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Correlation and prediction of the solubility of the racemic tartaric acid–ethanol–water system with the NRTL model
Journal of Molecular Liquids 216 (2016) 476–483
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Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq
Correlation and prediction of the solubility of the racemic tartaric acid–ethanol–water system with the NRTL model Qian Tan, Yixin Leng ⁎, Jun Wang, Chunxiang Huang, Ye Yuan School of Petrochemical Engineering, Changzhou University, No. 1, Gehu Road, Changzhou 213164, China
a r t i c l e
i n f o
Article history: Received 30 July 2015 Received in revised form 22 January 2016 Accepted 24 January 2016 Available online xxxx Keywords: Racemic tartaric acid Solid–liquid equilibria Solubility-temperature dependence Correlation NRTL model
a b s t r a c t The solubility data on solid–liquid equilibria (SLE) of racemic tartaric acid in ethanol + water mixtures were measured in the temperature range of (293.15 to 318.15) K at 0.1 MPa by acid–base titration method. In the binary solvent mixtures the solubility of racemic tartaric acid increases with rising temperature and decreases with increasing ethanol content. The modified Apelblat equation, λh equation and CNIBS/R–K equations were applied to describe and predict the change tendency of solubility. Computational results show that the modified Apelblat equation is superior to the others. Furthermore, a predictive version of the NRTL model was proposed for the description of the non-ideality of the racemic tartaric acid–ethanol–water system. The predicted values were compared with the experimental data. The agreements are good. By using the van't Hoff equation the molar enthalpy, entropy and Gibbs free energy changes of solution were calculated. A linear ΔsolH versus ΔsolS compensation plot with a positive slope was obtained by means of enthalpy–entropy compensation effect. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Racemic tartaric acid (C4H6O6, molar mass 150.09 g/mol) is a racemic mixture of optically active (2S,3S)- and (2R,3R)-isomers. Racemic tartaric acid appears white crystalline diprotic organic acid with a sour taste, which is used in soft drinks as food additives, effervescent tablets, chemical resolving agents and electroplating [1–3]. For most solid products, solution crystallization is one of the most common operations employed in the downstream recovery or purification steps [4]. Now in industrial manufacturing, racemic tartaric acid is often chemically synthesized with high quality and purity through crystallization refinement, so the knowledge of the solid–liquid equilibria (SLE) thermodynamics has a significant effect on the design, analysis and optimization of crystallization process [5]. Additionally, the solvent is also one of the key points which determine the success or failure, the yield and productivity of the crystallization process [6,7]. Since the binary solvent mixtures are highly versatile and have powerful means of altering the solubility of a solute [8], which play a major role in the solubility behavior, thus it is necessary to measure the solubility of racemic tartaric acid in binary solvent mixtures. To our knowledge, the solubility data of tartaric acid in pure solvents have been extensively reported [1,9–11], however, the solubility data of tartaric acid in solvent mixtures were
⁎ Corresponding author. E-mail addresses: [email protected] (Q. Tan), [email protected] (Y. Leng).
http://dx.doi.org/10.1016/j.molliq.2016.01.080 0167-7322/© 2016 Elsevier B.V. All rights reserved.
scarce [12]. Furthermore, water and ethanol are common green solvents, which are chosen for this study because they can be easily separated from the systems. The purpose of this work is to extend the database on experimental solubility. To conveniently use the solubility data, the ternary system (racemic tartaric acid–ethanol–water) phase equilibrium values were predicted by using the NRTL model. The predicted results were compared with experimental results. The key parameters involved in the NRTL model were obtained by regressing the experimental data of racemic tartaric acid in pure water and ethanol. Besides that, the modified Apelblat, the λh and the CNIBS/R–K equations were also applied to correlate the solubility data, respectively. The thermodynamic prosperities of the solution process, including the molar enthalpy, entropy and Gibbs free energy changes were calculated by the van't Hoff equation. By using the enthalpy–entropy compensation analysis, a linear plot between ΔsolH and ΔsolS was obtained. 2. Experimental 2.1. Materials Anhydrous racemic tartaric acid (mass fraction ≥0.999) used in the experiments was obtained from Changmao Biochemical Engineering Co., Ltd., China. It was kept in a desiccator with dry silica gel. Ethanol (mass fraction ≥0.997) was purchased from Jiangsu Yongfeng chemical Co., Ltd., China. Distilled–deionized water was prepared in our
Q. Tan et al. / Journal of Molecular Liquids 216 (2016) 476–483
477
Table 1 Provenance and mass fraction purity for materials used in the experiment. Material
Source
CAS RN
Mass fraction purity
Purification method
Analytical method
Racemic tartaric acid Ethanol Water Sodium hydroxide Phenolphthalein
Changmao Biochemical Engineering Co., Ltd. Jiangsu Yongfeng chemical Co., Ltd. Our laboratory Aladdin Reagent Co., Ltd. Aladdin Reagent Co., Ltd.
133–37-9 64–17-5 7732–18-5 1310–73-2 77–09-8
0.999 0.997 – 0.9999 0.980
None None – None None
HPLCa – – – –
a
High-performance liquid chromatography.
laboratory. All chemicals were employed without further purification. The detailed information for each material studied in this paper is summarized in Table 1.
2.2. Apparatus and procedures The solubility of racemic tartaric acid in water, ethanol, and binary ethanol + water solvent mixtures were measured by a static method [13–15]. The apparatus for the measurement was similar to that described in the literature [16,17]. A cylindrical double-jacketed glass vessel was used as the equilibrium cell. The jacket temperature could be kept within ±0.01 K at a desired temperature by water circulated from a thermostat (type DC-1006, Shanghai Hengping Scientific Instrument Co. Ltd., China). The glass vessel has a condenser to prevent solvents from evaporating through which a mercury-in-glass thermometer with an accuracy of ±0.01 K was inserted. Solvents and solutes were prepared by mass using an electronic analytical balance (type FA2004B Shanghai Yueping Science Instrument Co. Ltd., China) with an accuracy of ± 0.0001 g. Predetermined excess amounts of racemic tartaric acid were added to the liquid phase. During the whole process, continuous stirring was performed with a magnetic stir bar. The attaining of equilibrium was verified by successive concentration measurements over time and when the concentration was nearly invariable, that time was considered as the time to reach solid–liquid equilibrium [18]. Several equilibrium times were tested and it appeared that 24 h was always sufficient to reach equilibrium. Additionally, the solution was also kept still at least 2 h in order to settle the suspension media. After enough time of solid– liquid mixing and gravitational settling, a sample of liquid phase (2 to 4) mL was extracted by the syringe from the vessel and the solution was transferred into a conical flask through a 0.25 μm hydrophilic PTFE membrane filter mounted on the syringe. The solid phase was collected and characterized by TG (thermal gravimetric analyzer) and XRD pattern (X-ray diffraction) to determine the solid form present in equilibrium. TG (STA6000, USA) was conducted to quantitatively estimate the weight loss. Samples of approximately 3–6 mg were measured at a heating rate of 10 °C/min from 30 to 350 °C under nitrogen atmosphere. XRD (Rigaku D/max 2500 PC, Japan) was adopted to identify the crystal structure of the sample using Cu Kα radiation at 200 mA and 40 kV with a scan speed of 0.02°/s. Subsequently the filtrate including racemic tartaric acid present in the filtrate in equilibrium, was neutralized with standardized solutions of sodium hydroxide and phenolphthalein used as indicator [9,19,20]. Phenolphthalein is an appropriate indicator for the titration of tartaric acid. In this work, the titration is to the second endpoint for tartaric acid. It's titration endpoint when the color change of the solution appeared from colorless to reddish and didn't fade in thirty seconds. The pH of titration endpoint around 8.3 is in the transition range for phenolphthalein. The error of overtitration or undertitration induced when titrating was estimated to be ±0.1% for different ethanol + water solvents mixtures according to the pKa values (pKa1 = 2.96, pKa2 = 4.24) of tartaric acid in aqueous solution at 298.15 K [2]. All experiments were repeated three times for reproducibility to obtain the mean values, and the mean values were used to calculate the mole fraction solubility.
3. Thermodynamic basis 3.1. Three empirical equations The temperature dependence of racemic tartaric acid solubility in solvents can be well correlated by the modified Apelblat equation, which is deduced from the Clausius–Clapeyron equation [21,22]. ln ðxA Þ ¼ A þ
B þ C ln ðT=KÞ T=K
ð1Þ
where xA refers to the mole fraction solubility of racemic tartaric acid. T is the absolute temperature, respectively. A, B and C are regression parameters. The Buchowski–Ksiazczak λh equation is also used to describe the solution behavior [23] and could fit the solid–liquid equilibria systems with only two adjustable parameters [24]. The λh equation can be applied to eutectic system by taking into account the action of its intermolecular association, which is on the basis of general solubility equation. λð1−xA Þ 1 1 ¼ λh − ln 1 þ xA T=K T m =K
ð2Þ
where xA is the mole fraction solubility of racemic tartaric acid, T is the absolute temperature, and Tm is the atmospheric melting point of racemic tartaric acid. λ is the enthalpy factor. h is a measure of the non-ideal property of saturated solution. The Combined Nearly Ideal Binary Solvent/Redlich–Kister (CNIBS/ R–K) model proposed by Acree and his co-workers is commonly used to calculate the solute solubility in binary solvent systems [25,26]. The function is described as follows: ln ðxA Þ ¼ xB 0 ln ðxA ÞB þ xC 0 ln ðxA ÞC þ xB 0 xC 0
N X i Si xB 0 −xC 0
ð3Þ
i¼0
where Si is the model constant and N can be equal to 0, 1, 2, and 3. xA is the mole fraction solubility of racemic tartaric acid in binary solvent system. x0B and x0C are the initial mole fraction solubility of the binary solvent mixtures when the racemic tartaric acid is not added. (xA)B and (xA)C refer to the mole fraction solubility of racemic tartaric acid in pure water (B) and ethanol (C), respectively. When N = 2, Eq. (3) is rewritten as Eq. (4) where x0C is replaced with (1 − x0B). lnxA − 1−xB 0 ln ðxA ÞC −xB 0 ln ðxA ÞB h 2 i ¼ 1−xB 0 xB 0 S0 þ S1 2xB 0 −1 þ S2 2xB 0 −1
ð4Þ
In order to judge the fitting of each model to the experimental data, the root mean square deviation (RMSD) is used: RMSD ¼
" #1=2 n X ðxA −xcal Þ2 i¼1
n
ð5Þ
478
Q. Tan et al. / Journal of Molecular Liquids 216 (2016) 476–483
where n is the number of experimental points. xA and xcal denote the mole fraction solubility of the experimental and calculated values, respectively.
where σ refers to the molecular rotational symmetry number, R is the universal gas constant, and τ is the number of torsional angles calculated from Eq. (14) [25]:
3.2. Solid–liquid equilibria thermodynamics
τ ¼ SP3 þ 0:5 SP2 þ 0:5 RING−1
The fugacity of supercooled liquid at a temperature T and a pressure p is defined as the fugacity of standard state. Supposing that the solubility of the solvent in the solid phase is neglected, thermodynamic equilibrium condition between solid and liquid phases [27] is expressed as follows:
where SP3 is the number of sp3 chain atoms, SP2 is the number of sp2 chain atoms, and RING is the number of fused-ring systems. The detailed parameters of Eqs. (13) and (14) are listed in Table 2.
