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Measurement and correlation for solubilities of isophthalic acid and m-toluic acid in binary acetic acid + water and acetic acid + m-xylene solvent mixtures
Journal of Molecular Liquids 262 (2018) 549–555
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Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq
Measurement and correlation for solubilities of isophthalic acid and m-toluic acid in binary acetic acid + water and acetic acid + m-xylene solvent mixtures Bao Tao a, Zhipeng Sheng a, Weiping Luo a,⁎, Xiaoxiao Sheng a, Qinbo Wang b,⁎ a b
Department of Chemical Engineering, Hunan University, Changsha, 410082, Hunan, PR China Jiangxi Keyuan Boipharm Co. Ltd., Jiujiang, 332000, Jiangxi, PR China
a r t i c l e
i n f o
Article history: Received 19 March 2018 Received in revised form 12 April 2018 Accepted 16 April 2018 Available online 24 April 2018 Keywords: Solubility Isophthalic acid m-Toluic acid Water Acetic acid m-Xylene
a b s t r a c t In this study, the solubilities of isophthalic acid (IPA) and m-toluic acid (m-TA) in binary acetic acid (HAc) + (water or m-xylene) solvent mixtures were measured by using a synthetic method at atmospheric pressure. The mole fraction of HAc in the corresponding solvent mixtures ranges from 0.0000 to 1.000. The measured data show that within the temperature range studied, the solubilities of IPA and m-TA increase with increasing temperature at constant solvent composition. At a given temperature, the solubilities of IPA and m-TA decrease with the decreasing mole fraction of HAc in HAc + water solvent mixtures; whereas the “maximum-solubility effect” was observed in HAc + m-xylene solvent mixtures, and that with the mole fraction of HAc at 0.8761 has the best dissolving capacity for IPA at constant temperature. The experimental solubilities were well correlated by both the nonrandom two-liquid (NRTL) and Apelblat equations, and the calculated solubilities agree satisfactorily with the measured results. Furthermore, the thermodynamic functions including dissolution enthalpy, entropy and Gibbs energy were obtained from the solubility data by using the van't Hoff equation. © 2018 Elsevier B.V. All rights reserved.
1. Introduction Isophthalic acid (IPA) is a commercially important aromatic compound and widely applied in synthesis of acid-modified copolyester, surface coating, and unsaturated polyester [1]. Currently, the majority of IPA is produced by liquid-phase catalytic oxidation of m-xylene under the Co–Mn–Br catalyst system with air in a conventional oxidation reactor [2–4]. During the oxidation process, HAc is used as the solvent, which is a more environmentally friendly way than using nitric acid as an oxidant [5]. In this technique, m-xylene is oxidized by air and converted into IPA; water and m-TA are the main byproducts. Sequentially, the reaction mixtures comprising crude IPA, m-TA products and mother liquor must be separated to produce pure IPA. Usually, crystallization is used in the relevant purification process for obtaining products with high purity [6]. It is well-known that solubility data is indispensable for designing the separation equipment, as well as for setting the relevant operating conditions. From the literature survey results, some reports on the solubilities of IPA in pure water [7–11] and HAc [11–13] could be found. Many scientists have studied the solubility of IPA in HAc + water solvent mixtures with the mole fraction of HAc ranged from 0.034 to 0.739 [9,11–13]. ⁎ Corresponding authors. E-mail addresses: [email protected], (W. Luo), [email protected] (Q. Wang).
https://doi.org/10.1016/j.molliq.2018.04.086 0167-7322/© 2018 Elsevier B.V. All rights reserved.
Unfortunately, no reports on the solubility of IPA in HAc + m-xylene solvent mixtures are available. Meanwhile, only a few reports on the solubility of m-TA in pure water [14–17] could be found. Furthermore, there are no reports or publications for the solubility of m-TA in HAc + water solvent mixtures, let alone that in HAc + m-xylene solvent mixtures. Thus, it is necessary to measure the solubilities of IPA and m-TA in the aforementioned solvent mixtures. The aim of this work is to measure the solubilities of IPA and m-TA in the HAc + water mixtures and HAc + m-xylene mixtures at different temperature by using the synthetic method. The reliability of the experimental solubility data will be verified by comparison with the literature data. Moreover, the experimental solubility data will be correlated with the nonrandom two-liquid (NRTL) [18] and modified Apelblat [19,20] equations, and the equation parameters are expected to be obtained. Thermodynamic functions including dissolution enthalpy, entropy and Gibbs energy will be calculated from the solubility data by using the van't Hoff equation. 2. Experimental 2.1. Materials IPA (mass fraction N 0.990) and m-TA (mass fraction N 0.980) were purchased from Adamas Reagent Co., Ltd. and Tokyo Chemical Industry
550
B. Tao et al. / Journal of Molecular Liquids 262 (2018) 549–555 Table 1 Suppliers and mass fraction purity of the chemicals. Components
Suppliers
Mass fraction purity
Analysis method
Isophthalic acid m-Toluic acid Acetic acid m-Xylene Water
Adamas Reagent Co., Ltd. Tokyo Chemical Industry Co., Ltd. Sinopharm Chemical Reagent Co. Sinopharm Chemical Reagent Co. Hangzhou Wahaha Group Co.
N0.990 N0.980 N0.990 N0.990 N0.999
HPLCa HPLCa GCb GCb
a b
High-performance liquid chromatograph. Gas chromatograph.
Co., Ltd., respectively. Acetic acid (mass fraction N 0.990) and mxylene (mass fraction N 0.990) were purchased from Sinopharm Chemical Reagent Co. Purified water produced by Hangzhou Wahaha Group Co was bought from supermarket (596 mL each bottle) and had the measured resistivity of 18.2 MΩ·cm. The mass fraction of IPA and m-TA were checked by high-performance liquid chromatography (HPLC). The purities of HAc and m-xylene were checked by gas chromatograph (GC) and no impurity peaks were detected. All the chemicals were used in the experiments without further purifications. The detailed suppliers and mass fraction of the used chemicals are listed in Table 1. 2.2. Apparatus and procedures The solid-liquid equilibrium (SLE) experiment was carried out by a synthetic method. The details of apparatus and procedures used in this work have been described in detail by Wang et al. [21,22], Chen et al. [23] and Luo et al. [24–29], which have good use for reference to this work. Briefly, the apparatus is comprised of a solid-liquid equilibrium cell, a magnetic stirring system, a temperature-controlling and measurement system, and a laser-detecting system. The experiment was carried out in a 125 mL equilibrium cell that was heated in a thermostatic water bath. Continuous stirring was achieved by the magnetic stirrer system, and the dissolution temperature of a (solid + liquid) mixture of known composition was determined by the laser-detecting system. In the experiment, the equilibrium cell can let the laser beam to pass through it, and the intensity of laser beam was recorded in real time by a computer in terms of the photovoltage. In each experiment, predetermined amounts of solvent and solute were accurately weighed by an electronic balance (type AL204, Mettler Toledo instrument Co. Ltd.,) and added into the equilibrium cell. Then, the cell was put into a thermostatic water bath, and the mixture was heated very slowly (at b0.2 K·h−1 near the equilibrium temperature) with continuous stirring. At the early stages of the experiment, the laser beam was partly passed the solvent-solute mixture due to the existence of unsolved particles of solute in the solution. Thus, the intensity of the laser beam passing through the mixture was lower. The intensity increased gradually with the decrease of amount of solute undissolved. At last when crystal disappeared, the intensity of the laser beam reached a maximum value and kept steady, the SLE was considered to be reached. The temperature corresponding to the maximum intensity was taken as SLE temperature of the mixture. The mole fraction of solubility (x1) of IPA or m-TA was calculated according to Eq. (1), and the mole fraction of HAc (x2, solv) in binary HAc + water or HAc + m-xylene solvent mixtures was calculated based on Eq. (2). m1, m2 and m3 denote the mass of IPA or m-TA, HAc and water or m-xylene, respectively. M1, M2 and M3 represent the molecular weight of IPA or m-TA, HAc and water or m-xylene, respectively. m1 M1 x1 ¼ m m2 m3 1 þ þ M1 M2 M3
