Solubility Modeling and Mixing Properties for Benzoin in Different

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

pubs.acs.org/jced

Solubility Modeling and Mixing Properties for Benzoin in Different Monosolvents and Solvent Mixtures at the Temperature Range from 273.15 to 313.15 K Yanqing Zhu,† Chao Cheng,‡ Gaoquan Chen,‡ and Hongkun Zhao*,‡ †

School of Environmental & Municipal Engineering, North China University of Water Resources and Electric Power, ZhengZhou, He’nan 450011, People’s Republic of China ‡ College of Chemistry & Chemical Engineering, YangZhou University, YangZhou, Jiangsu 225002, People’s Republic of China S Supporting Information *

ABSTRACT: In the present work, the benzoin solubility in ethanol, methanol, n-propanol, isopropyl alcohol, n-butanol, acetone, ethyl acetate, acetonitrile, cyclohexane, butyl acetate, isobutyl alcohol, and toluene and ethyl acetate + ethanol solvent mixtures was measured by using the static method at the temperature range from 273.15 to 313.15 K under atmospheric pressure (101.1 kPa). The solubilities in mole fraction increased with increasing temperature and followed the order from high to low in the selected monosolvents: ethyl acetate > acetone > butyl acetate > (acetonitrile, toluene) > methanol > ethanol > n-propanol > n-butanol > isobutyl alcohol > isopropyl alcohol > cyclohexane; and for the ethyl acetate + ethanol mixture, the mole fraction solubilities of benzoin increased with the increase in temperature and ethyl acetate mass fraction. The obtained solubility of benzoin in neat solvents was correlated with the Apelblat equation, λh equation, and Wilson and NRTL models; and in solvent mixtures of ethyl acetate (w) + ethanol (1 − w), with the Jouyban−Acree, van’t Hoff−Jouyban−Acree and Apelblat−Jouyban−Acree models. The largest value of root-mean-square deviation was 4.02 × 10−4, and relative average deviation was 2.36 × 10−2. Furthermore, the mixing enthalpy, mixing Gibbs energy, mixing entropy, activity coefficients under E,∞ infinitesimal concentration (γ∞ 1 ), and reduced excess enthalpy (H1 ) were deduced.

■

INTRODUCTION Benzoin (CAS No. 119-53-9, chemical structure given in Figure 1) appears as off-white crystals with a light camphor-like odor. As an

it possible to select suitable solvents for dissolving a drug and solves different problems, for example, medical solutions and low bioavailability of drugs.7 There is a strong need for accurate solubility data in industry. Therefore, the thermodynamics data play an essential role in the improvement of the crystallization procedure. In this way, it is of great significance to determine the thermodynamic properties and solubility of a solution of benzoin in some neat solvents and mixed solvents. It is regrettable that the results of benzoin solubility in normal solvents are very limited in previous works. Up to now, the solubility of benzoin in supercritical carbon dioxide,8−13 some halogenated hydrocarbons,14 and dry octan-1-ol15 are reported. In addition, Stephens16 and Yang17 have determined the solubilities of benzoin in some organic monosolvents and solvent mixtures. Nevertheless, a large difference is observed between the reported solubility data in the literature. Furthermore, these data are not sufficient for the industrial requirement and for deeply understanding the dissolution procedure of benzoin in solvents. On the basis of the considerations mentioned above, the objects of the present work are to (1) measure the solubility of

Figure 1. Chemical structure of benzoin.

important drug, it is employed on minor skin sores1,2 and wounds in order to keep the region from irritation and infection,3 and employed on canker sores around and in the mouth.4 Benzoin can also be used to soothe and relieve slight irritation of the throat, nose, and airways.5 Crystallization of a drug is a significant factor to control the yield and quality of the final product. The process requires solubility data to control low energy and high yield. Liquid− solid phase equilibrium data constitute the significant thermodynamic property.6 The solubility of the drug plays a very important role and is still a challenging subject in the pharmaceutical industry, because the knowledge of solubility makes © XXXX American Chemical Society

Received: August 21, 2017 Accepted: December 8, 2017

A

DOI: 10.1021/acs.jced.7b00743 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

For a binary solid−liquid system, the activity coefficient γ for component i can be obtained by using the famous Wilson equation.22

benzoin in neat solvents (ethanol, methanol, n-butanol, isopropyl alcohol, ethyl acetate, acetone, acetonitrile, cyclohexane, butyl acetate, isobutyl alcohol, n-butanol, and toluene) and (ethyl acetate + ethanol) mixtures at the temperature range from 273.15 to 313.15 K under atmospheric pressure; (2) correlate the solubility data by using some thermodynamics models; and (3) calculate the mixing properties of benzoin in different monosolvents.

