Solubility of Veratric Acid in Eight Monosolvents and Ethanol + 1

7 Mar 2013 - State Key Laboratory of Chemical Resource Engineering, Beijing ... College of Chinese Pharmacology, Beijing University of Chinese ... and...
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Solubility of Veratric Acid in Eight Monosolvents and Ethanol + 1‑Butanol at Various Temperatures Qunsheng Li,† Fenghua Lu,† Yuanming Tian,† Sijia Feng,† Yang Shen,† and Baohua Wang*,‡ †

State Key Laboratory of Chemical Resource Engineering, Beijing University of Chemical Technology, Box 35, Beijing, 100029, China College of Chinese Pharmacology, Beijing University of Chinese Medicine and Pharmacology, Beijing, 100029, China

‡

ABSTRACT: The solubility of veratric acid (3,4-dimethoxybenzoic acid, with measured melting point of 453.12 K by differential scanning calorimetry, DSC) in eight monosolvents, including ethanol, 1-propanol, 2-propanol, 1-butanol, 2-methyl-1-propanol, methyl acetate, ethyl acetate, and 2-butanone, and binary mixtures of ethanol + 1-butanol was determined at (278 to 323) K and atmospheric pressure using a dynamic method. The modified Apelblat equation and two local composition models (NRTL and UNIQUAC) were used to correlate the solubility of veratric acid in pure solvents. The modified Apelblat and the Jouyban−Acree model were used to correlate the solute solubility in binary mixtures. A combination of the Jouyban−Acree model and van’t Hoff equation was used to predict solubility data in the mixed solvents at different temperatures and gives a reasonable prediction. Each of the correlation equations selected gives a good description of the relationship of solubility and the temperature, and correlated data of the modified Apelblat equation show the best agreement with the experimental data, with the overall relative average deviations values of 0.61 % and 0.62 % in pure solvents and binary mixtures, respectively.

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INTRODUCTION Veratric acid (3,4-dimethoxybenzoic acid, CAS Registry No. 93-07-2, Figure 1) is an important pharmaceutical intermediate for preparation

2-methyl-1-propanol, methyl acetate, ethyl acetate, and 2-butanone, and binary mixtures of ethanol + 1-butanol was determined by a dynamic method at (278 to 323) K and atmospheric pressure. In addition, solubility correlations of veratric acid in monosolvents and binary mixtures at different temperatures were investigated. The modified Apelblat equation and two local composition models (NRTL and UNIQUAC) were selected to correlate the solute solubility in monosolvents. The modified Apelblat equation and the Jouyban−Acree model were selected to correlate the solute solubility in the binary mixtures. Furthermore, a combination of the Jouyban−Acree and van’t Hoff models was trained to predict the solubility of veratric acid in mixed solvents at different temperatures.

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EXPERIMENTAL SECTION Materials. Information concerning all of the samples used in this work, including veratric acid, gallic acid, ethanol, 1-propanol, 2-propanol, 1-butanol, 2-methyl-1-propanol, methyl acetate, ethyl acetate, and 2-butanone, are listed in Table 1. Melting Properties. The melting temperature, Tm, and enthalpy of fusion, ΔfusH, of veratric acid were determined by a differential scanning calorimetric instrument (TGA/DSC1/1600LF, Mettler Toledo Co., Switzerland) and carried out under a nitrogen atmosphere. The temperature and heat flow calibration of the calorimeter were carried out by using the phase-transition temperature and phase-transition enthalpy of National Institute of Standards and Technology (NIST) reference materials (indium: Tm = 429.75 K,

Figure 1. Chemical structure of veratric acid.

of several drugs, such as gefitinib,1 alfuzosin hydrochloride,2 inhibitors of tumor necrosis factor alpha production,3 and desleucyl glycopeptide antibiotics.4 Additionally, the fungistatic activity and antihypertensive and antioxidant bioactivities of veratric acid are reported in literature.5,6 It is well-known that solubility data are essential for designing chemical and pharmaceutical industry processes, such as crystallization and liquid extraction processes, and conducting further thermodynamic research.7 Hence, solubility data of veratric acid in different solvent systems at various temperatures are needed in the purification process to get high purity products. To the best of our knowledge, there are no published solubility data of veratric acid. In this work, the solubility of veratric acid in eight organic monosolvents, including ethanol, 1-propanol, 2-propanol, 1-butanol, © 2013 American Chemical Society

Received: January 11, 2013 Accepted: February 25, 2013 Published: March 7, 2013 1020

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phase equilibrium. The total amount of the solute added in the vessel was recorded. The same solubility experiment was conducted three times. The mean value was used to calculate the mole fraction solubility. The mole fraction solubility x1 of veratric acid in pure solvents is defined as

Table 1. Sources and Purity of the Materials Used in This Work material gallic acid

purity (mass fraction) ≥ 0.990

source

Alfa Aesar China (Tianjin) Co., Ltd. veratric acid ≥ 0.990 Alfa Aesar China (Tianjin) Co., Ltd. ≥ 0.997 Beijing Chemical ethanol (AR)b Works, China 1-propanol (AR) ≥ 0.998 Beijing Chemical Works, China 2-propanol (AR) ≥ 0.997 Beijing Chemical Works, China 1-butanol (AR) ≥ 0.995 Beijing Chemical Works, China 2-methyl-1-propanol (AR) ≥ 0.995 Beijing Chemical Works, China 2-butanone (AR) ≥ 0.995 Beijing Chemical Works, China methyl acetate (AR) ≥ 0.995 Beijing Chemical Works, China ethyl acetate (AR) ≥ 0.995 Beijing Chemical Works, China water double distilled lab made

analysis method HPLCa HPLC

x1 =

GCc GC

m1/Μ1 m1/M1 + m2 /M 2

(1)

where m1 and m2 represent the mass of the solute and the solvent, respectively; M1 and M2 represent respective molecular weights. The mole fraction solubility x1 of veratric acid in the binary mixtures of ethanol + 1-butanol is defined as

