Measurement and Correlation of the Solubility of Vanillic Acid in Eight

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Measurement and Correlation of the Solubility of Vanillic Acid in Eight Pure and Water + Ethanol Mixed Solvents at Temperatures from (293.15 to 323.15) K Yuqiang Zhang,† Fan Guo,† Qiao Cui,† Muyao Lu,† Xiaolin Song,‡ Hongjian Tang,‡ and Qunsheng Li*,† †

State Key Laboratory of Chemical Resource Engineering, Beijing University of Chemical Technology, Box 35, Beijing, 100029, China Xinjiang Tianye Group Co., Ltd., Shihezi, Xinjiang 832000, China

‡

ABSTRACT: The solubility of vanillic acid in eight pure solvents, including ethanol, 1-propanol, 2-propanol, n-butanol, isobutanol, acetone, methyl acetate, water, and binary mixtures of water + ethanol have been measured at (293.15 to 323.15) K and atmospheric pressure by using a gravimetric method. The experimental solubility in the pure solvents was correlated by the modified Apelblat equation, van’t Hoff equation, λh equation, nonrandom two-liquid (NRTL) equation, universal quasichemical (UNIQUAC) equation, and Wilson equation. The solubility in the binary mixed solvents was correlated by the modified Apelblat equation and the Jouyban−Acree equation. The correlated values based on all the selected equations showed good agreement with the experimental values, and the correlated data of the modified Apelblat equation show the best agreement with the experimental data.

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reactions and properties of vanillic acid;7 however, it was found that no experimental solubility data in water and organic solvents have been reported. Thus, it is necessary to study the experimental data of solubility of vanillic acid in pure and mixed solvents. In this work, the solubility of vanillic acid in eight pure solvents, including ethanol, 1-propanol, 2-propanol, n-butanol, isobutanol, acetone, methyl acetate, water, and binary mixtures of water + ethanol was measured by a gravimetric method from (293.15 to 323.15) K at atmospheric pressure. Moreover, the experimental solubility values in eight pure solvents were correlated by the modified Apelblat equation, van’t Hoff equation, λh equation, nonrandom two-liquid (NRTL) equation, universal quasichemical (UNIQUAC) equation, and Wilson equation. The modified Apelblet equation and the Jouyban−Acree equation were used to correlate the solubility of water + ethanol mixed solvents. Furthermore, the enthalpy change (ΔHsol), the entropy change (ΔSsol), and the Gibbs free energy change (ΔGsol) in the dissolution process of vanillic acid in pure solvents and mixed solvents were calculated.

INTRODUCTION Vanillic acid (4-hydroxy-3-methoxybenzoic acid, formula: C8H8O4, molecular weight: 168.15 g·mol−1, CAS Registry No. 121-34-6, Figure 1) is a pale yellow crystalline powder. Vanillic

Figure 1. Chemical structure of vanillic acid.

acid is a natural substance; it is found in vanilla bean, benzoin, soybeans, and many other plants. Vanillic acid is an important chemical raw materials; it is an important ingredient for the synthesis of tolcapone. It has been reported to exhibit potential antiulcer activity in ulcerative colitis.1 Moreover, vanillic acid is an important ingredient for the synthesis of spices; it is a flavoring compound in soy sauce. It is well-known that solubility data is essential for designing industry processes and making further thermodynamic research.2−5 To determine the parameters, proper temperature, and solvent for the industrial production, it is necessary to know the solubility in different solvents.6 From a review of the literature on vanillic acid, there are lots of literature about © XXXX American Chemical Society

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EXPERIMENTAL SECTION Materials. The vanillic acid was supplied by Beijing Bailingwei Technology Co., Ltd., with a mass fraction higher than 0.99. The solvents of ethanol, 1-propanol, 2-propanol, nbutanol, isobutanol, acetone, and methyl acetate were purchased from Beijing Chemical Works of China, with the

Received: July 20, 2015 Accepted: December 17, 2015

A

DOI: 10.1021/acs.jced.5b00619 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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mass fraction higher than 0.995. The water was obtained from ultra pure water machine. The details of materials are listed in Table 1.

x1 =

purity (mass fraction)

vanillic acid

≥ 0.990

ethanol (AR)b 1-propanol 2-propanol n-butanol isobutanol acetone methyl acetate water

source

Beijing Bailingwei Technology Co., Ltd. ≥ 0.997 Beijing Chemical Works, China ≥ 0.998 Beijing Chemical Works, China ≥ 0.997 Beijing Chemical Works, China ≥ 0.995 Beijing Chemical Works, China ≥ 0.995 Beijing Chemical Works, China ≥ 0.995 Beijing Chemical Works, China ≥ 0.995 Beijing Chemical Works, China made from ultra pure water machine

(1)

where m1 and m2 are the mass of vanillic acid and the solvent, respectively; M1 and M2 are the respective molar mass. The mass fraction of water (w2) in mixed solvents varied from 0.1 to 0.9 in intervals of 0.1; the mass fraction of water (w2) in mixed solvents was calculated by eq 2 m2 w2 = m 2 + m3 (2)

Table 1. Sources and Purity of Chemicals chemical

m1/M1 m1/M1 + m2 /M 2

analysis method HPLCα GCc

where m2 and m3 are the mass of the water and ethanol, respectively. The mole fraction solubility of vanillic acid (x1) in different compositions of the mixed solvents at different temperatures was obtained by eq 3

GC GC GC GC

x1 =

GC

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

(3)

where m1, m2, and m3 represent the mass of vanillic acid, water, and ethanol, respectively; M1, M2, and M3 are the molar mass of vanillic acid, water, and ethanol, respectively.

