Solubility and Thermodynamic Functions of Isatin in Pure Solvents

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Solubility and Thermodynamic Functions of Isatin in Pure Solvents Jin-Qiang Liu, Si-Yu Chen, and Baoming Ji* College of Chemistry and Chemical Engineering, Luoyang Normal University, Luoyang, 471022, P. R. China ABSTRACT: The solubility of isatin in eight pure solvents including dichloromethane, toluene, acetone, ethyl acetate, 1,4-dioxane, N,N-dimethylformamide, tetrahydrofuran, and acetonitrile were determined from (278.15 to 333.15) K at atmospheric pressure using the synthetic method. The solubility was determined by a laser monitoring observation technique and found to increase with the rise of temperature. The experimental solubilities were correlated by four models including the ideal solution model, the modified Apelblat equation, λh (Buchowski) equation, and Wilson models with the overall average percentage deviations less than 0.52% in all cases. Thermodynamic functions of the solution of isatin in these solvents including apparent standard enthalpy and entropy of solution were obtained by van’t Hoff plot, and the apparent standard Gibbs energy change of solution was also calculated.

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INTRODUCTION Isatin, or chemically, 1H-indole-2,3-dione or indoline-2,3-dione (chemical structure drawn in Figure 1, C8H5NO2, CAS registry

solvents to achieve a high reaction yield, and even can be used to determine why the yield and enantiomeric excess of the reaction of isatin is low.8 Because of the high importance in chemical transformation and little reported solubility data of isatin, we investigate the solubilities of isatin in this study. Employing a laser monitoring observation technique, the solubilities of isatin in eight organic solvents including dichloromethane, toluene, acetone, ethyl acetate, 1,4-dioxane, N,N-dimethylformamide (DMF), tetrahydrofuran (THF), and acetonitrile were measured with the synthetic method at temperatures ranging from (283.15 to 358.15) K. Also, the experimental solubility data were correlated with the ideal solution, modified Apelblat equation, and λh equation, and the solubilities correlated by the model agreed with the experimental data. The thermodynamic functions of the solutions of isatin in these solvents such as apparent dissolution enthalpy and entropy were calculated from the experimental solubility data with the van’t Hoff plot, and the apparent dissolution Gibbs free energy changes were also calculated with the Gibbs equation.

Figure 1. Chemical structure of isatin.

no. 91-56-5), was first obtained from the oxidation of indigo in 19th century, and its chemical structure was initially proposed by Kekule.1 It is a versatile natural product which can be isolated from leaves of Isatis Tinctoria (Woad), Wrightia tinctoria, Wrightia tomentosa, and Couropita guianancis aubl, etc. It could also be found in humans as a metabolic derivative of adrenaline. Its unique structure, containing an indole motif, a ketone, and a γ-lactam moiety, attracts a great amount of investigation of its chemical transformations including the reactions on every functional group.1−3 The reason for its popularity is partly due to the fact that it is the most direct way to the synthesis of pharmaceutical candidates4 and natural products,5 especially in those in the asymmetric mode.5,6 The last decade has witnessed a boom in this open research area.1 Substituted and naked isatins are the most common raw materials for the syntheses of these compounds. Along with the investigation of chemical reactions of isatin, the physical properties of isatin have also been studied, such as the melting point (475.13 K), density, dipole moment, enthalpy of combustion, enthalpy of formation (251.8 kJ·mol−1), enthalpy of fusion (27.82 kJ·mol−1), and enthalpy of sublimation (146.3· kJ·mol−1 at 297.14 K).7 However, as far as we know, the solubility of isatin in different solvents is scarcely reported. The solubility of isatin in different solvents is not only a fundamental thermoproperty for purification and industrial design, but the data are also useful in the choice of suitable © XXXX American Chemical Society

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EXPERIMENTAL PART Materials. Isatin is purchased from the Aladdin Chemistry Co., Ltd. and recrystallized twice from acetone prior to the solubility measurement. The purity of purified isatin crystal is more than 0.998 in mass fraction according to high performance liquid chromatography (HPLC). All the solvents, purchased from Tianjin Yongda Chemical Reagent Co., Ltd. of China, are analytical pure reagent with the purity of higher than 0.995 in mass fraction, dried, and stored over 0.3 nm molecular sieves and used without any further purification. The mass fraction of water in the organic solvents was determined