S
f 1 ¼ γ 1 x1 f 1
L
ð6Þ
where x1 is the mole fraction of a solid solute. fS1 and fL1 are the fugacity of a solute in the solid phase and in the supercooled liquid phase. γ1 represents the activity coefficient. The molar Gibbs free energy, ΔG, is related to the fugacity of the solid and supercooled liquid:
3.3. The NRTL activity coefficient model The NRTL model is one of the most widely applied activity coefficient models in phase equilibrium, which was developed by Renon and Prausnitz in 1968 [29], based on the local composition theory of Wilson [30] and the two-liquid solution theory of Scott. [31]. The detailed expression of NRTL model of multi-component systems is expressed as follows [32], Xδ
L
ΔG f ¼ ln 1 S RT f1
ð7Þ
where R is the universal gas constant. The molar Gibbs free energy is derived from the molar enthalpy (ΔH) and entropy (ΔS). It is due to the fact that both of ΔH and ΔS are state functions irrelevant to the approaches. ln
1 ΔH ΔS ¼ − x1 γ 1 RT R
ð8Þ
ln
ΔC p T t ΔC p 1 Δ Ht T t Tt −1 − −1 þ ln ¼ fus RT t T R T R T x1 γ 1
ð9Þ
where the heat capacity change (cCp) is considered to be constant. Since the temperature of triple point (Tt) and ΔfusHt are not available, it is presumed that they can be substituted by the atmospheric melting point (Tm) and the molar enthalpy of fusion (ΔfusHm) at Tm. The second and the third terms are omitted because they are much smaller than the first terms, and then Eq. (9) simplifies to Eq. (10): ln
1 Δ Hm T m −1 : ¼ fus RT m T x1 γ 1
ð10Þ
Δfus H m : Tm
0 0 11 Xδ δ X x τ G x j Gi j m¼1 m mj mj AA @ @ þ τij − Xδ ð15Þ Xδ x G x G j¼1 k¼1 k kj k¼1 k kj
with τij = aij + bij/T, Gij = exp(−αijτij) and αij = αji, where γi represents the activity coefficient of the component i. δ stands for the number of components. xi is the mole fraction of the component i. Gij is a dimensionless equation parameter. αij is a measure of the non-randomness of systems and R is the universal gas constant. For binary systems, the NRTL model is written as follows [33]: ln γ 1 ¼ x22 τ21
G21 x1 þ x2 G21
2 þ
τ12 G12
# ð16Þ
ðx2 þ x1 G12 Þ2
with τ12 = (g12 − g22)/RT = a12 + b12/T, τ21 = (g21 − g11)/RT = a21 + b21/T, G12 = exp(−α12τ12), and G21 = exp(−α21τ21). The interaction energy parameters, (g12-g22) and (g21-g11), are adjustable parameters obtained by non-linear least-square correlation. For great quantities of binary systems, the non-randomness factor (α12) varies from 0.20 to 0.47. We set α12 to be a typical value of 0.3. One of the most prominent advantages of this model is that the correlated binary parameters are used to predict the thermodynamic properties of multi-component systems. 3.4. Thermodynamic functions of solution If the melting point Tm and fusion molar enthalpy ΔfusS of the ideal solution are known, solubility data can be deduced from the van't Hoff equation [34].
The entropy change of fusion is also calculated from Eq. (11): Δfus Sm ¼
ln γi ¼
xτ G j¼1 i ji ji Xδ x G k¼1 k ki
"
At the triple point, a thermodynamic cycle is used to evaluate the enthalpy and entropy changes, so the following equation is obtained [24]:
ð14Þ
ð11Þ
∂ ln x Δ H ¼ − fus R ∂ð1=T Þ
ð17Þ
Substitution of Eq. (11) into Eq. (10) yields: 1 Δ Sm T m −1 : ln ¼ fus R T x1 γ 1
ð12Þ
The knowledge of the molar entropy of fusion at Tm (ΔfusSm) is of great interest in the accurate prediction of chemical properties such as phase equilibrium solubility. Nevertheless, values of ΔfusSm are usually not available. It is required to build up a correlation for their prediction. On the basis of a modification of Walden's rule, a correlation was proposed in detail for the first time by Dannenfelser and Yalkowsky in 1996 [28] which is used to predicting the molar entropy of fusion. This method is defined as follows:
However, racemic tartaric acid–ethanol–water solution is often regarded as a non-ideal system, which causes a certain margin of error when using the van't Hoff equation to predict the solubility data of the non-ideal solution and analyze the thermodynamic properties. Therefore, here the fusion enthalpy (ΔfusH) and entropy (ΔfusS) are replaced
Table 2 Parameters of Eqs. (13) and (14). Parameter
σ
ΔfusSma
τb
SP3
SP2
RING
Value
2
79.1
4
4
2
0
a
Δfus Sm ¼ 50−R ln σ þ 1:047Rτ
ð13Þ
b
ΔfusSm is calculated from Eq. (13). τ is calculated from Eq. (14).
Q. Tan et al. / Journal of Molecular Liquids 216 (2016) 476–483 Table 3 Solubility of racemic tartaric acid in water, ethanol and binary ethanol + water solvent mixtures at the temperature range of (293.15 to 333.15) K and pressure p =
Table 3 (continued)
0.1 MPa. T/K
10
wAb
10
2
xAb
102xApel A
102xλh A
102xCNIBS A
102xNRTL A
wC = 0(water) 293.15 15.57 298.15 18.54 303.15 21.47 308.15 23.98 313.15 26.74 318.15 29.07 323.15 32.00 328.15 35.26 333.15 38.25
2.17(M)c 2.66(M) 3.18(M) 3.65(M) 4.20(M) 4.69(M) 5.35(M) 6.14(M) 6.92(M)
2.25 2.65 3.10 3.60 4.15 4.76 5.42 6.13 6.90
2.29 2.68 3.10 3.59 4.12 4.72 5.39 6.12 6.94
2.17 2.66 3.18 3.65 4.20 4.69 – – –
2.34 2.72 3.14 3.62 4.16 4.75 5.40 6.11 6.90
wC = 0.1 293.15 298.15 303.15 308.15 313.15 318.15
14.28 17.32 20.08 22.93 25.51 28.00
2.08(M) 2.61(M) 3.11(M) 3.66(M) 4.19(M) 4.74(M)
2.09 2.59 3.12 3.67 4.21 4.72
2.20 2.60 3.06 3.58 4.16 4.82
2.18 2.67 3.19 3.68 4.20 4.75
2.39 2.79 3.24 3.74 4.30 4.92
wC = 0.2 293.15 298.15 303.15 308.15 313.15 318.15
13.97 16.76 19.49 21.87 24.20 27.03
2.17(M) 2.68(M) 3.20(M) 3.68(M) 4.18(M) 4.82(A)c
2.20 2.66 3.16 3.69 4.24 4.79
2.27 2.67 3.12 3.63 4.21 4.85
2.20 2.70 3.20 3.71 4.21 4.79
2.43 2.84 3.30 3.82 4.40 5.04
wC = 0.3 293.15 298.15 303.15 308.15 313.15 318.15
13.62 15.90 18.11 20.71 23.20 25.76
2.26(M) 2.70(M) 3.14(M) 3.69(M) 4.25(A) 4.85(A)
2.27 2.69 3.16 3.68 4.24 4.86
2.29 2.69 3.15 3.66 4.23 4.88
2.24 2.72 3.20 3.71 4.21 4.81
2.44 2.86 3.33 3.86 4.45 5.11
wC = 0.4 293.15 298.15 303.15 308.15 313.15 318.15
12.96 15.07 17.22 19.31 21.32 23.78
2.31(M) 2.74(M) 3.20(A + M) 3.66(A) 4.12(A) 4.72(A)
2.32 2.73 3.18 3.65 4.16 4.70
2.36 2.73 3.15 3.62 4.15 4.73
2.28 2.72 3.19 3.68 4.19 4.78
2.41 2.83 3.29 3.83 4.42 5.08
wC = 0.5 293.15 298.15 303.15 308.15 313.15 318.15
12.15 14.07 16.20 18.11 20.06 22.15
2.33(M) 2.75(M) 3.23(A) 3.68(A) 4.15(A) 4.68(A)
2.33 2.75 3.20 3.68 4.17 4.67
2.39 2.76 3.17 3.64 4.15 4.72
2.29 2.68 3.12 3.59 4.10 4.66
2.33 2.74 3.19 3.71 4.29 4.93
wC = 0.6 293.15 298.15 303.15 308.15 313.15 318.15
10.75 12.15 13.78 15.68 17.77 19.54
2.23(A) 2.55(A) 2.94(A) 3.40(A 3.93(A) 4.39(A)
2.21 2.56 2.96 3.40 3.88 4.41
2.22 2.56 2.96 3.39 3.88 4.42
2.25 2.56 2.95 3.39 3.89 4.41
2.19 2.57 3.00 3.49 4.04 4.65
wC = 0.7 293.15 298.15 303.15 308.15 313.15 318.15
9.03 9.89 11.25 12.82 14.52 16.40
2.04(A) 2.24(A) 2.58(A) 2.98(A) 3.43(A) 3.94(A)
2.02 2.28 2.59 2.96 3.42 3.96
1.96 2.27 2.62 3.01 3.44 3.91
2.08 2.30 2.64 3.02 3.48 3.95
1.97 2.31 2.70 3.12 3.61 4.16
wC = 0.8 293.15 7.13 298.15 7.56 303.15 8.43 308.15 9.65 313.15 11.09 318.15 12.76
1.77(A) 1.88(A) 2.11(A) 2.44(A) 2.84(A) 3.31(A)
1.73 1.91 2.14 2.44 2.82 3.31
1.65 1.90 2.19 2.50 2.85 3.24
1.74 1.87 2.14 2.48 2.83 3.27
1.66 1.94 2.25 2.61 3.01 3.46
102wAb
102xAb
102xApel A
102xλh A
102xCNIBS A
102xNRTL A
4.57 4.91 5.72 6.63 7.24 8.31
1.26(A) 1.35(A) 1.58(A) 1.85(A) 2.03(A) 2.35(A)
1.23 1.40 1.59 1.81 2.06 2.35
1.22 1.40 1.60 1.82 2.06 2.33
1.25 1.33 1.52 1.80 2.01 2.39
1.26 1.46 1.69 1.94 2.23 2.55
wC = 1.0 (ethanol) 293.15 2.57 298.15 2.90 303.15 3.22 308.15 3.73 313.15 4.14 318.15 4.77 323.15 5.39 328.15 6.05 333.15 6.49
0.80(A) 0.91(A) 1.01(A) 1.17(A) 1.31(A) 1.51(A) 1.72(A) 1.94(A) 2.09(A)
0.80 0.90 1.02 1.18 1.32 1.51 1.70 1.90 2.11
0.79 0.91 1.03 1.18 1.33 1.50 1.69 1.90 2.13
0.80 0.91 1.01 1.17 1.31 1.51 – – –
0.79 0.91 1.03 1.17 1.33 1.50 1.69 1.90 2.13
Ideal 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15
0.24 0.31 0.40 0.51 0.64 0.81 1.01 1.26 1.55
0.24 0.31 0.40 0.51 0.64 0.81 1.01 1.26 1.55
0.24 0.31 0.40 0.51 0.64 0.81 1.01 1.26 1.55
– – – – – – – – –
– – – – – – – – –
T/K
a
2
479
wC = 0.9 293.15 298.15 303.15 308.15 313.15 318.15
1.96 2.52 3.23 4.09 5.13 6.38 7.85 9.58 11.57
a Standard uncertainties u are u(T) = 0.01 K, u(wA) = 0.02, u(wC) = 0.01, u(xA) = 0.006 and u(p) = 0.003 MPa. b wA and xA are the mass and mole fractions solubility of racemic tartaric acid. c (M) and (A) indicate racemic tartaric acid monohydrate and racemic tartaric acid anhydrate, respectively, at equilibrium.