GC

■

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

RESULTS AND DISCUSSION Thermodynamic Properties. The melting temperature Tm and the heat of fusion ΔfusH of vanillic acid are 484.9 K and 32.8 kJ·mol−1, corresponding to the literature data of 485.15 K and 29.1 kJ·mol−1, respectively.13−15 The difference of the melting temperature Tm is very small. The difference of the ΔfusH is mainly due to the distinction of the purity of the vanillic acid. Solubility Data. The experimental data and the solubility data reported in the literature are shown in Figure 2. We can

Apparatus and Procedure. Melting Properties Measurements. As the basic thermal characteristics, the melting temperature Tm and heat of fusion ΔfusH were measured by a differential scanning calorimetric instrument (DSC). The standard uncertainty of the Tm was estimated to be 0.2K. The relative standard uncertainty of ΔfusH was estimated to be 0.02. The apparatus (TGA/DSC1/1600LF, Mettler Toledo Co., Switzerland) was calibrated with a 0.999999 mole fraction purity indium and tin sample under a nitrogen atmosphere.8 Vanillic acid sample (about 5 mg) was added to a hermetically sealed DSC pan, with a heating rate of 10 K·min−1. Solubility Measurements. The gravimetric method was used to measure the solubility of vanillic acid in pure solvents and mixed solvents from (293.15 to 323.15) K at atmospheric pressure. An excess amount of vanillic acid was added in a conical flask with a solvent volume of 40 mL.9 The conical flask was maintained at a certain temperature by a water bath shaking table (Shanghai Yiheng Scientific Instrument Co., LTD). The actual temperature was measured by a mercury-in-glass thermometer (the standard uncertainty of temperature u(T) = 0.1 K) inside the flask. The flask was shaken for 72 h to reach the solid−liquid equilibrium. The solution should be settled for 12 h or more before sampling. Subsequently, the supernatant was taken (syringe, the volume is 5 mL) and filtered (vacuum filtration, the pore size of filter membrane is 0.22 μm), and the filtrate was poured into an evaporating dish, which had been preweighed by an analytical balance (Sartorius CP124S, Germany) with an accuracy of ±0.0001 g. The solution (4−5 mL) was transferred into the preweighed evaporating dish and weighted immediately, and then the samples were dried in vacuum drying oven (Tianjin Taisite Instrument Co., Ltd.) at 318.15 K and weighted every 2 h until reaching constant weight.10 All experiments were repeated three times to obtain the mean values.11 The mole fraction solubility of vanillic acid (x1) in pure solvents was calculated by eq 112

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

learn from Figure 2 that the mean variation between the experimental values and literature values16,17 from 293.15 to 308.15 K is about 4.1%. The variation between the experimental values and literature values of 313.15 and 318.15 K is relatively large. The variation between the experimental values and literature values is mainly due to the distinction of the impurities in the vanillic acid. Except for the influence of the purity of the vanillic acid, the experimental values show good agreement with the literature values. The comparison indicates that the determination method is reasonable and reliable. The standard uncertainty of the temperature u(T) is 0.1 K; the relative standard uncertainty of the experimental data ur is about 0.02. The experimental solubility of vanillic acid in eight pure solvents at the temperature ranging from (293.15 to 323.15) K are presented B

DOI: 10.1021/acs.jced.5b00619 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 2. Experimental Mole Fraction Solubility (x1) and Relative Deviations, RD, of Vanillic Acid in Eight Pure Solvents at Temperature T and Pressure p = 0.1 MPaα 100RD T/K

