 2.72 2.99 10.30 T = 268.15 K 3.09 3.48 3.15 3.35 2.75 2.18 2.52 4.19 3.30 3.57 14.20 T = 273.15 K 3.52 4.00 3.72 3.90 3.41

λh 10xcal

NRTL 10xcal

solvent

10xexp

2.16 2.23 1.79 2.02 1.29 0.78 1.00 2.87 1.81 2.08 5.50

2.16 2.24 1.80 2.03 1.28 0.75 0.90 2.87 1.80 2.10 5.20

isobutyl alcohol sec-butyl alcohol acetone methyl acetate ethyl acetate n-hexaneb

2.87 3.21 4.70 3.92 4.16 19.38

2.43 2.58 2.16 2.39 1.65 1.09 1.35 3.22 2.20 2.48 7.00

2.43 2.58 2.15 2.40 1.62 1.04 1.35 3.23 2.20 2.47 6.80


4.01 4.56 4.33 4.46 4.12 3.66 3.95 5.26 4.52 4.86 24.77

2.74 2.97 2.58 2.80 2.09 1.50 1.79 3.62 2.66 2.94 8.90

2.74 2.97 2.57 2.80 2.08 1.54 1.82 3.63 2.64 2.90 9.30


4.66 5.20 4.96 5.12 4.79 4.31 4.59 5.79 5.23 5.47 29.38

3.10 3.42 3.06 3.28 2.62 2.02 2.34 4.06 3.18 3.45 11.40

3.10 3.40 3.04 3.25 2.60 2.06 2.44 4.07 3.17 3.43 12.40


5.36 5.90 5.67 5.82 5.53 4.98 5.30 6.25 5.91 6.10 35.15

3.52 3.93 3.61 3.82 3.24

3.51 3.93 3.61 3.81 3.28


6.10 6.52 6.34 6.49 6.08 5.76 5.92 6.74 6.46 6.59 41.82

Apelblat 10xcal T = 273.15 K 2.86 3.21 4.70 3.91 4.18 18.90 T = 278.15 K 4.02 4.57 4.33 4.49 4.10 3.59 3.92 5.22 4.56 4.80 24.20 T = 283.15 K 4.62 5.19 4.98 5.13 4.80 4.34 4.64 5.74 5.21 5.43 29.90 T = 288.15 K 5.32 5.85 5.65 5.80 5.48 5.06 5.31 6.26 5.86 6.05 35.70 T = 293.15 K 6.14 6.55 6.34 6.50 6.11 5.71 5.90 6.76 6.49 6.64 41.40

λh 10xcal

NRTL 10xcal

2.66 3.00 4.55 3.78 4.03 14.70

2.77 3.13 4.55 3.79 4.03 16.80

4.01 4.51 4.25 4.43 3.95 3.44 3.78 5.10 4.45 4.67 19.30

3.99 4.49 4.24 4.41 4.02 3.59 3.92 5.09 4.47 4.71 22.30

4.59 5.17 4.97 5.12 4.77 4.36 4.68 5.72 5.21 5.39 25.90

4.59 5.16 4.96 5.12 4.82 4.40 4.71 5.70 5.25 5.43 28.60

5.29 5.92 5.79 5.91 5.69 5.40 5.68 6.41 6.05 6.19 36.30

5.31 5.93 5.79 5.92 5.72 5.30 5.61 6.36 6.09 6.23 37.00

6.14 6.79 6.72 6.80 6.71 6.54 6.76 7.19 6.97 7.07 54.20

6.19 6.77 6.69 6.80 6.60 6.33 6.53 7.10 6.95 7.05 47.70

a exp x is the experimental solubility; xcal is the calculated solubility according to the Apelblat model, the λh model and the NRTL model. The standard uncertainty of T is u(T) = 0.1 K. The relative standard uncertainty of the solubility is ur(x) = 0.05. The relative uncertainty of pressure is ur(P) = 0.05. bIn addition, the xexp and xcal of cinnamyl alcohol in n-hexane in this table represent 1000 xexp and xcal.

D


Journal of Chemical & Engineering Data x exp − x cal x exp

RD =

ARD =

1 N

N i=1

where ΔfusH and ΔfusS represent the melting enthalpy and the melting entropy, respectively. 4.2. X-ray Powder Diffraction (XPRD) Analysis. The XRPD patterns of raw cinnamyl alcohol, dried products from the supernatant, and residual cinnamyl alcohol after 8 h dissolution were analyzed by the X-ray powder diffraction. Results were shown in Figure 3 which depicted that all the samples shared the same crystal form. 4.3. Solubility of Cinnamyl Alcohol. The experimental solubility data of salicylic acid in methanol, acetic acid, acetone, and ethyl acetate were determined to prove the reliability of the experimental method used in this manuscript. The experimental data, together with the reported solubility data,19 are presented in Table 2 Figure 4. We have compared our measured solubility data with the available literature data and the deviations are less than 5.0%. So the experimental method used is reasonable and reliable. The experimental solubility of cinnamyl alcohol in 11 solvents were presented in Table 3 and Figure 5. As shown, the solubility