with the molar enthalpy (ΔsolH) and entropy (ΔsolS) of the non-ideal solution to take into account the influence of solvents.
∂ ln x Δ H ¼ − sol R ∂ð1=T Þ
ð18Þ
Since the heat capacity change of solution is assumed as constant in the temperature interval of (293.15 to 318.15) K, the molar enthalpy change of the solution process can be considered useful for the mean harmonic temperature (Thm), which is calculated as follows: T hm ¼
n n X ð1=T Þ
ð19Þ
i¼1
where n is the number of experimental points. Substitution of Eq. (19) into Eq. (18) yields: Δsol H ¼ −R
∂ ln xA : ∂ð1=T−1=T hm Þ
ð20Þ
The lnxA versus 104(1/T − 1/Thm) curves of racemic tartaric acid in the binary solvent mixtures are shown in Fig. 4. The molar Gibbs free energy change of the solution process (ΔsolG) is obtained at Thm with the approach of Krug et al. [35]: Δsol G ¼ −RT hm intercept
ð21Þ
where the intercept is determined from the plots of ln x versus (1/T-1/ Thm). The molar entropy change of solution (ΔsolS) is derived from Eq. (22): Δsol S ¼
Δsol H−Δsol G : T hm
ð22Þ
480
Q. Tan et al. / Journal of Molecular Liquids 216 (2016) 476–483
Eqs. (23) and (24) are applied to compare the relative contribution to the molar Gibbs free energy by enthalpy and entropy in the solution process: ζH ¼
jΔsol H j jΔsol H j þ jT hm Δsol Sj
ð23Þ
ζ TS ¼
jT hm Δsol Sj : jΔsol H j þ jT hm Δsol Sj
ð24Þ
4. Results and discussions 4.1. Solubility data The experimental solubility (expressed in mole fraction and mass fraction) of racemic tartaric acid anhydrate or racemic tartaric acid monohydrate are presented in Table 3, in which “A” and “M” represent racemic tartaric acid anhydrate and racemic tartaric acid monohydrate at equilibrium, respectively. The mole fraction solubility values in water or ethanol are close to the data of Li et al. [1] and Zhang et al. [11]. Besides that, the solubility values in water are almost 10% higher than the ones measured by Mullin et al. (i.e. 2.11 × 10−2 at 293.15 K and 2.94 × 10−2 at 303.15 K) except at 313.15 K and 333.15 K [10]. Unfortunately, experimental solubility data in pure water are smaller by one order of magnitude than the ones reported by Apelblat et al. [9]. Nevertheless, it is worth noting that the solubilities of D-, L-, mesomeric and racemic tartaric acid in water, are quite different. The mole fraction solubilities of four forms in water, as compared at 293.15 K, can be arranged in the following series: racemic tartaric acid (xA = 0.02) b mesomeric tartaric acid (xA = 0.13) b D- or L-tartaric acid (xA = 0.14) [2,10]. This is because racemic crystals are indeed more stable (and denser) than their chiral counterparts. In order to verify this methodology, the gravimetric analysis method [3,7] and a direct titration method were implemented. Finally, these results measured by the gravimetric analysis method are consistent with the solubility data measured by acid–base method. On the other hand, racemic tartaric acid, of known mass, was titrated with standardized solutions of NaOH which was calibrated by potassium hydrogen phthalate centigrade. The relative deviations between true values and experimental values for different solvents are less than ± 0.1%. Therefore the data and methodology are considered reliable in this work. Physico-chemical properties of the solvent such as polarity, intermolecular interactions, and the ability of the solvent to form a hydrogen bond with the acid molecules play an important role in the dissolution process [36]. Water has a smaller molecular structure, stronger polarity with sizable dielectric constant (εr = 78.36) [14], large surface tension, and a high level of hydrogen bonding. It can be said that the solubility of organic acids were significantly influenced by water as a co-solvent. As shown in Table 3, the solubility data increase with an increase of temperature, and the racemic tartaric acid dissolves more in pure water than ethanol. This is because racemic tartaric acid can effectively break into the lattice structure of water, overcome electrostatic interaction with positive and negative ions and eventually form solvated ions [37]. Hence racemic tartaric acid solubility is highly miscible with water. In this experimental work, solubility decreases with the addition of ethanol by reducing the polarity of solvents which may indicate that the polarity of the solvent is an important factor governing the solubility of acid [38]. It is in accord with the general rule “like dissolves like”. The polar protic solvent molecules (such as ethanol) interact by forming strong hydrogen bonds with each other. In order to dissolve, the solute must break these bonds and replace them with bonds of similar strength [10]. In a general way, the hydroxyl groups of racemic tartaric acid could associate with ethanol to form hydrogen bonds. Nevertheless, the strength was significantly weakened by intermolecular hydrogen bonds with water molecules. Moreover, Ethanol as a polar
Fig. 1. Experimental solubility of racemic tartaric acid in ethanol + water versus the mass fraction of ethanol.
protic solvent has weak polarity with lower dielectric constant (εr = 24.3) [39]. The addition of ethanol gradually provides environments of lower dielectric constant, which makes it difficult for them to overcome electrostatic interaction and form solvated ions. Thus the solubility of the solute declines with the enhancement of the ethanol content. Fig. 1 presents that the solubility of racemic tartaric acid investigated in binary ethanol + water solvent mixtures decreases slowly at first and quickly at the high mass fraction of ethanol content (wC N 0.4) in ternary systems. It can be explained in the way that water molecules outnumber ethanol molecules (wC b 0.4), which makes water molecules easier to form intermolecular hydrogen bonds with racemic tartaric acid molecules. While wC N 0.4, the hydroxyl group from water will associate with the ethanol via hydrogen bonds more closely than that with racemic tartaric acid [40,41]. Therefore the solubility of racemic tartaric acid in mixtures decreases quickly with rising ethanol content in solvent mixtures. So to some extent, we can draw a conclusion that the polarity of solvents and the intermolecular hydrogen bonds play a leading role in the dissolution process. This conclusion is also verified by ideal model fraction solubility of racemic tartaric acid (xideal) which was calculated by Eq. (25) with Tm = 479.15 K [42]. The ideal mole fraction solubility exhibited in Table 3 are much lower than the experimental data obtained in all cases.
ln
1 xideal
¼
ΔSm T m −1 R T
ð25Þ
Table 4 Regression parameters of the modified Apelblat equation for racemic tartaric acid in water, ethanol and binary ethanol + water solvent mixtures at the temperature range of (293.15 to 318.15) K and pressure p = 0.1 MPa. wCa
A
B
C
104RMSDb
rc
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
65.35 496.1 298.3 97.21 143.4 219.4 26.79 −277.7 −483.9 −136.0 21.98
−5.504 × 103 −2.528 × 104 −1.618 × 104 −6.981 × 103 −8.904 × 103 −1.232 × 104 −3.573 × 103 1.031 × 104 1.974 × 104 3.944 × 103 −3.289 × 103
−8.867 −72.83 −43.47 −13.59 −20.55 −31.88 −3.235 42.01 72.62 20.79 −2.754
3.985 1.278 3.362 1.111 2.066 1.335 2.469 1.988 2.341 2.975 1.703
0.9993 0.9999 0.9993 0.9999 0.9997 0.9999 0.9995 0.9996 0.9991 0.9970 0.9986
a b c
wC is the mass fraction of ethanol in binary solvents. RMSD is the root-mean-square deviation. r is the coefficient of determination.
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Table 5 Regression parameters of the λh equation for racemic tartaric acid in water, ethanol and binary ethanol + water solvent mixtures at the temperature range of (293.15 to 318.15) K and pressure p = 0.1 MPa. wCa 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 a b c
λ
h 3
0.7824 1.067 0.9638 0.9416 0.6915 0.6395 0.6216 0.5363 0.4082 0.2502 0.1460
3.413 × 10 2.746 × 103 2.938 × 103 2.980 × 103 3.702 × 103 3.899 × 103 4.067 × 103 4.681 × 103 5.981 × 103 9.232 × 103 1.530 × 104
104RMSDb
rc
5.955 7.293 5.859 2.276 3.159 6.156 2.526 3.758 6.957 3.143 2.421
0.9992 0.9968 0.9978 0.9997 0.9992 0.9988 0.9994 0.9984 0.9919 0.9966 0.9984
wC is the mass fraction of ethanol in binary solvents. RMSD is the root-mean-square deviation. r is the coefficient of determination.
