Article pubs.acs.org/jced
Solid−Liquid Phase Equilibrium of trans-Cinnamic Acid in Several Alcohols: Measurements and Thermodynamic Modeling Juan Li, Zuo-Xiang Zeng, Li Sun, Wei-Lan Xue,* and Hui-Hui Wang Institute of Chemical Engineering, East China University of Science and Technology, 200237 Shanghai, China ABSTRACT: The solubilities of trans-cinnamic acid (t-CA) in methanol, ethanol, propanol, n-butanol, isopropyl alcohol, and isobutyl alcohol were measured by a synthetic method at temperatures ranging from (283.15 to 333.15) K. The modified Apelblat equation, the λh equation, and activity coefficient models (nonrandom two-liquid, NRTL; universal quasichemical, UNIQUAC) were used to correlate these data. It was found that all of the models show good agreement with the experimental data, and the modified Apelblat equation and NRTL model give better correlation results. Furthermore, on the basis of the NRTL model and experimental data, the thermodynamic excess functions (GE, SE, HE) of t-CA + alcohols (methanol, ethanol, propanol, n-butanol, isopropyl alcohol, and isobutyl alcohol) system were determined.
1. INTRODUCTION
2. EXPERIMENTAL SECTION
trans-Cinnamic acid (t-CA, C9H8O2, CAS Registry No. 140-103), a white oily phenolic powder, exists in some dietary plants, fruits, and herbs.1 It can be used as a preservative for grain, fruits, and vegetables.2,3 It is also an important raw material or intermediate in organic synthesis industry. For example, t-CA is an important material for the production of L-phenylalanine, which is a precursor required for the synthesis of artificial sweetener aspartame.4 Especially, the esterification of t-CA with short chain alcohols plays an important role in industrial production. Cinnamates produced from esterification are used in the food, perfumery, cosmetic, and pharmaceutical industries.5 For example, methyl cinnamate is a compound widely used in foodstuffs as a flavoring agent or to control food browning.6 Butyl cinnamate is a fragrance ingredient used in many fragrance compounds.7 The solubility of t-CA in the alcohols can provide basic data for the esterification and the separation of reaction mixture. The solubility data of t-CA in several solvents were reported previously. Mota et al. determined the solubility of t-CA in water between 288.15 K and 323.15 K.8 Timofeiew determined the solubility of t-CA in methanol, ethanol, propanol and isobutyl alcohol at four temperatures (255.15, 260.65, 273.15, and 292.65 K).9,10 However, the solubilities of t-CA in other alcohols were not found in the literature, so an additional study is needed. In this work, the solubilities of t-CA in methanol, ethanol, propanol, n-butanol, isopropyl alcohol, and isobutyl alcohol were measured at temperatures ranging from (283.15 to 333.15) K, then the modified Apelblat equation, the λh equation and activity coefficient models (nonrandom twoliquid, NRTL; universal quasichemical, UNIQUAC) were used to correlate these measurements. Furthermore, the thermodynamic excess functions (GE, SE, HE) of t-CA + alcohols system were determined.
2.1. Materials. t-CA (99% purity), was purchased from Aladdin Industrial Corporation. All the alcohols used in this study including methanol, ethanol, propanol, n-butanol, isopropyl alcohol, and isobutyl alcohol were obtained from Shanghai Lingfeng Chemical Reagent Co., Ltd. with purities greater than 99.5%. The water used was distilled and deionized before use. All above chemicals were used as received. The description about these materials is summarized in Table 1. 2.2. DSC and TGA Measurements. The DSC (Auto Q20, TA Instruments, USA) analysis was performed under a stream of nitrogen, with a 10 K/min increasing rate program at a temperature ranging from 313.15 K to 463.15 K. The endothermic peak of the DSC curve shown in Figure 1 results most probably from a melting procedure, and the onset temperature and peak’s integration should correspond to melting temperature Tm and enthalpy of fusion ΔfusHm respectively. Besides, thermogravimetric analysis (TGA) (TGA/ SDTA851, Mettler Instrument Inc.) was used to evaluate thermal stability of t-CA. It was also performed at nitrogen atmosphere and a heating rate of 10 K/min, with a temperature standard uncertainty of 0.3 K. The TGA curve is presented in Figure 2. As shown, a decomposition stage begins at a higher temperature than the onset temperature determined by DSC. It indicates that for t-CA, decomposition takes place following melting, so the temperature (406.15 K) and peak’s integration (22.21 kJ/mol) determined by DSC are actually the normal melting point temperature Tm and enthalpy of fusion ΔfusHm of the initial material. Benzoic acid was taken as the calibration
© 2016 American Chemical Society
Received: September 22, 2015 Accepted: January 26, 2016 Published: February 11, 2016 1192
DOI: 10.1021/acs.jced.5b00814 J. Chem. Eng. Data 2016, 61, 1192−1198
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Table 1. Source and Purity of the Materials Used chemical name trans-cinnamic acid (t-CA) water methanol ethanol propanol n-butanol isopropyl alcohol isobutyl alcohol a
source Aladdin Industrial Co., Shanghai, China prepared by us Shanghai Lingfeng Chemical Reagent Co., Shanghai Lingfeng Chemical Reagent Co., Shanghai Lingfeng Chemical Reagent Co., Shanghai Lingfeng Chemical Reagent Co., Shanghai Lingfeng Chemical Reagent Co., Shanghai Lingfeng Chemical Reagent Co.,
Ltd. Ltd. Ltd. Ltd. Ltd. Ltd.