GC GC GC

x1 =

GC GC

m1/M1 m1/M1 + m2 /M 2 + m3 /M3

(2)

where m1, m2, and m3 represent the mass of veratric acid, ethanol, and 1-butanol, respectively; M1, M2, and M3 represent respective molecular weights.

GC

■

a

HPLC means high-performance liquid chromatography. bAR means analytical reagent. cGC means gas chromatography.

THEORETICAL BASIS Modified Apelblat Equation. The temperature dependence of the mole fraction experimental solubility of solute in various solvents can be well-correlated by the modified Apelblat equation derived from the Williamson equation.10,11

ΔfusH = 28.45 J·g−1; stannum: Tm = 505.10 K, ΔfusH = 60.21 J·g−1). Approximately 5 mg of veratric acid powder was added to a hermetically sealed DSC pan. The analyses were performed over the temperature range of (313.15 to 573.15) K at a 10 K·min−1 heating rate. The uncertainties of the measurements are ± 0.2 K for the temperature and ± 2 % for the enthalpy of fusion. Solubility Measurements. The solubility of veratric acid was determined by a laser monitoring dynamic method with an apparatus similar to that described in the literature.8,9 The measurement was carried out in a jacked glass vessel (200 mL) with a magnetic stirrer (type 85-2, China). The temperature in the vessel was controlled at a required temperature by circulating water through the outer jacket from a thermostatic water bath (type MPG-10C, China). A mercury-in-glass thermometer (uncertainty of ± 0.05 K) was used to determine the temperature of the solution in the vessel. To prevent the evaporation of the solvent, a condenser was directly connected to the vessel. The mass of samples and solvents were weighed by an electronic analytical balance (uncertainty of ± 0.0001 g, Sartorius CP124S, Germany). The dissolution rate of the solute was examined by the laser beam intensity displayed by the monitoring sensor. At the beginning of the experiment, a predetermined excess mass of solvent and a known mass of solute were added to the inner chamber of the vessel. The dissolution of the solute was facilitated by the continuously stirring at a desired temperature. As the solid particles dissolved, the intensity of the laser beam increased. When the solid particles dissolved completely, the laser beam intensity reached a maximum level, and the solution in the vessel was clear. Then an additional solid solute of known mass (about 1 mg to 3 mg) was added to the solution in the vessel. This process was repeated several times until the maximum intensity of laser beam started to decline after the last addition of solute. The interval time of the addition depended on the dissolution speed of solute, usually longer than 30 min. When the intensity of the laser beam was no more than 90 % of the maximum, the mixture was considered to have reached

ln x1 = a +

b T + c ln T /Κ Κ

(3)

where a, b, and c are model constants; T is the absolute temperature of the system. The Local Composition Models. According to the solid− liquid phase equilibrium theory, the relationship between equilibrium solubility and temperature is described as7 ⎛ 1 ⎞ Δ H ⎛T ⎞ ΔCp ⎛ Tt ⎞ ⎜ ⎟⎟ = fus ⎜ t − 1⎟ − − 1⎟ ln⎜⎜ ⎝ ⎠ ⎝ ⎠ x RT T R T γ ⎝ 1 1⎠ t ΔCp Tt + ln R T

(4)

where γ1 is the solute activity coefficient in solution, Tt is the triple-point temperature of veratric acid, R is the gas constant, and ΔCp is the change of the heat capacity. There are two assumptions commonly employed: first, for most substances there is a little difference between the triple-point temperature and the normal melting point temperature, Tm, and therefore, the triple-point temperature can be submitted by the melting point temperature. Second, ΔCp is set equal to zero. Therefore, eq 4 can be simplified as ⎛ 1 ⎞ Δ H ⎛T ⎞ ⎟⎟ = fus ⎜ m − 1⎟ ln⎜⎜ ⎠ ⎝ γ x RT T ⎝ 1 1⎠ m

(5)

In this study, two local composition models (NRTL and UNIQUAC) were used to calculate the solute activity coefficient γ1 in the binary systems. The mathematical forms of the equations for binary systems are given as follows. (1) NRTL equation.12 The activity coefficient of this equation is given by 1021

dx.doi.org/10.1021/je400029t | J. Chem. Eng. Data 2013, 58, 1020−1028

Journal of Chemical & Engineering Data ⎡ τ G 2 ⎤ τ12G12 21 21 ⎥ ln γ1 = x 2 2⎢ + (G12x1 + x 2)2 ⎦ ⎣ (x1 + G21x 2)2

Article

Table 2. Experimental Mole Fraction Solubility (x1) and Literature Solubility Values of Gallic Acid in Water at Temperature Ta