⎤ ⎡ Λ12 Λ 21 ln γ1 = −ln(x1 + Λ12x 2) + x 2⎢ − ⎥ x 2 + Λ 21x1 ⎦ ⎣ x1 + Λ12x 2 (5)

■

SOLUBILITY MODELS In the present work, four models such as the Apelblat equation,18−20 Buchowski−Ksiazaczak λh equation,21 Wilson model,22 and NRTL model,23 are used to describe the solubility behavior of benzoin in the selected monosolvents, and the solubility of benzoin in ethyl acetate + ethanol mixtures is correlated with the Jouyban−Acree equation,24 a combination of Jouyban−Acree equation with van’t Hoff equation,25,26 and a combination of Jouyban−Acree equation with modified Apelblat equation.25,26 Modified Apelblat Equation. The modified Apelblat equation is proposed by Apelblat and may provide a relatively precise correlation using three parameters.18−20 It is expressed as eq 1. ln x = A + B /(T /K) + C ln(T /K)

Λ 21 =

⎛ Δλ ⎞ V1 ⎛ λ 21 − λ 22 ⎞ V ⎟ = 1 exp⎜ − 21 ⎟ exp⎜ − V2 ⎝ RT ⎠ V2 ⎝ RT ⎠

(7)

ln γi =

(1)

∑ j = 1 τjiGjixj N

∑i = 1 Gijx i

N

+

∑ j=1

N ⎡ ∑ xτ G ⎤ ⎢τ − i = 1 i ij ij ⎥ ij N N ∑i = 1 Gijxi ⎢⎣ ∑i = 1 Gijxi ⎥⎦

xjGij

(8)

Gji = exp( −αjiτji)

(9)

αij = αji = α τij =

gij − gjj RT

(10)

=

Δgij R(T /K)

(11)

Here Δgij are model constants relating to the energy of cross interaction. The value of α reveals the nonrandomness of a solution. Supposing that the relationship between the cross-interaction parameter and temperature is linear,33Λij in the Wilson equation and τij in the NRTL equation may be described as eqs 12 and 13.

(2)

τij = aij + Λij =

bij T/K

(12)

⎡ ⎛ bij ⎞⎤ exp⎢ −⎜aij + ⎟⎥ ⎢⎣ ⎝ T /K ⎠⎥⎦ Vi

Vj

(13)

In eqs 12 and 13, aij and bij refer to the parameters being independent upon composition and temperature. Jouyban-Acree Model. This model24 expressed as eq 14 may provide accurate correlation for the dependence of solubility on both solvent composition and temperature for binary solvent mixtures.

(3)

In eq 3, γ denotes the activity coefficient of a solid in equilibrium liquor. ΔfusH stands for the fusion enthalpy at fusion temperature Tfus. ΔCp refers to the difference of the molar heat capacity between in solid and in hypothetical supercooled liquid form. The ΔCp can be roughly regarded as the fusion entropy (ΔfusS).29−32 Therefore, eq 3 can be written as eq 4.27−29 −ΔfusH(Tfus − T ) ln(xγ ) = RTfusT ⎛ T ⎞⎤ Δ S ⎡ (T − T ) + fus ⎢ fus + ln⎜ ⎟⎥ R ⎢⎣ T ⎝ Tfus ⎠⎥⎦

(6)

N

here, λ and h denote the two model parameters. Also x is the solubility of benzoin in mole fraction. T is the experimental temperature, and Tm is the absolute fusion temperature of benzoin. Wilson Equation. In terms of the theory of liquid−solid phase equilibrium and a series of hypothesis and simplifications, the dependence of the mole fraction solubility of a solid upon the absolute temperature may be described as eq 3.27−29 −ΔfusH(Tfus − T ) ln(xγ ) = RTfusT ⎛ T ⎞⎤ ΔCp ⎡ (Tfus − T ) ⎢ + + ln⎜ ⎟⎥ R ⎢⎣ T ⎝ Tfus ⎠⎥⎦

V2 ⎛ λ12 − λ11 ⎞ V2 ⎛ Δλ12 ⎞ ⎟ = exp⎜ − ⎟ exp⎜ − V1 ⎝ RT ⎠ V1 ⎝ RT ⎠

here V1 and V2 refer to the molar volume of the solute and corresponding solvent, respectively. Δλij are equation parameters, which are relevant to the interaction of cross energy. NRTL Model. This model based on the concept of molecular local composition is first put forward by Renon.23 This model has been widely applied in solid−liquid equilibrium. The equation described by the NRTL model is shown as eqs 8−11.

here x is the benzoin solubility in mole fraction at experimental temperature T in K, and A, B, and C are the regression parameters in this equation. Buchowski−Ksiazaczak λh Equation. The λh equation having only two parameters λ and h is put forward to study the relationship between solid solubility and temperature.21 This equation may be described as eq 2: ⎛ 1 ⎡ λ(1 − x) ⎤ 1 ⎞ − ln⎢1 + ⎟ ⎥ = λh⎜ ⎣ ⎦ x Tm/K ⎠ ⎝ T /K

Λ12 =

ln x w,T = w1 ln x1,T + w2 ln x 2,T +

w1w2 T /K

2

∑ Ji (w1 − w2)i i=0

(14)

here xw,T stands for the solubility of solid in mole fraction in solvent mixtures at temperature T/K; w1 and w2 refer to the mass fraction of solvents 1 and 2 free of the benzoin, respectively; x1,T and x2,T are the benzoin solubility in the monosolvent; and Ji are the parameters in Jouyban−Acree model.