ð1Þ
m2 M2
x2;solv ¼ m m3 2 þ M2 M3
ð2Þ
2.3. Verification of the experimental methods To verify the reliability of the measured solubility data, comparisons have been made between the experimental solubilities data and those available in the literature. The experimental solubilities data together with the literature data [7–17] are illustrated in Figs. 1–3, as can be seen, the measured solubilities data of IPA and m-TA in pure water and IPA in pure HAc have good agreement with the literature data, which indicates the measured solubilities data are convincing and accurate. 3. Results and discussion 3.1. Experimental results In this work, the measured solubilities of IPA and m-TA in HAc + water and HAc + m-xylene mixtures are summarized in Tables S1– S4, and plotted in Figs. 4–7, respectively. However, the solubility data of IPA in m-xylene cannot be obtained because IPA is not detectably soluble in m-xylene. From Figs. 4–7, it can be seen that the solubilities of IPA and m-TA in HAc + water and HAc + m-xylene mixtures increase with the increase of temperature at constant solvent composition. Furthermore, it can be concluded from Figs. 4 and 6 that the effect of solvent composition on the solubility of IPA and m-TA in HAc + water mixtures is apparent. Within the temperature range studied, the solubilities of IPA and m-TA in pure HAc are the highest, and it decreases with an increasing concentration of water in the mixed HAc + water at constant temperature. Fig. 5 gives an interesting result that the solvent mixtures with HAc mole fraction of 0.8761 has the best dissolving capacity for IPA within the solvent composition range of the measurements. This phenomenon can be rightly explained by the “maximum solubility effect” predicted by the Hildebrand-Scatchard's theory [30]. Chen et al. [23] verified the theory by experimentally measuring the solubility of terephthalic acid in the mixture of acetic acid and water, and Wang et al. [22] also verified the theory by experimentally measuring the solubility of benzoic acid in the mixtures of methylbenzene + benzyl alcohol and methylbenzene + benzaldehyde. A similar conclusion can be drawn from them works. Fig. 7 shows that the binary solvent mixtures have better dissolving capacity for m-TA than pure HAc or m-xylene. However, the effect of solvent composition on the solubilities of m-TA in HAc + m-xylene mixtures is not apparent. In order to illustrate it more clearly, the solubility of m-TA in HAc + m-xylene mixtures at (293.15–338.15) K were calculated by the Apelblat model (Eq. (8)) by using the obtained model parameters listed in Table S5, and the results are illustrated in Fig. 8. As shown in Fig. 8, below 318.15 K, the solubility of m-TA increases with the increase of mole fraction of HAc in HAc + mxylene mixtures solvent mixtures at constant temperature, and then reaches the maximum solubility at the mole fraction of HAc at 0.5410. When the mole fraction of HAc is bigger than 0.5410, the solubility of
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Fig. 1. Solubilities x1 of IPA in water: ●, measured in this work; □, Ref. [7]; ○, Ref. [8]; Δ, Ref. [9]; ◁, Ref. [10]; ◇, Ref. [11].
Fig. 3. Solubilities x1 of m-TA in water: ●, measured in this work; □, Ref. [14]; ○, Ref. [15]; Δ, Ref. [16]; ∇, Ref. [17].
m-TA decreases with the increase of mole fraction of HAc. However, above 318.15 K, the solubility of m-TA reaches the maximum at the HAc mole fraction of 0.7262 at constant temperature. Similarly, the result also can be explained by the “maximum solubility effect”.
transition. Tfus and Ttrs are the fusion temperature and transition temperature. R is the universal gas constant, and T is the absolute temperature. Because activity coefficient (γ1) depends on the mole fraction and temperature, Eq. (4) must be solved iteratively. For the calculation of activity coefficient, the NRTL activity coefficient model was employed in this work as [18]:
3.2. Correlation of experimental data 3.2.1. NRTL correlation The SLE can be approximated in a general manner by the Eq. (3) that involves such properties of pure solute as enthalpy of fusion, melting point, and so forth [23,31]. Δfus H 1 1 Δtrs H 1 1 ln ðγ1 x1 Þ ¼ − − − − R T T fus R T T trs
ð3Þ
For the four studied systems, the solid-solid phase does not occur, and thus the Eq. (3) can be simplified to the form shown as Eq. (4). ln ðγ1 x1 Þ ¼ −
Δfus H 1 1 − T T fus R
P3 ln γi ¼
j¼1 τ ji Gji x j P3 k¼1 Gki xk
τij ¼ aij þ
þ
3 X j¼1
Gij x j
P3
k¼1
Gkj xk
P3 τij −
k¼1 τ kj Gkj xk P3 k¼1 Gkj xk
!
bij ; Gij ¼ exp −α ij τ ij ; α ij ¼ α ji ; τ ij ≠τji ; τii ¼ 0 T
ð5Þ
ð6Þ
where, xi and γi denote the mole fraction and the activity coefficient of component i, respectively. aij and bij are the parameters needed to be regressed. The term αij in the NRTL model was fixed at 0.3, as proposed by Prausnitz [30] according to the molecular polarity.
ð4Þ
In Eqs. (3) and (4), γ1 is the activity coefficient of solute, and x1 is the real mole fraction of solute in solution. ΔfusH and ΔtrsH are the molar fusion enthalpy of solute and molar enthalpy of solid-solid phase
Fig. 2. Solubilities x1 of IPA in HAc: ●, measured in this work; ◇, Ref. [11]; ▷, Ref. [12]; ⊕, Ref. [13].
Fig. 4. Mole fraction solubility (x1) of IPA depending on temperature T and the mole fraction of HAc (x2, solv) in (HAc + water) solvent mixtures: ●, x 2, solv = 0.0000; □, x 2, solv = 0.0698; ☆, x 2, solv = 0.1667; ◇, x 2, solv = 0.3104; ▲, x 2, solv = 0.5455; ▼, x2, solv = 1.000. Scatter, experimental data; — (solid line), NRTL equation correlated, the averaged relative deviation is 1.73%; — (dotted line), Apelblat equation correlated, the averaged relative deviation is 2.23%.
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Fig. 5. Mole fraction solubility (x1) of IPA depending on temperature T and the mole fraction of HAc (x2, solv) in (HAc + m-xylene) solvent mixtures: ●, x2, solv = 0.3067; □, x2, solv = 0.5419; ☆, x2, solv = 0.7263; ◇, x2, solv = 0.8761; ▲, x2, solv = 1.000. Scatter, experimental data; — (solid line), NRTL equation correlated, the averaged relative deviation is 1.73%; — (dotted line), Apelblat equation correlated, the averaged relative deviation is 0.715%.
Fig. 7. Mole fraction solubility (x1) of m-TA depending on temperature T and the mole fraction of HAc (x2, solv) in (HAc + m-xylene) solvent mixtures: ●, x2, solv = 0.0000; □, x2, solv = 0.3066; ☆, x2, solv = 0.5410; ◇, x2, solv = 0.7262; ▲, x2, solv = 0.8760; ▼, x2, solv = 1.000. Scatter, experimental data; — (solid line), NRTL equation correlated, the averaged relative deviation is 2.19%; — (dotted line), Apelblat equation correlated, the averaged relative deviation is 0.667%.
In order to calculate the solubility, the molar fusion enthalpy of solute (ΔfusH) and the fusion temperature (Tfus) are required. ΔfusH and Tfus used in this work for IPA are 48,194.3 J·mol−1 and 621.2 K [32], and that for m-TA are 15,730 J·mol−1 and 383 K [33], which are acquired from the literature. By using model Eqs. (3)–(6), the measured solubilities data for the four studied systems were correlated and shown in Tables S1–S4. The optimized model parameters are listed in Table S6. The regression of model parameters was performed using the Matlab program, and the procedure is based on the Simplex approach proposed by Nelder and Mead [34]. Function fminsearch in the optimization toolbox of Matlab (Mathwork, MA) uses the Nelder-Mead Simplex approach and can be
applied for the minimization of the objective function, which is the averaged relative deviation (ARD) between experimental and calculated solubility defined in this work as:
Fig. 6. Mole fraction solubility (x 1 ) of m-TA depending on temperature T and the mole fraction of HAc (x 2, solv ) in (HAc + water) solvent mixtures: ●, x 2, solv = 0.0000; □, x2, solv = 0.0699; ☆, x 2, solv = 0.1669; ◇, x2, solv = 0.3104; ▲, x2, solv = 0.5456; ▼, x2, solv = 1.000. Scatter, experimental data; — (solid line), NRTL equation correlated, the averaged relative deviation is 2.19%; — (dotted line), Apelblat equation correlated, the averaged relative deviation is 1.45%.