(6)

where G12 = exp( −α12τ12) τ12 =

G21 = exp( −α12τ21)

g12 − g22

τ21 =

RT

(7)

g21 − g11 RT

(8)

in eqs 6 to 8, x1 and x2 represent the mole fraction of the solute and the solvent, respectively; Δg12 (= g12 − g22) and Δg21 (= g21 − g11) are two binary interaction parameters independent from temperature and composition, two fitting parameters calculated by regression; the parameter α12 is a measure of the nonrandomness of the mixture and set equal to 0.3 in this work. (2) UNIQUAC equation.13 The activity coefficient of this equation is given by ln γ1 = ln γ1C + ln γ1R

ln γ1C = ln

φ1 x1

+

103 x1exp

Tlit

292.18 298.00 303.09 308.21 313.04 318.15 323.15 327.85 333.15

0.98 1.10 1.42 1.90 2.44 3.28 4.27 5.23 6.93

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

mlit 0.96 1.00 1.38 1.79 2.36 3.07 4.02 5.15 6.86

± ± ± ± ± ± ± ± ±

103 x1,callit 0.01 0.02 0.01 0.01 0.02 0.05 0.06 0.06 0.06

1.01 1.06 1.46 1.89 2.49 3.24 4.24 5.42 7.21

a exp

T and Tlit are the temperatures of the system in our measurement and the literature,19 respectively, mlit is the mass solubility of gallic acid in 100 g of water, and x1exp and x1,callit are the mole fraction solubility in our measurement and back-calculated by mlit, respectively. The relative standard uncertainty for the solubility is less than ± 4 %, and the uncertainty of determining temperature is ± 0.05 K. The measurements were made at atmospheric pressure.

(9)

⎛ v r ⎞ z q1 ln 1 + φ2⎜l1 − 1 l 2⎟ r2 ⎠ 2 φ1 ⎝

Texp

(10)

⎛ τ21 ln γ1R = −q1 ln(v1 + v2τ21) + v2q1⎜ ⎝ v1 + v2τ21 τ12 ⎞ ⎟ v1τ12 + v2 ⎠

−

(11)

where z (r1 − q1) − (r1 − 1); 2 z l 2 = (r2 − q2) − (r2 − 1) 2

l1 =

(12)

with φ1 = v1 =

x1r1 x1r1 + x 2r2

φ2 =

x1q1

v1 =

x1q1 + x 2q2 m

ri =

∑ njR j j=1

x 2r2 x1r1 + x 2r2

Figure 2. Mole fraction solubility of gallic acid (x1) in water in our experiment and literature: ■, experimental values; ○, literature values.

(13)

x1q1 x1q1 + x 2q2

(14)

ln x1 = w2 ln(x1)2 + w3 ln(x1)3 +

m

qi =

∑ njQ j j=1

(17) (15)

with

z is the number of close interacting molecules around a central molecule and set equal to 10 in this work; ri and qi are the structure parameters of pure component i; m is the number of functional groups in the molecule; n is the repeating number of each functional group in the molecule. The structural parameters Rj and Qj of functional group j are taken from the literature.14 Two adjustable parameters, τ12 and τ21, are expressed as ⎛ Δu ⎞ τ12 = exp⎜ − 12 ⎟ ⎝ RT ⎠

w2w3 2 ·∑ J (w2 − w3)i T i=0 i

⎛ Δu ⎞ τ21 = exp⎜ − 21 ⎟ ⎝ RT ⎠

w2 =

m2 m 2 + m3

w3 =

m3 m 2 + m3

(18)

where x1, (x1)2, and (x1)3 represent the mole fraction solubility of solute in the mixed solvent, ethanol, and 1-butanol, respectively; w2 and w3 respectively represent the mass fractions of ethanol and 1-butanol in the absence of the solute; m2 and m3 respectively represent the mass of ethanol and 1-butanol in the mixed solvent; the Ji terms are the model constants calculated using a no intercept least-squares regression.15 The solubility of solute in monosolvent at different temperatures can be represented by the van’t Hoff equation.16 The equation is given as

(16)

where Δu12 (= u12 − u22) and Δu21 (= u21 − u11) are the two interaction energy parameters unrelated to both composition and temperature. The Jouyban−Acree Model. The Jouyban−Acree model can provide accurate descriptions of the solute solubility in mixed solvents respecting to both temperature and solvent composition variations. This model is given by15

ln(x1)i = Ai + 1022

Bi T

(19)

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Table 3. Experimental Mole Fraction Solubility (x1) and Calculated Mole Fraction Solubility Values (x1Apel, x1NRTL, and x1UNIQ) of Veratric Acid in Eight Monosolvents at Temperature Ta T/K