100x1exp

Apelblat

293.15 298.15 303.15 308.15 313.15 318.15 323.15

2.98 3.45 3.84 4.34 4.93 5.44 6.15

−0.67 1.16 −0.52 −0.46 0.61 −0.92 0.33

293.15 298.15 303.15 308.15 313.15 318.15 323.15

2.00 2.41 2.82 3.35 3.98 4.72 5.48

0.50 1.24 −0.71 −0.90 −0.25 0.64 −0.18

293.15 298.15 303.15 308.15 313.15 318.15 323.15

2.56 2.92 3.34 3.80 4.26 4.75 5.32

−0.39 −0.34 0.30 0.79 0.23 −0.42 0.00

293.15 298.15 303.15 308.15 313.15 318.15 323.15

2.29 2.63 3.09 3.57 4.08 4.68 5.36

0.44 −1.14 0.32 0.56 −0.25 −0.21 0.00

293.15 298.15 303.15 308.15 313.15 318.15 323.15

1.13 1.42 1.75 2.17 2.68 3.34 4.08

0.88 1.41 −0.57 −0.46 −0.75 0.30 0.00

293.15 298.15 303.15 308.15 313.15 318.15 323.15

5.86 6.61 7.43 8.25 9.16 10.14 11.07

−0.68 −0.15 0.40 0.12 0.22 0.39 −0.45

293.15 298.15 303.15 308.15 313.15 318.15 323.15

2.07 2.57 3.16 3.79 4.62 5.52 6.63

−0.48 0.39 0.63 −0.53 0.22 −0.36 0.15

van’t Hoff Ethanol −0.67 1.16 −0.52 −0.46 0.61 −0.92 0.49 1-Propanol 0.50 0.83 −1.06 −0.90 −0.25 0.85 0.18 2-Propanol −0.39 −0.34 0.30 0.79 0.23 −0.42 −0.38 n-Butanol 0.44 −1.14 0.32 0.28 −0.25 −0.21 0.37 Isobutanol 0.88 0.70 −1.14 −0.92 −1.12 0.60 0.98 Acetone −0.51 0.00 0.54 0.24 0.22 0.30 −0.72 Methyl Acetate −0.48 0.39 0.63 −0.53 0.22 −0.36 0.15

C

λh

NRTL

UNIQUAC

Wilson

−1.01 0.87 −0.78 −0.69 0.41 −1.10 0.00

−1.34 1.16 −0.52 −0.23 1.01 −1.10 0.16

−0.67 1.16 −1.04 −0.92 0.61 −0.92 0.98

2.35 3.48 0.00 −1.15 −0.81 −3.86 −2.93

1.00 1.24 −1.06 −0.90 −0.25 0.64 0.00

1.00 1.24 −1.42 −1.19 −0.50 1.06 0.91

1.00 0.83 −1.42 −1.49 −0.50 1.27 1.46

1.50 1.24 −1.42 −1.49 −0.50 1.06 1.09

1.17 0.68 0.90 1.05 0.00 −1.05 −1.50

0.00 0.34 1.20 1.58 0.47 −0.84 −1.69

−0.39 −0.68 0.00 0.79 0.23 −0.63 −0.38

3.13 2.05 1.80 1.32 −0.70 −2.74 −3.95

2.18 0.38 0.97 0.28 −0.74 −1.07 −1.12

0.87 −1.14 0.32 0.28 −0.25 0.00 0.56

0.87 −1.14 0.32 0.28 −0.49 0.00 0.56

0.87 −1.14 0.32 0.28 −0.49 −0.21 0.75

1.77 1.41 −0.57 −1.38 −1.49 0.00 0.00

−7.96 −5.63 −4.57 −1.84 0.75 5.09 8.09

−8.85 −6.34 −5.14 −2.30 1.12 5.69 9.07

−7.08 −4.93 −4.00 −1.84 0.75 5.09 7.84

−0.85 −0.15 0.54 0.24 0.33 0.39 −0.54

−0.51 −0.15 0.54 0.00 0.22 0.59 −0.63

0.00 −0.15 0.27 −0.36 −0.11 0.49 −0.45

−0.51 −0.15 0.40 0.00 0.11 0.59 −0.63

0.00 0.39 0.63 −1.06 −0.22 −0.54 0.15

−7.25 −4.28 −1.58 −1.06 2.16 3.80 6.94

−11.59 −7.39 −3.48 −1.58 3.25 6.52 11.31

−6.28 −3.50 −1.27 −1.06 1.95 3.44 6.18

DOI: 10.1021/acs.jced.5b00619 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 2. continued 100RD T/K

100x1exp

Apelblat

van’t Hoff

λh

NRTL

UNIQUAC

Wilson

0.00 0.00 1.95 0.79 0.95 0.00 −1.29

0.79 0.63 1.95 0.40 0.32 −0.78 −2.36

−0.79 −0.62 1.46 0.40 0.95 0.00 −1.07

0.00 0.00 1.46 0.40 0.63 −0.52 −1.72

Water 293.15 298.15 303.15 308.15 313.15 318.15 323.15 α

1.26 1.60 2.05 2.53 3.15 3.85 4.66

× × × × × × ×

10−2 10−2 10−2 10−2 10−2 10−2 10−2

−3.17 −1.87 0.98 0.40 1.27 0.52 −0.86

−0.79 −0.62 1.46 0.40 0.63 0.00 −1.07

Standard uncertainty u is u(T) = 0.1 K; the relative standard uncertainty u are ur(p) = 0.05, ur(x1) = 0.02.

corresponding graph was plotted in Figure 4. The solubility in the mixed solvents increased with the temperature increased. The solubility of vanillic acid in the mixed solvents decreases with the increasing of the mass fraction of water, since the solubility of vanillic acid in ethanol is much larger than that in water. Solubility Correlation. The experimental solubility data of vanillic acid in eight pure solvents were correlated by the modified Apelblat equation, Van’t Hoff equation, λh equation, NRTL equation, UNIQUAC equation, and Wilson equation, respectively. The modified Apelblat equation and Jouyban− Acree model were used to correlate the solubility of vanillic acid in water + ethanol mixed solvents. We can predict the solubility data in different temperatures by using thermodynamic models. The predicted solubility data could be used for industrial production. The relative average deviation of the modified Apelblat equation, van’t Hoff equation, and λh equation is smaller. We can refer more to those models in the prediction of the solubility.

in Table 2,which were correlated by the modified Apelblat equation, van’t Hoff equation, λh equation, NRTL equation, UNIQUAC equation, and Wilson equation, the corresponding graph plotted in Figure 3. It can be seen obviously that the

Figure 3. Mole fraction solubility of vanillic acid (x1) in eight pure solvents: ■, ethanol; □, 1-propanol; ●, 2-propanol; ○, n-butanol; ▲, isobutanol; △, acetone; ☆, methyl acetate; ★, water. The solid line solubility curve was calculated by the modified Apelblat equation.