(4) B



Article

Table 1. Details of Benzoin and the Selected Solvents molar mass g·mol−1

material benzoin

212.24

molar volume (295 K) ml·mol−1

purification method

mass fraction purity

analysis method

Beijing HWRK Chem Co. Ltd. China

164.53g

recrystallization

0.996

HPLCi

Shanghai Chemical Reagent Co., Ltd., China

40.4h

melting point melting enthalpy (Tm) K kJ·mol−1 410.9a

40.88a

409−410b

source

410c 408.5−410.5d 408e 407−409f methanol

32.04

58.68

none

0.997

GCj

h

ethanol

46.07

none

0.995

GC

isopropyl alcohol

60.06

76.92h

none

0.994

GC

n-butanol

74.12

91.97h

none

0.995

GC

h

acetone

58.05

73.4

none

0.994

GC

ethyl acetate

88.11

79.8h

none

0.996

GC

acetonitrile

41.05

52.86h

none

0.996

GC

toluene

92.14

106.85h

none

0.993

GC

cyclohexane

84.16

108.57h

none

0.994

GC

h

butyl acetate

116.16

132.5

none

0.995

GC

n-propanol

60.06

75.14h

none

0.993

GC

isobutyl alcohol

74.12

92.91h

none

0.995

GC

−1 b

a

This work, determined under 101.1 kPa. The standard uncertainties u are u(T) = 0.5 K, u(p) = 0.45 kPa, u(ΔfusH) = 0.45 kJ·mol . Taken from ref 41. cTaken from ref 42. dTaken from ref 43. eTaken from ref 44. fTaken from ref 45. gTaken from ref 46. hTaken from ref 47. iHighperformance liquid chromatography. jGas chromatography.

van’t Hoff-Jouyban-Acree Model. The equation is expressed as eq 15. ln x T = A +

B T

liquid-phase chromatograph (HPLC, Shimadzu-6A). The details of the benzoin and solvents employed in this work, such as ethanol, methanol, n-butanol, isopropyl alcohol, ethyl acetate, acetone, acetonitrile, cyclohexane, butyl acetate, isobutyl alcohol, n-butanol, and toluene was tabulated in Table 1. These solvents were provided by Sinopharm Chemical Reagent Co., Ltd., China, and employed in experiment without additional treatment. Characterization of Benzoin. The solid in equilibrium with the liquid was analyzed by TGA/DSC thermal analyzer (METTLER TOLEDO, Swizerland) calibrated by indium and zinc and X-ray powder diffraction (type R-AXIS-RAPID, Rigaku, Japan). The melting temperature Tm and the melting enthalpy ΔfusH of benzoin were determined by DSC. Nitrogen was used as a protection gas, for which a flow rate was 10 mL·min−1. About 5 mg of benzoin was added into a standard DSC aluminum pan. Then the pan was heated from 300 to 420 K with a heating rate of 5 K·min−1. X-ray powder diffraction was used to determine the form of solid benzoin. The determination was performed by Cu Kα radiation (0.15405 nm) within the range from 10 to 60° (2-theta) at a scanning rate of five steps per second. Solubility Determination. In the work, the liquid−solid equilibrium for benzoin in different neat solvents was built with the static method33−37 at the temperatures ranging from 273.15 to 313.15 K, and the HPLC was used to test the benzoin solubility in the studied solvents. The apparatus for solubility determination and the experimental procedure for solubility determination were demonstrated detailedly in the previous publications.33−39 Here they were described briefly. The apparatus, which is presented in Figure S1 in the Supporting Information, comprises a jacketed glass vessel of 100 mL, a magnetic stirrer, a condenser, and a

(15)

By combining eq 15 and eq 14, the van’t Hoff−Jouyban−Acree model is derived25,26 and described as eq 16. ⎛ ⎛ B1 ⎞ B2 ⎞ ⎟ ⎟ + w2⎜A 2 + ln xw ,T = w1⎜A1 + ⎝ ⎝ T /K ⎠ T /K ⎠ +

w1w2 T /K

2

∑ Ji (w1 − w2)i i=0

(16)

Modified Apelblat−Jouyban−Acree model. In the same way, by substituting eq 1 into eq 14, the modified Apelblat− Jouyban−Acree model is acquired as eq 17.25,26 ⎡ ⎤ B1 ln x w,T = w1⎢A1 + + C1 ln(T /K)⎥ ⎣ ⎦ T /K ⎡ ⎤ B2 + w2⎢A 2 + + C2 ln(T /K)⎥ ⎦ ⎣ T /K +

■

w1w2 T /K

2

∑ Ji (w1 − w2)i i=0

(17)

EXPERIMENTAL SECTION Materials. Benzoin having a mass fraction of 0.982 was purchased from Beijing HWRK Chemical Co., Ltd., China. The crude raw material was recrystallized triple times in methanol. The crystallized benzoin had a mass fraction composition of 0.996, which was determined by using a high-performance C