(11)

x exp − x cal x exp

∑

Article

(12)

N

∑i = 1 (xiexp − xical)2

RMSD =

N−1

(13)

3.4. Mixing Thermodynamic Properties. The system studied is a nonideal solution. It is necessary to discuss the mixing thermodynamic properties of the solute in pure and binary solvents, such as the mixing enthalpy (ΔmixH), the mixing Gibbs energy (ΔmixG), and the mixing entropy (ΔmixS) which could be calculated as follows,18 Δmix G = Δmix Gid + ΔGE

(14)

Δmix H = Δmix H id + ΔHE

(15)

Δmix S = Δmix S id + ΔS E

(16)

where ΔmixM, ΔmixM , ΔmixM represent the mixing properties, the ideal mixing properties, and the excess properties, respectively. Furthermore, the mixing properties of the ideal solution and the excess properties of the nonideal solution can be calculated by the following equations. id

E

n id

Δmix G = RT ∑ xi ln xi i=1

(17)

n

Δmix S id = −R ∑ xi ln xi i=1

Δmix H id = 0

(18)

Figure 5. Mole-fraction solubility of cinnamyl alcohol (xc) in 11 pure solvents: ▼, acetone; ●, ethyl acetate; ▲, methyl acetate; ■, ethanol; ●, isopropyl alcohol; ★, n-propanol; ▼, n-butyl alcohol; ★, methanol; ⧫, sec-butyl alcohol; ▲, isobutyl alcohol; ■, n-hexane.

(19)

where xi represents the mole fraction of each component of solution. For a pure solvent, i = 2; for a binary solvent, i = 3. n

in all selected solvents increased dramatically with the increasing temperature, suggesting that the cooling crystallization method would be suitable for the recrystallization of cinnamyl alcohol. Generally, as cinnamyl alcohol was a polar reagent, its solubility would decrease with less polar solvent, thus n-hexane manifested the least soluble drug as compared with other 10 tested solvents because of its lowest polarity. Besides polarity, other physicochemical properties of the solvents,20,21 including functional groups, viscosity, as well as intermolecular association between solutes and solvent could also affect the solubility of the solute.22 For example, the cinnamyl alcohol molecules could form hydrogen bonds with several kinds of solvent molecules such as acetone, esters, and alcohols, which could help to enhance the dissolution of the solutes,23 and various strength of hydrogen bonds between solutes and the solvents could lead to solubility diversity of cinnamyl alcohol in different solvents. Furthermore, steric effects also played a role in solutes−solvent interactions, in which higher solute content was usually found in the solvent with less steric hindrances. Thus, the solubility of cinnamyl alcohol in n-butyl alcohol, isobutyl alcohol, and sec-butyl alcohol followed the order of n-butyl alcohol > sec-butyl alcohol > isobutyl alcohol.24 Above all, at temperatures above 273.15 K, the solubility of cinnamyl alcohol in pure solvents follows the order acetone > ethyl acetate > methyl acetate > ethanol > isopropyl

E

ΔG = RT ∑ xi ln γi i=1

n ⎛ ∂ ln γi ⎞ ΔHE = −RT 2 ∑ xi⎜ ⎟ ⎝ ∂T ⎠ p , x i=1

(20)

(21)

ΔHE − ΔGE (22) T where γi stands for the activity coefficient, which can be calculated by the NRTL model. ΔS E =

4. RESULT AND DISCUSSION 4.1. Melting Properties of Cinnamyl Alcohol. As shown in Figure 2, the melting temperature Tm of cinnamyl alcohol is 305.62 ± 0.5 K (P < 0.05) and the melting enthalpy is measured as 13.72 ± 1.16 kJ·mol−1 (P < 0.05). During the phase transition stage, the system is in equilibrium, so ΔfusG = 0, for which the entropy of fusion of cinnamyl alcohol can be calculated by eq 23, giving the value of 44.68 ± 3.80 J·K−1·mol−1. Δ H ΔfusS = fus Tm (23) E



Article

Table 4. Experimental (xexp) and Calculated (xcal) Mole-Fraction Solubility of Cinnamyl Alcohol in n-Propanol + n-Hexane Solvents at Atmosphere Pressure (p = 0.1 MPa) at Temperatures Ranging from 253.15 K to 293.15 Ka ω10