RDi ¼
n xci −xi 1X 100; ARD ¼ absðRDi Þ n i¼1 xi
ð7Þ
where xci and xi are the ith calculated and experimental solubility, n is the total number of experimental points. The corresponding RD are presented in Tables S1–S4, respectively. The obtained NRTL model parameters and the averaged relative deviation (ARD) defined in Eq. (7) are listed in Table S6. For comparison, the calculated data along with the experimental data are illustrated in Figs. 4–7. As can be seen from these figures, the calculated data have good agreement with the experimental data. It indicates that the NRTL model was successfully applied to
Fig. 8. Solubilities (x1) of m-TA (1) in HAc (2) + m-xylene (3) solvent mixtures: ■, 293.15 K; ●, 303.15 K; ▲, 313.15 K; ▼, 318.15 K; ◆, 323.15 K; ◄, 328.15 K; ►, 338.15 K. x2, solv is the mole fraction of HAc in HAc + m-xylene solvent mixtures.
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correlate the solubilities of IPA and m-TA in binary HAc + water and HAc + m-xylene solvent mixtures.
In the special case of least-squares estimation with normal distributed errors, apart from an additive constant, AIC can be simplified to:
3.2.2. Modified Apelblat correlation The modified Apelblat equation was also used to correlate the experimental solubility data in this work. The form of equation proposed by Apelblat is shown as
AIC ¼ NlnðRSS=NÞ þ 2k
ln x1 ¼ A þ
B þ C ln T T
ð8Þ
In Eq. (8), x1 is the mole fraction of IPA or m-TA, T is the absolute temperature, A, B and C are the empirical model parameters. In order to use Eq. (8) to correlate the solubility of IPA and m-TA at various solvent compositions, the following empirical correlations were adopted [35–37]. C ¼ C 0 þ C 1 x2 þ C 2 x22 þ C 3 x32 þ C 4 x42
ð9Þ
where Ai, Bi and Ci are model parameters, x2 is the mole fraction of water or m-xylene in HAc + water or HAc + m-xylene mixtures, respectively. Once again, the measured solubilities data for the four studied systems were correlated by using model Eqs. (8) and (9), and the model parameters were optimized. The optimum algorithm used in the parameter estimation program was same as to that applied in the NRTL correlation, and the objective function was chosen as that defined in Eq. (7). The calculated results with Apelblat model along with the corresponding RD are listed in Tables S1–S4, and the obtained model parameters and the ARD are given in Table S5. For comparison, the calculated results are also plotted in Figs. 4–7, respectively. It clearly shows that a good agreement between the experimental solubilities with that calculated. Therefore, the modified Apelblat equation is suitable to correlate the solubilities of IPA and m-TA in binary HAc + water and HAc + mxylene solvent mixtures. 3.2.3. Evaluation of thermodynamic models In order to choose the best model for isophthalic acid (IPA) and mtoluic acid (m-TA), the Akaike Information Criterion (AIC) [38–41] was used to compare the applicability of the Apelblat model and NRTL model. In general, the model with the low value of AIC can be the best-fit model. The AIC is given as follow: AIC ¼ −2 ln LðθÞ þ 2k
ð10Þ
where L(θ) and k represent the maximized likelihood value and the number of estimable parameters for the evaluated model, respectively.
RSS ¼
N X
ð11Þ
ðxi −xci Þ2
ð12Þ
i¼1
where N is the number of observations; RSS is the residual sum of squares; xi and xci are the experimental and calculated values of solubility for solute, respectively. The calculated results of AIC for the three models are shown in Table 2. Akaike weights, ωi, are employed to determine the best model with highest Akaike weights in order to illustrate the results more intuitively, which is expressed as: ωi ¼ expððAIC min −AIC i Þ=2Þ PM i¼1 expððAIC min −AIC i Þ=2Þ
ð13Þ
where M is the number of the selected models in the comparison; AICmin is the minimum value of AIC for the selected models; AICi is the AIC value of the ith model. The values of Akaike weights are also displayed in Table 2. From Table 2,for isophthalic acid (IPA) and m-toluic acid (m-TA) in binary acetic acid (HAc) + (water or m-xylene) system, the low AIC value and the high Akaike weight value indicate that the Apelblat equation could be used to correlate the solubility better between the two models. 3.3. Thermodynamic functions of solution Thermodynamic properties are very important for further studies. The thermodynamic functions of solution such as dissolution enthalpy, entropy and Gibbs free energy are useful to understand the dissolution process of IPA and m-TA in HAc + water and HAc + m-xylene solvent mixtures. Thus, they were evaluated from the measured solubility data by van't Hoff analysis, which is shown as [42]. ΔH sol ∂ ln_ x1 ¼− R ∂ð1=T−1=T hm Þ
! ð14Þ
where R is the gas constant; Thm is the mean harmonic [calculated as: Thm = n/∑ni=1(1/T), where n is the number of temperatures studied], the corresponding Thm are presented in Tables S7, respectively. The logarithm of mole fraction of the solute (ln x1) is linearly related to the
Table 2 Value of the akaike information criterion of the apelblat model and the modified NRTL model for isophthalic acid (IPA) and m-toluic acid (m-TA) in binary acetic acid (HAc) + (water or mxylene) mixed solvents. Models
RSSa
N
Parameters
AICb
e((AICmin-AICi)/2)c
Akaike weight ωid
IPA in HAc + water NRTL model Apelblat model
1.93563e−08 1.76809e−08
10 10
4 3
−192.628 −195.534
0.233944 1
0.18959 0.81041
IPA in HAc + m-xylene NRTL model Apelblat model
3.11444e−08 9.17849e−09
10 10
4 3
−187.872 −202.09
0.000817824 1
0.000817156 0.999183
m-TA in HAc + water NRTL model Apelblat model
0.00089 0.000122
10 10
4 3
−85.265 −107.165
1.75569e−05 1
1.75566e−05 0.999982
m-TA in HAc + m-xylene NRTL model Apelblat model
0.002345 0.000405
10 10
4 3
−75.5796 −95.1532
5.61875E−05 1
5.61843E−05 0.999944
a b c d
RSS is the residual sum of squares. AIC is the Akaike Information Criterion value for each model. AICmin is the minimum value of the compared models, and AICi is the value of the ith model. Akaike weight is the probabilities of each model within the interval [0,1] and they sum to 1.