102 x1

102 x1Apel

102 RDApel

278.15 282.93 288.21 293.08 298.00 303.33 307.90 313.30 317.15 323.30

0.35 0.42 0.51 0.62 0.74 0.93 1.10 1.36 1.61 2.03

0.35 0.42 0.51 0.62 0.75 0.92 1.10 1.37 1.60 2.04

0.10 −0.32 0.22 0.40 −0.62 0.35 −0.12 −0.75 1.06 −0.33

278.37 283.05 288.39 293.30 299.00 303.17 308.27 313.13 318.15 323.20

0.27 0.33 0.42 0.51 0.66 0.79 0.97 1.18 1.46 1.77

0.27 0.33 0.42 0.52 0.66 0.78 0.97 1.18 1.45 1.78

0.36 −0.34 0.30 −0.78 −0.11 0.27 0.34 0.03 0.46 −0.53

278.37 283.05 288.39 294.07 299.00 303.17 308.27 313.13 318.15 323.20

0.24 0.30 0.39 0.51 0.63 0.74 0.95 1.18 1.50 1.83

0.24 0.30 0.38 0.50 0.63 0.76 0.95 1.17 1.46 1.82

−0.68 −0.61 1.22 2.09 1.18 −2.00 −0.23 0.35 2.23 0.41

277.90 283.25 288.15 293.04 298.15 302.94 308.10 313.15 318.01 323.33

0.25 0.30 0.37 0.46 0.57 0.70 0.89 1.10 1.34 1.68

0.24 0.30 0.37 0.46 0.57 0.70 0.88 1.09 1.35 1.70

1.71 −1.33 −1.89 0.76 −0.66 0.39 1.05 1.06 −0.14 −1.00

277.90 283.25 288.15 293.04 298.15 302.94 308.10 313.15 318.01 323.33

0.15 0.20 0.26 0.32 0.41 0.52 0.66 0.83 1.05 1.32

0.15 0.20 0.25 0.32 0.41 0.52 0.66 0.84 1.04 1.32

−1.03 1.29 1.20 −1.62 −0.05 0.44 −0.19 −0.83 0.89 −0.12

278.30 283.01 288.05 293.15

0.42 0.49 0.58 0.68

0.42 0.49 0.58 0.69

0.05 0.57 −0.32 −0.68

102 x1NRTL Ethanol 0.33 0.41 0.51 0.63 0.77 0.95 1.15 1.42 1.66 2.12 1-Propanol 0.27 0.34 0.43 0.54 0.68 0.82 1.00 1.22 1.47 1.78 2-Propanol 0.24 0.31 0.40 0.52 0.64 0.77 0.95 1.17 1.43 1.74 1-Butanol 0.23 0.30 0.38 0.47 0.59 0.72 0.89 1.09 1.31 1.61 2-Methyl-1-propanol 0.16 0.21 0.26 0.33 0.42 0.52 0.65 0.81 0.99 1.23 Methyl Acetate 0.38 0.46 0.57 0.69 1023

102 RDNRTL

102 x1UNIQ

102 RDUNIQ

4.48 1.71 0.11 −1.17 −3.16 −3.03 −3.83 −4.60 −3.12 −4.32

0.34 0.41 0.51 0.63 0.76 0.94 1.12 1.37 1.57 1.95

3.47 1.49 −0.16 −1.22 −2.79 −1.64 −1.40 −0.56 2.59 3.96

2.06 −0.75 −1.91 −4.09 −4.01 −3.64 −3.15 −2.67 −1.04 −0.49

0.27 0.33 0.42 0.52 0.67 0.79 0.98 1.18 1.43 1.73

3.08 0.71 −0.02 −1.83 −1.43 −0.89 −0.26 0.30 1.89 2.38

−2.62 −3.41 −1.98 −0.98 −1.37 −3.78 −0.84 1.11 4.48 4.57

0.23 0.30 0.39 0.50 0.63 0.76 0.95 1.17 1.45 1.79

1.65 0.27 0.92 1.12 0.05 −2.92 −0.81 0.35 2.87 2.10

4.95 −1.13 −3.69 −2.13 −3.91 −2.40 −0.55 1.23 2.31 4.47

0.24 0.31 0.38 0.47 0.59 0.72 0.89 1.09 1.32 1.64

2.95 −2.11 −3.89 −1.89 −3.27 −1.76 −0.18 1.09 1.48 2.55

−6.92 −3.85 −3.06 −4.81 −1.84 0.10 1.19 2.33 5.64 6.61

0.16 0.20 0.26 0.33 0.42 0.52 0.65 0.81 1.00 1.24

−5.43 −2.60 −2.02 −3.95 −1.23 0.47 1.30 2.16 5.18 5.81

8.20 5.62 1.81 −1.20

0.41 0.49 0.58 0.70

1.99 1.22 −0.78 −2.01

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Table 3. continued T/K

102 x1

102 x1Apel

102 RDApel

298.00 303.13 308.07 313.15 318.06 323.37

0.80 0.95 1.11 1.31 1.52 1.77

0.80 0.95 1.11 1.30 1.51 1.78

−0.58 0.47 0.31 0.56 0.26 −0.63

278.30 283.01 288.05 293.15 298.00 303.13 308.07 313.15 318.06 323.37

0.37 0.44 0.52 0.61 0.72 0.83 0.99 1.16 1.33 1.57

0.37 0.43 0.52 0.61 0.71 0.84 0.98 1.15 1.34 1.57

−0.85 0.99 0.64 −0.61 0.36 −1.20 0.44 0.36 −0.31 0.16

278.95 283.15 287.95 293.32 298.13 303.15 308.37 313.05 318.15 323.49

0.68 0.77 0.89 1.04 1.20 1.40 1.62 1.84 2.12 2.46

0.68 0.77 0.89 1.05 1.20 1.39 1.61 1.84 2.12 2.46

0.11 −0.09 0.17 −0.32 −0.39 0.39 0.15 0.15 −0.09 −0.11

102 x1NRTL Methyl Acetate 0.83 0.99 1.18 1.40 1.64 1.93 Ethyl Acetate 0.33 0.40 0.49 0.60 0.72 0.87 1.04 1.23 1.45 1.72 2-Butanone 0.60 0.70 0.84 1.03 1.22 1.45 1.72 2.00 2.34 2.75