Received: May 6, 2014 Accepted: September 4, 2014

A

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Table 1. Provenance and Purities of the Materials material isatin dichloromethane toluene acetone ethyl acetate 1,4-dioxane N,N-dimethylformamide (DMF) tetrahydrofuran (THF) acetonitrile a

source Aladdin Chemistry Co., Ltd. Tianjin Yongda Chemical Reagent Ltd. Tianjin Yongda Chemical Reagent Ltd. Tianjin Yongda Chemical Reagent Ltd. Tianjin Yongda Chemical Reagent Ltd. Tianjin Yongda Chemical Reagent Ltd. Tianjin Yongda Chemical Reagent Ltd. Tianjin Yongda Chemical Reagent Ltd. Tianjin Yongda Chemical Reagent Ltd.

IUPAC name

initial mass fraction purity

purification method

analysis methoda

Co.,

1H-indole-2,3-dione dichloromethane

0.98 0.995

recrystallization none

HPLC GC

Co.,

methylbenzene

0.995

none

GC

Co.,

propanone

0.995

none

GC

Co.,

ethyl acetate

0.995

none

GC

Co.,

1,4-dioxacyclohexane

0.995

none

GC

Co.,

0.995

none

GC

Co.,

N,Ndimethylformamide oxolane

0.995

none

GC

Co.,

acetonitrile

0.995

none

GC

Notation: HPLC, high performance liquid chromatography; GC, gas chromatography.

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RESULTS AND DISCUSSION Experimental Solubility Data. The determined solubility data of isatin in different organic solvents at different temperatures are collected in Table 2, where T represents temperature in Kelvin and x1, xcal,id, xcal,Apel, xcal,λh and xcal,Wilson are the solubility of the experimental, calculated values from the ideal solution model, modified Apelblat equation, λh equation, and Wilson model, respectively. To illustrate the solubility vividly, the plot of the solubility data (ln x1) of isatin in these solvents in the experimental temperature range is shown in Figure 2. From Table 2, it can be seen that the solubility of isatin increases nonlinearly with the rise of temperature in all solvents. Figure 2 also demonstrates that the solubility of isatin roughly follows the order of DMF > THF > 1,4-dioxane > acetone > acetonitrile > ethyl acetate > dichloromethane > toluene. From the data listed in Table 2 and Figure 2, it is obvious that the solubility of isatin in DMF is almost 200 times higher than that in toluene. DMF, THF, and 1,4-dioxane are good solvents to dissolve isatin. Modest solubility of isatin in acetone, acetonitrile, and ethyl acetate is enough for reaction solvent optimization. This result is in agreement with Zhao’s report.8 Besides, from the data in Table 2, we can see the ratio of solubility change in the experimental range is acetonitrile (3.24) > 1,4-dioxane (2.99) > ethyl acetate (2.45) > acetone (2.21) > dichloromethane (2.16) > THF (2.03) > DMF (1.72) > toluene (1.57). The high solubility of isatin in DMF, THF, 1,4-dioxane, and acetone at low temperature made these solvents unsuitable for the recrystallization of isatin, while the opposite situation occurred in the dichloromethane and toluene for the low solubility of isatin at high temperature. Considering that the solubility of isatin in ethyl acetate and acetonitrile is low at lower temperature and relatively high at higher temperature, ethyl acetate is thought to be the suitable solvent for the recrystallization of isatin, especially considering the facile availability, low price, and toxicity of ethyl acetate. In addition, all the crystals obtained from these solvents except toluene are prismatical, while that in toluene is powder. To confirm the crystals obtained from different solvents, XRD powder analysis is employed, and the results are presented in Figure 3, which demonstrates that there is no difference between them.