10xexp

0.40 0.50 0.60 0.70 0.80 0.90 1.00

1.03 1.24 1.55 1.76 1.84 1.89 1.74

0.40 0.50 0.60 0.70 0.80 0.90 1.00

1.30 1.56 1.83 2.06 2.26 2.24 2.13

0.40 0.50 0.60 0.70 0.80 0.90 1.00

1.47 2.03 2.35 2.51 2.66 2.69 2.66

0.40 0.50 0.60 0.70 0.80 0.90 1.00

1.85 2.34 2.76 2.95 3.11 3.18 3.13

0.40 0.50 0.60

2.46 3.03 3.39

Apelblat

λh

NRTL

10xcal

10xcal

10xcal

ω10

10xexp

0.98 1.25 1.52 1.72 1.86 1.90 1.79

1.02 1.28 1.54 1.73 1.84 1.88 1.80

0.70 0.80 0.90 1.00

3.59 3.70 3.79 3.73

1.25 1.57 1.89 2.10 2.23 2.27 2.16

1.26 1.58 1.86 2.08 2.22 2.25 2.15

0.40 0.50 0.60 0.70 0.80 0.90 1.00

3.20 3.78 4.20 4.48 4.54 4.50 4.33

1.58 1.97 2.31 2.53 2.66 2.69 2.58

1.52 1.99 2.32 2.51 2.65 2.68 2.57

0.40 0.50 0.60 0.70 0.80 0.90 1.00

3.97 4.60 4.99 5.19 5.19 5.12 4.96

1.98 2.44 2.81 3.03 3.16 3.17 3.06

1.83 2.39 2.78 3.00 3.13 3.18 3.04

0.40 0.50 0.60 0.70 0.80 0.90 1.00

4.81 5.26 5.55 5.78 5.87 5.80 5.67

2.48 3.00 3.39

2.44 3.02 3.39

0.40 0.50 0.60 0.70 0.80 0.90 1.00

5.68 6.07 6.41 6.54 6.50 6.41 6.34

T = 253.15 1.01 1.23 1.50 1.76 1.83 1.86 1.74 T = 258.15 1.25 1.57 1.88 2.11 2.23 2.26 2.15 T = 263.15 1.56 1.99 2.33 2.52 2.69 2.72 2.62 T = 268.15 1.95 2.47 2.84 3.00 3.20 3.23 3.15 T = 273.15 2.43 3.04 3.42

K

K

K

K

K

Apelblat

λh

NRTL

10xcal

10xcal

10xcal

3.61 3.72 3.72 3.61

3.60 3.72 3.78 3.61

3.08 3.66 4.05 4.26 4.36 4.35 4.25

3.14 3.74 4.12 4.35 4.43 4.46 4.24

3.80 4.43 4.82 5.01 5.08 5.06 4.97

3.94 4.54 4.89 5.07 5.13 5.16 4.96

4.68 5.32 5.68 5.84 5.90 5.86 5.79

4.85 5.33 5.61 5.79 5.88 5.96 5.79

5.73 6.35 6.65 6.78 6.81 6.78 6.72

5.82 6.21 6.47 6.60 6.68 6.79 6.69

T = 273.15 3.56 3.77 3.79 3.72 T = 278.15 3.04 3.69 4.08 4.21 4.39 4.40 4.33 T = 283.15 3.80 4.43 4.81 4.97 5.08 5.06 4.98 T = 288.15 4.74 5.27 5.62 5.84 5.83 5.77 5.65 T = 293.15 5.93 6.20 6.50 6.85 6.63 6.51 6.34

K

K

K

K

K

ω10 is the initial mass fraction of n-propanol in the binary solvents; xexp is the experimental solubility; xcal is the calculated solubility according to the Apelblat model, the λh model, and the NRTL model. The standard uncertainty of T is u(T) = 0.1 K. The relative standard uncertainty of the solubility is ur(x) = 0.05. The relative standard uncertainty of n-propanol + n-hexane solvents is ur(x) = 0.0001. The relative uncertainty of pressure is ur(P) = 0.05. a

4.4. Model Correlation. In the study, three solid−liquid phase equilibrium models were used to correlate the solubility data of cinnamyl alcohol. The tested solubility in 11 pure solvents or the binary solvents was fitted by Apelblat equation, λh equation, and NRTL equation. The model parameters, the average relative deviation (ARD) and the root-mean square deviations (RMSD) of these models were summarized in Tables 6−9. The values of ARD and RMSD listed in Tables 6−9 showed that the experimental solubility data were in good agreement with the calculated values within the experimental temperature range, suggesting that these three models were suitable for correlating the solubility data of cinnamyl alcohol. Furthermore, The solubility data of cinnamyl alcohol in pure and mixed solvents were better fitted with the modified Apelblat model as compared with the other models (Table 5), indicating that the semiempirical model was more suitable than the theoretical model for correlating the solubility data of cinnamyl alcohol.