Article

circulating bath (QYHX-1030), which was provided by Shanghai Joyn Electronic Co., Ltd., China, and had a standard uncertainty of 0.05 K. The actual temperature of the system was shown using a mercury glass microthermometer, which was inserted in the inner chamber of the vessel. Before determination, the verification for reliability of the apparatus was made via determination of the solubility of benzoic acid in toluene.38,39 Excess benzoin was introduced into the glass vessel filled with about 60 mL of solvent. The system was controlled at a given temperature via circulating the mixture of (isopropyl alcohol + water) from the circulator bath. The ratio of isopropyl alcohol to water was approximately 1:4 (volume). So as to decide the equilibrium time, the liquor was withdrawn every 2 h with a 3 mL syringe connected using a pore syringe filter (0.2 μm), and then analyzed by using the HPLC (Shimadzu-6A). Once the content of liquor did not change, the solution was believed to reach equilibrium. The analysis showed that it took approximately 12 h to equilibrate the system. Then, the stirring was stopped to let any solid precipitate completely. Then, nearly 3 mL of the supernatant was withdrawn with the 3 mL syringe, and transferred cautiously and rapidly to a 25 mL volumetric flask. The sample was diluted with corresponding solvent and tested by the HPLC. In each experiment, three analyses were made for every system at a given temperature. During the whole experiment process, the atmospheric pressure was around 101.1 kPa. Analysis. The benzoin solubility in studied solvents was analyzed using a high-performance liquid-phase chromatograph (HPLC, Shimadzu-6A). The chromatographic column was the Eurospher 100−5 Si (120 mm × 4 mm) column, which temperature was about 303 K. The mobile phase was neat methanol at a flow rate of 1 mL·min−1, and the wavelength of UV detector was 248 nm.40 Each sample was analyzed three times, and the mean data was regarded as the final value of the analysis. The relative standard uncertainty of mole fraction solubility was estimated to be 2.42%. The uncertainty may be due to the uncertainties in the HPLC tests and weighing process.

ΔfusS =

ΔfusH Tm

(18)

Solubility in Monosolvents. The saturated mole fraction solubility (xe) of benzoin in ethanol, methanol, n-propanol, isopropyl alcohol, acetone, acetonitrile, ethyl acetate, cyclohexane, butyl acetate, isobutyl alcohol, n-butanol, and toluene are presented in Table 2, and the x/T curves of benzoin are shown graphically in Figure 2. It can be seen from Figure 2 and Table 2 that the mole fraction solubility of benzoin increases in temperature. The benzoin solubilities are more sensitive to temperature for ethyl acetate, acetone, and butyl acetate, where the solubility changes obviously with temperature. For example, when the temperature rises from 273.15 to 313.15 K, the mole fraction solubility of benzoin in ethyl acetate increases from 0.5211 × 10−2 to 2.235 × 10−2. This tendency shows that cooling crystallization is appropriate for crystallization of benzoin using these solvents, especially in acetone and ethyl acetate. The mole fraction solubility of benzoin in the selected monosolvents ranks as ethyl acetate > acetone > butyl acetate > (acetonitrile, toluene) > methanol > ethanol > n-propanol > n-butanol > isobutyl alcohol > isopropyl alcohol > cyclohexane. Benzoin is soluble in all the studied monosolvents and most soluble in acetone and ethyl acetate. Figure 2 further shows that for the solvents of toluene and acetonitrile, when the temperature is below about 286.3 K, the mole fraction solubility of benzoin is larger in toluene than in acetonitrile; while when the temperature is above 286.3 K, this case is vice versa. The benzoin molecule has one hydroxyl group, and acetone, ethyl acetate, and butyl acetate molecules have a O group. The solubility of benzoin in ethyl acetate, acetone, and butyl acetate are higher than those in the other solvents. Obviously, the case may be resulted from formation of H-bonds between the benzoin and the free electron pairs of the oxygen atoms of ethyl acetate, acetone, and butyl acetate. The polarity of the benzoin molecule is relatively weak; while the polarities of ethanol, methanol, isopropyl alcohol, n-propanol, and n-butanol are relatively strong,46 so the benzoin solubility in the selected alcohols is not large. On the whole, it is very difficult to illustrate the solubility shown in Table 2 in terms of one reason. The situation results from a lot of factors, for example, solvent− solute interactions, solvent−solvent interactions, and molecular sizes and shapes. The solubility data of benzoin in ethanol, n-propanol, isopropyl alcohol, ethyl acetate, butyl acetate, isobutyl alcohol, n-butanol and toluene and in mixed solvents of ethyl acetate + ethanol have been reported at 298.15 K in the previous publications.16,17 These data together with that determined in this work are shown graphically in Figure S4 in Supporting Information. Obviously, these data reported by Stephens16 are very close to our measured ones. A maximum relative error of approximately 3.90% is observed between them. However, there are large difference between our measured solubility data and the values determined by Yang.17 The lagest relative deviations are 26.00%, 18.31%, 20.15%, 34.14%, 49.09%, and 31.54% for methanol, ethanol, ethyl acetate, n-propanol, n-butanol, and acetone, respectively; and 18.31%, 17.81%, 21.65%, 25.08%, 23.47%, 19.17%, 17.65%, 15.19%, and 9.60% for the solvent mixtures of ethyl acetate (w) + ethanol (1 − w) with composition w = 0.1000, 0.2000, 0.3000, 0.4000, 0.5000, 0.6000, 0.7000, 0.8000, and 0.9000, respectively. The result may be due to many factors, such as instrumental error,

■

RESULTS AND DISCUSSION X-ray Powder Diffraction Analysis. To illustrate the solid transformations happening, the excess benzoin in the selected solvents together with the raw material are analyzed by the X-ray powder diffraction. The obtained PXRD patterns of the equilibrium liquid solid are shown graphically in Figure S2 in Supporting Information, which illustrates that all the XPRD patterns of the solid benzoin in equilibration with its liquid and the raw material have the same characteristic peaks. The result demonstrates that benzoin does not display any solvates, amorphous or polymorphism during the entire investigational procedure. Melting Properties of Benzoin. The TG/DSC curves of benzoin are given in Figure S3. The calorimetric determination of benzoin shows a clear fusion peak, while the sample mass is almost the same with the increasing temperature. It indicates that the fusion temperature Tm and fusing enthalpy ΔfusH are 410.9 K and 40.88 kJ·mol−1, respectively, which are very close to the values determined by Yang.17 The obtained value of Tm in the present work is a slight large than those reported in refs 41−45. It is perhaps resulted from the difference in sample purity, equipment, and/or experimental conditions. The fusion entropy ΔfusS may be computed to be 65.99 J·(K·mol)−1 through the eq 18. D