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THEORETICAL BASIS van’t Hoff Equation. The van’t Hoff equation is a simplified formula of activity coefficient equation. The logarithm of mole fraction of the solute is linearly related to the reciprocal of the absolute temperature in the ideal solution.20 In the real solution, the nonideality of the real solution should be considered, so it is a certain physical meaning of the semiempirical equation, the formula is as follows:

solubility of vanillic acid in pure solvents and mixed solvents increased with the increasing temperature, and the maximum solubility of vanillic acid was observed in acetone and the minimum was in water. Moreover, the solubility of solute in five alcohols follows the order of ethanol > 2-propanol > n-butanol > 1-propanol > isobutanol, which is consistent with the polarity order of solvents except for 1-propanol and 2-propanol: ethanol (65.4) > 1-propanol (61.7) > n-butanol (60.2) > isobutanol (55.2) > 2-propanol (54.6). Thus, the solubility behavior of vanillic acid is mostly corresponded with the popular rule “like dissolves like”.18 Based on the popular rule “like dissolves like”, the polarity of vanillic acid is very big. In addition, the molecule was found to possess high polarity judged by the structure of vanillic acid. The solubility is different from each other in different types of solvents. The polarity order of solvents is water > acetone > methyl acetate > ethanol > 2-propanol > 1propanol > n-butanol > isobutanol, well the solubility in eight solvents follows the order: acetone > ethanol > 2-propanol > nbutanol > methyl acetate > 1-propanol > isobutanol > water, the solubility in solvents is related to the polarity of the solvents; it is influenced by many other factors. The solubility in solvents may be caused by the effects of the solvating interactions and the chemical properties of solute and solvent, such as the structure and functional group.19 The experimental solubility of vanillic acid in mixed solvents at the temperature ranging from (293.15 to 323.15) K are presented in Table 3, which were correlated by the modified Apelblat equation and the Jouyban-Acree model, and the

ln x1 = −

ΔHd° ΔSd° + RT R

(4)

where x1 is mole fraction solubility, T is the absolute temperature, R is the gas constant, and ΔHdo and ΔSdo represent the dissolution enthalpy and dissolution entropy, respectively. λh Equation. Buchowski first proposed the λh equation with certain physical and chemical meaning;21 the formula is as follows: ⎛1 ⎛ 1 − x1 ⎞ 1 ⎞ ln⎜1 + λ ⎟ ⎟ = λh⎜ − x1 ⎠ Tm ⎠ ⎝T ⎝

(5)

where x1 is mole fraction solubility, T is the absolute temperature, λ and h are the model parameters, and Tm is the melting temperature of solute. Modified Apelblat Equation. The modified Apelblat equation is a semiemprical model. Because of its simplicity, it D

DOI: 10.1021/acs.jced.5b00619 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 3. Experimental Mole Fraction Solubility (x1) and Relative Deviations (RD) of Vanillic Acid in Mixtures of Water + Ethanol at Temperature T and Pressure p = 0.1 MPaα T/K

100x1exp

293.15 298.15 303.15 308.15 313.15 318.15 323.15

2.83 3.11 3.44 3.82 4.25 4.68 5.39

293.15 298.15 303.15 308.15 313.15 318.15 323.15

2.48 2.77 3.08 3.44 3.81 4.23 4.70

293.15 298.15 303.15 308.15 313.15 318.15 323.15

1.97 2.18 2.47 2.77 3.08 3.35 3.84

293.15 298.15 303.15 308.15 313.15 318.15 323.15

1.42 1.60 1.84 2.07 2.31 2.53 2.88

293.15 298.15 303.15 308.15 313.15

9.07 × 10−1 1.05 1.22 1.40 1.57

100x1Apel w 2.77 3.10 3.46 3.86 4.30 4.77 5.29 w 2.46 2.76 3.09 3.44 3.83 4.24 4.68 w 1.97 2.20 2.47 2.76 3.07 3.43 3.81 w 1.42 1.61 1.82 2.05 2.30 2.57 2.86 w 0.927 1.06 1.21 1.37 1.54