Table 6 Regression parameters of the CNIBS/Redlich–Kister equation for racemic tartaric acid in water, ethanol and binary ethanol + water solvent mixtures at the temperature range of (293.15 to 318.15) K and pressure p = 0.1 MPa. T/K
S0
S1
S2
104RMSDa
rb
293.15 298.15 303.15 308.15 313.15 318.15
1.726 1.445 1.420 1.399 1.469 1.464
0.2598 0.6018 0.4983 0.4311 0.4175 0.3167
−0.9429 −0.8801 −0.7326 −0.4679 −0.7428 −0.3179
3.829 3.431 5.130 3.751 3.453 3.010
0.9968 0.9984 0.9976 0.9990 0.9994 0.9996
a b
RMSD is the root-mean-square deviation. r is the coefficient of determination.
4.2. Correlated results of three empirical equations The experimental solubility data of the racemic tartaric acid in water, ethanol, and binary ethanol + water solvent mixtures during the temperature range from (293.15 to 318.15) K, were fitted by the modified Apelblat, the λh and the CNIBS/R–K equations, respectively. Tables 4–6 show that the 104RMSD values in various ethanol + water solvent mixtures were observed in the range of 1.11–3.98 for the modified Apelblat equation, 2.28–7.29 for the λh equation and 3.01– 5.13 for the CNIBS/R–K equation, respectively. This result demonstrates that the calculated solubility of racemic tartaric acid in solvent mixtures agree well with experimental data, and the modified Apelblat equation correlates the solubility data best owing to its lowest value of the 104RMSD.
Fig. 2. Experimental values and predicted values of the NRTL model for the solubility data of racemic tartaric acid in binary mixtures of ethanol + water: (■) T = 293.15 K; (●) T = 298.15 K; (▲) T = 303.15 K; (▼) T = 308.15 K; (◄) T = 313.15 K; (►) T = 318.15 K; (−) predicted values of the NRTL model.
(293.15 to 333.15) K were used to fitting the interaction energy parameters of the NRTL model, which are summarized in Table 7. From Table 3, the calculated values are consistent with the experimental values in pure water and ethanol, so the obtained NRTL interaction parameters in this work are potential to predict the ternary phase equilibrium. Fig. 2 exhibits that the predicted values increase with the rising temperature and with a decrease in the concentration of ethanol. More accurately, the predicted values decrease slowly at the low mass fraction of ethanol content while a rapid reduction is seen between wC = 0.4 up to wC = 0.9. In addition, the trends of predicted values as a function of wC and T are in very good agreement with the experimental values. Although the predicted values are slightly greater than the experimental solubility, the relative deviations between them are mostly within ±5% (cf. Fig. 3), which is applicable in industrial crystallization process. These comparative results show that the NRTL model is well performed with good predictions for the phases in equilibrium and will provide a thermodynamic basis for the crystallization process of the racemic tartaric acid–ethanol–water system.
4.3. The NRTL prediction of the ternary systems In this work, the experimental solubility values of racemic tartaric acid in pure water and ethanol over the temperature range from
Table 7 The available interaction energy parameters of the NRTL model for the racemic tartaric acid–ethanol–water system.a System
a12
a21
b12
b21
Racemic tartaric acid(1)/water(2) Racemic tartaric acid(1)/ethanol(2) Ethanol(1)/water(2)
−1.665 −2.530 3.458
3.899 7.645 −0.8009
1000 1000 −586.1
−2123 −2794 246.2
a
a12, a21, b12, and b12 are parameters of the NRTL model.
Fig. 3. The relative deviation of experimental values and predicted values of the NRTL model: (□) wC = 0.1; (○) wC = 0.2; (△) wC = 0.3; (▽) wC = 0.4; (◇) wC = 0.5; (×) wC = 0.6; (☉) wC = 0.7; (+) wC = 0.8; (☆) wC = 0.9.
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Q. Tan et al. / Journal of Molecular Liquids 216 (2016) 476–483
Fig. 6. ΔsolH versus ΔsolS enthalpy–entropy compensation plot for dissolution process of racemic tartaric acid in binary ethanol + water solvent mixtures. Fig. 4. A van't Hoff plot of the mole fraction solubility (lnxA) of racemic tartaric acid in binary mixtures of ethanol + water against 104(1/T − 1/Thm) with a straight line to correlate the data: (□) wC = 0.1; (○) wC = 0.2; (△) wC = 0.3; (▽) wC = 0.4; (◇) wC = 0.5; (×) wC = 0.6; (☉) wC = 0.7; (+) wC = 0.8; (☆) wC = 0.9.
4.4. Thermodynamic quantities of solution The mean harmonic temperature (Thm) value calculated is just 305.41 K from (293.15 to 318.15) K. The values of ΔsolH, ΔsolS, ΔsolG, T ΔsolS, ζH and ζTS are listed in Table 8. It is clear to see that the main contributor to the molar Gibbs free energy change of solution is the positive molar enthalpy with ζH N 0.6, which demonstrates the solution process is endothermic predominance and the enthalpy to the Gibbs free energy change contributes more than the entropy. Furthermore, ζTS for the ideal solution process is greater than values obtained for some cases meaning that the entropy contribution is limited during the real solution process [43]. From Fig. 5, ΔsolH and T ΔsolS present a slight fluctuation with the mass fraction of ethanol in ternary systems due to the excess molar Gibbs free energy change of the solution process. The molar enthalpy change of solution is the integration of several kinds of interactions, therefore high value of the enthalpy signifies that high energy is required to overcome the cohesive force of the solute molecules and the solvent molecules in the solution process [11,44].
4.5. Enthalpy–entropy compensation of solution The chemical compensation has effect on the solubility of several compounds in solvent mixtures, which has been reported in some literatures [45–47]. In biochemical and chemistry literature, this analysis is attributed to the structural property of solvent water [48] and get a better understanding of dissolution process. Enthalpy–entropy compensation describes the behavior of ΔsolH and ΔsolS for a series of systems driven by changes in solvation. The making weighted graph of ΔsolH as a function of ΔsolS at the mean harmonic temperature permits the observation of the dissolution process according to the tendencies obtained. For concentration dependent enthalpy–entropy compensation is expressed by a linear relation, ΔsolH = a + bΔsolS. In this relation, a and b are constants. Obviously b, (the slope of the plot ΔsolH versus ΔsolS) has the dimension of temperature, while a (the intercept of this plot) has the dimension of free energy. In the case of the ethanolwater mixture (Fig. 6), the relationship is linear and ascendant, according to the following expression: Δsol H ¼ 11:66926 þ 0:24294Δsol Sðr ¼ 0:9799Þ:
High values of correlation coefficient certify the existence of compensation effect. As can be seen, there is a good linear correlation between the enthalpy and entropy changes, therefore a compensation effect exists.
Table 8 Thermodynamic functions relative to solution process of racemic tartaric acid in binary ethanol + water solvent mixtures at the mean temperature.
Fig. 5. The thermodynamic properties of the solution for racemic tartaric acid in ethanol + water as functions of wC: (◄): ΔsolH; (●): TΔsolS; (★): ΔsolG.
wCa
xCa
ΔsolH (kJ mol−1)
ΔsolS (J mol−1 K−1)
ΔsolG (kJ mol−1)
TΔsolS (kJ mol−1)
ζH
ζTS
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Ideal
0.042 0.089 0.143 0.207 0.281 0.370 0.477 0.610 0.779
25.3 24.3 23.6 22.3 21.5 21.4 20.9 20.0 19.9 22.0
54.4 51.2 49.2 44.8 42.4 41.4 38.8 34.1 31.4 43.8
8.68 8.63 8.61 8.59 8.60 8.78 9.08 9.54 10.4 8.30
16.6 15.6 15.0 13.7 12.9 12.6 11.8 10.4 9.59 13.4
0.604 0.608 0.611 0.620 0.625 0.629 0.639 0.657 0.675 0.622
0.396 0.392 0.389 0.380 0.375 0.371 0.361 0.343 0.325 0.378
a
wC and xC are the mass fractions of ethanol in binary solvents.
Q. Tan et al. / Journal of Molecular Liquids 216 (2016) 476–483
5. Conclusion In this work, the solubility of racemic tartaric acid in water, ethanol, and binary solvents of ethanol + water were measured in the temperature range of (293.15 to 318.15) K by acid–base titration method. The experimental results showed that the solubility of racemic tartaric acid in mixtures increased with rising temperature and decreased with increasing ethanol content. The experimental data were well fitted with the modified Apelblat, the λh and the CNIBS/R–K equations by adjusting the binary interaction parameters. By comparison of these three models in terms of 104RMSD, the modified Apelblat equation was more accurate than the others in this system. Moreover, the modeling results of the NRTL model provided good predictions with the experimental values as shown by the relative deviation which were within ±5%. The simplicity of the model, the robustness of the predictions, and the applicability of the model to the ternary system made this a useful thermodynamic framework for solubility modeling in support of crystallization process design. The thermodynamic properties, the molar enthalpy, entropy and Gibbs free energy changes of solution were calculated by the van't Hoff equation. Values of the thermodynamic parameters indicated that the solution process was endothermic and the main contributor to the molar Gibbs free energy change of solution was the positive molar enthalpy. In this context, the linear enthalpy–entropy compensation effect has been observed for the studied system, and the compensation temperature along with entropic parameter is reported. For solvent mixtures, the linear plot means the enthalpy–entropy compensation is in the dissolution processes. List of symbols A, B, C ΔCP f S1 f L1 Gij ΔG ΔsolG ΔfusHm ΔfusHt ΔsolH Ka1 Ka2 n p R RING RMSD r S0, S1, S2 ΔfusSm ΔsolS SP2 SP3 T Thm Tm Tt
regression parameters of the modified Apelblat equation the heat capacity change (J mol−1 K−1) the fugacity of solute in the solid phase the fugacity of solute in the supercooled liquid a dimensionless equation parameter the molar Gibbs free energy change of the solid (J mol−1) the molar Gibbs free energy change of the solution process (J mol−1) the molar enthalpy change of fusion of solute at melting point (J mol−1) the molar enthalpy change of fusion of solute at triple point (J mol−1) the molar enthalpy change of the solution process (J mol−1) first acidity constant of racemic tartaric acid second acidity constant of racemic tartaric acid number of experimental points pressure (Pa) gas constant (J mol−1 K−1) the number of fused-ring systems the root-mean-square deviation coefficient of determination regression parameters of the CNIBS/R–K equation the molar entropy change of fusion of solute at melting point (J mol−1 K−1) the molar entropy change of the solution process (J mol−1 K−1) the number of sp2 chain atoms the number of sp3 chain atoms absolute temperature (K) the mean harmonic temperature (K) melting point (K) the absolute temperature of triple point (K)
xA wA wC
483
mole fraction solubility of racemic tartaric acid mass fraction solubility of racemic tartaric acid and ethanol the mass fraction of ethanol
Greek letters αij γ1 γi δ ζH ζTS λ, h
a measure of the non-randomness of systems the activity coefficient of a solid solute the activity coefficient of the component i the number of components the contribution of enthalpy to the standard Gibbs energy the contribution of entropy to the standard Gibbs energy regression parameters of the λh equation
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Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq
Correlation and prediction of the solubility of the racemic tartaric acid–ethanol–water system with the NRTL model Qian Tan, Yixin Leng ⁎, Jun Wang, Chunxiang Huang, Ye Yuan School of Petrochemical Engineering, Changzhou University, No. 1, Gehu Road, Changzhou 213164, China
a r t i c l e
i n f o
Article history: Received 30 July 2015 Received in revised form 22 January 2016 Accepted 24 January 2016 Available online xxxx Keywords: Racemic tartaric acid Solid–liquid equilibria Solubility-temperature dependence Correlation NRTL model
a b s t r a c t The solubility data on solid–liquid equilibria (SLE) of racemic tartaric acid in ethanol + water mixtures were measured in the temperature range of (293.15 to 318.15) K at 0.1 MPa by acid–base titration method. In the binary solvent mixtures the solubility of racemic tartaric acid increases with rising temperature and decreases with increasing ethanol content. The modified Apelblat equation, λh equation and CNIBS/R–K equations were applied to describe and predict the change tendency of solubility. Computational results show that the modified Apelblat equation is superior to the others. Furthermore, a predictive version of the NRTL model was proposed for the description of the non-ideality of the racemic tartaric acid–ethanol–water system. The predicted values were compared with the experimental data. The agreements are good. By using the van't Hoff equation the molar enthalpy, entropy and Gibbs free energy changes of solution were calculated. A linear ΔsolH versus ΔsolS compensation plot with a positive slope was obtained by means of enthalpy–entropy compensation effect. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Racemic tartaric acid (C4H6O6, molar mass 150.09 g/mol) is a racemic mixture of optically active (2S,3S)- and (2R,3R)-isomers. Racemic tartaric acid appears white crystalline diprotic organic acid with a sour taste, which is used in soft drinks as food additives, effervescent tablets, chemical resolving agents and electroplating [1–3]. For most solid products, solution crystallization is one of the most common operations employed in the downstream recovery or purification steps [4]. Now in industrial manufacturing, racemic tartaric acid is often chemically synthesized with high quality and purity through crystallization refinement, so the knowledge of the solid–liquid equilibria (SLE) thermodynamics has a significant effect on the design, analysis and optimization of crystallization process [5]. Additionally, the solvent is also one of the key points which determine the success or failure, the yield and productivity of the crystallization process [6,7]. Since the binary solvent mixtures are highly versatile and have powerful means of altering the solubility of a solute [8], which play a major role in the solubility behavior, thus it is necessary to measure the solubility of racemic tartaric acid in binary solvent mixtures. To our knowledge, the solubility data of tartaric acid in pure solvents have been extensively reported [1,9–11], however, the solubility data of tartaric acid in solvent mixtures were
⁎ Corresponding author. E-mail addresses: [email protected] (Q. Tan), [email protected] (Y. Leng).