by the Karl Fischer method and found to be no more than 0.002. All the information about the materials used is listed in Table 1. Apparatus and Procedure. The synthetic method is employed to measure the solubility of isatin. Our co-workers have described the detailed procedure previously9−13 and we made little improvement in this study. Following is a concise description. Our solubility measurement equipment is composed of a thermostat, a double-wall glass vessel (about 200 mL), a magnetic stirrer, and a mercury-in-glass thermometer (uncertainty of 0.05 K). A laser beam is used to observe the dissolution of the solid + liquid mixture. A detector is employed to collect the light signal transmitted through the vessel and to guarantee the complete dissolution of the last crystal. The maximum signal strength based on the signal change is recorded to be the equilibrium point of the given system. At the start of each experiment, a known mass of solute and solvent measured by an electronic analytical balance (type BS210S, Sartorius Scientific Instrument Co. Ltd., uncertainty of 0.0001 g) was introduced to the solubility measurement equipment at a known temperature. The undissolved solute particles were completely suspended in the double-wall vessel by continuous stirring for 1 h, and then a quantitative additional solvent was added into the vessel through a buret. Every addition of solvent was followed by an additional 1 h of stirring. When the last portion of the solid solute just disappeared, the penetrated light intensity reached its maximum value. The mass of the solute and the total solvent were recorded. The saturated mole fraction (x1) could be obtained from the following eq 1: x1 =

m1/M1 m1/M1 + m2 /M 2

(1)

where m1 and m2 are the mass consumed of the solute and the solvent, and M1 and M2 represent the molecular weight of the solute and the solvent, respectively. All the experiments were independently run at least three times with different solute mass, and the relative uncertainties of the experimental data were within 1%, obtained from the mass ratio of the additional solute to the dissolved solute. B

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Table 2. Experimental and Calculated Solubilities of Isatin in Different Organic Solvents from T = (278.15 to 333.15) K at 0.1 MPaa 103x1cal T/K

3

10 x1

ideal

102RD λh

Apelblat

ideal

Apelblat

λh

Wilson

0.7900 0.8774 0.9833 1.0993 1.1979 1.3164 1.4123 1.5313 1.6958

0.63 −0.85 −0.29 −0.76 0.97 0.58 0.28 −0.06 −0.49 0.54

0.75 −0.84 −0.33 −0.84 0.88 0.52 0.24 −0.03 −0.37 0.53

0.47 −0.84 −0.16 −0.58 1.13 0.68 0.30 −0.19 −0.90 0.58

−0.29 −0.19 −0.10 −0.03 0.01 0.06 0.09 0.12 0.15 0.11

0.5911 0.6392 0.6861 0.7138 0.7700 0.8170 0.8820 0.9228

−0.24 0.63 0.98 −1.58 −0.32 −0.54 1.14 −0.10 0.69

−0.61 0.55 1.05 −1.43 −0.18 −0.49 1.02 −0.48 0.73

−0.82 0.63 1.33 −1.07 0.14 −0.31 0.94 −0.95 0.77

−0.51 −0.33 −0.17 −0.03 0.09 0.19 0.28 0.36 0.24

Wilson

278.15 282.35 286.25 290.55 293.15 296.95 299.85 303.25 307.65 ARD

0.78767 0.87582 0.98231 1.0990 1.1980 1.3171 1.4135 1.5331 1.6983

0.78267 0.88328 0.98512 1.1073 1.1864 1.3095 1.4096 1.5340 1.7067

0.78175 0.88315 0.98558 1.1082 1.1874 1.3103 1.4101 1.5336 1.7046

Dichloromethane 0.78400 0.88317 0.98392 1.1054 1.1845 1.3081 1.4093 1.5360 1.7135