alcohol > n-propanol > n-butyl alcohol > methanol > sec-butyl alcohol > isobutyl alcohol > n-hexane. The experimental solubility of cinnamyl alcohol in binary solvents (n-hexane with n-propanol, or n-butyl alcohol) is presented in Tables 4 and 5 and Figures 6 and 7. Of note, when an alcohols mass fraction of less than 0.4 was applied, the solvent formed a heterogeneously double-layered system which is unfavorable for solubility determination. Thus, the mass fraction of alcohols in the range of 0.4−1 are applied in the present study. As shown, the solubility of cinnamyl alcohol in both binary solvents increases with the increasing temperature. At a constant temperature, the solubility in both solvents changes with different solvent compositions, showing a rising solubility in solvents with increasing alcohol content, which reaches a maximum point where the mass fraction of alcohols reaches to 0.8−0.9. However, further increasing alcohol content leads to decreased solubility because of strong intermolecular interactions between the solvent molecules. F



Article

Table 5. Experimental (xexp) and Calculated (xcal) Mole-Fraction Solubility of Cinnamyl Alcohol in n-Butyl Alcohol + n-Hexane Solvents at Atmosphere Pressure (p = 0.1 MPa) at Temperatures Ranging from 253.15 K to 293.15 Ka ω10

10xexp

0.40 0.50 0.60 0.70 0.80 0.90 1.00

0.65 0.98 1.16 1.24 1.28 1.32 1.25

0.40 0.50 0.60 0.70 0.80 0.90 1.00

0.90 1.25 1.40 1.52 1.62 1.68 1.62

0.40 0.50 0.60 0.70 0.80 0.90 1.00

1.25 1.67 1.90 2.07 2.18 2.22 2.14

0.40 0.50 0.60 0.70 0.80 0.90 1.00

1.77 2.02 2.34 2.63 2.80 2.78 2.69

0.40 0.50 0.60

2.22 2.83 3.11

Apelblat

λh

NRTL

10xcal

10xcal

10xcal

ω10

10xexp

0.66 0.97 1.14 1.23 1.30 1.36 1.29

0.65 0.98 1.16 1.24 1.29 1.31 1.25

0.70 0.80 0.90 1.00

3.32 3.51 3.46 3.42

0.92 1.28 1.47 1.60 1.68 1.73 1.65

0.90 1.24 1.41 1.52 1.62 1.69 1.62

0.40 0.50 0.60 0.70 0.80 0.90 1.00

3.16 3.72 3.94 4.17 4.28 4.21 4.12

1.26 1.66 1.89 2.04 2.14 2.17 2.09

1.25 1.66 1.91 2.06 2.18 2.23 2.14

0.40 0.50 0.60 0.70 0.80 0.90 1.00

3.89 4.26 4.52 4.75 4.91 4.88 4.79

1.70 2.14 2.39 2.58 2.69 2.70 2.62

1.78 2.02 2.34 2.63 2.79 2.79 2.69

0.40 0.50 0.60 0.70 0.80 0.90 1.00

4.77 5.18 5.43 5.70 5.74 5.65 5.53

2.26 2.71 2.98

2.23 2.80 3.14

0.40 0.50 0.60 0.70 0.80 0.90 1.00

5.44 5.74 5.99 6.14 6.14 6.11 6.08

T = 253.15 0.63 0.94 1.10 1.18 1.24 1.29 1.19 T = 258.15 0.91 1.27 1.47 1.60 1.68 1.72 1.63 T = 263.15 1.28 1.69 1.92 2.09 2.21 2.23 2.15 T = 268.15 1.75 2.18 2.44 2.66 2.82 2.82 2.75 T = 273.15 2.32 2.77 3.05

K

K

K

K

K

Apelblat

λh

NRTL

10xcal

10xcal

10xcal

3.21 3.34 3.32 3.24

3.34 3.46 3.50 3.41

2.95 3.40 3.69 3.94 4.08 4.03 3.95

3.17 3.69 3.99 4.16 4.24 4.24 4.11

3.80 4.22 4.50 4.77 4.91 4.84 4.77

3.89 4.25 4.54 4.75 4.88 4.90 4.79

4.80 5.17 5.43 5.71 5.84 5.75 5.69

4.78 5.15 5.47 5.67 5.73 5.66 5.52

5.97 6.25 6.48 6.73 6.86 6.76 6.71

5.44 5.74 6.00 6.13 6.15 6.10 6.08

T = 273.15 3.31 3.49 3.46 3.41 T = 278.15 3.00 3.45 3.74 4.01 4.19 4.14 4.10 T = 283.15 3.79 4.21 4.50 4.77 4.91 4.84 4.80 T = 288.15 4.67 5.06 5.32 5.54 5.62 5.55 5.48 T = 293.15 5.64 5.98 6.20 6.33 6.28 6.23 6.11

K

K

K

K

K

ω10 is the initial mass fraction of n-butyl alcohol in the binary solvents; xexp is the experimental solubility; xcal is the calculated solubility according to the Apelblat model, the λh model, and the NRTL model. The standard uncertainty of T is u(T) = 0.1 K. The relative standard uncertainty of the solubility is ur(x) = 0.05. The relative standard uncertainty of n-butyl alcohol + n-hexane solvents is ur(x) = 0.0001. The relative uncertainty of pressure is ur(P) = 0.05. a

Figure 6. Mole-fraction solubility of cinnamyl alcohol (xc) in (n-propanol + n-hexane) mixed solvents.