Article

Table 2. Experimental and Correlated Mole Fraction Solubility (x) of Benzoin in Different Mono-Solvents at Temperatures Ranging from (273.15 to 313.15) K under p = 101.1 kPaa 100xλh

100xWilson

100xNRTL

0.07864

0.08055

0.08018

0.08013

0.1003

0.1005

0.1014

0.1012

0.1012

0.1245

0.1269

0.1266

0.1267

0.1268

288.15

0.1571

0.1585

0.1571

0.1575

0.1576

293.15

0.1952

0.1961

0.1938

0.1944

0.1945

298.15

0.2432

0.2403

0.2376

0.2383

0.2384

303.15

0.2928

0.2918

0.2899

0.2903

0.2904

308.15

0.3497

0.3512

0.352

0.3517

0.3516

313.15

0.4196

0.4195

0.4258

0.4238

0.4234

1.08

1.00

0.97

T/K

100xexp

100xApel

273.15

0.08116

278.15 283.15

Methanol

100RAD

0.95 Ethanol

273.15

0.07712

0.07504

0.07780

0.07745

0.07736

278.15

0.09856

0.09666

0.09798

0.09785

0.09781

283.15

0.1214

0.1228

0.1225

0.1226

0.1227

288.15

0.1520

0.1541

0.1521

0.1525

0.1526

293.15

0.1859

0.1910

0.1877

0.1883

0.1885

298.15

0.2402

0.2341

0.2304

0.2311

0.2312

303.15

0.2801

0.2838

0.2813

0.2817

0.2818

308.15

0.3464

0.3406

0.3418

0.3414

0.3413

313.15

0.4019

0.4048

0.4136

0.4116

0.4110

1.81

1.36

1.34

1.34

10 RAD

Isopropyl Alcohol 273.15

0.04370

0.04259

0.04509

0.04486

0.04489

278.15

0.05798

0.05756

0.05872

0.05857

0.05858

283.15

0.07810

0.07628

0.07580

0.07577

0.07575

288.15

0.09724

0.09925

0.0971

0.09718

0.09712

293.15

0.1237

0.1269

0.1234

0.1236

0.1235

298.15

0.1587

0.1597

0.1557

0.1561

0.1560

303.15

0.2020

0.1979

0.1952

0.1956

0.1956

308.15

0.2421

0.2417

0.2434

0.2436

0.2436

313.15

0.2899

0.2911

0.3018

0.3014

0.3018

1.91

1.80

1.75

100RAD

1.51 n-Butanol

273.15

0.07172

0.07039

0.07282

0.07240

0.07236

278.15

0.0903

0.09162

0.09236

0.09213

0.09212

283.15

0.1155

0.1174

0.1163

0.1163

0.1163

288.15

0.1476

0.1483

0.1453

0.1456

0.1457

293.15

0.1856

0.1848

0.1805

0.1810

0.1811

298.15

0.2334

0.2272

0.2228

0.2234

0.2235

303.15

0.2737

0.2760

0.2735

0.2741

0.2741

308.15

0.3266

0.3314

0.3341

0.3341

0.3341

313.15

0.3963

0.3937

0.4064

0.4052

0.4048

1.28

2.04

1.83

1.80

100RAD

Acetone 273.15

0.4651

0.6697

0.4755

0.4724

0.4621

278.15

0.5753

0.648

0.5808

0.5796

0.5735

283.15

0.6906

0.8236

0.705

0.7059

0.7069

288.15

0.8597

1.028

0.8511

0.8540

0.8649

293.15

1.078

1.261

1.0222

1.027

1.0487

E



Article

Table 2. continued T/K

100xexp

100xλh

100xApel

100xWilson

100xNRTL

Acetone 298.15

1.267

1.522

1.222

1.227

1.2574

303.15

1.463

1.811

1.455

1.458

1.4852

308.15

1.712

2.123

1.725

1.723

1.7192

313.15

1.945

2.456

2.039

2.026

1.9365

2.35

2.03

1.09

100RAD

1.45 Ethyl Acetate

273.15

0.5211

0.5197

0.5221

0.5189

0.5185

278.15

0.6281

0.6377

0.6382

0.6371

0.6369

283.15

0.7786

0.7769

0.7754

0.7765

0.7767

288.15

0.9466

0.9403

0.9367

0.9400

0.940

293.15

1.145

1.131

1.126

1.131

1.131

298.15

1.335

1.352

1.346

1.352

1.352

303.15

1.608

1.606

1.603

1.607

1.607

308.15

1.897

1.899

1.902

1.900

1.899

313.15

2.235

2.233

2.249

2.235

2.233

0.61

0.78

0.62

0.62

100RAD

Acetonitrile 273.15

0.2025