288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 ARD

0.5881 0.6371 0.6849 0.7136 0.7707 0.8186 0.8844 0.9261

0.5895 0.6331 0.6782 0.7249 0.7732 0.8230 0.8743 0.9270

0.5917 0.6336 0.6777 0.7238 0.7721 0.8226 0.8754 0.9305

Toluene 0.5929 0.6331 0.6758 0.7212 0.7696 0.8211 0.8761 0.9349

287.25 292.75 298.45 302.65 308.35 312.65 318.15 323.35 ARD

10.887 12.513 14.044 15.808 17.432 19.259 21.676 24.077

10.887 12.433 14.193 15.598 17.656 19.329 21.625 23.962

10.921 12.432 14.164 15.556 17.612 19.298 21.633 24.036

Acetone 10.927 12.432 14.159 15.549 17.607 19.301 21.660 24.105

11.097 12.660 14.103 15.844 17.377 19.164 21.530 23.878

0.00 0.64 −1.06 1.33 −1.28 −0.36 0.24 0.48 0.67

−0.31 0.65 −0.85 1.59 −1.03 −0.20 0.20 0.17 0.63

−0.37 0.65 −0.82 1.64 −1.00 −0.22 0.07 −0.12 0.61

−1.93 −1.17 −0.43 −0.22 0.32 0.49 0.68 0.83 0.76

288.15 293.35 298.25 303.65 308.65 313.35 318.15 323.35 ARD

4.2066 4.7991 5.6544 6.3674 7.3259 8.2201 9.2017 10.316

4.1993 4.8655 5.5636 6.4171 7.2912 8.1907 9.1912 10.373

4.1854 4.8641 5.5719 6.4321 7.3068 8.2000 9.1853 10.338

Ethyl Acetate 4.2030 4.8592 5.5502 6.4011 7.2803 8.1944 9.2233 10.457

4.2233 4.8083 5.6626 6.3671 7.3230 8.2130 9.1899 10.3004

0.17 −1.38 1.61 −0.78 0.47 0.36 0.11 −0.55 0.68

0.50 −1.35 1.46 −1.02 0.26 0.24 0.18 −0.21 0.65

0.09 −1.25 1.84 −0.53 0.62 0.31 −0.23 −1.37 0.78

−0.40 −0.19 −0.14 0.00 0.04 0.08 0.12 0.15 0.14

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 ARD

16.176 18.827 21.824 25.213 28.999 33.091 37.755 42.821 48.382

16.183 18.857 21.863 25.226 28.974 33.135 37.736 42.805 48.373

16.165 18.838 21.844 25.208 28.959 33.125 37.734 42.814 48.397

1,4-Dioxane 16.185 18.836 21.821 25.170 28.917 33.097 37.745 42.903 48.613

16.239 18.871 21.851 25.225 28.996 33.071 37.722 42.774 48.321

−0.04 −0.16 −0.18 −0.05 0.09 −0.13 0.05 0.04 0.02 0.08

0.07 −0.06 −0.09 0.02 0.14 −0.10 0.06 0.02 −0.03 0.06

−0.06 −0.05 0.01 0.17 0.28 −0.02 0.03 −0.19 −0.48 0.14

−0.39 −0.23 −0.12 −0.05 0.01 0.06 0.09 0.11 0.13 0.13

0.13 0.16 −0.22 −0.20 −0.08

0.10 0.14 −0.23 −0.20 −0.07

−0.45 0.02 −0.03 0.20 0.41

0.021 0.001 −0.002 −0.007 −0.011

283.15 288.25 293.25 298.15 303.15

126.50 134.95 142.89 151.42 160.49

126.33 134.73 143.20 151.72 160.62

126.37 134.76 143.22 151.72 160.61

N,N-Dimethylformamide (DMF) 127.07 126.30 134.92 134.95 142.93 142.89 151.12 151.43 159.83 160.51

C

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Table 2. continued 103x1cal T/K 308.25 313.25 318.45 323.15 328.15 333.15 ARD

a

103x1 170.32 178.80 189.84 198.03 208.76 217.57

ideal 169.91 179.22 189.11 198.23 208.10 218.14

102RD λh

Apelblat 169.91 179.22 189.13 198.25 208.15 218.22

Wilson

N,N-Dimethylformamide (DMF) 169.09 170.35 178.57 178.81 188.86 189.86 198.56 198.02 209.32 208.75 220.56 217.53