Figure 7. Mole-fraction solubility of cinnamyl alcohol (xc) in (n-butyl alcohol + n-hexane) mixed solvents. G



Article

Table 6. Model Parameters of the Apelblat Model for Cinnamyl Alcohol in the Pure Solvents and the Binary Mixtures 10−2A methanol ethanol n-propanol isopropyl alcohol n-butyl alcohol isobutyl alcohol sec-butyl alcohol acetone methyl acetate ethyl acetate n-hexane ω10 0.40 0.50 0.60 0.70 0.80 0.90 ω10 0.40 0.50 0.60 0.70 0.80 0.90

10−3B

C

102RAD

Pure Solvents 5.45 27.15 1.25 −3.98 −7.08 0.99 −9.08 −24.54 0.66 −6.26 −14.88 3.22 −20.72 −64.98 1.50 −29.80 −95.55 2.54 −26.99 −86.76 1.99 −6.99 −19.56 0.93 −13.15 −39.29 1.04 −12.33 −37.01 2.14 −27.33 −85.53 3.15 n-Propanol + n-Hexane 3.69 25.63 3.67 −6.71 −13.63 1.98 −6.41 −13.58 2.21 0.00 9.25 2.38 −5.37 −10.97 1.69 −6.49 −15.28 1.18 n-Butyl alcohol + n-Hexane −17.05 −47.71 3.10 −12.42 −33.00 3.56 −12.34 −33.59 3.19 −16.02 −47.45 2.50 −19.69 −61.27 1.84 −17.09 −52.04 1.45

−1.73 0.53 1.70 1.05 4.39 6.44 5.84 1.35 2.68 2.52 5.74 −1.59 1.00 0.99 −0.53 0.80 1.08 3.29 2.29 2.32 3.24 4.15 3.53

Table 8. Model Parameters of the NRTL Model for Cinnamyl Alcohol in the Pure Solvents

103RMSD

methanol ethanol n-propanol isopropyl alcohol n-butyl alcohol isobutyl alcohol sec-butyl alcohol acetone methyl acetate ethyl acetate n-hexane

3.84 3.70 1.93 3.22 3.69 5.33 3.68 3.69 3.43 6.57 0.04

10−3Δg12

10−3Δg21

a

102RAD

103RMSD

7.93 2.47 1.96 2.03 1.65 1.84 1.74 2.67 1.37 1.40 −4.23

−3.60 0.02 0.89 0.41 2.01 3.31 3.33 −0.70 1.05 0.53 21.42

0.16 0.88 0.96 0.92 0.83 0.72 0.80 0.96 0.93 0.95 0.29

1.28 1.37 2.56 2.29 3.15 4.50 4.16 2.21 3.01 2.37 9.78

0.54 1.02 1.49 1.33 2.11 2.44 2.53 1.63 1.96 1.88 0.03

Table 9. Model Parameters of the NRTL Model for Cinnamyl Alcohol in the n-Propanol + n-Hexane and n-Butyl Alcohol + n-Hexane Binary Mixtures

1.32 0.94 0.94 1.69 0.90 0.59 1.12 1.51 1.22 1.08 0.80 0.67

parameters

n-propanol + n-hexane

n-butyl alcohol + n-hexane

a1 a2 a3 10−4Δg12 10−4Δg13 10−4Δg21 10−4Δg23 10−4Δg31 10−4Δg32 102RAD 103RMSD

0.17 0.35 0.29 0.07 5.44 0.10 −0.43 1.14 0.19 1.63 11.93

0.18 0.40 0.24 0.02 4.41 0.23 −0.49 2.96 9.98 2.02 14.40

Table 7. Model Parameters of the λh Model for Cinnamyl Alcohol in the Pure Solvents and the Binary Mixtures λ methanol ethanol n-propanol isopropyl alcohol n-butyl alcohol isobutyl alcohol sec-butyl alcohol acetone methyl acetate ethyl acetate n-hexane ω10 0.40 0.50 0.60 0.70 0.80 0.90 ω10 0.40 0.50 0.60 0.70 0.80 0.90