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reciprocal of the absolute temperature (1/T). The slope of the plot ln x1 against (1/T − 1/Thm) is the value of −ΔHsol/R. ΔHsol was the mean value of the dissolution enthalpy over the considered temperature range. The Gibbs free energy change for the solution process (ΔGsol) was calculated by the following equations [43]. ΔGsol ¼ −RT hm intercept
ð15Þ
in which, the intercept used is the one obtained in the analysis by treatment of ln x1 as a function of (1/T − 1/Thm). Finally, the entropic change for solution process (ΔSsol) can be obtained by the following equation ΔSsol ¼
ΔH sol −ΔGsol T hm
ð16Þ
The thermodynamic functions of solution ΔHsol, ΔGsol, ΔSsol, for IPA and m-TA in HAc + water and HAc + m-xylene solvent mixtures, are summarized in Tables S7. The relative contributions of enthalpy %ζH and entropy %ζTS in the dissolution process were calculated by the following equations [44]. %ξH ¼
jΔH sol j 100 jΔH sol j þ jTΔSsol j
ð17Þ
%ξTS ¼
jTΔSsol j 100 jΔH sol j þ jTΔSsol j
ð18Þ
The calculated values of %ζH and %ζTS are also given in Tables S7. The results indicate that in all case the main contributor to Gibbs free energy of the dissolving process of IPA or m-TA in HAc + water and HAc + mxylene solvent mixtures is the enthalpy. Moreover, as shown in Tables S7, the values of ΔHsol and ΔGsol are positive at the measured temperature, which shows that the four dissolving process are endothermic and not spontaneous. From Table S7, in the dissolution process of IPA in HAc + water, it can be seen that the ΔGsol decreases with the increase of mole fraction of HAc in HAc + water solvent mixtures. It indicates that less energy is required to overcome the cohesive force between the solute IPA and the solvent in the dissolving process when HAc added into the solvent system. From Table S7, in the dissolution process of IPA in HAc + m-xylene, one can see that when the mole fraction of HAc is b0.8761, ΔGsol decreases gradually with the increase of mole fraction of HAc; when the mole fraction of HAc is N0.8761, the value of ΔGsol increases with the HAc mole fraction increasing. In other words, when the mole fraction of HAc is 0.8761, the cohesive force between the solute IPA and the solvent reaches a minimum. From Table S7, in the dissolution process of m-TA in HAc + water, ΔGsol for m-TA in HAc + water solvent mixtures decreases with the increasing mole fraction of HAc. Similar to the results for the IPA in HAc + water solvent mixtures, the results demonstrate that when HAc is added into the solvent system, less energy is required to overcome the cohesive force between the solute m-TA and the solvent in the dissolving process. As can be seen from Table S7, in the dissolution process of m-TA in HAc + m-xylene, when the mole fraction of HAc is b0.5410, ΔGsol decreases gradually with the increase of mole fraction of HAc and reaches a minimum with HAc mole fraction of 0.5410; when the mole fraction of HAc is N0.5410, the value of ΔGsol increases with the HAc mole fraction increasing. 4. Conclusions In this work, the solubilities of IPA and m-TA in HAc + water and HAc + m-xylene solvent mixtures at atmospheric pressure have been measured by a synthetic method. The solubilities of IPA and m-TA in
the investigated solvent mixtures increase with the increase of temperature at constant solvent composition. The effects of mole fraction of HAc in the solvent mixtures at 0.0000 to 1.000 on the solubility were studied. The solubility of IPA and m-TA in HAc + water mixtures increase with the increasing mole fraction of HAc at constant temperature. Meanwhile, it can be found that the HAc + m-xylene solvent mixtures with the mole fraction of HAc at 0.8761 has the highest dissolving capacity for IPA at constant temperature. The binary HAc + mxylene solvent mixture has better dissolving capacity for m-TA than pure HAc or m-xylene. However, the effect of solvent composition on the solubilities of m-TA in HAc + m-xylene mixtures is not apparent. The measured solubility data were correlated by applying both the NRTL equation and the modified Apelblat equation. The calculated solubilities of IPA and m-TA based on the aforementioned equations agree satisfactorily with the experimental results. In addition, for isophthalic acid (IPA) and m-toluic acid (m-TA) in binary acetic acid (HAc) + (water or m-xylene) system, the low AIC value and the high Akaike weight value indicate that the Apelblat equation could be used to correlate the solubility better between the two models. Finally, the thermodynamic functions including dissolution enthalpy, entropy and Gibbs energy were obtained from the solubility data by using the van't Hoff equation. The results indicate that the dissolution process is not spontaneous and endothermic. The obtained thermodynamic functions are helpful to understand the dissolution process of IPA and m-TA in HAc + water and HAc + m-xylene solvent mixtures. The measured solubility data could be applied for the separation and purification of IPA and m-TA in the related process. Acknowledgments This work was supported by the Fundamental Research Funds for the Central Universities and the National Nature Science Fund (21302049). Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.molliq.2018.04.086. References [1] G.G. Zhang, C.Y. Zhu, J.L. Li, Y.G. Ma, Production technology and application of isophthalic acid, China Synth. Fiber Ind. 28 (2005) 43–45. [2] W. Partenheimer, Methodology and scope of metal/bromide autoxidation of hydrocarbons, Catal. Today 23 (1995) 69–158. [3] Q.B. Wang, Y.Z. Zhang, Y.W. Cheng, X. Li, Reaction mechanism and kinetics for the liquid-phase catalytic oxidation of meta-xylene to meta-phthalic acid, AIChE J 54 (2008) 2674–2688. [4] H. Ly, S. Wu, N. Liu, X. Long, W. Yuan, A study on the m-xylene oxidation to isophthalic acid under the catalysis of bromine-free homogeneous catalytic system, Chem. Eng. J. 172 (2011) 1045–1053. [5] Y.W. Cheng, MC Liquid-phase Catalytic Oxidation of Hydrocarbonsto Polycarboxylic Acids(Dissertation) Zhejiang University, China's Hangzhou, 2004. [6] Q.B. Wang, Reactive Crystallization in the Oxidation of para-Xylene(Dissertation) Zhejiang University, China's Hangzhou, 2006. [7] N.Y. Han, L. Zhu, L.S. Wang, R.N. Fu, Aqueous solubility of m-phthalic acid, o-phthalic acid and p-phthalic acid from 298 to 483 K, Sep. Purif. Technol. 16 (1999) 175–180. [8] L. Zhu, L.S. Wang, Solubility of o-phthalic, m-phthalic acid and p-phthalic acid in water, J. Ind. Eng. Chem. 16 (1999) 52–54. [9] B.W. Long, L.S. Wang, Crystallization thermodynamics of m-phthalic acid in water and aqueous acetic acid solutions, J. Biomed. Instrum. Technol. 25 (2005) 749–752. [10] L.S. Wang, B.W. Long, Aqueous solubilities of 1, 3-benzenedicarboxylic acid from 301.45 to 463.15 K, Comput. Appl. Chem. 22 (2005) 477–480. [11] Y.W. Cheng, L. Huo, X. Li, Solubilities of isophthalic acid in acetic acid + water solvent mixtures, Chin. J. Chem. Eng. 21 (2013) 754–758. [12] L. Feng, Q.B. Wang, X. Li, Solubilities of 1,3,5-benzenetricarboxylic acid and 1,3benzenedicarboxylic acid in acetic acid + water solvent mixtures, J. Chem. Eng. Data 53 (2008) 2501–2504. [13] Y. Li, Determination and Correlation of Solubilities of Components Involving in TA Manufacture Residues with Aqueous HAc and Ethanol as Solvent(Dissertation) Tianjin University, China's Tianjin, 2006. [14] L.E. Strong, R.M. Neff, I. Whitesel, Thermodynamics of dissolving and solvation processes for benzoic acid and the toluic acids in aqueous solution, J. Solut. Chem. 18 (1989) 101–114.
B. Tao et al. / Journal of Molecular Liquids 262 (2018) 549–555 [15] Q.Z. Jia, P.S. Ma, H. Zhou, S.Q. Xia, Q. Wang, Y. Qiao, The effect of temperature on the solubility of benzoic acid derivatives in water, Fluid Phase Equilib. 250 (2006) 165–172. [16] S. Sugunan, B. Thomas, Salting coefficients of 2-, 3-, and 4-methylbenzoic acids, J. Chem. Eng. Data 38 (1993) 520–521. [17] N.V. Sidgwick, W.J. Spurrell, T.E. Davies, The solubility of the nitrophenols and other isomeric disubstitution products of benzene, J. Chem. Soc. 107 (1915) 1202–1213. [18] H. Renon, J.M. Prausnitz, Local compositions in thermodynamic excess functions for liquid mixtures, AIChE J 14 (1968) 135–144. [19] A. Apelblat, E. Manzurola, Solubilities of o-acetylsalicylic, 4-aminosalicylic, 3,5dinitrosalicylic, and p-toluic acid, and magnesium-DL-aspartate in water from T = (278 to 348) K, J. Chem. Thermodyn. 31 (1999) 85–91. [20] E. Manzurola, A. Apelblat, Solubilities of l-glutamic acid, 3-nitrobenzoic acid, p-toluic acid, calcium-L-lactate, calcium gluconate, magnesium-DL-aspartate, and magnesium-L-lactate in water, J. Chem. Thermodyn. 34 (2002) 1127–1136. [21] H. Wang, Q.B. Wang, Z.H. Xiong, C.X. Chen, B.W. Shen, Solubilities of benzoic acid in binary (benzyl alcohol + benzaldehyde) solvent mixtures, J. Chem. Thermodyn. 83 (2015) 61–66. [22] H. Wang, Q.B. Wang, Z.H. Xiong, C.X. Chen, B.W. Shen, Solubilities of benzoic acid in binary methylbenzene + benzyl alcohol and methylbenzene + benzaldehyde solvent mixtures, J. Chem. Eng. Data 60 (2015) 643–652. [23] M.M. Chen, P.S. Ma, Solid−liquid equilibria of several systems containing acetic acid, J. Chem. Eng. Data 49 (2004) 756–759. [24] W.P. Luo, X.Q. Li, D. Ruan, D.W. Liu, K.L. Xie, Z.K. Chen, Measurement and correlation for solubilities of adipic acid, glutaric acid and succinic acid in acetic acid + cyclohexanone mixtures, J. Chem. Eng. Data 62 (2017) 1269–1277. [25] W.P. Luo, D. Ruan, D.W. Liu, K.L. Xie, X.Q. Li, C.C. Guo, Measurement and correlation for solubilities of adipic acid in acetic acid + ε-caprolactone mixtures and cyclohexanone + ε-caprolactone mixtures, J. Chem. Eng. Data 61 (2016) 2474–2480. [26] X.X. Sheng, W.P. Luo, Q.B. Wang, Determination and correlation for the solubilities of succinic acid in cyclohexanol + cyclohexanone + cyclohexane solvent mixtures, J. Chem. Eng. 63 (2018) 801–811. [27] W.P. Luo, X.Q. Li, D. Ruan, K.L. Xie, B. Tao, C.C. Guo, Measurement and correlation for solubilities of succinic acid and glutaric acid in ε-caprolactone + acetic acid mixtures and ε-caprolactone + cyclohexanone mixtures, J. Chem. Eng. Data 63 (2018) 298–304. [28] W.P. Luo, K.L. Xie, D.W. Liu, X.Q. Li, B. Tao, J. Hao, W. Deng, Q. Liu, C.C. Guo, Measurement and correlation for solubilities of adipic acid, glutaric acid, and succinic acid in dimethyl adipate + methanol mixtures, J. Chem. Eng. Data 62 (2017) 3124–3137. [29] X.J. Liao, X.Q. Li, Y.J. Han, J. Song, Y.J. Gao, A. Yang, Y. Zhu, W.P. Luo, Measurement and correlation for the solubility of adipic acid and succinic acid in glutaric acid + cyclohexanone and glutaric acid + acetic acid mixtures, J. Chem. Eng. Data 62 (2017) 3473–3482.