mass fraction purity
analysis method
purification method
0.99 > 0.999 > 0.995 > 0.995 > 0.995 > 0.995 > 0.995 > 0.995
HPLCa GCb GCb GCb GCb GCb GCb GCb
none three times distillation none none none none none none
High-performance liquid chromatography. bGas−liquid chromatography.
work to obtain the solubility of t-CA. The detailed procedure was described previously in the literature by our co-workers.16,17 A known mass of solvent (about 20 ± 0.001 g) was added to a three-necked flask equipped with a condenser, stirrer, and glass stopper. The actual temperature was measured by a mercury thermometer (standard uncertainty of 0.05 K) with its glass bulb immersed in the solvent. The constant temperature of the apparatus was controlled by a cylindrical glass thermostatic water bath (standard uncertainty of 0.05 K). A known mass of t-CA was added into the flask by the reducing weight method when the system stabilized at the desired temperature, and the solute was weighed with an analytical balance (standard uncertainty of 0.0001 g). After the solid introduced into the flask dissolved completely, a next portion was added in. This operation was repeated until the last piece (less than 0.01 g) only partly dissolved for 2 h. All solubility experiments were performed at least in triplicate, and the averaged value was used to calculate the mole fraction of solute. The same process was operated to obtain the solubility of t-CA at different temperatures. The solubilities of t-CA in water were determined to check the reliability of the apparatus. The deviations between experimental results and literature values8 are less than 2%, which was shown in Figure 3. It suggests that the solubility measurement performed with this apparatus is reliable. The solubility in mole fraction of t-CA (x1) in solvents can be calculated according to the following equation:
Figure 1. DSC curve of t-CA.
Figure 2. TGA curve of t-CA.
material for the determination, and the standard uncertainties for DSC are u(Tm) = 0.3 K and ur(ΔfusHm) = 1.6%, respectively. Comparable with all the collected data in previous literature,8,11,12 the relative deviations for measured melting temperature and enthalpy of fusion of t-CA were less than 0.5% and 0.1%, respectively. 2.3. Solubility Measurement. Two methods are generally used to achieve the solid−liquid equilibrium: analytical method and synthetic method.13,14 The last crystal disappearance method,15 one of the synthetic methods, was used in this
Figure 3. Mole fraction solubility (x1) of t-CA in water: ▲, this work; ○, ref 8 1193
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Table 2. Solubilities and Excess Function Values of t-CA in Methanol, Ethanol, Propanol, Isopropyl Alcohol, and Isobutyl Alcohol at Temperature T and Pressure p = 0.1 MPaa 100(x1exp − x1cal)/x1exp
T K
100x1exp
Apeblat
λh
283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 100ARD
4.68 5.30 5.81 6.42 7.10 7.87 8.68 9.67 10.58 11.47 12.53
−0.03 1.47 −0.23 −0.71 −0.76 −0.44 −0.36 0.96 0.69 −0.28 −0.25 0.56
−2.71 −0.02 −0.78 −0.50 0.00 0.63 0.79 1.92 1.21 −0.48 −1.51 0.96
283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 100ARD