102 RDNRTL

102 x1UNIQ

102 RDUNIQ

−3.28 −4.12 −5.81 −6.78 −7.98 −9.58

0.82 0.97 1.14 1.33 1.54 1.81

−2.48 −1.76 −2.06 −1.74 −1.82 −2.31

9.65 8.14 4.70 0.61 −0.88 −4.79 −5.02 −6.81 −8.92 −9.61

0.36 0.43 0.52 0.62 0.73 0.86 1.01 1.18 1.37 1.60

1.22 1.82 0.42 −1.66 −1.24 −3.23 −1.75 −1.86 −2.41 −1.63

12.93 9.25 5.77 1.49 −1.64 −3.65 −6.44 −8.36 −10.35 −11.77

0.67 0.77 0.90 1.06 1.23 1.42 1.65 1.88 2.15 2.48

2.05 0.59 −0.30 −1.73 −2.34 −1.80 −2.04 −1.79 −1.55 −0.81

a

x1Apel, x1NRTL, and x1UNIQ are the calculated solubility of the Apelblat, NRTL, and UNIQUAC equations, respectively, and RDApel, RDNRTL, and RDUNIQ are respective RD values. The relative standard uncertainty for the solubility is less than ± 4 %, the uncertainty of determining temperature is ± 0.05 K. The measurements were made at atmospheric pressure.

where Ai and Bi are the model constants regressed by solute solubility in monosolvent i. A combination of the Jouyban− Acree and van’t Hoff models can be used to predict the solubility in mixed solvents at different temperatures using two solubility data points, for example, at the lowest and highest temperatures for each solvent.17,18 The combined equation could be represented as ⎛ B ⎞ ww ⎛ B ⎞ ln x1 = w2⎜A 2 + 2 ⎟ + w3⎜A3 + 3 ⎟ + 2 3 ⎝ ⎝ T⎠ T⎠ T 2

·∑ Ji (w2 − w3)i i=0

(20)

where A2, B2, A3, and B3 are parameters of van’t Hoff equation; and Ji terms are the model parameters of the Jouyban−Acree model.

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Figure 3. Mole fraction solubility of veratric acid (x1) in eight monosolvents with error bars representing the standard uncertainty: ■, ethanol; □, 1-propanol; ●, 2-propanol; ○, 1-butanol; ▲, 2-methyl1-propanol; △, methyl acetate; ▼, ethyl acetate; ▽, 2-butanone. Solid line, calculated data based on the modified Apelblat equation.

RESULTS AND DISCUSSION Thermodynamic Properties. The melting temperature Tm and heat of fusion ΔfusH of veratric acid were determined by DSC to be 453.12 K and 29.60 kJ·mol−1, respectively. These data were used in the calculation of this work. Solubility Data. The experimental solubility data of gallic acid in water were measured to prove the reliability of the experimental method used in this work. The experimental data, together with the solubility data reported in the literature,19 are listed in Table 2 and shown in Figure 2. Figure 2 shows the

experimental values show good agreement with the literature values. The comparison indicates that the determination method is reasonable and reliable. Table 3 lists the experimental and calculated solubility of veratric acid in eight monosolvents, which are also shown in Figure 3. The maximum solubility was observed in 2-butanone, 1024

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Table 4. Experimental Mole Fraction Solubility (x1) and Calculated Mole Fraction Solubility Values (x1Apel, x1eq 17, and x1eq 20) of Veratric Acid in Binary Mixtures of Ethanol + 1-Butanol at Temperature Ta T/K