100RDApel

100x1JA

100RDJA

T/K 318.15 323.15

1.74 1.89

293.15 298.15 303.15 308.15 313.15 318.15 323.15

5.09 5.84 6.91 7.86 8.91 9.69 1.10

× × × × × ×

10−1 10−1 10−1 10−1 10−1 10−1

293.15 298.15 303.15 308.15 313.15 318.15 323.15

2.35 2.78 3.12 3.68 4.21 4.73 5.37

× × × × × × ×

10−1 10−1 10−1 10−1 10−1 10−1 10−1

293.15 298.15 303.15 308.15 313.15 318.15 323.15

9.05 1.03 1.25 1.44 1.74 1.92 2.24

× × × × × × ×

10−2 10−1 10−1 10−1 10−1 10−1 10−1

293.15 298.15 303.15 308.15 313.15 318.15 323.15

2.83 3.43 4.01 4.83 5.66 6.73 7.72

× × × × × × ×

10−2 10−2 10−2 10−2 10−2 10−2 10−2

100x1exp

= 0.1 2.12 0.32 −0.58 −1.05 −1.18 −1.92 1.86

2.76 3.11 3.49 3.91 4.36 4.84 5.36

2.47 0.00 −1.45 −2.36 −2.59 −3.42 0.56

0.81 0.36 −0.32 0.00 −0.52 −0.24 0.43

2.40 2.71 3.04 3.40 3.80 4.22 4.68

3.23 2.17 1.30 1.16 0.26 0.24 0.43

0.00 −0.92 0.00 0.36 0.32 −2.39 0.78

1.95 2.20 2.48 2.78 3.10 3.45 3.83

1.02 −0.92 −0.40 −0.36 −0.65 −2.99 0.26

0.00 −0.62 1.09 0.97 0.43 −1.58 0.69

1.43 1.63 1.83 2.06 2.31 2.58 2.87

−0.70 −1.87 0.54 0.48 0.00 −1.98 0.35

−2.21 −0.95 0.82 2.14 1.91

0.929 1.06 1.20 1.36 1.53

−2.43 −0.95 1.64 2.86 2.55

= 0.2

= 0.3

= 0.4

= 0.5

100x1Apel w= 1.72 1.92 w= 0.518 0.596 0.680 0.773 0.874 0.984 1.10 w= 0.237 0.275 0.317 0.365 0.417 0.475 0.538 w= 0.0897 0.106 0.124 0.145 0.169 0.195 0.224 w= 0.0286 0.0341 0.0405 0.0479 0.0565 0.0664 0.0778

100RDApel

100x1JA

100RDJA

0.5 1.15 −1.59

1.71 1.92

1.72 −1.59

−1.77 −2.05 1.59 1.65 1.91 −1.55 0.00

0.517 0.594 0.679 0.773 0.876 0.989 1.11

−1.57 −1.71 1.74 1.65 1.68 −2.06 −0.91

−0.85 1.08 −1.60 0.82 0.95 −0.42 −0.19

0.241 0.280 0.323 0.372 0.426 0.485 0.551

−2.55 −0.72 −3.53 −1.09 −1.19 −2.54 −2.61

0.88 −2.91 0.80 −0.69 2.87 −1.56 0.00

0.0924 0.109 0.128 0.149 0.172 0.199 0.229

−2.10 −5.83 −2.40 −3.47 1.15 −3.65 −2.23

−1.06 0.58 −1.00 0.83 0.18 1.34 −0.78

0.0286 0.0343 0.0409 0.0484 0.0571 0.0669 0.0781

−1.06 0.00 −2.00 −0.21 −0.88 0.59 −1.17

0.6

0.7

0.8

0.9

α

Standard uncertainty u is u(T) = 0.1 K; the relative standard uncertainty u are ur(p) = 0.05, ur(x1) = 0.02.

ln x1 = a +

b T + c ln T /K K

(6)

where a, b, and c are the model parameters; T is the absolute temperature; x1 is the experimental mole fraction solubility of vanillic acid. Local Composition Model. Based on the solid−liquid phase equilibrium theory, the relationship between solubility and temperature is shown as23 ⎛ 1 ⎞ Δ H ⎛T ⎞ ⎟⎟ = fus ⎜ m − 1⎟ ln⎜⎜ ⎠ ⎝ RTm T ⎝ γ1x1 ⎠

Figure 4. Mole fraction solubility of vanillic acid (x1) in mixed solvents of water + ethanol: ■, 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. The solid line solubility curve was calculated by the modified Apelblat equation.

(7)

In this paper, three local composition models (NRTL, UNIQUAC, and Wilson) were used to calculate the solute activity coefficient γ1 and correlate the solubility values. NRTL Equation.24,25 The solute’s activity coefficient of this equation is given by

is widely used for the correlation of the solubility. It is shown as eq 622 E

DOI: 10.1021/acs.jced.5b00619 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 4. Parameters of the Modified Apelblat Equation, Van’t Hoff Equation, λh Equation, NRTL Equation, UNIQUAC Equation, and Wilson Equation for Vanillic Acid in Eight Pure Solvents Apelblat solvent

a

b

ethanol 1-propanol 2-propanol n-butanol isobutanol acetone methyl acetate water

−1.766 −5.413 15.530 −16.987 −33.984 9.684 −5.110 −79.960

−1986.193 −2639.233 −2818.204 −1671.211 −2103.463 −2261.315 −3025.379 −169.907 NRTL

λh

Van’t Hoff ΔH° J·mol−1

c 0.886 1.848 −1.686 3.328 6.454 −0.845 2.035 12.603

ΔS° J·mol−1 ·K−1

18766.65 26516.43 19205.84 22408.58 33688.96 16744.91 30401.42 34402.43 UNIQUAC

λ

34.8510 57.8932 35.0690 44.9902 77.5742 33.5790 71.5022 42.7645

h

0.5544 1.616 0.5786 0.9696 3.136 0.8289 3.403 0.03378 Wilson

3927 2016 4034 2883 1333 2373 1108 122839

solvent

Δg12 (J·mol−1)