5.15 5.78 6.48 7.33 8.09 8.90 9.86 10.96 12.15 13.27 14.45
0.09 −0.18 −0.22 0.98 0.19 −0.77 −0.71 −0.01 0.72 0.25 −0.33 0.40
−2.78 −1.80 −0.80 1.19 0.96 0.33 0.47 0.98 1.25 0.04 −1.60 1.11
283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 100ARD
4.69 5.30 6.08 6.80 7.61 8.62 9.57 10.75 11.83 12.93 14.21
0.96 −0.37 0.65 −0.61 −1.05 0.06 −0.34 0.85 0.44 −0.32 −0.12 0.52
−3.50 −2.89 −0.25 −0.31 0.08 1.62 1.33 2.22 1.18 −0.61 −1.85 1.44
283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 100ARD
4.55 5.39 6.19 6.91 7.91 9.06 10.15 11.84 13.45 15.17 16.85
−1.05 1.78 1.70 −0.88 −0.82 −0.38 −1.99 0.72 1.02 0.81 −0.80 1.09
−0.42 2.04 1.73 −0.99 −0.99 −0.55 −2.12 0.66 1.03 0.86 −0.73 1.10
4.65 5.35 6.15 7.12 8.11
−0.03 −0.48 −0.63 0.54 0.73
−3.92 −2.69 −1.50 0.69 1.58
283.15 288.15 293.15 298.15 303.15
NRTL Methanol 0.76 1.98 −0.13 −0.85 −1.01 −0.71 −0.61 0.91 0.70 −0.26 −0.11 0.73 Ethanol 0.20 −0.19 −0.28 1.02 0.16 −0.86 −0.76 0.03 0.84 0.30 −0.42 0.46 Propanol 0.05 −0.92 0.51 −0.54 −0.82 0.45 0.05 1.23 0.64 −0.44 −0.59 0.57 n-Butanol 0.38 2.56 2.00 −0.96 −1.09 −0.73 −2.36 0.48 0.91 0.86 −0.55 1.17 Isopropyl Alcohol −1.06 −1.05 −0.81 0.68 1.07
1194
GE UNIQUAC
SE −1
J·mol
−1
J·mol ·K
HE −1
J·mol−1
−1.11 1.02 −0.60 −0.85 −0.68 −0.13 0.11 1.55 1.02 −0.37 −0.87 0.75
19.60 28.64 38.19 49.83 63.63 79.90 98.42 121.25 145.04 170.46 200.79
−1.03 −1.16 −1.26 −1.38 −1.52 −1.66 −1.82 −2.00 −2.17 −2.32 −2.50
−271.56 −305.16 −331.05 −362.05 −396.09 −433.16 −470.88 −515.85 −554.69 −590.62 −632.19
−1.97 −1.40 −0.65 1.05 0.68 −0.09 0.09 0.61 1.06 0.11 −1.10 0.80
9.24 16.33 24.98 35.90 47.90 61.66 78.33 98.27 121.32 145.70 172.72
−0.96 −1.06 −1.18 −1.32 −1.44 −1.56 −1.71 −1.87 −2.04 −2.20 −2.35
−261.50 −290.03 −320.84 −357.44 −388.86 −420.57 −457.14 −497.49 −539.03 −575.18 −610.42
−2.74 −2.55 −0.09 −0.50 −0.20 1.30 0.97 1.88 0.96 −0.47 −1.36 1.18
20.26 27.25 36.48 46.49 58.61 73.91 90.38 111.06 132.60 156.16 184.16
−0.72 −0.81 −0.94 −1.05 −1.18 −1.34 −1.49 −1.67 −1.84 −2.01 −2.20
−182.52 −207.12 −238.84 −267.57 −300.23 −339.79 −376.80 −421.72 −462.29 −502.42 −548.00
−0.75 1.83 1.59 −0.99 −0.79 −0.34 −1.82 0.72 1.03 0.75 −0.79 1.04
24.56 31.62 39.06 46.58 56.61 68.53 80.67 98.56 116.76 136.75 157.02
0.22 0.23 0.24 0.23 0.23 0.22 0.21 0.19 0.16 0.12 0.08
87.30 99.14 108.99 116.51 126.91 137.86 146.25 159.59 169.30 177.28 182.12
−3.95 −2.74 −1.47 0.66 1.51
20.74 27.00 34.62 44.30 55.34
−0.50 −0.57 −0.66 −0.76 −0.87
−119.74 −138.20 −158.81 −183.49 −208.55
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Table 2. continued 100(x1exp − x1cal)/x1exp
T
a
K
100x1exp
Apeblat
λh
308.15 313.15 318.15 323.15 328.15 333.15 100ARD
9.14 10.23 11.50 12.86 14.21 15.86
0.25 −0.36 −0.10 0.09 −0.49 0.31 0.36
1.51 1.00 1.05 0.73 −0.69 −1.05 1.49
283.35 288.15 293.65 298.15 303.15 308.15 314.15 318.35 323.85 329.15 335.35 100ARD
3.25 3.91 4.76 5.51 6.44 7.58 9.20 10.72 12.48 14.56 16.84
1.81 1.70 1.03 −0.25 −1.75 −1.90 −1.33 1.30 0.54 1.15 −0.82 1.23
−1.43 −0.35 0.06 −0.53 −1.45 −1.22 −0.48 2.09 1.07 1.22 −1.59 1.05
NRTL Isopropyl Alcohol 0.69 0.07 0.25 0.27 −0.63 −0.18 0.61 Isobutyl Alcohol −2.78 −1.26 −0.42 −0.69 −1.30 −0.91 −0.11 2.23 1.19 1.13 −1.69 1.25
GE
SE