102 x1

102 x1Apel

102 RDApel

278.75 283.26 288.15 293.18 298.41 303.15 308.01 313.15 317.94 323.12

0.28 0.36 0.45 0.54 0.67 0.83 1.02 1.25 1.52 1.89

0.28 0.35 0.43 0.54 0.68 0.83 1.02 1.26 1.53 1.87

−2.73 2.18 2.55 −0.20 −1.30 −0.31 −0.46 −0.60 −0.32 1.09

278.65 283.15 288.21 293.18 298.41 303.35 308.01 313.15 317.94 323.10

0.30 0.37 0.45 0.55 0.69 0.85 1.03 1.26 1.52 1.86

0.30 0.37 0.46 0.56 0.69 0.85 1.03 1.26 1.52 1.86

−0.59 1.39 −0.35 −0.90 −0.03 0.09 0.58 0.08 −0.30 −0.01

277.94 283.05 288.38 293.45 298.25 303.55 308.13 313.15 318.29 323.06

0.28 0.36 0.45 0.55 0.67 0.83 1.01 1.23 1.50 1.80

0.28 0.35 0.45 0.55 0.67 0.84 1.01 1.23 1.50 1.80

−1.16 1.86 0.19 −0.52 −0.60 −0.41 0.42 0.12 0.22 −0.15

279.20 283.45 288.03 292.91 298.02 303.66 307.94 313.10 318.15 323.05

0.29 0.34 0.43 0.52 0.64 0.80 0.95 1.18 1.43 1.73

0.29 0.35 0.42 0.52 0.64 0.80 0.95 1.17 1.43 1.73

0.51 −1.96 1.65 −0.02 0.57 −0.43 −0.83 0.27 0.00 0.17

279.20 283.45 288.03 292.91 298.02 303.66 307.94 313.10 318.15 323.05

0.34 0.40 0.48 0.58 0.71 0.90 1.06 1.29 1.56 1.88

0.34 0.40 0.48 0.59 0.72 0.89 1.05 1.29 1.57 1.89

0.51 −0.41 0.04 −0.39 −0.62 0.35 0.77 0.23 −0.26 −0.24

278.04 283.16 288.15 293.14

0.32 0.41 0.49 0.60

0.32 0.40 0.49 0.60

−1.33 2.07 −0.35 −0.31

102 x1eq w2 = 0.100 0.28 0.34 0.42 0.51 0.64 0.78 0.96 1.20 1.47 1.84 w2 = 0.200 0.30 0.36 0.44 0.54 0.67 0.82 1.00 1.24 1.52 1.90 w2 = 0.300 0.29 0.36 0.45 0.55 0.67 0.84 1.01 1.25 1.56 1.90 w2 = 0.400 0.31 0.37 0.44 0.54 0.67 0.84 1.01 1.25 1.54 1.90 w2 = 0.500 0.32 0.38 0.45 0.55 0.68 0.85 1.02 1.26 1.55 1.90 w2 = 0.600 0.31 0.38 0.47 0.57 1025

102 RDeq 17

102 x1eq 20

102 RDeq 20

−2.16 4.77 6.73 5.20 4.73 5.69 5.15 4.13 3.17 2.80

0.28 0.34 0.43 0.54 0.68 0.82 1.00 1.22 1.46 1.77

−0.72 3.41 3.34 0.48 −0.43 0.98 1.52 2.35 3.74 6.48

2.02 4.74 3.55 3.14 3.73 3.27 2.93 1.23 −0.56 −2.08

0.29 0.36 0.45 0.56 0.70 0.86 1.03 1.26 1.51 1.82

4.33 4.27 0.85 −0.87 −0.71 −0.80 −0.10 0.05 0.63 2.31

−4.81 0.19 −0.22 −0.30 −0.27 −0.47 −0.39 −1.93 −3.54 −5.92

0.29 0.36 0.46 0.58 0.71 0.88 1.05 1.28 1.54 1.83

−2.41 −0.85 −3.72 −5.15 −5.56 −5.34 −4.17 −3.86 −2.84 −2.14

−6.44 −7.97 −3.37 −4.68 −4.01 −5.46 −6.50 −6.41 −8.09 −9.57

0.31 0.38 0.46 0.57 0.71 0.89 1.06 1.29 1.55 1.85

−6.00 −10.39 −7.88 −10.71 −10.56 −11.65 −11.68 −9.55 −8.55 −6.78

7.25 6.34 6.52 5.66 4.75 4.69 4.19 2.40 0.48 −1.07

0.32 0.39 0.47 0.59 0.72 0.91 1.07 1.31 1.57 1.87

7.06 3.64 1.83 −0.40 −1.90 −1.57 −1.15 −1.19 −0.67 0.77

1.23 5.63 3.92 4.20

0.31 0.39 0.49 0.61

1.93 3.10 −0.92 −2.00

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Table 4. continued T/K

102 x1

102 x1Apel

102 RDApel

298.08 303.13 307.94 313.05 318.19 323.33

0.73 0.89 1.08 1.30 1.60 1.95

0.73 0.89 1.08 1.31 1.59 1.94

0.61 −0.58 0.01 −0.67 0.03 0.47

278.04 283.16 288.15 293.14 298.08 303.13 307.94 313.05 318.19 323.33

0.34 0.40 0.50 0.61 0.74 0.90 1.09 1.32 1.61 1.94

0.33 0.41 0.50 0.61 0.74 0.90 1.08 1.32 1.61 1.95

1.47 −2.09 0.12 −0.20 0.06 0.11 0.89 −0.01 0.14 −0.53

278.50 283.15 288.15 293.16 298.29 303.22 308.31 312.99 318.25 323.42

0.34 0.41 0.50 0.61 0.77 0.93 1.15 1.37 1.68 2.07

0.34 0.41 0.50 0.62 0.76 0.93 1.14 1.37 1.69 2.06

−0.08 0.70 −0.60 −1.01 0.98 −0.17 0.68 −0.11 −0.71 0.30

278.37 283.05 288.39 293.16 298.29 303.22 308.31 312.99 318.25 323.42

0.35 0.43 0.51 0.62 0.77 0.91 1.12 1.33 1.62 1.96

0.35 0.42 0.52 0.62 0.76 0.92 1.11 1.33 1.62 1.97

0.38 0.80 −1.79 −0.85 1.16 −0.14 0.50 0.35 0.13 −0.57

102 x1eq w2 = 0.600 0.70 0.86 1.04 1.28 1.59 1.96 w2 = 0.700 0.33 0.40 0.49 0.59 0.72 0.89 1.08 1.33 1.64 2.02 w2 = 0.800 0.35 0.42 0.51 0.62 0.76 0.93 1.13 1.37 1.69 2.09 w2 = 0.900 0.36 0.43 0.53 0.64 0.78 0.94 1.16 1.39 1.72 2.11