Δg21 (J·mol−1)

Δu12 (J·mol−1)

Δu21 (J·mol−1)

Δλ12 (J·mol−1)

Δλ21 (J·mol−1)

ethanol 1-propanol 2-propanol n-butanol isobutanol acetone methyl acetate water

−7484.5 −2147.4 −8166 −5746.1 948.3 −4759.7 1826.5 25852

8984.1 −1021.7 11877 5140.7 −3156.6 −209.0 −5359.7 5829

4735.0 608.1 5274.2 3464.2 290.2 −184.8 674.6 2233.3

−2758.2 −1106.0 −2868.1 −2558.1 −663.7 −1096.9 −1259.1 −709.7

3511.5 −2174.8 4467.5 1231.7 −3140.7 −3044.8 −5274.1 1754

−2243.3 −579.3 −2789.5 −2348.6 876.8 −1698.3 1583.7 48183

⎛ τ G 2 ⎞ τ12G12 21 21 ⎟ ln γ1 = x 2 2⎜ + 2 (G12x1 + x 2)2 ⎠ ⎝ (x1 + G21x 2)

(8)

G12 = exp( −α12τ12)G21 = exp( −α12τ21)

(9)

τ12 =

g12 − g22

τ21 =

RT

v1 =

ln γ1 = ln

ln γ1C = ln

+ ln γ1

ϕ1 x1

+

R

(10)

τ12 ⎞ ⎟ v1τ12 + v2 ⎠

x1q1 + x 2q2

qi =

∑ njQ j (17)

j=1

⎛ Δu ⎞ τ21 = exp⎜ − 21 ⎟ ⎝ RT ⎠

(18)

where Δu12(= u12 − u22) and Δu21(= u21 − u11) are the two adjustable interaction energy parameters independent from both composition and temperature. Wilson Equation.27 The solute’s activity coefficient of this equation is given by

(12)

⎤ ⎡ Λ12 Λ 21 ln γ1 = −ln(x1 + Λ12x 2) + x 2⎢ − ⎥ x 2 + Λ 21x1 ⎦ ⎣ x1 + Λ12x 2 (19)

⎤ ⎡ Λ12 Λ 21 ln γ2 = −ln(x 2 + Λ 21x1) + x1⎢ − ⎥ x 2 + Λ 21x1 ⎦ ⎣ x1 + Λ12x 2

(13)

(20)

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

l1 =

Λ12 = (14)

Λ 21 =

with x1r1 ϕ1 = x1r1 + x 2r2

(16)

m

∑ njR j

⎛ Δu ⎞ τ12 = exp⎜ − 12 ⎟ ⎝ RT ⎠

⎛ τ21 ln γ1R = −q1 ln(v1 + v2τ21) + v2q1⎜ ⎝ v1 + v2τ21 −

x 2q2

z is the number of adjacent interacting molecules around the central molecule, and it is usually set equal to 10; ri and qi are the structure parameters of pure component i; Rj and Qj represent the molecular’s size and surface area, respectively. τ12 and τ21 are two adjustable parameters, which are expressed as

(11)

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

x1q1 + x 2q2

j=1

x1 and x2 represent the mole fraction of the solute and the solvent; Δg12 (= g12 − g22) and Δg21 (= g21 − g11) are two binary interaction parameters that are independent of temperature and composition, and they are obtained by regression. The parameter α12 is a measure of the nonrandomness of the mixture, which generally varies from 0.20 to 0.47; it is set equal to 0.2 in this work. UNIQUAC Equation.26 The solute’s activity coefficient of this equation is given by γ1C

v2 =

m

ri =

g21 − g11 RT

x1q1

x 2r2 ϕ2 = x1r1 + x 2r2

⎡ (λ − λ11) ⎤ exp⎢ − 12 ⎥ ⎣ ⎦ V1,m RT

(21)

⎡ (λ − λ 22) ⎤ exp⎢ − 21 ⎥ ⎦ V2,m ⎣ RT

(22)

V2,m

V1,m

γ1 and γ2 are the activity coefficient of solute and solvent, respectively; Λ12 and Λ21 are the Wilson equation parameters;

(15) F

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where x1,i is the experimental solubility data and x1,ical is the calculated solubility; N is the number of experimental points. The values of RAD are shown in Table 7 and Table 8. The mean values of RAD in eight pure solvents of these equations are 0.650%, 0.728%, 0.675%, 1.903%, 2.281%, and 2.142%, respectively. The mean values of RAD in mixed solvents of the modified Apelblat equation and the Jouyban−Acree equation are 1.024% and 1.590%, respectively. It can be clearly found that they are both very small. They give good correction with the solubility data of vanillic acid in eight pure solvents and water + ethanol mixed solvents.