HE
UNIQUAC
J·mol−1
J·mol−1·K−1
J·mol−1
1.40 0.97 0.94 0.69 −0.65 −0.91 1.44
67.78 81.99 99.10 118.58 139.51 165.28
−0.98 −1.09 −1.22 −1.36 −1.50 −1.66
−233.96 −260.43 −290.45 −321.67 −351.57 −386.72
−3.49 −1.65 −0.50 −0.72 −1.08 −0.67 0.24 2.45 1.31 1.09 −1.92 1.37
43.15 51.85 63.00 72.80 84.76 99.14 119.18 137.39 157.94 181.21 205.70
−0.04 −0.05 −0.05 −0.06 −0.07 −0.07 −0.09 −0.09 −0.10 −0.11 −0.12
31.97 38.70 47.40 55.13 64.66 76.19 92.45 107.33 124.45 144.06 165.12
Standard uncertainties u are u(T) = 0.05 K, u(p) = 0.5 KPa, ur(x1) = 0.02.
x1 =
m1/M1 m1/M1 + m2 /M 2
parameter λ is a function of association constants and of mole fraction x1, whereas h is related to the enthalpy of solution.21,22 3.3. Local Composition Activity Coefficient Models. For the calculation of solid solubility, the standard thermodynamic equation is applied:23
(1)
where m and M represent the mass and molecular weight, respectively. The subscripts, 1and 2, denote solute and solvent, respectively.
⎡Δ H ⎛ Tm ⎞ T ⎞ ΔfusCp ⎛ ⎜1 − ⎟ ln(γ1x1) = −⎢ fus m ⎜1 − ⎟+ ⎢⎣ RT ⎝ Tm ⎠ R ⎝ T ⎠
3. RESULTS AND DISCUSSION Table 2 presents the experimental solubility of t-CA in methanol, ethanol, propanol, n-butanol, isopropyl alcohol, and isobutyl alcohol from (283.15 to 333.15) K at atmospheric pressure of 0.1 MPa. Four thermodynamic models, the modified Apelblat equation, the λh equation, and activity coefficient models (NRTL and UNIQUAC) were used to correlate the relationship between solubility and temperature. 3.1. Modified Apelblat Equation. The temperaturedependent solubility of t-CA can be correlated with the modified Apelblat equation, which is obtained from the Clausius−Clapeyron equation and expressed as18,19 ln x1 = a +
b + c ln T T
+
R
ln
Tm ⎤ ⎥ T ⎥⎦
(4)
where γ1 stands for the activity coefficient of the solute, whereas ΔfusCp is the heat capacity variation between the solid and the hypothetic supercooled liquid at the melting temperature. In some cases, the terms containing ΔfusCp could be neglected.23 Then the equation becomes ln(γ1x1) = −
(2)
where a, b, and c are empirical parameters, which can be regressed by experimental solubility data. The values of a and b reflect the effect of solution non-ideality on the solubility of the solute. The parameter c reveals the relationship between temperature and the fusion enthalpy.20 3.2. λh (Buchwski−Ksiazaczak) Equation. The λh equation, proposed by Buchwski−Ksiazaczak, is given in the following expression: ⎛1 ⎛ 1 − x1 ⎞ 1 ⎞ ln⎜1 + λ ⎟ ⎟ = λh⎜ − x1 ⎠ Tm ⎠ ⎝T ⎝
ΔfusCp
ΔfusHm ⎛ T ⎞ ⎟ ⎜1 − RT ⎝ Tm ⎠
(5)
For a given solid−liquid system, if the average relative deviations (ARDs) with eq 5 are larger than ur(x1) (2%, Table 2), the effect of the terms containing ΔfusCp on calculation of solubility could not be neglected; conversely, if the ARDs are smaller than ur(x1), the effect of the terms could be neglected. Two classical local composition activity coefficient models (NRTL model and UNIQUAC model) were selected to describe the relationship between the activity coefficient and the composition. 3.3.1. NRTL Model. The NRTL model originally proposed by Renon and Prausnitz contains three adjustable parameters, and is given as24,25