102 RDeq 17

102 x1eq 20

102 RDeq 20

4.94 3.33 3.12 1.32 0.54 −0.8

0.75 0.91 1.10 1.33 1.61 1.93

−1.72 −3.14 −2.35 −2.42 −0.72 1.05

2.83 −0.02 2.44 2.11 2.05 1.51 1.48 −0.54 −1.77 −4.1

0.32 0.41 0.51 0.63 0.77 0.94 1.13 1.37 1.65 1.97

4.15 −2.04 −1.85 −3.63 −4.24 −4.54 −3.59 −3.90 −2.65 −1.82

−3.94 −1.63 −1.72 −1.25 1.3 0.38 1.18 0.1 −1.09 −0.9

0.34 0.43 0.53 0.65 0.80 0.98 1.18 1.41 1.70 2.03

−2.09 −2.91 −5.43 −6.45 −4.37 −5.09 −3.20 −2.71 −1.43 1.81

−1.6 −0.97 −3.63 −2.9 −1.3 −3.26 −3.43 −4.51 −5.96 −8.07

0.35 0.43 0.55 0.67 0.82 1.00 1.21 1.43 1.73 2.06

0.33 −2.18 −7.52 −8.22 −7.17 −9.01 −8.12 −7.59 −6.49 −5.38

a

x1Apel, x1eq 17, and x1eq 20 are the calculated solubility of the modified Apelblat equation, eq 17 and eq 20, respectively, and RDApel, RDeq 17, and RDeq 20 are respective RD values. w2 represent the mass fractions of ethanol in the mixed solvents in the absence of the solute. The relative standard uncertainty for the solubility is less than ± 4 %, and the uncertainty of the determining temperature is ± 0.05 K. The measurements were made at atmospheric pressure.

and the minimum value was observed in 2-methyl-1-propanol. The solubility in each solvent increases with the increasing of temperature. The solubility in five alcohols at the overall temperature range according to the following order: ethanol > 1-propanol > 2-propanol > 1-butanol > 2-methyl-1-propanol, which is consistent with the polarity order of the solvents except for 2-propanol [polarity: ethanol (65.4) > 1-propanol (61.7) > 1-butanol (60.2) > 2-methyl-1-propanol (55.2) > 2-propanol (54.6)].20 As the five alcohols have the same hydroxyl functional group, this phenomenon could be due to the interaction between the solvent molecule and the solute molecule get stronger as the polarity of solvents get larger. The solubility is different in different types of solvents. The solubility in eight monosolvents at the temperature range of (278 to 308 K) follows the order: 2-butanone > methyl acetate > ethanol > ethyl acetate > 1-propanol > 2-propanol > 1-butanol > 2-methyl-1-propanol, which is not consistent with

the order of solubility at temperature from 308 K to 323 K. This phenomenon could be due to the combined effects of the solvating interactions and the nature of solute and solvent, such as the structure and functional group. The solubility data of veratric acid in the binary mixtures of ethanol + 1-butanol (w2 of 0.100, 0.200, 0.300, 0.400, 0.500, 0.600, 0.700, 0.800, and 0.900) at different temperatures are listed in Table 4 and shown in Figure 4. The solubility in the binary mixtures increases with the increase in temperature. The solubility of veratric acid in the binary mixture of ethanol + 1-butanol is at a maximum in the solvent with ethanol mass fraction of 0.800 and a minimum in the solvent with the ethanol mass fraction of 0.400. Regression Analysis and Prediction. The experimental solubility data of veratric acid in the eight monosolvents were correlated by the modified Apelblat equation, NRTL and 1026

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respectively. The parameters of NRTL and UNIQUAC equations are listed in Table 6, together with the RAD values. RD =

x1, i − x1,calc i x1, i

(21)

⎡ 1 rmsd = ⎢ ⎢⎣ N − 1

RAD =

1 N

N

∑

N

∑ (x1,i −

⎤1/2

2⎥ x1,calc i )

⎥⎦

i=1

(22)

x1, i − x1,calc i

i=1

x1, i

(23)

calc

where x1,i and x1,i represent the experimental and calculated mole fraction solubility, respectively; N is the number of experimental points. The overall RAD values of the calculated solubility data of the modified Apelblat, NRTL and UNIQUAC equations are 0.61 %, 4.08 %, and 1.84 %, respectively, and the modified Apelblat equation gives the best description of the relationship between equilibrium solubility and temperature. The experimental solubility data of veratric acid in the binary mixtures of ethanol + 1-butanol were correlated by the modified Apelblat equation and the Jouyban−Acree model (eq 17), respectively. In the second correlation, all experimental solubility in binary mixtures (experimental points number, N = 90), together with the solubility in two monosolvents which were back-calculated by the modified Apelblat equation, were correlated by the Jouyban−Acree equation (eq 17). The correlative parameters of the modified Apelblat and Jouyban− Acree (eq 17) equations were regressed by a nonlinear leastsquares method, listed in Tables 7 and 8, respectively. The experimental solubility in mixed solvents could be well-fitted by the modified Apelblat and Jouyban−Acree (eq 17) equations, with overall RAD values of 0.62 % and 3.25 %, respectively. Furthermore, a combination of the van’t Hoff and Jouyban− Acree equation, eq 20, was used to predict the solubility of veratric acid in the binary mixtures of ethanol + 1-butanol at different temperatures. To reduce the number of experimental data points needed in this calculation, we regressed Ai and Bi terms of the van’t Hoff equation employing the solubility in two monosolvents at the lowest and highest temperatures (N = 4), trained the Jouyban−Acree model (eq 20) employing the solubility data in binary mixtures at the lowest and highest temperatures (N = 18) and the Ai and Bi terms, and then used this trained model to predict the solubility at other temperatures.