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Measurement and correlation for solubilities of isophthalic acid and m-toluic acid in binary acetic acid + water and acetic acid + m-xylene solvent mixtures Bao Tao a, Zhipeng Sheng a, Weiping Luo a,⁎, Xiaoxiao Sheng a, Qinbo Wang b,⁎ a b
Department of Chemical Engineering, Hunan University, Changsha, 410082, Hunan, PR China Jiangxi Keyuan Boipharm Co. Ltd., Jiujiang, 332000, Jiangxi, PR China
a r t i c l e
i n f o
Article history: Received 19 March 2018 Received in revised form 12 April 2018 Accepted 16 April 2018 Available online 24 April 2018 Keywords: Solubility Isophthalic acid m-Toluic acid Water Acetic acid m-Xylene
a b s t r a c t In this study, the solubilities of isophthalic acid (IPA) and m-toluic acid (m-TA) in binary acetic acid (HAc) + (water or m-xylene) solvent mixtures were measured by using a synthetic method at atmospheric pressure. The mole fraction of HAc in the corresponding solvent mixtures ranges from 0.0000 to 1.000. The measured data show that within the temperature range studied, the solubilities of IPA and m-TA increase with increasing temperature at constant solvent composition. At a given temperature, the solubilities of IPA and m-TA decrease with the decreasing mole fraction of HAc in HAc + water solvent mixtures; whereas the “maximum-solubility effect” was observed in HAc + m-xylene solvent mixtures, and that with the mole fraction of HAc at 0.8761 has the best dissolving capacity for IPA at constant temperature. The experimental solubilities were well correlated by both the nonrandom two-liquid (NRTL) and Apelblat equations, and the calculated solubilities agree satisfactorily with the measured results. Furthermore, the thermodynamic functions including dissolution enthalpy, entropy and Gibbs energy were obtained from the solubility data by using the van't Hoff equation. © 2018 Elsevier B.V. All rights reserved.
1. Introduction Isophthalic acid (IPA) is a commercially important aromatic compound and widely applied in synthesis of acid-modified copolyester, surface coating, and unsaturated polyester [1]. Currently, the majority of IPA is produced by liquid-phase catalytic oxidation of m-xylene under the Co–Mn–Br catalyst system with air in a conventional oxidation reactor [2–4]. During the oxidation process, HAc is used as the solvent, which is a more environmentally friendly way than using nitric acid as an oxidant [5]. In this technique, m-xylene is oxidized by air and converted into IPA; water and m-TA are the main byproducts. Sequentially, the reaction mixtures comprising crude IPA, m-TA products and mother liquor must be separated to produce pure IPA. Usually, crystallization is used in the relevant purification process for obtaining products with high purity [6]. It is well-known that solubility data is indispensable for designing the separation equipment, as well as for setting the relevant operating conditions. From the literature survey results, some reports on the solubilities of IPA in pure water [7–11] and HAc [11–13] could be found. Many scientists have studied the solubility of IPA in HAc + water solvent mixtures with the mole fraction of HAc ranged from 0.034 to 0.739 [9,11–13]. ⁎ Corresponding authors. E-mail addresses: [email protected], (W. Luo), [email protected] (Q. Wang).
https://doi.org/10.1016/j.molliq.2018.04.086 0167-7322/© 2018 Elsevier B.V. All rights reserved.
Unfortunately, no reports on the solubility of IPA in HAc + m-xylene solvent mixtures are available. Meanwhile, only a few reports on the solubility of m-TA in pure water [14–17] could be found. Furthermore, there are no reports or publications for the solubility of m-TA in HAc + water solvent mixtures, let alone that in HAc + m-xylene solvent mixtures. Thus, it is necessary to measure the solubilities of IPA and m-TA in the aforementioned solvent mixtures. The aim of this work is to measure the solubilities of IPA and m-TA in the HAc + water mixtures and HAc + m-xylene mixtures at different temperature by using the synthetic method. The reliability of the experimental solubility data will be verified by comparison with the literature data. Moreover, the experimental solubility data will be correlated with the nonrandom two-liquid (NRTL) [18] and modified Apelblat [19,20] equations, and the equation parameters are expected to be obtained. Thermodynamic functions including dissolution enthalpy, entropy and Gibbs energy will be calculated from the solubility data by using the van't Hoff equation. 2. Experimental 2.1. Materials IPA (mass fraction N 0.990) and m-TA (mass fraction N 0.980) were purchased from Adamas Reagent Co., Ltd. and Tokyo Chemical Industry
550
B. Tao et al. / Journal of Molecular Liquids 262 (2018) 549–555 Table 1 Suppliers and mass fraction purity of the chemicals. Components
Suppliers
Mass fraction purity
Analysis method
Isophthalic acid m-Toluic acid Acetic acid m-Xylene Water
Adamas Reagent Co., Ltd. Tokyo Chemical Industry Co., Ltd. Sinopharm Chemical Reagent Co. Sinopharm Chemical Reagent Co. Hangzhou Wahaha Group Co.
N0.990 N0.980 N0.990 N0.990 N0.999
HPLCa HPLCa GCb GCb
a b
High-performance liquid chromatograph. Gas chromatograph.