ideal

Apelblat

λh

Wilson

0.24 −0.23 0.38 −0.10 0.32 −0.26 0.21

0.24 −0.23 0.37 −0.11 0.29 −0.30 0.21

0.72 0.13 0.52 −0.27 −0.27 −1.37 0.40

−0.015 −0.005 −0.008 0.003 0.005 0.018 0.01

289.85 297.15 301.15 305.15 308.95 314.05 318.35 323.15 ARD

19.694 23.443 25.413 27.975 30.110 33.459 36.657 39.894

19.732 23.358 25.532 27.842 30.168 33.495 36.489 40.040

19.697 23.355 25.541 27.858 30.183 33.498 36.467 39.974

THF 19.764 23.324 25.475 27.778 30.116 33.496 36.578 40.286

19.833 23.524 25.452 27.988 30.083 33.389 36.551 39.741

−0.19 0.36 −0.47 0.48 −0.19 −0.11 0.46 −0.37 0.33

−0.02 0.38 −0.50 0.42 −0.24 −0.12 0.52 −0.20 0.30

−0.36 0.51 −0.24 0.70 −0.02 −0.11 0.22 −0.98 0.39

−0.70 −0.35 −0.16 −0.04 0.09 0.21 0.29 0.39 0.28

283.15 288.35 294.65 298.15 303.15 308.15 313.15 318.15 323.15 ARD

4.2029 4.9805 6.0799 6.7486 7.8880 8.9335 10.281 11.810 13.597

4.2031 4.9807 6.0691 6.7490 7.8212 9.0205 10.356 11.839 13.477

4.2134 4.9833 6.0633 6.7396 7.8090 9.0093 10.352 11.848 13.509

Acetonitrile 4.2119 4.9801 6.0582 6.7340 7.8042 9.0086 10.360 11.874 13.566

4.3476 5.0841 6.1373 6.7783 7.8901 8.8825 10.1984 11.6991 13.4651

0.00 0.00 0.18 −0.01 0.85 −0.97 −0.73 −0.25 0.88 0.43

−0.25 −0.06 0.27 0.13 1.00 −0.85 −0.69 −0.32 0.65 0.47

−0.21 0.01 0.36 0.22 1.06 −0.84 −0.77 −0.54 0.23 0.47

−3.44 −2.08 −0.94 −0.44 −0.03 0.57 0.80 0.94 0.97 1.14

. Standard uncertainties u are u(T) = 0.05 K, ur(p) = 0.05, ur(x) = 0.01.

Modified Apelblat Equation. The temperature dependence of solubility of isatin in different pure solvents was described by the modified Apelblat equation,14,15 which is the most popular and has been widely used in the correlation and prediction of solubility data of different substances because of its simplicity.16−20 Hence, the temperature dependence of solubilities of isatin in different pure solvents was predicted by the modified Apelblat equation, whose formula is

To further understand the different solubility behavior of isatin in these solvents, we examined the solvent properties including polarity, dipole moments, dielectric constants, and δ Hildebrand solubility parameters. The solubilities of isatin are in the order of DMF > THF > 1,4-dioxane > acetone > acetonitrile > ethyl acetate > dichloromethane > toluene. That is not the order of polarity [acetonitrile (46) > DMF (40.4) > acetone (35.5) > dichloromethane (30.9) > ethyl acetate (23) > THF (21) > 1,4-dioxane (16.4) > toluene (9.9)], nor the order of dipole moments [DMF (3.8) > acetonitrile (3.2) > acetone (2.9) > dichloromethane (1.8) > THF (1.75) > ethyl acetate (1.7) > 1,4-dioxane = toluene (0.4)] and dielectric constants [acetonitrile (37.5) > DMF (36.7) > acetone (20.6) > dichloromethane (9.1) > THF (7.6) > ethyl acetate (6.02) > toluene (2.38) > 1,4-dioxane (2.21)]. Thus, the polarity of the solvent is not the sole reason for the solubility behavior. The same situation lies in solubility parameter, dipole moments and dielectric constants. All these data indicate a net contribution of the parameters mentioned above to the solubility behavior. Further study on the thermodynamic functions gives a reasonable explanation (vide infra). Data Correlation. Ideal Solution Model. For an ideal solution, the relationship between the mole fraction of a solute and the temperature is ln

x1cal,id

= a + b/T

ln x1cal,Apel = A + B /T + C ln T

(3)

x1cal,Apel

where is the calculated mole fraction solubility of isatin, T is the absolute temperature in Kelvin; and A, B, and C are the empirical model parameters, which can be obtained from the correlation of solubility data. λh (Buchowski) equation. This equation is initially proposed by Buchowski et al.21,22 The λh equation has only two adjustable parameters, and thus is always used in the correlation of solid−liquid equilibrium for its simplicity.18,23 It has the equation form as ⎛ ⎛1 1 − x1cal, λh ⎞ 1 ⎞ ⎟⎟ = λh⎜ − ln⎜⎜1 + λ ⎟ cal, λh Tm ⎠ ⎝T x1 ⎝ ⎠

(4)

where λ and h are model parameters, Tm is the normal melting point of isatin (475.13 K7), and T and x are temperature in Kelvin and mole fraction solubility of solute, respectively. Wilson Model. Based on the solid−liquid equilibrium criteria, the solubility of a solute in liquid solvents can be