0.1955

0.2044

0.2036

0.2015

278.15

0.2586

0.2559

0.2600

0.2596

0.2583

283.15

0.3305

0.3295

0.3280

0.3283

0.3283

288.15

0.4053

0.4180

0.4109

0.4119

0.4138

293.15

0.5061

0.5227

0.5113

0.5128

0.5175

298.15

0.6675

0.6450

0.6323

0.6340

0.6419

303.15

0.7873

0.7859

0.7775

0.7786

0.7883

308.15

0.9439

0.9463

0.9509

0.9502

0.9534

313.15

1.125

1.127

1.158

1.153

1.122

1.68

1.62

1.53

1.21

100RAD

Toluene 273.15

0.2644

0.2661

0.2591

0.2665

0.2584

278.15

0.3103

0.3057

0.3039

0.3063

0.3042

283.15

0.3557

0.3523

0.355

0.3528

0.3563

288.15

0.4005

0.4071

0.4132

0.4071

0.4152

293.15

0.4667

0.4716

0.4794

0.4708

0.4817

298.15

0.5515

0.5475

0.5547

0.5459

0.5565

303.15

0.6347

0.6368

0.6403

0.6349

0.6405

308.15

0.7494

0.7421

0.7378

0.7414

0.7346

313.15

0.8622

0.8662

0.8487

0.8701

0.8401

0.92

1.64

0.94

1.96 0.06060

100RAD

Cyclohexane 283.15

0.05955

0.06005

0.06077

0.06063

288.15

0.08002

0.08016

0.08009

0.08002

0.08002

293.15

0.1074

0.1055

0.1046

0.1047

0.1047

298.15

0.1358

0.1370

0.1356

0.1357

0.1358

303.15

0.1748

0.1757

0.1744

0.1745

0.1746

308.15

0.2236

0.2226

0.2227

0.2228

0.2228

313.15

0.2786

0.2789

0.2825

0.2825

0.2823

0.67

0.99

0.91

0.87

100RAD

Butyl Acetate 273.15

0.4512

0.4594

0.4564

0.4563

0.4564

278.15

0.5608

0.5496

0.5484

0.5488

0.5487

F



Article

Table 2. continued 100xexp

100xApel

283.15 288.15 293.15 298.15 303.15 308.15 313.15 100RAD

0.6456 0.7880 0.9288 1.077 1.277 1.507 1.758

0.6552 0.7784 0.9218 1.088 1.281 1.503 1.758 0.99

273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 100RAD

0.07478 0.09472 0.1191 0.1489 0.1862 0.2339 0.2768 0.3294 0.3978

0.07373 0.09478 0.1203 0.1507 0.1867 0.2288 0.2774 0.3331 0.3962 0.87

273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 100RAD

0.05749 0.07252 0.09413 0.1234 0.1554 0.1924 0.2324 0.2816 0.3452

0.0569 0.07434 0.09582 0.1219 0.1532 0.1904 0.2341 0.2848 0.3432 1.27

T/K

100xλh

100xWilson

100xNRTL

0.6556 0.7800 0.9239 1.090 1.282 1.502 1.756 0.94

0.6562 0.7804 0.9238 1.089 1.280 1.501 1.758 0.91

0.656 0.7802 0.9237 1.089 1.280 1.501 1.757 0.92

0.07578 0.09553 0.1195 0.1486 0.1835 0.2254 0.2753 0.3348 0.4054 1.33

0.07535 0.09531 0.1196 0.1489 0.1841 0.2261 0.2759 0.3347 0.4039 1.09

0.07531 0.09529 0.1196 0.1490 0.1842 0.2268 0.2759 0.3346 0.4035 1.06

0.05813 0.0746 0.09496 0.1200 0.1506 0.1877 0.2326 0.2868 0.3518 1.89

0.05781 0.07441 0.09495 0.1202 0.1509 0.1882 0.2331 0.2869 0.3510 1.73

0.05777 0.07440 0.09497 0.1202 0.1510 0.1883 0.2331 0.2868 0.3506 1.69

Butyl Acetate

n-Propanol

Isobutyl Alcohol

a Standard uncertainties u are u(T) = 0.05 K, u(p) = 0.45 kPa; relative standard uncertainty ur is ur(x) = 0.0242. RAD refers to the relative average deviation,

RAD =

1 N

N

∑ i=1

xie − x ic xie

Figure 2. Experimental mole fraction solubility x of benzoin in different solvents: ■, methanol; ●, ethanol; ▲, isopropyl alcohol; ▼, n- propanol; ◀, acetonitrile; ▶, acetone; □, ethyl acetate; ○, toluene; △, cyclohexane; ◇, butyl acetate; ☆, isobutyl alcohol; ★, n-butanol. , calculated curves by Apelblat equation.