Co., Ltd., respectively. Acetic acid (mass fraction N 0.990) and mxylene (mass fraction N 0.990) were purchased from Sinopharm Chemical Reagent Co. Purified water produced by Hangzhou Wahaha Group Co was bought from supermarket (596 mL each bottle) and had the measured resistivity of 18.2 MΩ·cm. The mass fraction of IPA and m-TA were checked by high-performance liquid chromatography (HPLC). The purities of HAc and m-xylene were checked by gas chromatograph (GC) and no impurity peaks were detected. All the chemicals were used in the experiments without further purifications. The detailed suppliers and mass fraction of the used chemicals are listed in Table 1. 2.2. Apparatus and procedures The solid-liquid equilibrium (SLE) experiment was carried out by a synthetic method. The details of apparatus and procedures used in this work have been described in detail by Wang et al. [21,22], Chen et al. [23] and Luo et al. [24–29], which have good use for reference to this work. Briefly, the apparatus is comprised of a solid-liquid equilibrium cell, a magnetic stirring system, a temperature-controlling and measurement system, and a laser-detecting system. The experiment was carried out in a 125 mL equilibrium cell that was heated in a thermostatic water bath. Continuous stirring was achieved by the magnetic stirrer system, and the dissolution temperature of a (solid + liquid) mixture of known composition was determined by the laser-detecting system. In the experiment, the equilibrium cell can let the laser beam to pass through it, and the intensity of laser beam was recorded in real time by a computer in terms of the photovoltage. In each experiment, predetermined amounts of solvent and solute were accurately weighed by an electronic balance (type AL204, Mettler Toledo instrument Co. Ltd.,) and added into the equilibrium cell. Then, the cell was put into a thermostatic water bath, and the mixture was heated very slowly (at b0.2 K·h−1 near the equilibrium temperature) with continuous stirring. At the early stages of the experiment, the laser beam was partly passed the solvent-solute mixture due to the existence of unsolved particles of solute in the solution. Thus, the intensity of the laser beam passing through the mixture was lower. The intensity increased gradually with the decrease of amount of solute undissolved. At last when crystal disappeared, the intensity of the laser beam reached a maximum value and kept steady, the SLE was considered to be reached. The temperature corresponding to the maximum intensity was taken as SLE temperature of the mixture. The mole fraction of solubility (x1) of IPA or m-TA was calculated according to Eq. (1), and the mole fraction of HAc (x2, solv) in binary HAc + water or HAc + m-xylene solvent mixtures was calculated based on Eq. (2). m1, m2 and m3 denote the mass of IPA or m-TA, HAc and water or m-xylene, respectively. M1, M2 and M3 represent the molecular weight of IPA or m-TA, HAc and water or m-xylene, respectively. m1 M1 x1 ¼ m m2 m3 1 þ þ M1 M2 M3
ð1Þ
m2 M2
x2;solv ¼ m m3 2 þ M2 M3
ð2Þ
2.3. Verification of the experimental methods To verify the reliability of the measured solubility data, comparisons have been made between the experimental solubilities data and those available in the literature. The experimental solubilities data together with the literature data [7–17] are illustrated in Figs. 1–3, as can be seen, the measured solubilities data of IPA and m-TA in pure water and IPA in pure HAc have good agreement with the literature data, which indicates the measured solubilities data are convincing and accurate. 3. Results and discussion 3.1. Experimental results In this work, the measured solubilities of IPA and m-TA in HAc + water and HAc + m-xylene mixtures are summarized in Tables S1– S4, and plotted in Figs. 4–7, respectively. However, the solubility data of IPA in m-xylene cannot be obtained because IPA is not detectably soluble in m-xylene. From Figs. 4–7, it can be seen that the solubilities of IPA and m-TA in HAc + water and HAc + m-xylene mixtures increase with the increase of temperature at constant solvent composition. Furthermore, it can be concluded from Figs. 4 and 6 that the effect of solvent composition on the solubility of IPA and m-TA in HAc + water mixtures is apparent. Within the temperature range studied, the solubilities of IPA and m-TA in pure HAc are the highest, and it decreases with an increasing concentration of water in the mixed HAc + water at constant temperature. Fig. 5 gives an interesting result that the solvent mixtures with HAc mole fraction of 0.8761 has the best dissolving capacity for IPA within the solvent composition range of the measurements. This phenomenon can be rightly explained by the “maximum solubility effect” predicted by the Hildebrand-Scatchard's theory [30]. Chen et al. [23] verified the theory by experimentally measuring the solubility of terephthalic acid in the mixture of acetic acid and water, and Wang et al. [22] also verified the theory by experimentally measuring the solubility of benzoic acid in the mixtures of methylbenzene + benzyl alcohol and methylbenzene + benzaldehyde. A similar conclusion can be drawn from them works. Fig. 7 shows that the binary solvent mixtures have better dissolving capacity for m-TA than pure HAc or m-xylene. However, the effect of solvent composition on the solubilities of m-TA in HAc + m-xylene mixtures is not apparent. In order to illustrate it more clearly, the solubility of m-TA in HAc + m-xylene mixtures at (293.15–338.15) K were calculated by the Apelblat model (Eq. (8)) by using the obtained model parameters listed in Table S5, and the results are illustrated in Fig. 8. As shown in Fig. 8, below 318.15 K, the solubility of m-TA increases with the increase of mole fraction of HAc in HAc + mxylene mixtures solvent mixtures at constant temperature, and then reaches the maximum solubility at the mole fraction of HAc at 0.5410. When the mole fraction of HAc is bigger than 0.5410, the solubility of
B. Tao et al. / Journal of Molecular Liquids 262 (2018) 549–555
551
Fig. 1. Solubilities x1 of IPA in water: ●, measured in this work; □, Ref. [7]; ○, Ref. [8]; Δ, Ref. [9]; ◁, Ref. [10]; ◇, Ref. [11].
Fig. 3. Solubilities x1 of m-TA in water: ●, measured in this work; □, Ref. [14]; ○, Ref. [15]; Δ, Ref. [16]; ∇, Ref. [17].
m-TA decreases with the increase of mole fraction of HAc. However, above 318.15 K, the solubility of m-TA reaches the maximum at the HAc mole fraction of 0.7262 at constant temperature. Similarly, the result also can be explained by the “maximum solubility effect”.
transition. Tfus and Ttrs are the fusion temperature and transition temperature. R is the universal gas constant, and T is the absolute temperature. Because activity coefficient (γ1) depends on the mole fraction and temperature, Eq. (4) must be solved iteratively. For the calculation of activity coefficient, the NRTL activity coefficient model was employed in this work as [18]:
3.2. Correlation of experimental data 3.2.1. NRTL correlation The SLE can be approximated in a general manner by the Eq. (3) that involves such properties of pure solute as enthalpy of fusion, melting point, and so forth [23,31]. Δfus H 1 1 Δtrs H 1 1 ln ðγ1 x1 Þ ¼ − − − − R T T fus R T T trs
ð3Þ
For the four studied systems, the solid-solid phase does not occur, and thus the Eq. (3) can be simplified to the form shown as Eq. (4). ln ðγ1 x1 Þ ¼ −
Δfus H 1 1 − T T fus R
P3 ln γi ¼
j¼1 τ ji Gji x j P3 k¼1 Gki xk
τij ¼ aij þ
þ
3 X j¼1
Gij x j
P3
k¼1
Gkj xk
P3 τij −
k¼1 τ kj Gkj xk P3 k¼1 Gkj xk
!
bij ; Gij ¼ exp −α ij τ ij ; α ij ¼ α ji ; τ ij ≠τji ; τii ¼ 0 T
ð5Þ
ð6Þ
where, xi and γi denote the mole fraction and the activity coefficient of component i, respectively. aij and bij are the parameters needed to be regressed. The term αij in the NRTL model was fixed at 0.3, as proposed by Prausnitz [30] according to the molecular polarity.
ð4Þ
In Eqs. (3) and (4), γ1 is the activity coefficient of solute, and x1 is the real mole fraction of solute in solution. ΔfusH and ΔtrsH are the molar fusion enthalpy of solute and molar enthalpy of solid-solid phase
Fig. 2. Solubilities x1 of IPA in HAc: ●, measured in this work; ◇, Ref. [11]; ▷, Ref. [12]; ⊕, Ref. [13].
Fig. 4. Mole fraction solubility (x1) of IPA depending on temperature T and the mole fraction of HAc (x2, solv) in (HAc + water) solvent mixtures: ●, x 2, solv = 0.0000; □, x 2, solv = 0.0698; ☆, x 2, solv = 0.1667; ◇, x 2, solv = 0.3104; ▲, x 2, solv = 0.5455; ▼, x2, solv = 1.000. Scatter, experimental data; — (solid line), NRTL equation correlated, the averaged relative deviation is 1.73%; — (dotted line), Apelblat equation correlated, the averaged relative deviation is 2.23%.
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B. Tao et al. / Journal of Molecular Liquids 262 (2018) 549–555
Fig. 5. Mole fraction solubility (x1) of IPA depending on temperature T and the mole fraction of HAc (x2, solv) in (HAc + m-xylene) solvent mixtures: ●, x2, solv = 0.3067; □, x2, solv = 0.5419; ☆, x2, solv = 0.7263; ◇, x2, solv = 0.8761; ▲, x2, solv = 1.000. Scatter, experimental data; — (solid line), NRTL equation correlated, the averaged relative deviation is 1.73%; — (dotted line), Apelblat equation correlated, the averaged relative deviation is 0.715%.