(3)
where λ and h are two regression curve parameters in this model and Tm is the melting temperature of t-CA. The 1195
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Table 3. Model Parameters in Different Solvents λh
Apeblat
NRTL
UNIQUAC
system
a
b
c
λ
h
Δg12
Δg21
a
Δu12
Δu21
methanol ethanol propanol n-butanol isopropyl alcohol isobutyl alcohol
−16.16 −4.48 30.64 −43.14 29.35 39.23
−966.04 −1571.34 −3307.72 −243.06 −3415.45 −4514.04
2.92 1.25 −3.90 7.25 −3.60 −4.74
0.14 0.19 0.23 0.48 0.35 0.74
8991.51 7208.62 6896.80 4650.48 5516.15 3973.08
21053.89 16728.55 20649.23 7551.13 13172.07 1573.77
−3187.14 −3170.98 −1387.39 −3456.54 −912.03 214.07
0.20 0.23 0.28 0.20 0.41 0.47
7976.30 5821.00 4889.90 2685.30 3775.10 725.34
−1885.00 −2342.20 −2174.90 −1657.10 −1989.00 −485.08
Figure 4. Experimental mole fraction solubility (x1) of t-CA in different alcohols: ■, methanol; ●, ethanol; △, propanol; −, correlation results: (a) modified Apelblat equation; (b) λh equation; (c) NRTL model; (d) UNIQUAC model.
⎡ τ G 2 ⎤ τ12G12 21 21 ⎥ ln γ1 = x 2 2⎢ + 2 2 (x 2 + x1G12) ⎦ ⎣ (x1 + x 2G21)
ln γ1 = ln
(6)
(7)
G21 = exp( −a 21τ21)
(8)
τ12 =
τ21 =
g12 − g21 RT
g21 − g12 RT
=
Δg12
=
Δg21
RT
RT
x1
+
⎛ r ⎞ θ z q1 ln 1 + ϕ2⎜l1 − 1 l 2⎟ r2 ⎠ 2 ϕ1 ⎝
⎞ ⎛ τ21 τ12 − q1 ln(θ1 + θ2τ21) + θ2q1⎜ − ⎟ θ2 + θ1τ12 ⎠ ⎝ θ1 + θ2τ21
with
G12 = exp( −a12τ12)
ϕ1
(11)
with
(9)
(10)
⎛ Δu12 ⎞ ⎛ u − u 21 ⎞ ⎟ = exp⎜ − ⎟ τ12 = exp⎜ − 12 ⎝ ⎝ RT ⎠ RT ⎠
(12)
⎛ Δu 21 ⎞ ⎛ u − u12 ⎞ ⎟ = exp⎜ − ⎟ τ21 = exp⎜ − 21 ⎝ ⎝ RT ⎠ RT ⎠
(13)
where Δu12 and Δu21 are characteristic energy parameters of the 1−2 interactions. The experimental solubility data were correlated with the above models, and the model parameters are displayed in Table 3. The experimental data points (xexp 1,i ) and the fitted curves with these models are shown in Figure 4 (in three alcohols:
where Δg12 and Δg21 are two cross interaction energy parameters (J·mol−1) and a reflects the nonrandomness of the mixture with a12 = a21. 3.3.2. UNIQUAC Model. The UNIQUAC model based on the concept of local composition is given as26 1196
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methanol, ethanol, and propanol). The calculated solubility values (xcal 1,i ) based on these models and the average relative deviations (ARDs) are also listed in Table 2. ARD is determined by the equation: ARD =
1 N
N
∑ i=1
cal |x1,exp i − x1, i |
x1,exp i
(14)
⎛ ∂GE ⎞ S E = −⎜ ⎟ ⎝ ∂T ⎠
(16)
⎛ ∂ GE ⎞ H E = − T 2⎜ ⎟ ⎝ ∂T T ⎠
(17)
The values of GE, SE, and HE for t-CA + alcohols (methanol, ethanol, propanol, n-butanol, isopropyl alcohol, and isobutyl alcohol) systems are also displayed in Table 2.
where N denotes the number of data points for each solvent. As shown in Table 2, the solubilities of t-CA in all alcohols investigated increase with an increase in temperature. The overall ARDs for the above models in this work are 0.70% (Apelblat), 1.19% (λh), 0.80% (NRTL), and 1.10% (UNIQUAC). It proved that a good correlation of the experimental data can be obtained by each model, and Apelblat and NRTL are better than the other two models (λh and UNIQUAC). Besides, the ARDs with eq 5 are 0.80% (NRTL) and 1.10% (UNIQUAC) (