Solubility in mixed solvents. The mole fraction solubilities of benzoin are tabulated in Table 3 for the mixed solvents of ethyl acetate + ethanol. In addition, the dependence of determined solubility upon solvent composition and temperature is given in Figure 3. As can be observed from Table 3 that the benzoin solubility is a function of solvent composition and temperature. The solubilities of benzoin increase with increasing mass fraction of ethyl acetate and temperature.

measurement error, measurement methods and other error. The instrumental error is determined by instrumental accuracy. For example, accuracy of electric balance is ±0.0001 g, the accuracy of shaker is ±0.05 K; these all could bring about instrumental error. Measurement error is determined by the experiment process, some operations such as reading indicator and weighing could cause error. Moreover, the solubility determination method could also lead to error. G



Article

Table 3. Experimental Mole Fraction Solubility (xeT,m·102) of Benzoin in Mixed Solvents of Ethyl Acetate (w) + Ethanol (1 − w) with Various Mass Fractions within the Temperature Range from T/K = (273.15 to 313.15) under 101.1 kPaa w T/K 273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15

0

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1

0.07712 0.09856 0.1214 0.1520 0.1859 0.2402 0.2801 0.3464 0.4019

0.1046 0.1375 0.1848 0.2343 0.2956 0.3445 0.4069 0.5030 0.6127

0.1452 0.1951 0.2611 0.3268 0.4031 0.4902 0.5712 0.6938 0.8277

0.1977 0.2624 0.3292 0.4258 0.5308 0.5952 0.7018 0.8376 1.016

0.2575 0.332 0.4086 0.5272 0.6273 0.753 0.853 0.9822 1.185

0.2977 0.3775 0.4779 0.5983 0.7144 0.8352 0.9853 1.151 1.457

0.3404 0.4231 0.5334 0.6713 0.7939 0.9494 1.176 1.406 1.661

0.3932 0.495 0.6031 0.746 0.8727 1.053 1.307 1.551 1.834

0.4524 0.5612 0.6749 0.8516 1.005 1.196 1.470 1.698 1.971

0.4862 0.5975 0.7414 0.9043 1.095 1.289 1.539 1.815 2.120

0.5211 0.6281 0.7786 0.9466 1.145 1.335 1.608 1.897 2.235

a

Standard uncertainties u are u(T) = 0.05 K, u(p) = 0.45 kPa; relative standard uncertainty ur is ur(x) = 0.0242. Solvent mixtures were prepared by mixing different masses of the solvents with relative standard uncertainty ur(w) = 0.0002. w represents the mass fraction of ethyl acetate in mixed solvents of (ethyl acetate + ethanol).

The maximum solubilities of benzoin are observed in neat ethyl acetate. Solubility Modeling. The benzoin solubility in the selected monosolvents is correlated by using eqs 1−13; and in mixed solvents of ethyl acetate (w) + ethanol (1 − w), with eqs 14−17. The objective function for the selected models is expressed as F=

∑ (ln γie − ln γic)2 i=1

(19)

and for λh and Apelblat equations F=

∑ (xie − xic)2 i=1

(20)

γei

here ln refers to the logarithm of activity coefficient attained using eq 4; and ln γci , the logarithm of activity coefficient evaluated using corresponding model. Additionally, the relative average deviation (RAD) and rootmean-square deviation (RMSD) are used to evaluate the studied solubility models, which are described as eqs 21 and 22, respectively. RAD =

1 N

N

∑ i=1

xie − xic xie

⎡ ∑N (x c − x e)2 ⎤1/2 i i ⎥ RMSD = ⎢ i = 1 ⎢⎣ ⎥⎦ N

Figure 3. Mole fraction solubility (x) of benzoin in ethyl acetate (w) + ethanol (1 − w) mixed solutions with various mass fractions at different temperatures: ★, w = 0; ▶, w = 0.1000; ◀, w = 0.2000; ▼, w = 0.3000; ▲, w = 0.4000; ●, w = 0.5000; △, w = 0.6000; ▽, w = 0.7000; ○, w = 0.8000; □, w = 0.9000, ☆, w = 1. w, mass fraction of ethyl acetate; , calculated curves by Apelblat−Jouyban−Acree model.

show the difference between the experimental and the calculated solubility values, the calculated solubility in monosolvents using the modified Apelblat equation is plotted in Figure 2; and in the mixed solvents of ethyl acetate (w) + ethanol (1 − w) with the Apelblat−Jouyban−Acree model, in Figure 3. As may be observed from Tables S1−S3 in the Supporting Information, the mole fraction solubility of benzoin calculated in the studied monosolvents and in mixed solvents of ethyl acetate + ethanol agrees well with the determined values. For the monosolvent, the largest RMSD value is 4.02 × 10−4, which is acquired with the λh equation for acetone, and the values of RAD are all no greater than 2.35 × 10−2. For the solvent mixtures of ethyl acetate + ethanol, the maximum of RMSD and RAD are 2.04 × 10−4 and 2.36 × 10−2, respectively, which are acquired with Apelblat−Jouyban−Acree model. Generally, the calculated solubility using the selected models agrees well with the determined ones. Mixing Properties of Solution. According to the LewisRandall rule, the mixing properties of solution may be acquired. For an ideal system, the mixing properties including mixing Gibbs energy change, mixing enthalpy, and mixing entropy in a monosolvent can be calculated using eqs 23−25.35,48

(21)

(22)

here N stands for the number of temperature points; xci and xei are the evaluated solubility and determined ones of benzoin, respectively. The molar volumes of the studied solvents presented in Table 1 are cited in ref 46, and of benzoin at 298 K, ref 47. The melting enthalpy (ΔfusH) and melting temperature (Tm) of benzoin are the values determined in this work. The acquired parameters’ values in the Apelblat equation, λh equation, NRTL, and Wilson models are tabulated in Tables S1 and S2 in Supporting Information together with the RMSD values. In addition, the parameters’ values in Jouyban−Acree, van’t Hoff−Jouyban−Acree and Apelblat−Jouyban−Acree models together with the values of RAD and RMSD are presented in Table S3 in the Supporting Information. On the basis of the obtained parameters’ values, the benzoin solubility in selected monosolvents at various temperatures are computed and listed in Table 2, together with the attained values of RAD. So as to