Fig. 7. Mole fraction solubility (x1) of m-TA depending on temperature T and the mole fraction of HAc (x2, solv) in (HAc + m-xylene) solvent mixtures: ●, x2, solv = 0.0000; □, x2, solv = 0.3066; ☆, x2, solv = 0.5410; ◇, x2, solv = 0.7262; ▲, x2, solv = 0.8760; ▼, x2, solv = 1.000. Scatter, experimental data; — (solid line), NRTL equation correlated, the averaged relative deviation is 2.19%; — (dotted line), Apelblat equation correlated, the averaged relative deviation is 0.667%.
In order to calculate the solubility, the molar fusion enthalpy of solute (ΔfusH) and the fusion temperature (Tfus) are required. ΔfusH and Tfus used in this work for IPA are 48,194.3 J·mol−1 and 621.2 K [32], and that for m-TA are 15,730 J·mol−1 and 383 K [33], which are acquired from the literature. By using model Eqs. (3)–(6), the measured solubilities data for the four studied systems were correlated and shown in Tables S1–S4. The optimized model parameters are listed in Table S6. The regression of model parameters was performed using the Matlab program, and the procedure is based on the Simplex approach proposed by Nelder and Mead [34]. Function fminsearch in the optimization toolbox of Matlab (Mathwork, MA) uses the Nelder-Mead Simplex approach and can be
applied for the minimization of the objective function, which is the averaged relative deviation (ARD) between experimental and calculated solubility defined in this work as:
Fig. 6. Mole fraction solubility (x 1 ) of m-TA depending on temperature T and the mole fraction of HAc (x 2, solv ) in (HAc + water) solvent mixtures: ●, x 2, solv = 0.0000; □, x2, solv = 0.0699; ☆, x 2, solv = 0.1669; ◇, x2, solv = 0.3104; ▲, x2, solv = 0.5456; ▼, x2, solv = 1.000. Scatter, experimental data; — (solid line), NRTL equation correlated, the averaged relative deviation is 2.19%; — (dotted line), Apelblat equation correlated, the averaged relative deviation is 1.45%.
RDi ¼
n xci −xi 1X 100; ARD ¼ absðRDi Þ n i¼1 xi
ð7Þ
where xci and xi are the ith calculated and experimental solubility, n is the total number of experimental points. The corresponding RD are presented in Tables S1–S4, respectively. The obtained NRTL model parameters and the averaged relative deviation (ARD) defined in Eq. (7) are listed in Table S6. For comparison, the calculated data along with the experimental data are illustrated in Figs. 4–7. As can be seen from these figures, the calculated data have good agreement with the experimental data. It indicates that the NRTL model was successfully applied to
Fig. 8. Solubilities (x1) of m-TA (1) in HAc (2) + m-xylene (3) solvent mixtures: ■, 293.15 K; ●, 303.15 K; ▲, 313.15 K; ▼, 318.15 K; ◆, 323.15 K; ◄, 328.15 K; ►, 338.15 K. x2, solv is the mole fraction of HAc in HAc + m-xylene solvent mixtures.
B. Tao et al. / Journal of Molecular Liquids 262 (2018) 549–555
553
correlate the solubilities of IPA and m-TA in binary HAc + water and HAc + m-xylene solvent mixtures.
In the special case of least-squares estimation with normal distributed errors, apart from an additive constant, AIC can be simplified to:
3.2.2. Modified Apelblat correlation The modified Apelblat equation was also used to correlate the experimental solubility data in this work. The form of equation proposed by Apelblat is shown as
AIC ¼ NlnðRSS=NÞ þ 2k
ln x1 ¼ A þ
B þ C ln T T
ð8Þ
In Eq. (8), x1 is the mole fraction of IPA or m-TA, T is the absolute temperature, A, B and C are the empirical model parameters. In order to use Eq. (8) to correlate the solubility of IPA and m-TA at various solvent compositions, the following empirical correlations were adopted [35–37]. C ¼ C 0 þ C 1 x2 þ C 2 x22 þ C 3 x32 þ C 4 x42
ð9Þ
where Ai, Bi and Ci are model parameters, x2 is the mole fraction of water or m-xylene in HAc + water or HAc + m-xylene mixtures, respectively. Once again, the measured solubilities data for the four studied systems were correlated by using model Eqs. (8) and (9), and the model parameters were optimized. The optimum algorithm used in the parameter estimation program was same as to that applied in the NRTL correlation, and the objective function was chosen as that defined in Eq. (7). The calculated results with Apelblat model along with the corresponding RD are listed in Tables S1–S4, and the obtained model parameters and the ARD are given in Table S5. For comparison, the calculated results are also plotted in Figs. 4–7, respectively. It clearly shows that a good agreement between the experimental solubilities with that calculated. Therefore, the modified Apelblat equation is suitable to correlate the solubilities of IPA and m-TA in binary HAc + water and HAc + mxylene solvent mixtures. 3.2.3. Evaluation of thermodynamic models In order to choose the best model for isophthalic acid (IPA) and mtoluic acid (m-TA), the Akaike Information Criterion (AIC) [38–41] was used to compare the applicability of the Apelblat model and NRTL model. In general, the model with the low value of AIC can be the best-fit model. The AIC is given as follow: AIC ¼ −2 ln LðθÞ þ 2k
ð10Þ
where L(θ) and k represent the maximized likelihood value and the number of estimable parameters for the evaluated model, respectively.
RSS ¼
N X
ð11Þ
ðxi −xci Þ2
ð12Þ
i¼1
where N is the number of observations; RSS is the residual sum of squares; xi and xci are the experimental and calculated values of solubility for solute, respectively. The calculated results of AIC for the three models are shown in Table 2. Akaike weights, ωi, are employed to determine the best model with highest Akaike weights in order to illustrate the results more intuitively, which is expressed as: ωi ¼ expððAIC min −AIC i Þ=2Þ PM i¼1 expððAIC min −AIC i Þ=2Þ
ð13Þ
where M is the number of the selected models in the comparison; AICmin is the minimum value of AIC for the selected models; AICi is the AIC value of the ith model. The values of Akaike weights are also displayed in Table 2. From Table 2,for isophthalic acid (IPA) and m-toluic acid (m-TA) in binary acetic acid (HAc) + (water or m-xylene) system, the low AIC value and the high Akaike weight value indicate that the Apelblat equation could be used to correlate the solubility better between the two models. 3.3. Thermodynamic functions of solution Thermodynamic properties are very important for further studies. The thermodynamic functions of solution such as dissolution enthalpy, entropy and Gibbs free energy are useful to understand the dissolution process of IPA and m-TA in HAc + water and HAc + m-xylene solvent mixtures. Thus, they were evaluated from the measured solubility data by van't Hoff analysis, which is shown as [42]. ΔH sol ∂ ln_ x1 ¼− R ∂ð1=T−1=T hm Þ
! ð14Þ
where R is the gas constant; Thm is the mean harmonic [calculated as: Thm = n/∑ni=1(1/T), where n is the number of temperatures studied], the corresponding Thm are presented in Tables S7, respectively. The logarithm of mole fraction of the solute (ln x1) is linearly related to the
Table 2 Value of the akaike information criterion of the apelblat model and the modified NRTL model for isophthalic acid (IPA) and m-toluic acid (m-TA) in binary acetic acid (HAc) + (water or mxylene) mixed solvents. Models
RSSa
N
Parameters
AICb
e((AICmin-AICi)/2)c
Akaike weight ωid
IPA in HAc + water NRTL model Apelblat model
1.93563e−08 1.76809e−08
10 10
4 3
−192.628 −195.534
0.233944 1
0.18959 0.81041
IPA in HAc + m-xylene NRTL model Apelblat model
3.11444e−08 9.17849e−09
10 10
4 3
−187.872 −202.09
0.000817824 1
0.000817156 0.999183
m-TA in HAc + water NRTL model Apelblat model
0.00089 0.000122
10 10
4 3
−85.265 −107.165
1.75569e−05 1
1.75566e−05 0.999982
m-TA in HAc + m-xylene NRTL model Apelblat model
0.002345 0.000405
10 10
4 3
−75.5796 −95.1532
5.61875E−05 1
5.61843E−05 0.999944
a b c d
RSS is the residual sum of squares. AIC is the Akaike Information Criterion value for each model. AICmin is the minimum value of the compared models, and AICi is the value of the ith model. Akaike weight is the probabilities of each model within the interval [0,1] and they sum to 1.