10−3h

102RAD

Pure Solvents 0.24 3.76 1.24 0.63 2.67 1.19 0.91 2.60 2.51 0.80 2.57 2.07 1.42 2.40 3.73 1.97 2.33 7.12 1.91 2.19 7.23 0.53 2.29 2.36 1.17 2.26 2.99 1.04 2.22 2.52 2.62 × 10−03 964.21 17.12 n-Propanol + n-Hexane 0.84 3.73 3.95 1.07 2.89 2.36 1.09 2.58 2.35 1.04 2.48 2.35 0.95 2.49 1.76 0.87 2.56 1.73 n-Butyl Alcohol + n-Hhexane 1.48 3.01 3.25 1.30 2.85 3.64 1.33 2.63 3.25 1.52 2.34 3.18 1.60 2.21 3.87 1.40 2.36 3.52

103RMSD 0.51 1.06 1.54 1.30 2.49 3.40 3.51 1.89 2.00 1.97 0.05

Figure 8. Scheme of dissolution of solid particles. 1.10 1.29 1.29 1.39 1.36 1.47

4.5. Mixing Thermodynamic Properties of Solution. It was well-known that in the dissolution process of solid particles, the solute molecules first overcame the intermolecular force to separate from the crystalline lattices, which then interacted with the solvent and spread, finally forming a homogeneous solution25 (Figure 8). The thermodynamic properties of the dissolution process of cinnamyl alcohol could be calculated by the NRTL model. All calculated values of the mixing thermodynamics in the binary solvents were listed in Tables 10 and 11. As shown, the molar mixing Gibbs energy was negative, whereas the molar mixing enthalpy in binary solvents was positive, suggesting that

2.07 2.21 2.03 2.31 2.77 2.50 H



Article

Table 10. Calculated Values of Mixing Thermodynamic Properties of Cinnamyl Alcohol in (n-Propanol + n-Hexane) Mixed Solventsa ω10

ΔmixG (kJ·mol−1)

ΔmixH (kJ·mol−1)

0.40 0.50 0.60 0.70 0.80 0.90

−0.17 −0.28 −0.45 −0.61 −0.73 −0.82

1.58 1.54 1.42 1.21 0.92 0.56

0.40 0.50 0.60 0.70 0.80 0.90

−0.27 −0.39 −0.55 −0.70 −0.84 −0.92

1.60 1.55 1.41 1.19 0.91 0.50

0.40 0.50 0.60 0.70 0.80 0.90

−0.35 −0.53 −0.68 −0.81 −0.94 −1.01

1.60 1.54 1.38 1.17 0.88 0.53

0.40 0.50 0.60 0.70 0.80 0.90

−0.44 −0.62 −0.78 −0.91 −1.03 −1.09

1.60 1.52 1.34 1.12 0.84 0.50

0.40 0.50 0.60 0.70 0.80 0.90

−0.58 −0.75 −0.89 −1.02 −1.11 −1.17

1.57 1.45 1.26 1.03 0.77 0.46

0.40 0.50 0.60 0.70 0.80 0.90

−0.70 −0.85 −0.99 −1.10 −1.17 −1.22

1.50 1.33 1.12 0.88 0.65 0.39

0.40 0.50 0.60 0.70 0.80 0.90

−0.78 −0.93 −1.04 −1.13 −1.20 −1.24

1.38 1.16 0.94 0.73 0.54 0.34

0.40 0.50 0.60 0.70 0.80 0.90

−0.84 −0.96 −1.06 −1.13 −1.19 −1.23

1.19 0.99 0.79 0.59 0.41 0.27

0.40 0.50 0.60

−0.86 −0.96 −1.02

0.95 0.75 0.56

ΔmixS (J·mol−1·K−1) T = 253.15 K 6.93 7.20 7.35 7.16 6.54 5.46 T = 258.15 K 7.24 7.52 7.57 7.35 6.78 5.50 T = 263.15 K 7.40 7.84 7.85 7.54 6.90 5.85 T = 268.15 K 7.63 7.95 7.92 7.58 6.94 5.94 T = 273.15 K 7.89 8.04 7.89 7.50 6.87 5.94 T = 278.15 K 7.90 7.86 7.58 7.12 6.55 5.79 T = 283.15 K 7.63 7.38 7.00 6.58 6.12 5.55 T = 288.15 K 7.05 6.77 6.43 5.98 5.55 5.21 T = 293.15 K 6.16 5.82 5.38 I

T·S (kJ·mol−1)