http://dx.doi.org/10.1016/j.molliq.2016.01.080 0167-7322/© 2016 Elsevier B.V. All rights reserved.
scarce [12]. Furthermore, water and ethanol are common green solvents, which are chosen for this study because they can be easily separated from the systems. The purpose of this work is to extend the database on experimental solubility. To conveniently use the solubility data, the ternary system (racemic tartaric acid–ethanol–water) phase equilibrium values were predicted by using the NRTL model. The predicted results were compared with experimental results. The key parameters involved in the NRTL model were obtained by regressing the experimental data of racemic tartaric acid in pure water and ethanol. Besides that, the modified Apelblat, the λh and the CNIBS/R–K equations were also applied to correlate the solubility data, respectively. The thermodynamic prosperities of the solution process, including the molar enthalpy, entropy and Gibbs free energy changes were calculated by the van't Hoff equation. By using the enthalpy–entropy compensation analysis, a linear plot between ΔsolH and ΔsolS was obtained. 2. Experimental 2.1. Materials Anhydrous racemic tartaric acid (mass fraction ≥0.999) used in the experiments was obtained from Changmao Biochemical Engineering Co., Ltd., China. It was kept in a desiccator with dry silica gel. Ethanol (mass fraction ≥0.997) was purchased from Jiangsu Yongfeng chemical Co., Ltd., China. Distilled–deionized water was prepared in our
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Table 1 Provenance and mass fraction purity for materials used in the experiment. Material
Source
CAS RN
Mass fraction purity
Purification method
Analytical method
Racemic tartaric acid Ethanol Water Sodium hydroxide Phenolphthalein
Changmao Biochemical Engineering Co., Ltd. Jiangsu Yongfeng chemical Co., Ltd. Our laboratory Aladdin Reagent Co., Ltd. Aladdin Reagent Co., Ltd.
133–37-9 64–17-5 7732–18-5 1310–73-2 77–09-8
0.999 0.997 – 0.9999 0.980
None None – None None
HPLCa – – – –
a
High-performance liquid chromatography.
laboratory. All chemicals were employed without further purification. The detailed information for each material studied in this paper is summarized in Table 1.
2.2. Apparatus and procedures The solubility of racemic tartaric acid in water, ethanol, and binary ethanol + water solvent mixtures were measured by a static method [13–15]. The apparatus for the measurement was similar to that described in the literature [16,17]. A cylindrical double-jacketed glass vessel was used as the equilibrium cell. The jacket temperature could be kept within ±0.01 K at a desired temperature by water circulated from a thermostat (type DC-1006, Shanghai Hengping Scientific Instrument Co. Ltd., China). The glass vessel has a condenser to prevent solvents from evaporating through which a mercury-in-glass thermometer with an accuracy of ±0.01 K was inserted. Solvents and solutes were prepared by mass using an electronic analytical balance (type FA2004B Shanghai Yueping Science Instrument Co. Ltd., China) with an accuracy of ± 0.0001 g. Predetermined excess amounts of racemic tartaric acid were added to the liquid phase. During the whole process, continuous stirring was performed with a magnetic stir bar. The attaining of equilibrium was verified by successive concentration measurements over time and when the concentration was nearly invariable, that time was considered as the time to reach solid–liquid equilibrium [18]. Several equilibrium times were tested and it appeared that 24 h was always sufficient to reach equilibrium. Additionally, the solution was also kept still at least 2 h in order to settle the suspension media. After enough time of solid– liquid mixing and gravitational settling, a sample of liquid phase (2 to 4) mL was extracted by the syringe from the vessel and the solution was transferred into a conical flask through a 0.25 μm hydrophilic PTFE membrane filter mounted on the syringe. The solid phase was collected and characterized by TG (thermal gravimetric analyzer) and XRD pattern (X-ray diffraction) to determine the solid form present in equilibrium. TG (STA6000, USA) was conducted to quantitatively estimate the weight loss. Samples of approximately 3–6 mg were measured at a heating rate of 10 °C/min from 30 to 350 °C under nitrogen atmosphere. XRD (Rigaku D/max 2500 PC, Japan) was adopted to identify the crystal structure of the sample using Cu Kα radiation at 200 mA and 40 kV with a scan speed of 0.02°/s. Subsequently the filtrate including racemic tartaric acid present in the filtrate in equilibrium, was neutralized with standardized solutions of sodium hydroxide and phenolphthalein used as indicator [9,19,20]. Phenolphthalein is an appropriate indicator for the titration of tartaric acid. In this work, the titration is to the second endpoint for tartaric acid. It's titration endpoint when the color change of the solution appeared from colorless to reddish and didn't fade in thirty seconds. The pH of titration endpoint around 8.3 is in the transition range for phenolphthalein. The error of overtitration or undertitration induced when titrating was estimated to be ±0.1% for different ethanol + water solvents mixtures according to the pKa values (pKa1 = 2.96, pKa2 = 4.24) of tartaric acid in aqueous solution at 298.15 K [2]. All experiments were repeated three times for reproducibility to obtain the mean values, and the mean values were used to calculate the mole fraction solubility.
3. Thermodynamic basis 3.1. Three empirical equations The temperature dependence of racemic tartaric acid solubility in solvents can be well correlated by the modified Apelblat equation, which is deduced from the Clausius–Clapeyron equation [21,22]. ln ðxA Þ ¼ A þ
B þ C ln ðT=KÞ T=K
ð1Þ
where xA refers to the mole fraction solubility of racemic tartaric acid. T is the absolute temperature, respectively. A, B and C are regression parameters. The Buchowski–Ksiazczak λh equation is also used to describe the solution behavior [23] and could fit the solid–liquid equilibria systems with only two adjustable parameters [24]. The λh equation can be applied to eutectic system by taking into account the action of its intermolecular association, which is on the basis of general solubility equation. λð1−xA Þ 1 1 ¼ λh − ln 1 þ xA T=K T m =K
ð2Þ
where xA is the mole fraction solubility of racemic tartaric acid, T is the absolute temperature, and Tm is the atmospheric melting point of racemic tartaric acid. λ is the enthalpy factor. h is a measure of the non-ideal property of saturated solution. The Combined Nearly Ideal Binary Solvent/Redlich–Kister (CNIBS/ R–K) model proposed by Acree and his co-workers is commonly used to calculate the solute solubility in binary solvent systems [25,26]. The function is described as follows: ln ðxA Þ ¼ xB 0 ln ðxA ÞB þ xC 0 ln ðxA ÞC þ xB 0 xC 0
N X i Si xB 0 −xC 0
ð3Þ
i¼0
where Si is the model constant and N can be equal to 0, 1, 2, and 3. xA is the mole fraction solubility of racemic tartaric acid in binary solvent system. x0B and x0C are the initial mole fraction solubility of the binary solvent mixtures when the racemic tartaric acid is not added. (xA)B and (xA)C refer to the mole fraction solubility of racemic tartaric acid in pure water (B) and ethanol (C), respectively. When N = 2, Eq. (3) is rewritten as Eq. (4) where x0C is replaced with (1 − x0B). lnxA − 1−xB 0 ln ðxA ÞC −xB 0 ln ðxA ÞB h 2 i ¼ 1−xB 0 xB 0 S0 þ S1 2xB 0 −1 þ S2 2xB 0 −1
ð4Þ
In order to judge the fitting of each model to the experimental data, the root mean square deviation (RMSD) is used: RMSD ¼
" #1=2 n X ðxA −xcal Þ2 i¼1
n
ð5Þ
478
Q. Tan et al. / Journal of Molecular Liquids 216 (2016) 476–483
where n is the number of experimental points. xA and xcal denote the mole fraction solubility of the experimental and calculated values, respectively.
where σ refers to the molecular rotational symmetry number, R is the universal gas constant, and τ is the number of torsional angles calculated from Eq. (14) [25]:
3.2. Solid–liquid equilibria thermodynamics
τ ¼ SP3 þ 0:5 SP2 þ 0:5 RING−1
The fugacity of supercooled liquid at a temperature T and a pressure p is defined as the fugacity of standard state. Supposing that the solubility of the solvent in the solid phase is neglected, thermodynamic equilibrium condition between solid and liquid phases [27] is expressed as follows:
where SP3 is the number of sp3 chain atoms, SP2 is the number of sp2 chain atoms, and RING is the number of fused-ring systems. The detailed parameters of Eqs. (13) and (14) are listed in Table 2.