Figure 4. Mole fraction solubility of veratric acid (x1) in binary mixtures of ethanol + 1-butanol: ■, w2 = 0.100; □, w2 = 0.200; ●, w2 = 0.300; ○, w2 = 0.400; ▲, w2 = 0.500; △, w2 = 0.600; ▼, w2 = 0.700; ▽, w2 = 0.800; ★, w2 = 0.900. Solid line, calculated data based on the modified Apelblat equation.

Table 5. Correlative Parameters, Root-Mean-Square Deviation (rmsd) Values, and Relative Average Deviations (RAD) of the Modified Apelblat Equation for Veratric Acid in Eight Monosolvents solvent

a

b

c

104 rmsd

102 RAD

ethanol 1-propanol 2-propanol 1-butanol 2-methyl-1propanol methyl acetate ethyl acetate 2-butanone

−179.892 −120.239 −108.899 −187.012 −69.072

4830.140 1951.116 1184.711 4848.020 −831.534

27.872 19.067 17.518 29.062 11.649

0.74 0.43 1.34 0.83 0.46

0.43 0.35 1.10 1.00 0.77

−68.758 −62.515 −78.009

397.164 119.789 1085.742

10.988 10.035 12.277

0.56 0.49 0.32

0.44 0.59 0.20

UNIQUAC, respectively. The relative deviations (RD) between the experimental and calculated values of solubility were calculated by eq 21. The model parameters were regressed by a nonlinear least-squares method. The parameters of the modified Apelblat equation are listed in Table 5, together with the root-mean-square deviations (rmsd) and the relative average deviations (RAD), which were calculated by eq 22 and eq 23,

Table 6. Correlative Parameters and Relative Average Deviations (RADs) of the NRTL and UNIQUAC Equations for Veratric Acid in Eight Monosolventsa NRTL

a

UNIQUAC

Δg12

Δg21

Δu12

Δu21

solvent

J·mol−1

J·mol−1

102 RADNRTL

J·mol−1

J·mol−1

102 RADUNIQ

ethanol 1-propanol 2-propanol 1-butanol 2-methyl-1-propanol methyl acetate ethyl acetate 2-butanone

−4489.8 2905.4 −1249.8 3312.7 −570.0 17200.0 13899.0 15695.0

9950.9 300.6 3997.5 408.5 4101.9 −392.0 −501.0 −1568.0

2.95 2.38 2.51 2.68 3.64 5.44 5.91 7.17

2836.6 1706.1 −320.4 −1362.4 −193.4 4838.9 4878.0 5895.9

−1046.1 −641.4 972.8 2401.0 940.7 −1703.1 −1709.5 −2046.0

1.93 1.28 1.31 2.12 3.01 1.82 1.73 1.50

RADNRTL and RADUNIQ represent the RAD values of NRTL and UNIQUAC equations, respectively. 1027

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Table 7. Correlative Parameters, rmsd Values, and RADs of Modified Apelblat Equation for Veratric Acid in Binary Mixtures of Ethanol + 1-Butanola w2

a

b

c

104 rmsd

102 RAD

0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900

−62.561 −101.058 −69.121 −96.862 −129.979 −94.590 −112.182 −111.980 −132.847

−683.254 1174.010 −270.397 991.840 2596.306 975.147 1811.214 1705.930 2799.779

10.505 16.172 11.412 15.531 20.418 15.164 17.762 17.793 20.810

0.98 0.36 0.38 0.47 0.41 0.58 0.58 0.63 0.65

1.17 0.43 0.57 0.64 0.38 0.64 0.56 0.54 0.67

w2 represent the mass fractions of ethanol in the mixed solvents in the absence of the solute.

Table 8. Model Parameters of the Jouyban−Acree Model and the Overall RADs of Calculated Solubility of Veratric Acid in Binary Mixtures of Ethanol + 1-Butanol eq 17

eq 20

45.023 −51.970 268.010 3.25

6.965 −3511.5 7.671 −3801.5 27.724 −23.638 152.078 3.89

The parameters of eq 20 are listed in Table 7, together with the overall RAD value. The overall RAD value for calculated solubility of veratric acid in mixed solvents at other temperatures (expect the lowest and highest temperatures used, N = 72) of this method is 3.89 %. Hence, the prediction using the combined model which trained with solubility data at the lowest and highest temperatures is reasonable.

■

CONCLUSION The melting temperature Tm and heat of fusion ΔfusH of veratric acid were determined by DSC to be 453.12 K and 29.60 kJ·mol−1, respectively. The experimental solubility data of veratric acid in eight monosolvents and binary mixtures of ethanol + 1-butanol solvents were measured by a dynamic method. The solubility data of veratric acid in eight monosolvents can be well-correlated by the modified Apelblat, NRTL, and UNIQUAC equations; the solute solubility in mixed solvents can be well-correlated by the modified Apelblat and Jouyban−Acree equations. A combination of Jouyban-Acree and van’t Hoff equation was trained to predict the solubility in mixed solvents at different temperatures and can give a reasonable prediction. All of the solubility data and calculation equations in this work could be used as essential data for the purification of veratric acid and further thermodynamic research.

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a

A2 B2 A3 B3 J0 J1 J2 102 RAD

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +86-10-64446523. E-mail address: lufenghua1990@163. com. Notes

The authors declare no competing financial interest. 1028

dx.doi.org/10.1021/je400029t | J. Chem. Eng. Data 2013, 58, 1020−1028