100ζTS

100ζH

1.75 1.82 1.86 1.81 1.65 1.38

52.55 54.17 56.81 60.04 64.21 71.17

47.45 45.83 43.19 39.96 35.79 28.83

1.87 1.94 1.95 1.90 1.75 1.42

53.91 55.65 58.12 61.38 65.89 73.85

46.09 44.35 41.88 38.62 34.11 26.15

1.95 2.06 2.06 1.98 1.82 1.54

54.88 57.29 59.91 62.88 67.40 74.29

45.12 42.71 40.09 37.12 32.60 25.71

2.05 2.13 2.13 2.03 1.86 1.59

56.06 58.47 61.30 64.50 69.03 76.03

43.94 41.53 38.70 35.50 30.97 23.97

2.16 2.20 2.15 2.05 1.88 1.62

57.81 60.26 63.09 66.46 71.00 78.04

42.19 39.74 36.91 33.54 29.00 21.96

2.20 2.19 2.11 1.98 1.82 1.61

59.43 62.13 65.31 69.14 73.77 80.34

40.57 37.87 34.69 30.86 26.23 19.66

2.16 2.09 1.98 1.86 1.73 1.57

61.10 64.25 67.76 71.72 76.38 82.43

38.90 35.75 32.24 28.28 23.62 17.57

2.03 1.95 1.85 1.72 1.60 1.50

63.07 66.36 69.99 74.38 79.44 84.55

36.93 33.64 30.01 25.62 20.56 15.45

1.81 1.71 1.58

65.59 69.42 73.97

34.41 30.58 26.03



Article

Table 10. continued ω10 0.70 0.80 0.90

ΔmixG (kJ·mol−1) −1.08 −1.14 −1.19

ΔmixH (kJ·mol−1) 0.41 0.30 0.23

ΔmixS (J·mol−1·K−1) T = 293.15 K 5.10 4.93 4.85

T·S (kJ·mol−1)

100ζTS

100ζH

1.50 1.45 1.42

78.41 82.71 86.13

21.59 17.29 13.87

ΔmixH, ΔmixG, ΔmixS stand for the mixing enthalpy, the mixing Gibbs energy and the mixing entropy, calculated by eqs 14−22. The expanded uncertainties are U(ΔmixH) = 0.05 ΔmixH, U(ΔmixS) = 0.05 ΔmixS, U(ΔmixG) = 0.05 ΔmixG (0.95 level of confidence).

a

Table 11. Calculated Values of Mixing Thermodynamic Properties of Cinnamyl Alcohol in (n-Butyl Alcohol + n-Hexane) Mixed Solventsa ω10



0.40 0.50 0.60 0.70 0.80 0.90

−0.97 −0.92 −0.87 −0.82 −0.79 −0.74

0.21 0.56 0.76 0.83 0.76 0.56

0.40 0.50 0.60 0.70 0.80 0.90

−1.03 −0.99 −0.94 −0.91 −0.88 −0.83

0.30 0.63 0.82 0.88 0.81 0.61

0.40 0.50 0.60 0.70 0.80 0.90

−1.10 −1.07 −1.04 −1.02 −0.99 −0.94

0.41 0.73 0.90 0.95 0.87 0.66

0.40 0.50 0.60 0.70 0.80 0.90

−1.17 −1.14 −1.12 −1.11 −1.09 −1.02

0.54 0.79 0.95 0.99 0.91 0.70

0.40 0.50 0.60 0.70 0.80 0.90

−1.23 −1.22 −1.21 −1.19 −1.17 −1.10

0.49 0.88 0.99 1.01 0.92 0.72

0.40 0.50 0.60 0.70 0.80 0.90

−1.26 −1.26 −1.26 −1.25 −1.22 −1.16

0.73 0.90 0.98 0.98 0.90 0.72

0.40 0.50 0.60 0.70 0.80 0.90

−1.28 −1.29 −1.29 −1.28 −1.25 −1.19

0.76 0.88 0.94 0.94 0.86 0.70

ΔmixS (J·mol−1·K−1) T = 253.15 K 4.63 5.84 6.45 6.53 6.13 5.14 T = 258.15 K 5.16 6.29 6.81 6.90 6.55 5.58 T = 263.15 K 5.75 6.85 7.36 7.46 7.07 6.06 T = 268.15 K 6.40 7.20 7.71 7.83 7.44 6.42 T = 273.15 K 6.31 7.66 8.04 8.05 7.64 6.68 T = 278.15 K 7.17 7.78 8.06 8.02 7.62 6.76 T = 283.15 K 7.18 7.67 7.90 7.83 7.44 6.68 J

T·S (kJ·mol−1)