S
f 1 ¼ γ 1 x1 f 1
L
ð6Þ
where x1 is the mole fraction of a solid solute. fS1 and fL1 are the fugacity of a solute in the solid phase and in the supercooled liquid phase. γ1 represents the activity coefficient. The molar Gibbs free energy, ΔG, is related to the fugacity of the solid and supercooled liquid:
3.3. The NRTL activity coefficient model The NRTL model is one of the most widely applied activity coefficient models in phase equilibrium, which was developed by Renon and Prausnitz in 1968 [29], based on the local composition theory of Wilson [30] and the two-liquid solution theory of Scott. [31]. The detailed expression of NRTL model of multi-component systems is expressed as follows [32], Xδ
L
ΔG f ¼ ln 1 S RT f1
ð7Þ
where R is the universal gas constant. The molar Gibbs free energy is derived from the molar enthalpy (ΔH) and entropy (ΔS). It is due to the fact that both of ΔH and ΔS are state functions irrelevant to the approaches. ln
1 ΔH ΔS ¼ − x1 γ 1 RT R
ð8Þ
ln
ΔC p T t ΔC p 1 Δ Ht T t Tt −1 − −1 þ ln ¼ fus RT t T R T R T x1 γ 1
ð9Þ
where the heat capacity change (cCp) is considered to be constant. Since the temperature of triple point (Tt) and ΔfusHt are not available, it is presumed that they can be substituted by the atmospheric melting point (Tm) and the molar enthalpy of fusion (ΔfusHm) at Tm. The second and the third terms are omitted because they are much smaller than the first terms, and then Eq. (9) simplifies to Eq. (10): ln
1 Δ Hm T m −1 : ¼ fus RT m T x1 γ 1
ð10Þ
Δfus H m : Tm
0 0 11 Xδ δ X x τ G x j Gi j m¼1 m mj mj AA @ @ þ τij − Xδ ð15Þ Xδ x G x G j¼1 k¼1 k kj k¼1 k kj
with τij = aij + bij/T, Gij = exp(−αijτij) and αij = αji, where γi represents the activity coefficient of the component i. δ stands for the number of components. xi is the mole fraction of the component i. Gij is a dimensionless equation parameter. αij is a measure of the non-randomness of systems and R is the universal gas constant. For binary systems, the NRTL model is written as follows [33]: ln γ 1 ¼ x22 τ21
G21 x1 þ x2 G21
2 þ
τ12 G12
# ð16Þ
ðx2 þ x1 G12 Þ2
with τ12 = (g12 − g22)/RT = a12 + b12/T, τ21 = (g21 − g11)/RT = a21 + b21/T, G12 = exp(−α12τ12), and G21 = exp(−α21τ21). The interaction energy parameters, (g12-g22) and (g21-g11), are adjustable parameters obtained by non-linear least-square correlation. For great quantities of binary systems, the non-randomness factor (α12) varies from 0.20 to 0.47. We set α12 to be a typical value of 0.3. One of the most prominent advantages of this model is that the correlated binary parameters are used to predict the thermodynamic properties of multi-component systems. 3.4. Thermodynamic functions of solution If the melting point Tm and fusion molar enthalpy ΔfusS of the ideal solution are known, solubility data can be deduced from the van't Hoff equation [34].
The entropy change of fusion is also calculated from Eq. (11): Δfus Sm ¼
ln γi ¼
xτ G j¼1 i ji ji Xδ x G k¼1 k ki
"
At the triple point, a thermodynamic cycle is used to evaluate the enthalpy and entropy changes, so the following equation is obtained [24]:
ð14Þ
ð11Þ
∂ ln x Δ H ¼ − fus R ∂ð1=T Þ
ð17Þ
Substitution of Eq. (11) into Eq. (10) yields: 1 Δ Sm T m −1 : ln ¼ fus R T x1 γ 1
ð12Þ
The knowledge of the molar entropy of fusion at Tm (ΔfusSm) is of great interest in the accurate prediction of chemical properties such as phase equilibrium solubility. Nevertheless, values of ΔfusSm are usually not available. It is required to build up a correlation for their prediction. On the basis of a modification of Walden's rule, a correlation was proposed in detail for the first time by Dannenfelser and Yalkowsky in 1996 [28] which is used to predicting the molar entropy of fusion. This method is defined as follows:
However, racemic tartaric acid–ethanol–water solution is often regarded as a non-ideal system, which causes a certain margin of error when using the van't Hoff equation to predict the solubility data of the non-ideal solution and analyze the thermodynamic properties. Therefore, here the fusion enthalpy (ΔfusH) and entropy (ΔfusS) are replaced
Table 2 Parameters of Eqs. (13) and (14). Parameter
σ
ΔfusSma
τb
SP3
SP2
RING
Value
2
79.1
4
4
2
0
a
Δfus Sm ¼ 50−R ln σ þ 1:047Rτ
ð13Þ
b
ΔfusSm is calculated from Eq. (13). τ is calculated from Eq. (14).
Q. Tan et al. / Journal of Molecular Liquids 216 (2016) 476–483 Table 3 Solubility of racemic tartaric acid in water, ethanol and binary ethanol + water solvent mixtures at the temperature range of (293.15 to 333.15) K and pressure p =
Table 3 (continued)
0.1 MPa. T/K
10
wAb
10
2
xAb
102xApel A
102xλh A
102xCNIBS A
102xNRTL A
wC = 0(water) 293.15 15.57 298.15 18.54 303.15 21.47 308.15 23.98 313.15 26.74 318.15 29.07 323.15 32.00 328.15 35.26 333.15 38.25
2.17(M)c 2.66(M) 3.18(M) 3.65(M) 4.20(M) 4.69(M) 5.35(M) 6.14(M) 6.92(M)
2.25 2.65 3.10 3.60 4.15 4.76 5.42 6.13 6.90
2.29 2.68 3.10 3.59 4.12 4.72 5.39 6.12 6.94
2.17 2.66 3.18 3.65 4.20 4.69 – – –
2.34 2.72 3.14 3.62 4.16 4.75 5.40 6.11 6.90
wC = 0.1 293.15 298.15 303.15 308.15 313.15 318.15
14.28 17.32 20.08 22.93 25.51 28.00
2.08(M) 2.61(M) 3.11(M) 3.66(M) 4.19(M) 4.74(M)
2.09 2.59 3.12 3.67 4.21 4.72
2.20 2.60 3.06 3.58 4.16 4.82
2.18 2.67 3.19 3.68 4.20 4.75
2.39 2.79 3.24 3.74 4.30 4.92
wC = 0.2 293.15 298.15 303.15 308.15 313.15 318.15
13.97 16.76 19.49 21.87 24.20 27.03
2.17(M) 2.68(M) 3.20(M) 3.68(M) 4.18(M) 4.82(A)c
2.20 2.66 3.16 3.69 4.24 4.79
2.27 2.67 3.12 3.63 4.21 4.85
2.20 2.70 3.20 3.71 4.21 4.79
2.43 2.84 3.30 3.82 4.40 5.04
wC = 0.3 293.15 298.15 303.15 308.15 313.15 318.15
13.62 15.90 18.11 20.71 23.20 25.76
2.26(M) 2.70(M) 3.14(M) 3.69(M) 4.25(A) 4.85(A)
2.27 2.69 3.16 3.68 4.24 4.86
2.29 2.69 3.15 3.66 4.23 4.88
2.24 2.72 3.20 3.71 4.21 4.81
2.44 2.86 3.33 3.86 4.45 5.11
wC = 0.4 293.15 298.15 303.15 308.15 313.15 318.15
12.96 15.07 17.22 19.31 21.32 23.78
2.31(M) 2.74(M) 3.20(A + M) 3.66(A) 4.12(A) 4.72(A)
2.32 2.73 3.18 3.65 4.16 4.70
2.36 2.73 3.15 3.62 4.15 4.73
2.28 2.72 3.19 3.68 4.19 4.78
2.41 2.83 3.29 3.83 4.42 5.08
wC = 0.5 293.15 298.15 303.15 308.15 313.15 318.15
12.15 14.07 16.20 18.11 20.06 22.15
2.33(M) 2.75(M) 3.23(A) 3.68(A) 4.15(A) 4.68(A)
2.33 2.75 3.20 3.68 4.17 4.67
2.39 2.76 3.17 3.64 4.15 4.72
2.29 2.68 3.12 3.59 4.10 4.66
2.33 2.74 3.19 3.71 4.29 4.93
wC = 0.6 293.15 298.15 303.15 308.15 313.15 318.15
10.75 12.15 13.78 15.68 17.77 19.54
2.23(A) 2.55(A) 2.94(A) 3.40(A 3.93(A) 4.39(A)
2.21 2.56 2.96 3.40 3.88 4.41
2.22 2.56 2.96 3.39 3.88 4.42
2.25 2.56 2.95 3.39 3.89 4.41
2.19 2.57 3.00 3.49 4.04 4.65
wC = 0.7 293.15 298.15 303.15 308.15 313.15 318.15
9.03 9.89 11.25 12.82 14.52 16.40
2.04(A) 2.24(A) 2.58(A) 2.98(A) 3.43(A) 3.94(A)
2.02 2.28 2.59 2.96 3.42 3.96
1.96 2.27 2.62 3.01 3.44 3.91
2.08 2.30 2.64 3.02 3.48 3.95
1.97 2.31 2.70 3.12 3.61 4.16
wC = 0.8 293.15 7.13 298.15 7.56 303.15 8.43 308.15 9.65 313.15 11.09 318.15 12.76
1.77(A) 1.88(A) 2.11(A) 2.44(A) 2.84(A) 3.31(A)
1.73 1.91 2.14 2.44 2.82 3.31
1.65 1.90 2.19 2.50 2.85 3.24
1.74 1.87 2.14 2.48 2.83 3.27
1.66 1.94 2.25 2.61 3.01 3.46
102wAb
102xAb
102xApel A
102xλh A
102xCNIBS A
102xNRTL A
4.57 4.91 5.72 6.63 7.24 8.31
1.26(A) 1.35(A) 1.58(A) 1.85(A) 2.03(A) 2.35(A)
1.23 1.40 1.59 1.81 2.06 2.35
1.22 1.40 1.60 1.82 2.06 2.33
1.25 1.33 1.52 1.80 2.01 2.39
1.26 1.46 1.69 1.94 2.23 2.55
wC = 1.0 (ethanol) 293.15 2.57 298.15 2.90 303.15 3.22 308.15 3.73 313.15 4.14 318.15 4.77 323.15 5.39 328.15 6.05 333.15 6.49
0.80(A) 0.91(A) 1.01(A) 1.17(A) 1.31(A) 1.51(A) 1.72(A) 1.94(A) 2.09(A)
0.80 0.90 1.02 1.18 1.32 1.51 1.70 1.90 2.11
0.79 0.91 1.03 1.18 1.33 1.50 1.69 1.90 2.13
0.80 0.91 1.01 1.17 1.31 1.51 – – –
0.79 0.91 1.03 1.17 1.33 1.50 1.69 1.90 2.13
Ideal 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15
0.24 0.31 0.40 0.51 0.64 0.81 1.01 1.26 1.55
0.24 0.31 0.40 0.51 0.64 0.81 1.01 1.26 1.55
0.24 0.31 0.40 0.51 0.64 0.81 1.01 1.26 1.55
– – – – – – – – –
– – – – – – – – –
T/K
a
2
479
wC = 0.9 293.15 298.15 303.15 308.15 313.15 318.15
1.96 2.52 3.23 4.09 5.13 6.38 7.85 9.58 11.57
a Standard uncertainties u are u(T) = 0.01 K, u(wA) = 0.02, u(wC) = 0.01, u(xA) = 0.006 and u(p) = 0.003 MPa. b wA and xA are the mass and mole fractions solubility of racemic tartaric acid. c (M) and (A) indicate racemic tartaric acid monohydrate and racemic tartaric acid anhydrate, respectively, at equilibrium.