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reciprocal of the absolute temperature (1/T). The slope of the plot ln x1 against (1/T − 1/Thm) is the value of −ΔHsol/R. ΔHsol was the mean value of the dissolution enthalpy over the considered temperature range. The Gibbs free energy change for the solution process (ΔGsol) was calculated by the following equations [43]. ΔGsol ¼ −RT hm intercept
ð15Þ
in which, the intercept used is the one obtained in the analysis by treatment of ln x1 as a function of (1/T − 1/Thm). Finally, the entropic change for solution process (ΔSsol) can be obtained by the following equation ΔSsol ¼
ΔH sol −ΔGsol T hm
ð16Þ
The thermodynamic functions of solution ΔHsol, ΔGsol, ΔSsol, for IPA and m-TA in HAc + water and HAc + m-xylene solvent mixtures, are summarized in Tables S7. The relative contributions of enthalpy %ζH and entropy %ζTS in the dissolution process were calculated by the following equations [44]. %ξH ¼
jΔH sol j 100 jΔH sol j þ jTΔSsol j
ð17Þ
%ξTS ¼
jTΔSsol j 100 jΔH sol j þ jTΔSsol j
ð18Þ
The calculated values of %ζH and %ζTS are also given in Tables S7. The results indicate that in all case the main contributor to Gibbs free energy of the dissolving process of IPA or m-TA in HAc + water and HAc + mxylene solvent mixtures is the enthalpy. Moreover, as shown in Tables S7, the values of ΔHsol and ΔGsol are positive at the measured temperature, which shows that the four dissolving process are endothermic and not spontaneous. From Table S7, in the dissolution process of IPA in HAc + water, it can be seen that the ΔGsol decreases with the increase of mole fraction of HAc in HAc + water solvent mixtures. It indicates that less energy is required to overcome the cohesive force between the solute IPA and the solvent in the dissolving process when HAc added into the solvent system. From Table S7, in the dissolution process of IPA in HAc + m-xylene, one can see that when the mole fraction of HAc is b0.8761, ΔGsol decreases gradually with the increase of mole fraction of HAc; when the mole fraction of HAc is N0.8761, the value of ΔGsol increases with the HAc mole fraction increasing. In other words, when the mole fraction of HAc is 0.8761, the cohesive force between the solute IPA and the solvent reaches a minimum. From Table S7, in the dissolution process of m-TA in HAc + water, ΔGsol for m-TA in HAc + water solvent mixtures decreases with the increasing mole fraction of HAc. Similar to the results for the IPA in HAc + water solvent mixtures, the results demonstrate that when HAc is added into the solvent system, less energy is required to overcome the cohesive force between the solute m-TA and the solvent in the dissolving process. As can be seen from Table S7, in the dissolution process of m-TA in HAc + m-xylene, when the mole fraction of HAc is b0.5410, ΔGsol decreases gradually with the increase of mole fraction of HAc and reaches a minimum with HAc mole fraction of 0.5410; when the mole fraction of HAc is N0.5410, the value of ΔGsol increases with the HAc mole fraction increasing. 4. Conclusions In this work, the solubilities of IPA and m-TA in HAc + water and HAc + m-xylene solvent mixtures at atmospheric pressure have been measured by a synthetic method. The solubilities of IPA and m-TA in
the investigated solvent mixtures increase with the increase of temperature at constant solvent composition. The effects of mole fraction of HAc in the solvent mixtures at 0.0000 to 1.000 on the solubility were studied. The solubility of IPA and m-TA in HAc + water mixtures increase with the increasing mole fraction of HAc at constant temperature. Meanwhile, it can be found that the HAc + m-xylene solvent mixtures with the mole fraction of HAc at 0.8761 has the highest dissolving capacity for IPA at constant temperature. The binary HAc + mxylene solvent mixture has better dissolving capacity for m-TA than pure HAc or m-xylene. However, the effect of solvent composition on the solubilities of m-TA in HAc + m-xylene mixtures is not apparent. The measured solubility data were correlated by applying both the NRTL equation and the modified Apelblat equation. The calculated solubilities of IPA and m-TA based on the aforementioned equations agree satisfactorily with the experimental results. In addition, for isophthalic acid (IPA) and m-toluic acid (m-TA) in binary acetic acid (HAc) + (water or m-xylene) system, the low AIC value and the high Akaike weight value indicate that the Apelblat equation could be used to correlate the solubility better between the two models. Finally, the thermodynamic functions including dissolution enthalpy, entropy and Gibbs energy were obtained from the solubility data by using the van't Hoff equation. The results indicate that the dissolution process is not spontaneous and endothermic. The obtained thermodynamic functions are helpful to understand the dissolution process of IPA and m-TA in HAc + water and HAc + m-xylene solvent mixtures. The measured solubility data could be applied for the separation and purification of IPA and m-TA in the related process. Acknowledgments This work was supported by the Fundamental Research Funds for the Central Universities and the National Nature Science Fund (21302049). Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.molliq.2018.04.086. References [1] G.G. Zhang, C.Y. Zhu, J.L. Li, Y.G. Ma, Production technology and application of isophthalic acid, China Synth. Fiber Ind. 28 (2005) 43–45. [2] W. Partenheimer, Methodology and scope of metal/bromide autoxidation of hydrocarbons, Catal. Today 23 (1995) 69–158. [3] Q.B. Wang, Y.Z. Zhang, Y.W. Cheng, X. Li, Reaction mechanism and kinetics for the liquid-phase catalytic oxidation of meta-xylene to meta-phthalic acid, AIChE J 54 (2008) 2674–2688. [4] H. Ly, S. Wu, N. Liu, X. Long, W. Yuan, A study on the m-xylene oxidation to isophthalic acid under the catalysis of bromine-free homogeneous catalytic system, Chem. Eng. J. 172 (2011) 1045–1053. [5] Y.W. Cheng, MC Liquid-phase Catalytic Oxidation of Hydrocarbonsto Polycarboxylic Acids(Dissertation) Zhejiang University, China's Hangzhou, 2004. [6] Q.B. Wang, Reactive Crystallization in the Oxidation of para-Xylene(Dissertation) Zhejiang University, China's Hangzhou, 2006. [7] N.Y. Han, L. Zhu, L.S. Wang, R.N. Fu, Aqueous solubility of m-phthalic acid, o-phthalic acid and p-phthalic acid from 298 to 483 K, Sep. Purif. Technol. 16 (1999) 175–180. [8] L. Zhu, L.S. Wang, Solubility of o-phthalic, m-phthalic acid and p-phthalic acid in water, J. Ind. Eng. Chem. 16 (1999) 52–54. [9] B.W. Long, L.S. Wang, Crystallization thermodynamics of m-phthalic acid in water and aqueous acetic acid solutions, J. Biomed. Instrum. Technol. 25 (2005) 749–752. [10] L.S. Wang, B.W. Long, Aqueous solubilities of 1, 3-benzenedicarboxylic acid from 301.45 to 463.15 K, Comput. Appl. Chem. 22 (2005) 477–480. [11] Y.W. Cheng, L. Huo, X. Li, Solubilities of isophthalic acid in acetic acid + water solvent mixtures, Chin. J. Chem. Eng. 21 (2013) 754–758. [12] L. Feng, Q.B. Wang, X. Li, Solubilities of 1,3,5-benzenetricarboxylic acid and 1,3benzenedicarboxylic acid in acetic acid + water solvent mixtures, J. Chem. Eng. Data 53 (2008) 2501–2504. [13] Y. Li, Determination and Correlation of Solubilities of Components Involving in TA Manufacture Residues with Aqueous HAc and Ethanol as Solvent(Dissertation) Tianjin University, China's Tianjin, 2006. [14] L.E. Strong, R.M. Neff, I. Whitesel, Thermodynamics of dissolving and solvation processes for benzoic acid and the toluic acids in aqueous solution, J. Solut. Chem. 18 (1989) 101–114.
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