Δmix Gid = RT (x1 ln x1 + x 2 ln x 2) H

(23)



Article

Δmix S id = −R(x1 ln x1 + x 2 ln x 2)

(24)

Δmix H id = 0

(25)

highest in ethyl acetate, and lowest in cyclohexane. At the fixed temperature, they ranked as ethyl acetate > acetone > butyl acetate > (acetonitrile, toluene) > methanol > ethanol > n-propanol > n-butanol > isobutyl alcohol > isopropyl alcohol > cyclohexane. The solubility showed strong dependence upon temperature for acetone, ethyl acetate, and butyl acetate. For the solvent mixtures of ethanol + ethyl acetate, the solubilities of benzoin increased with the increase in mass fraction of ethyl acetate and temperature. The maximum solubilities of benzoin were observed in neat ethyl acetate. The experimental mole fraction solubility data were correlated with different solubility models. For the monosolvents, the maximum values of RAD and RMSD were 2.35 × 10−2 and 4.02 × 10−4, respectively; and for the solvent mixtures of ethanol + ethyl acetate, the maximum ones were 2.36 × 10−2 and 2.04 × 10−4. Furthermore, the mixing Gibbs energy change, mixing entropy, mixing enthalpy, and activity coefficient (γ∞ 1 ) under infinitesimal concentration and reduced excess enthalpy (HE,∞ 1 ) were derived based on the Wilson model and the benzoin solubility in 12 monosolvents. The values of ΔmixG were all negative and decreased with increasing temperature.

where x1 is the mole fraction of benzoin, and x2, corresponding solvent. For the real sysem, the mixing properties are attained using eq 26. Δmix M = ME + Δmix M id

(26)

for M = G , H , and S

ME stands for the excess property in a real system. ΔmixG, ΔmixH, and ΔmixS denote, respectively, the mixing Gibbs energy change, mixing enthalpy, and mixing entropy. The id stands for the ideal state. On the basis of the Wilson equation, the mixing properties in real solutions are expressed as eqs 27−29.49 GE = RT (x1 ln γ1 + x 2 ln γ2) = −RT[x1 ln(x1 + x 2 Λ12) + x 2 ln(x 2 + x1Λ 21)]

■

(27)

⎡ ∂(GE /T ) ⎤ H = −T ⎢ ⎥ ⎣ ∂T ⎦ E

⎛ b Λ b21Λ 21 ⎞ = x1x 2⎜ 12 12 + ⎟ x 2 + Λ 21x1 ⎠ ⎝ x1 + Λ12x 2

SE =

HE − GE T

coefficient (γ∞ 1 ) 50

The activity tration is computed by

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.7b00743. Experimental apparatus (Figure S1), XPRD patterns (Figure S2), DSC scan of benzoin (Figure S3), solubilities of adenosine determined in this work and reported in the previous publications (Figure S4), mixing Gibbs energy (Figure S5), and parameters of the equations (Tables S1, S2, and S3) and mixing properties (Table S4) (PDF)

(28)

(29)

under the infinitesimal concen-

ln γ1∞ = −ln Λ12 + 1 − Λ 21

The excess enthalpy at infinite dilution with eq 31.51,52 ⎡ ∂ lnγ ∞ ⎤ H E, ∞ 1 ⎢ ⎥ = 1 R ⎣ ∂(1/T ) ⎦ P , x

ASSOCIATED CONTENT

S Supporting Information *

2

■

(30)

(HE,∞ 1 )

AUTHOR INFORMATION

Corresponding Author

may be acquired

*Tel.: + 86 514 87975568. Fax: + 86 514 87975244. E-mail: [email protected]. ORCID

Hongkun Zhao: 0000-0001-5972-8352

(31)

Funding

On the basis of the acquired parameters in the Wilson model E,∞ presented in Table S2, the ΔmixG, ΔmixH, ΔmixS, lnγ∞ 1 , and H1 are computed and presented in Table S4 in Supporting Information. The change of mixing Gibbs energy (ΔmixG) may be employed to demostrate the dissolution ability of a benzoin. It can be found from Figure S5 and Table S4 in Supporting Information that the ΔmixG values are negative in all cases and decrease with increasing temperature, therefore, the dissolution procedure of benzoin is spontaneous and favorable in the studied monosolvents. The negative values of ΔmixH indicate that the mixing processes are exothermic for all the monosolvents, and the interactions between solute and solvent are attractive.

This work was supported by the Science and Technology Research Key Project of the Education Department of Henan Province (Project No. SJCX17_0621). Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors would like to express their gratitude for the Priority Academic Program Development of Jiangsu Higher Education Institutions.

■

■

REFERENCES

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CONCLUSION The solid−liquid equilibrium of benzoin in 12 organic monosolvents and in solvent mixtures of ethanol + ethyl acetate were established with the static method at temperatures ranging from 273.15 to 313.15 K under atmospheric pressure of 101.1 kPa, and the solubility of benzoin was determined with the HPLC. The solubility of benzoin in mole fraction was I



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