with the molar enthalpy (ΔsolH) and entropy (ΔsolS) of the non-ideal solution to take into account the influence of solvents.
∂ ln x Δ H ¼ − sol R ∂ð1=T Þ
ð18Þ
Since the heat capacity change of solution is assumed as constant in the temperature interval of (293.15 to 318.15) K, the molar enthalpy change of the solution process can be considered useful for the mean harmonic temperature (Thm), which is calculated as follows: T hm ¼
n n X ð1=T Þ
ð19Þ
i¼1
where n is the number of experimental points. Substitution of Eq. (19) into Eq. (18) yields: Δsol H ¼ −R
∂ ln xA : ∂ð1=T−1=T hm Þ
ð20Þ
The lnxA versus 104(1/T − 1/Thm) curves of racemic tartaric acid in the binary solvent mixtures are shown in Fig. 4. The molar Gibbs free energy change of the solution process (ΔsolG) is obtained at Thm with the approach of Krug et al. [35]: Δsol G ¼ −RT hm intercept
ð21Þ
where the intercept is determined from the plots of ln x versus (1/T-1/ Thm). The molar entropy change of solution (ΔsolS) is derived from Eq. (22): Δsol S ¼
Δsol H−Δsol G : T hm
ð22Þ
480
Q. Tan et al. / Journal of Molecular Liquids 216 (2016) 476–483
Eqs. (23) and (24) are applied to compare the relative contribution to the molar Gibbs free energy by enthalpy and entropy in the solution process: ζH ¼
jΔsol H j jΔsol H j þ jT hm Δsol Sj
ð23Þ
ζ TS ¼
jT hm Δsol Sj : jΔsol H j þ jT hm Δsol Sj
ð24Þ
4. Results and discussions 4.1. Solubility data The experimental solubility (expressed in mole fraction and mass fraction) of racemic tartaric acid anhydrate or racemic tartaric acid monohydrate are presented in Table 3, in which “A” and “M” represent racemic tartaric acid anhydrate and racemic tartaric acid monohydrate at equilibrium, respectively. The mole fraction solubility values in water or ethanol are close to the data of Li et al. [1] and Zhang et al. [11]. Besides that, the solubility values in water are almost 10% higher than the ones measured by Mullin et al. (i.e. 2.11 × 10−2 at 293.15 K and 2.94 × 10−2 at 303.15 K) except at 313.15 K and 333.15 K [10]. Unfortunately, experimental solubility data in pure water are smaller by one order of magnitude than the ones reported by Apelblat et al. [9]. Nevertheless, it is worth noting that the solubilities of D-, L-, mesomeric and racemic tartaric acid in water, are quite different. The mole fraction solubilities of four forms in water, as compared at 293.15 K, can be arranged in the following series: racemic tartaric acid (xA = 0.02) b mesomeric tartaric acid (xA = 0.13) b D- or L-tartaric acid (xA = 0.14) [2,10]. This is because racemic crystals are indeed more stable (and denser) than their chiral counterparts. In order to verify this methodology, the gravimetric analysis method [3,7] and a direct titration method were implemented. Finally, these results measured by the gravimetric analysis method are consistent with the solubility data measured by acid–base method. On the other hand, racemic tartaric acid, of known mass, was titrated with standardized solutions of NaOH which was calibrated by potassium hydrogen phthalate centigrade. The relative deviations between true values and experimental values for different solvents are less than ± 0.1%. Therefore the data and methodology are considered reliable in this work. Physico-chemical properties of the solvent such as polarity, intermolecular interactions, and the ability of the solvent to form a hydrogen bond with the acid molecules play an important role in the dissolution process [36]. Water has a smaller molecular structure, stronger polarity with sizable dielectric constant (εr = 78.36) [14], large surface tension, and a high level of hydrogen bonding. It can be said that the solubility of organic acids were significantly influenced by water as a co-solvent. As shown in Table 3, the solubility data increase with an increase of temperature, and the racemic tartaric acid dissolves more in pure water than ethanol. This is because racemic tartaric acid can effectively break into the lattice structure of water, overcome electrostatic interaction with positive and negative ions and eventually form solvated ions [37]. Hence racemic tartaric acid solubility is highly miscible with water. In this experimental work, solubility decreases with the addition of ethanol by reducing the polarity of solvents which may indicate that the polarity of the solvent is an important factor governing the solubility of acid [38]. It is in accord with the general rule “like dissolves like”. The polar protic solvent molecules (such as ethanol) interact by forming strong hydrogen bonds with each other. In order to dissolve, the solute must break these bonds and replace them with bonds of similar strength [10]. In a general way, the hydroxyl groups of racemic tartaric acid could associate with ethanol to form hydrogen bonds. Nevertheless, the strength was significantly weakened by intermolecular hydrogen bonds with water molecules. Moreover, Ethanol as a polar
Fig. 1. Experimental solubility of racemic tartaric acid in ethanol + water versus the mass fraction of ethanol.
protic solvent has weak polarity with lower dielectric constant (εr = 24.3) [39]. The addition of ethanol gradually provides environments of lower dielectric constant, which makes it difficult for them to overcome electrostatic interaction and form solvated ions. Thus the solubility of the solute declines with the enhancement of the ethanol content. Fig. 1 presents that the solubility of racemic tartaric acid investigated in binary ethanol + water solvent mixtures decreases slowly at first and quickly at the high mass fraction of ethanol content (wC N 0.4) in ternary systems. It can be explained in the way that water molecules outnumber ethanol molecules (wC b 0.4), which makes water molecules easier to form intermolecular hydrogen bonds with racemic tartaric acid molecules. While wC N 0.4, the hydroxyl group from water will associate with the ethanol via hydrogen bonds more closely than that with racemic tartaric acid [40,41]. Therefore the solubility of racemic tartaric acid in mixtures decreases quickly with rising ethanol content in solvent mixtures. So to some extent, we can draw a conclusion that the polarity of solvents and the intermolecular hydrogen bonds play a leading role in the dissolution process. This conclusion is also verified by ideal model fraction solubility of racemic tartaric acid (xideal) which was calculated by Eq. (25) with Tm = 479.15 K [42]. The ideal mole fraction solubility exhibited in Table 3 are much lower than the experimental data obtained in all cases.
ln
1 xideal
¼
ΔSm T m −1 R T
ð25Þ
Table 4 Regression parameters of the modified Apelblat equation for racemic tartaric acid in water, ethanol and binary ethanol + water solvent mixtures at the temperature range of (293.15 to 318.15) K and pressure p = 0.1 MPa. wCa
A
B
C
104RMSDb
rc
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
65.35 496.1 298.3 97.21 143.4 219.4 26.79 −277.7 −483.9 −136.0 21.98
−5.504 × 103 −2.528 × 104 −1.618 × 104 −6.981 × 103 −8.904 × 103 −1.232 × 104 −3.573 × 103 1.031 × 104 1.974 × 104 3.944 × 103 −3.289 × 103
−8.867 −72.83 −43.47 −13.59 −20.55 −31.88 −3.235 42.01 72.62 20.79 −2.754
3.985 1.278 3.362 1.111 2.066 1.335 2.469 1.988 2.341 2.975 1.703
0.9993 0.9999 0.9993 0.9999 0.9997 0.9999 0.9995 0.9996 0.9991 0.9970 0.9986
a b c
wC is the mass fraction of ethanol in binary solvents. RMSD is the root-mean-square deviation. r is the coefficient of determination.
Q. Tan et al. / Journal of Molecular Liquids 216 (2016) 476–483
481
Table 5 Regression parameters of the λh equation for racemic tartaric acid in water, ethanol and binary ethanol + water solvent mixtures at the temperature range of (293.15 to 318.15) K and pressure p = 0.1 MPa. wCa 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 a b c
λ
h 3
0.7824 1.067 0.9638 0.9416 0.6915 0.6395 0.6216 0.5363 0.4082 0.2502 0.1460
3.413 × 10 2.746 × 103 2.938 × 103 2.980 × 103 3.702 × 103 3.899 × 103 4.067 × 103 4.681 × 103 5.981 × 103 9.232 × 103 1.530 × 104
104RMSDb
rc
5.955 7.293 5.859 2.276 3.159 6.156 2.526 3.758 6.957 3.143 2.421
0.9992 0.9968 0.9978 0.9997 0.9992 0.9988 0.9994 0.9984 0.9919 0.9966 0.9984
wC is the mass fraction of ethanol in binary solvents. RMSD is the root-mean-square deviation. r is the coefficient of determination.
Table 6 Regression parameters of the CNIBS/Redlich–Kister equation for racemic tartaric acid in water, ethanol and binary ethanol + water solvent mixtures at the temperature range of (293.15 to 318.15) K and pressure p = 0.1 MPa. T/K
S0
S1
S2
104RMSDa
rb
293.15 298.15 303.15 308.15 313.15 318.15
1.726 1.445 1.420 1.399 1.469 1.464
0.2598 0.6018 0.4983 0.4311 0.4175 0.3167
−0.9429 −0.8801 −0.7326 −0.4679 −0.7428 −0.3179
3.829 3.431 5.130 3.751 3.453 3.010
0.9968 0.9984 0.9976 0.9990 0.9994 0.9996
a b
RMSD is the root-mean-square deviation. r is the coefficient of determination.