(2)

where a and b are parameters obtained from plotting ln(x1) versus 1/T. D

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Figure 3. X-ray powder diffraction pattern of isatin crystals obtained from different solvents: bottom line, toluene; top line, acetone. (Intensity (y axis) vs 2θ/° (x axis)).

ln x1γ1 =

⎞ ΔfusHtp ⎛ 1 Ttp 1 ⎞ ΔCp ⎛ Ttp ⎜⎜ − ⎟⎟ − − + 1⎟ ⎜ln R ⎝ Ttp T⎠ R ⎝ T T ⎠ ΔV − (P − Ptp) (5) RT

where γ1 is the liquid-phase activity coefficient of solute; ΔfusHtp is the molar enthalpy of fusion at the triple point; ΔCp denotes the molar heat capacity difference of the solute between the solid and the liquid; ΔV represents the volume difference between the solid and liquid phases; Ttp and Ptp represent the temperature and pressure of the triple point; P is the absolute pressure and R is the universal gas constant. Generally, the negligible difference between triple point and normal melting point makes it suitable to replace ΔfusHtp and Ttp by enthalpy of melting ΔfusHm and melting point Tm. Furthermore, the last two terms containing ΔCp and ΔV are the correction of heat capacity and pressure difference, which are often minor and also negligible. So, eq 5 can be simplified as ln x1γ1 =

ΔfusHm ⎛ 1 1⎞ − ⎟ ⎜ R ⎝ Tm T⎠

(6)

The enthalpy of fusion can be measured with the differential scanning calorimetry (DSC). The value of enthalpy of fusion of isatin was reported to be 27.82 KJ·mol−1.7 To use eq 6, a thermodynamic model is demanded to represent activity coefficients as a function of temperature and composition at constant pressure. In this article, the Wilson equation, a local composition model initially proposed by Wilson,25 was used to derive γ1, which can be expressed as eq 7 in the binary system:23,26 ⎞ ⎛ Λ12 Λ 21 ln γ1 = −ln(x1 + Λ12x 2) + x 2⎜ − ⎟ x 2 + Λ 21x1 ⎠ ⎝ x1 + Λ12x 2

Figure 2. Experimental mole fraction solubility (ln x1 (y axis)) of isatin in different solvents at different temperature (T/K (x axis)): ■, dichloromethane; ●, toluene; ▲, acetone; ▼ ethyl acetate; ⧫, 1,4dioxane; ◀, DMF; ▶, THF; ★ acetonitrile; ― calculated solubility values: (A) the ideal solution model; (B) the modified Apelblat equation; (C) λh equation; (D) Wilson model.

(7)

where Λ12 =

regressed by the frequently used thermodynamic equation expressed below:24

⎛ λ − λ11 ⎞ ⎛ Δλ ⎞ ν2 ν ⎟ = 2 exp⎜ − 12 ⎟ exp⎜ − 12 ⎝ ⎝ RT ⎠ RT ⎠ ν1 ν1

and E

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Table 3. Parameters of the Four Correlation Models Ideal solution model

Apelblat equation

λh (Buchowski) equation

Wilson model

Λ 21 =

dichloromethane

toluene

acetone

ethyl acetate

1,4-dioxane

DMF

THF

acetonitrile

0.97745 −2261.43 0.99928 11.536 −2723.6 −1.5809 0.99918 0.017993 118398.4 0.99917 −88922 3615.148 0.99999

−3.2563 −1204.45 0.99624 −25.186 −209.34 3.263 0.99575 0.00081772 775841.9 0.99593 −66748.5 3482.983 0.99999

2.5458 −2029.7 0.99879 −19.865 −1013.8 3.3350 0.99866 0.12505 14587.6 0.99878 2097.309 −426967 0.99999

2.8343 −2393.7 0.99903 25.961 −3443.3 −3.4409 0.99890 0.087156 25833.4 0.99857 −71.4527 −135659 0.99999

4.9961 −2673.5 0.99999 4.1487 −2637.6 0.12742 0.99999 0.47563 5468.4 0.99998 2902.855 −4983167 0.99999

1.5709 −1030.6 0.99980 0.80716 −995.74 0.11353 0.99978 0.23318 2873.7 0.99917 1216.244 4185.362 0.99999