ζTS

ζH

1.17 1.48 1.63 1.65 1.55 1.30

85.11 72.56 68.13 66.60 67.01 69.84

14.89 27.44 31.87 33.40 32.99 30.16

1.33 1.62 1.76 1.78 1.69 1.44

81.72 71.97 68.31 67.03 67.56 70.31

18.28 28.03 31.69 32.97 32.44 29.69

1.51 1.80 1.94 1.96 1.86 1.60

78.70 71.25 68.37 67.47 68.13 70.74

21.30 28.75 31.63 32.53 31.87 29.26

1.72 1.93 2.07 2.10 1.99 1.72

75.99 70.97 68.58 67.96 68.72 71.17

24.01 29.03 31.42 32.04 31.28 28.83

1.72 2.09 2.20 2.20 2.09 1.82

77.80 70.52 68.92 68.59 69.42 71.66

22.20 29.48 31.08 31.41 30.58 28.34

2.00 2.16 2.24 2.23 2.12 1.88

73.13 70.66 69.59 69.49 70.26 72.24

26.87 29.34 30.41 30.51 29.74 27.76

2.03 2.17 2.24 2.22 2.11 1.89

72.85 71.14 70.34 70.33 71.10 72.87

27.15 28.86 29.66 29.67 28.90 27.13



Article

Table 11. continued ω10



0.40 0.50 0.60 0.70 0.80 0.90

−1.26 −1.28 −1.29 −1.27 −1.24 −1.19

0.73 0.80 0.84 0.82 0.77 0.66

0.40 0.50 0.60 0.70 0.80 0.90

−1.23 −1.26 −1.27 −1.26 −1.24 −1.18

0.68 0.73 0.76 0.76 0.72 0.63

ΔmixS (J·mol−1·K−1)

T·S (kJ·mol−1)

ζTS

ζH

1.99 2.08 2.13 2.09 2.01 1.85

73.13 72.15 71.64 71.78 72.29 73.66

26.87 27.85 28.36 28.22 27.71 26.34

1.91 1.99 2.03 2.01 1.96 1.81

73.77 73.11 72.74 72.72 73.06 74.27

26.23 26.89 27.26 27.28 26.94 25.73

T = 288.15 K 6.90 7.22 7.38 7.25 6.98 6.42 T = 293.15 K 6.50 6.81 6.91 6.87 6.69 6.17

ΔmixH, ΔmixG, ΔmixS stand for the mixing enthalpy, the mixing Gibbs energy, and the mixing entropy, calculated by eqs 14−22. The expanded uncertainties are U(ΔmixH) = 0.05 ΔmixH, U(ΔmixS) = 0.05 ΔmixS, U(ΔmixG) = 0.05 ΔmixG (0.95 level of confidence).

a

indicated the mixing processes of cinnamyl alcohol in binary solvents were spontaneous and endothermic-driven. The thermodynamic properties provided us a better understanding about the dissolving behavior of cinnamyl alcohol in specific solvents. Most importantly, all experimental data provided a good guidance for the subsequent study of the crystallization and purification of cinnamyl alcohol.

the mixing of cinnamyl alcohol and solvents was a endothermic and spontaneous process,26 which explained why with increasing temperature the solubility increased in a binary solvent. Likewise, we could judge whether the dissolving process was either endothermic or exothermic depending on the net energy changes of the three stages. As shown in Figure 8, the ΔH of the cinnamyl alcohol−solvent interaction was lower than the sum of crystalline dissolution energy and solute diffuse energy to the solvent. In addition. The molar mixing entropy was positive, which was consistent with the systemic entropy increasing theory. To assess both enthalpy and entropy contributions to the Gibbs energy changes separately, the relative contribution of enthalpy (ζH) and entropy (ζTS) were calculated by eqs 24 and 25, and the results are listed in Tables 10 and 11. By assessing the relative contribution of enthalpy and entropy variations to the final Gibbs energy changes. It was found that when cinnamyl alcohol was dissolved in the binary solvents, the main contributor to the Gibbs energy change was from entropy.27 ζTS% =

|T Δmix S| × 100 |Δmix H | + |T Δmix S|

(24)

ζH % =

|Δmix H | × 100 |Δmix H | + |T Δmix S|

(25)

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: 86-22-27405754. Fax: + 86-22-27314971. ORCID

Junbo Gong: 0000-0002-3376-3296 Funding

The authors are grateful for the financial support from the National Natural Science Foundation of China (NNSFC 81361140344 and NNSFC 21376164), National 863 Program (2015AA021002), Major Science and Technology Program for Water Pollution Control and Treatment (NO.2015ZX07202-013), and Tianjin Science and Technology Project (15JCZDJC33200). Notes

The authors declare no competing financial interest.

■

5. CONCLUSIONS The solubility of cinnamyl alcohol was measured in 11 pure solvents, including methanol, ethanol, n-propanol, isopropyl alcohol, n-butyl alcohol, isobutyl alcohol, sec-butyl alcohol, acetone, methyl acetate, ethyl acetate and n-hexane as well as in the two binary mixtures, n-propanol + n-hexane and n-butyl alcohol + n-hexane. All measurements were under atmospheric pressure at temperatures ranging from 253.15 to 293.15 K by a gravimetric analysis method. On the basis of the experimental values, it could be seen that the solubility increased significantly with the increasing temperature in all selected solvents implying that cooling crystallization method would be suitable for the recrystallization to purify cinnamyl alcohol. The experimental solubility of cinnamyl alcohol in pure and binary solvents was correlated by the modified Apelblat model, the λh model, and the NRTL model. In addition, the mixing thermodynamic properties (Gibbs energy, entropy, and enthalpy) in binary mixtures were calculated by the NRTL model. The thermodynamic values

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Determination and Correlation of Solubility and Thermodynamic

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