V1,m and V2,m are mole volumes of solute and solvent, respectively; Δλ12 (= λ12 − λ21) and Δλ21 (= λ21 − λ12) are the cross interaction energy parameters of Wilson equation, γ12 and γ21 are the two adjustable interaction energy parameters. The Jouyban−Acree Model. The Jouyban−Acree model is based on the R-K model, establishing a relationship of solubility, temperature, and solvent composition. The form of the equation is as follows28 ω2ω3 T

ln x1 = ω2 ln(x1)2 + ω3 ln(x1)3 +

n

∑ Ji (ω2 − ω3)i

■

i=0

(23)

THERMODYNAMIC PARAMETERS FOR DISSOLUTION OF VANILLIC ACID Thermodynamic properties are very important for further studies. In our research, the enthalpy change (ΔHsolo), the entropy change (ΔSsolo), and the Gibbs free energy change (ΔGsolo) of solution of vanillic acid in eight pure solvents and binary water + ethanol solvent mixtures can be obtained by van’t Hoff analysis, which is shown as29

where Ji is the model parameter; w2 and w3 are the mass fraction of water and ethanol of the solution, respectively; (x1)2, and (x1)3 are the mole fraction solubility of vanillic acid in water and ethanol, respectively. When n = 2, the expression could be simplified as ln x1 = C1 + C2ω2 + + C7

C3 ω ω2 ω3 + C4 2 + C5 2 + C6 2 T T T T

ω2 4 T

⎛ ⎞ ΔHsol° ∂ ln x1 = −⎜ ⎟ R ⎝ ∂[(1/T ) − (1/Tmean)] ⎠ p

(24)

where C1, C2, C3, C4, C5, C6, and C7 are the model parameters. The parameters of the above-mentioned equation are listed in Table 4 to 6.

where x1 is the molar fraction of the solution of vanillic acid; R is the gas constant; Tmean is the mean harmonic of the experimental temperatures from 293.15 to 323.15 K, and the value is 307.825 K. The logarithm of mole fraction of the solute (lnx1) is linearly related to the reciprocal of the absolute temperature (1/T). The slope of the plot ln x1 against 1/T − 1/Tmean is the value of −ΔHsolo/R. The ΔHsolo was the mean value of the melting temperature over the considered temperature range, while the above-mentioned ΔHdo corresponds to the melting point at the considered temperature. The plots were shown in Figures 5 and 6. The Gibbs free energy change (ΔGsolo) for dissolution of vanillic acid was calculated by the following equation30

Table 5. Parameters of the Modified Apelblat Equation for Vanillic Acid in Mixed Solvents of Water and Ethanol Apelblat

a

w2a

a

b

c

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

−36.266 −7.736 −50.799 9.043 64.002 28.343 7.128 8.062 −47.863

−233.937 −1525.783 378.996 −2470.445 −5075.296 −3545.739 −2786.553 −3131.303 −850.174

5.893 1.626 8.023 −0.857 −9.043 −3.786 −0.645 −0.774 7.500

ΔGsol° = −RTmean × intercept

The entropy change for dissolution of vanillic acid can be obtained by the following equation ⎛ ΔHsol° − ΔGsol° ⎞ ΔSsol° = ⎜ ⎟ Tmean ⎝ ⎠

%ξH =

|ΔHsol°| × 100 |ΔHsol°| + |T ΔSsol°|

(30)

%ξTS =

|T ΔSsol°| × 100 |ΔHsol°| + |T ΔSsol°|

(31)

x1, i − x1, i cal

RAD =

1 N

N

∑ i=1

(25)

x1, i − x1, i

cal

x1, i

(29)

The relative contributions of enthalpy %ξH and entropy %ξTS in the dissolution process were calculated by the following equation31

The relative deviation (RD) was defined as eq 25 to show the deviations between the experimental and correlated values of solubility. The relative average deviation (RAD) was defined to identify differences between the measured and calculated data by eq 26 x1, i

(28)

(ΔSsolo)

w2 is the mass fraction of water in the mixed solvents.

RD =

(27)

The values of thermodynamic parameters ΔHsol°, ΔSsol°, ΔGsol°, %ξH, and %ξTS for vanillic acid in eight pure solvents are listed in Table 9. We can see from the Table 9 that the

(26)

Table 6. Parameters of the Jouyban−Acree Equation for Vanillic Acid in Mixed Solvents of Water + Ethanol parameters

C1

C2

C3

C4

C5

C6

C7

Jouyban−Acree

3.693

−1.159

−2104.425

47.580

21.681

−1834.829

324.732

G

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Table 7. Relative Average Deviations (RAD) of the Modified Apelblat Equation, Van’t Hoff Equation, λh Equation, NRTL Equation, UNIQUAC Equation, and Wilson Equation for Vanillic Acid in Eight Pure Solvents 100RAD solvent

Apelblat

Van’t Hoff

λh

NRTL

UNIQUAC

Wilson

ethanol 1-propanol 2-propanol n-butanol isobutanol acetone methyl acetate water (1/7)∑71RAD