4.2. Correlated results of three empirical equations The experimental solubility data of the racemic tartaric acid in water, ethanol, and binary ethanol + water solvent mixtures during the temperature range from (293.15 to 318.15) K, were fitted by the modified Apelblat, the λh and the CNIBS/R–K equations, respectively. Tables 4–6 show that the 104RMSD values in various ethanol + water solvent mixtures were observed in the range of 1.11–3.98 for the modified Apelblat equation, 2.28–7.29 for the λh equation and 3.01– 5.13 for the CNIBS/R–K equation, respectively. This result demonstrates that the calculated solubility of racemic tartaric acid in solvent mixtures agree well with experimental data, and the modified Apelblat equation correlates the solubility data best owing to its lowest value of the 104RMSD.
Fig. 2. Experimental values and predicted values of the NRTL model for the solubility data of racemic tartaric acid in binary mixtures of ethanol + water: (■) T = 293.15 K; (●) T = 298.15 K; (▲) T = 303.15 K; (▼) T = 308.15 K; (◄) T = 313.15 K; (►) T = 318.15 K; (−) predicted values of the NRTL model.
(293.15 to 333.15) K were used to fitting the interaction energy parameters of the NRTL model, which are summarized in Table 7. From Table 3, the calculated values are consistent with the experimental values in pure water and ethanol, so the obtained NRTL interaction parameters in this work are potential to predict the ternary phase equilibrium. Fig. 2 exhibits that the predicted values increase with the rising temperature and with a decrease in the concentration of ethanol. More accurately, the predicted values decrease slowly at the low mass fraction of ethanol content while a rapid reduction is seen between wC = 0.4 up to wC = 0.9. In addition, the trends of predicted values as a function of wC and T are in very good agreement with the experimental values. Although the predicted values are slightly greater than the experimental solubility, the relative deviations between them are mostly within ±5% (cf. Fig. 3), which is applicable in industrial crystallization process. These comparative results show that the NRTL model is well performed with good predictions for the phases in equilibrium and will provide a thermodynamic basis for the crystallization process of the racemic tartaric acid–ethanol–water system.
4.3. The NRTL prediction of the ternary systems In this work, the experimental solubility values of racemic tartaric acid in pure water and ethanol over the temperature range from
Table 7 The available interaction energy parameters of the NRTL model for the racemic tartaric acid–ethanol–water system.a System
a12
a21
b12
b21
Racemic tartaric acid(1)/water(2) Racemic tartaric acid(1)/ethanol(2) Ethanol(1)/water(2)
−1.665 −2.530 3.458
3.899 7.645 −0.8009
1000 1000 −586.1
−2123 −2794 246.2
a
a12, a21, b12, and b12 are parameters of the NRTL model.
Fig. 3. The relative deviation of experimental values and predicted values of the NRTL model: (□) wC = 0.1; (○) wC = 0.2; (△) wC = 0.3; (▽) wC = 0.4; (◇) wC = 0.5; (×) wC = 0.6; (☉) wC = 0.7; (+) wC = 0.8; (☆) wC = 0.9.
482
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Fig. 6. ΔsolH versus ΔsolS enthalpy–entropy compensation plot for dissolution process of racemic tartaric acid in binary ethanol + water solvent mixtures. Fig. 4. A van't Hoff plot of the mole fraction solubility (lnxA) of racemic tartaric acid in binary mixtures of ethanol + water against 104(1/T − 1/Thm) with a straight line to correlate the data: (□) wC = 0.1; (○) wC = 0.2; (△) wC = 0.3; (▽) wC = 0.4; (◇) wC = 0.5; (×) wC = 0.6; (☉) wC = 0.7; (+) wC = 0.8; (☆) wC = 0.9.
4.4. Thermodynamic quantities of solution The mean harmonic temperature (Thm) value calculated is just 305.41 K from (293.15 to 318.15) K. The values of ΔsolH, ΔsolS, ΔsolG, T ΔsolS, ζH and ζTS are listed in Table 8. It is clear to see that the main contributor to the molar Gibbs free energy change of solution is the positive molar enthalpy with ζH N 0.6, which demonstrates the solution process is endothermic predominance and the enthalpy to the Gibbs free energy change contributes more than the entropy. Furthermore, ζTS for the ideal solution process is greater than values obtained for some cases meaning that the entropy contribution is limited during the real solution process [43]. From Fig. 5, ΔsolH and T ΔsolS present a slight fluctuation with the mass fraction of ethanol in ternary systems due to the excess molar Gibbs free energy change of the solution process. The molar enthalpy change of solution is the integration of several kinds of interactions, therefore high value of the enthalpy signifies that high energy is required to overcome the cohesive force of the solute molecules and the solvent molecules in the solution process [11,44].
4.5. Enthalpy–entropy compensation of solution The chemical compensation has effect on the solubility of several compounds in solvent mixtures, which has been reported in some literatures [45–47]. In biochemical and chemistry literature, this analysis is attributed to the structural property of solvent water [48] and get a better understanding of dissolution process. Enthalpy–entropy compensation describes the behavior of ΔsolH and ΔsolS for a series of systems driven by changes in solvation. The making weighted graph of ΔsolH as a function of ΔsolS at the mean harmonic temperature permits the observation of the dissolution process according to the tendencies obtained. For concentration dependent enthalpy–entropy compensation is expressed by a linear relation, ΔsolH = a + bΔsolS. In this relation, a and b are constants. Obviously b, (the slope of the plot ΔsolH versus ΔsolS) has the dimension of temperature, while a (the intercept of this plot) has the dimension of free energy. In the case of the ethanolwater mixture (Fig. 6), the relationship is linear and ascendant, according to the following expression: Δsol H ¼ 11:66926 þ 0:24294Δsol Sðr ¼ 0:9799Þ:
High values of correlation coefficient certify the existence of compensation effect. As can be seen, there is a good linear correlation between the enthalpy and entropy changes, therefore a compensation effect exists.
Table 8 Thermodynamic functions relative to solution process of racemic tartaric acid in binary ethanol + water solvent mixtures at the mean temperature.
Fig. 5. The thermodynamic properties of the solution for racemic tartaric acid in ethanol + water as functions of wC: (◄): ΔsolH; (●): TΔsolS; (★): ΔsolG.
wCa
xCa
ΔsolH (kJ mol−1)
ΔsolS (J mol−1 K−1)
ΔsolG (kJ mol−1)
TΔsolS (kJ mol−1)
ζH
ζTS
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Ideal
0.042 0.089 0.143 0.207 0.281 0.370 0.477 0.610 0.779
25.3 24.3 23.6 22.3 21.5 21.4 20.9 20.0 19.9 22.0
54.4 51.2 49.2 44.8 42.4 41.4 38.8 34.1 31.4 43.8
8.68 8.63 8.61 8.59 8.60 8.78 9.08 9.54 10.4 8.30
16.6 15.6 15.0 13.7 12.9 12.6 11.8 10.4 9.59 13.4
0.604 0.608 0.611 0.620 0.625 0.629 0.639 0.657 0.675 0.622
0.396 0.392 0.389 0.380 0.375 0.371 0.361 0.343 0.325 0.378
a
wC and xC are the mass fractions of ethanol in binary solvents.
Q. Tan et al. / Journal of Molecular Liquids 216 (2016) 476–483
5. Conclusion In this work, the solubility of racemic tartaric acid in water, ethanol, and binary solvents of ethanol + water were measured in the temperature range of (293.15 to 318.15) K by acid–base titration method. The experimental results showed that the solubility of racemic tartaric acid in mixtures increased with rising temperature and decreased with increasing ethanol content. The experimental data were well fitted with the modified Apelblat, the λh and the CNIBS/R–K equations by adjusting the binary interaction parameters. By comparison of these three models in terms of 104RMSD, the modified Apelblat equation was more accurate than the others in this system. Moreover, the modeling results of the NRTL model provided good predictions with the experimental values as shown by the relative deviation which were within ±5%. The simplicity of the model, the robustness of the predictions, and the applicability of the model to the ternary system made this a useful thermodynamic framework for solubility modeling in support of crystallization process design. The thermodynamic properties, the molar enthalpy, entropy and Gibbs free energy changes of solution were calculated by the van't Hoff equation. Values of the thermodynamic parameters indicated that the solution process was endothermic and the main contributor to the molar Gibbs free energy change of solution was the positive molar enthalpy. In this context, the linear enthalpy–entropy compensation effect has been observed for the studied system, and the compensation temperature along with entropic parameter is reported. For solvent mixtures, the linear plot means the enthalpy–entropy compensation is in the dissolution processes. List of symbols A, B, C ΔCP f S1 f L1 Gij ΔG ΔsolG ΔfusHm ΔfusHt ΔsolH Ka1 Ka2 n p R RING RMSD r S0, S1, S2 ΔfusSm ΔsolS SP2 SP3 T Thm Tm Tt
regression parameters of the modified Apelblat equation the heat capacity change (J mol−1 K−1) the fugacity of solute in the solid phase the fugacity of solute in the supercooled liquid a dimensionless equation parameter the molar Gibbs free energy change of the solid (J mol−1) the molar Gibbs free energy change of the solution process (J mol−1) the molar enthalpy change of fusion of solute at melting point (J mol−1) the molar enthalpy change of fusion of solute at triple point (J mol−1) the molar enthalpy change of the solution process (J mol−1) first acidity constant of racemic tartaric acid second acidity constant of racemic tartaric acid number of experimental points pressure (Pa) gas constant (J mol−1 K−1) the number of fused-ring systems the root-mean-square deviation coefficient of determination regression parameters of the CNIBS/R–K equation the molar entropy change of fusion of solute at melting point (J mol−1 K−1) the molar entropy change of the solution process (J mol−1 K−1) the number of sp2 chain atoms the number of sp3 chain atoms absolute temperature (K) the mean harmonic temperature (K) melting point (K) the absolute temperature of triple point (K)
xA wA wC
483
mole fraction solubility of racemic tartaric acid mass fraction solubility of racemic tartaric acid and ethanol the mass fraction of ethanol
Greek letters αij γ1 γi δ ζH ζTS λ, h
a measure of the non-randomness of systems the activity coefficient of a solid solute the activity coefficient of the component i the number of components the contribution of enthalpy to the standard Gibbs energy the contribution of entropy to the standard Gibbs energy regression parameters of the λh equation
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