0.667 0.631 0.353 0.417 0.624 0.344 0.394 1.296 0.675

0.690 0.653 0.407 0.430 0.906 0.361 0.394 0.710 0.650

0.694 0.727 0.907 0.963 0.946 0.434 0.427 0.711 0.726

0.789 1.046 0.874 0.489 4.847 0.377 3.867 1.033 1.903

0.900 1.139 0.443 0.523 5.501 0.261 6.446 0.756 2.281

2.083 1.186 2.241 0.580 4.504 0.341 3.383 0.676 2.142

Table 8. Relative Average Deviations (RAD) of the Modified Apelblat Equation and the Jouyban−Acree Equation for Vanillic Acid in Mixed Solvents of Water + Ethanol 100RAD w1

modified Apelblat

Jouyban−Acree

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 (1/9)∑91RAD

1.290 0.383 0.681 0.769 1.539 1.503 0.844 1.387 0.824 1.024

1.836 1.256 0.943 0.846 1.963 1.617 2.033 2.976 0.844 1.590

Figure 6. van’t Hoff plot of the mole fraction solubility (ln x1) versus reciprocal of the temperature (1/T − 1/Tm) for vanillic acid in mixed solvents of water + ethanol: ■, 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.

force to the Gibbs free energy during the dissolution of vanillic acid in the studied pure solvents. The values of thermodynamic parameters ΔHsol°, ΔSsol°, ΔGsol°, %ξH, and %ξTS for vanillic acid in water + ethanol solvent mixtures are listed in Table 10. The ΔHsol° and ΔGsol° values in mixed solvents of vanillic acid are positive, indicating that the solution process is endothermic and spontaneous. The values of %ξH in the mixed solvents exceed 66.72%, which indicated that the enthalpy was the main contributing force to the Gibbs free energy during the dissolution of vanillic acid in the mixed solvents.

Figure 5. van’t Hoff plot of the mole fraction solubility (ln x1) versus reciprocal of the temperature (1/T − 1/Tm) for vanillic acid in eight pure solvents: ■, ethanol; □, 1-propanol; ●, 2-propanol; ○, nbutanol; ▲, isobutanol; △, acetone; ☆, methyl acetate; ★, water.

■

CONCLUSIONS The experimental solubility data of vanillic acid in eight monosolvents and binary mixtures of water + ethanol solvents were measured by a gravimetric method from 293.15 to 323.15 K. The solubility data of vanillic acid in eight monosolvents can be correlated very well by the Van’t Hoff equation, λh equation, modified Apelblat equation, NRTL equation, UNIQUAC equation, and the Wilson equation.33 The solubility data of vanillic acid in the mixed solvents can be well-correlated by the modified Apelblat and Jouyban−Acree equation. It was found that the modified Apelblat equation showed the best correlated results. The values of thermodynamic parameters ΔHsol°, ΔSsol°, and ΔGsol° suggested that the solution process of vanillic acid in the solvents is endothermic and spontaneous. In addition, the experimental solubility and the correlation equation would be used for the purification of the vanillic acid and further thermodynamic research.

ΔHsol° and ΔGsol° values are positive values, which indicating that the dissolution of vanillic acid in selected pure solvents was endothermic and spontaneous. This phenomenon means that the interactions between the vanillic acid molecules and solvent molecules are much stronger than those between the vanillic acid molecules and solvent−solvent molecules. In the process of dissolution, vanillic acid molecules and solvent molecules formed new bonds; meanwhile, the original bonds between solvent molecules were broken. However, the energy of newly formed bond is not strong enough to compensate the broken of the original bond energy in solvents intermolecular, thus the need to absorb more energy. The ΔSsol° values are also positive values, meaning entropy-driven dissolution of vanillic acid.32 The values of %ξH in the eight pure solvents exceed 58.00%, which indicated that the enthalpy was the main contributing H

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Table 9. Thermodynamic Parameters of Dissolution of Vanillic Acid in Eight Pure Solvents solvent

ΔdH°m (kJ·mol−1)

ΔdS°m (J·mol−1·K−1)

ΔdG°m (kJ·mol−1)

%ξH

%ξTS

ethanol 1-propanol 2-propanol n-butanol isobutanol acetone methyl acetate water

18.767 26.516 19.206 22.409 33.689 16.745 30.401 34.402

34.851 57.893 35.069 44.990 77.574 33.579 71.502 42.764

8.039 8.695 8.411 8.560 9.810 6.409 8.391 21.238

63.63 59.81 64.02 61.80 58.52 61.83 58.00 72.33

36.37 40.19 35.98 38.20 41.48 38.17 42.00 27.67

Table 10. Thermodynamic Parameters of Dissolution of Vanillic Acid in Mixed Solvents of Water + Ethanol

■

w2

ΔdH°m (kJ·mol−1)

ΔdS°m (J·mol−1·k−1)

ΔdG°m (kJ·mol−1)

%ξH

%ξTS

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

16.637 16.750 17.340 18.384 19.542 20.172 21.631 24.180 26.474

26.955 26.358 26.428 27.351 27.726 25.016 23.517 24.125 22.400

8.340 8.636 9.205 9.965 11.007 12.471 14.392 16.754 19.579

66.72 67.37 68.07 68.59 69.60 72.37 74.93 76.50 79.33

33.28 32.63 31.93 31.41 30.40 27.63 25.07 23.5 20.67

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +86-010-64446523. E-mail address: 18811179532@163. com. Notes

The authors declare no competing financial interest.

■

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