2.9415 −1990.4 0.99970 13.357 −2464.6 −1.5489 0.99966 0.20906 8642.5 0.99951 −6796.17 3362.487 0.99999

3.9411 −2665.3 0.99972 −8.3479 −2111.8 1.8308 0.99969 0.16116 15941.4 0.99980 365.5629 −188823 0.99999

a b R2 A B C R2 λ h R2 Δλ12 Δλ21 R2

⎛ Δλ ⎞ ⎛ λ − λ 22 ⎞ ν1 ν ⎟ = 2 exp⎜ − 21 ⎟ exp⎜ − 21 ⎝ ⎝ RT ⎠ RT ⎠ ν2 ν1

Using the van’t Hoff analysis, the apparent standard enthalpy change of solution is obtained from eq 11 employing the mean harmonic temperature (Thm), which is to reduce error and calculated using eq 12.

(8)

in eq 7, x2 is the mole fraction of the selected solvent. In eq 8, Δλ12 (= λ12 − λ11) and Δλ21 (= λ21 − λ22) are two binary cross interaction parameters which are independent of composition and temperature; v1 and v2 represent the molar volumes of solute and pure solvent, respectively. The values of v2 are obtained from literature and that of isatin is calculated from its density (v2 =100 mL·mol−3, ρ = 1.472 g·cm−3).27 In other words, the molar volume value of isatin referred to the solid molar volume, not liquid molar volume. The experimental solubility data of isatin in organic solvents shown in Table 2 are correlated with the ideal solution model, modified Apelblat equation, λh equation adjustable, and Wilson equation. The experimental data and calculated ones with the above models are collected in Table 2 and Figure 2. All the parameters of those models are listed in Table 3. The relative deviation (RD) and average relative deviations (ARDs) defined by eqs 9 and 10 are presented in Table 2 as well.

RD =

⎞ ⎛ Δ Ho ∂ lnx1 ⎟ = − soln ⎜ R ⎝ ∂(1/T − 1/Thm) ⎠ p

Thm =

(11)

n n 1 Ti

∑1

(12)

where n is the number of experimental temperatures. The plots for isatin solubility in different organic solvents are shown in Figure 4. It can be seen that linear trends with well

cal x1,exp i − x1, i

ARD% =

x1,exp i 100 N

(9) N

∑ i=1

cal |x1,exp i − x1, i |

x1,exp i

(10)

xexp 1,i

where N is the number of data points for each solvent, and xcal 1,i are the solubility values of experimental and calculated with those models, respectively. It is seen from Table 3 that the calculated solubilities of isatin by all the four models are in good agreement with the experimental values. As seen, the overall average ARDs of the four models are no more than 0.52% (λh equation) [0.46% (ideal solution), 0.45% (Apelblat), and 0.35% (Wilson)]. Thus, these models are suitable for correlation the solubility data of isatin in these organic solvents. Thermodynamic Functions of the Solution of Isatin. From the results obtained above, conclusions can be drawn that the solubility of isatin in organic solvents is a function of temperature. Furthermore, the relationship between solubility data and temperature provides the basis for the thermodynamic analysis which gives deep insight into the mechanism of the solution processes. Thus, the thermodynamic functions in the solution process of isatin are calculated on the basis of isatin solubility in different solvents.

Figure 4. Modified van’t Hoff plot of the mole fraction solubility of isatin in organic solvents ln x1 (y axis) vs 104(1/T − 1/Thm) (x axis): ■, dichloromethane; ●, toluene; ▲, acetone; ▼ ethyl acetate; ⧫ 1,4dioxane; ◀, DMF; ▶, THF; ★ acetonitrile.

determined ΔsolnH0 in all cases. Furthermore, the apparent standard Gibbs energy change of the solution process (ΔsolnG0) is calculated at Thm according to Krug28 with Δsoln Go = −R × Thm × intercept

(13)

where the intercept is obtained in plots of ln x1 versus (1/T − 1/Thm) (Figure 4). The standard apparent entropy change for F

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Table 4. Thermodynamic Functions of Isatin in Different Solvents ΔsolnH0

Thm solvent

K

dichloromethane toluene acetone ethyl acetate 1,4-dioxane DMF THF acetonitrile

292.84 305.22 305.00 305.43 312.62 307.40 306.87 302.80

KJ·mol

−1

18.80 10.01 16.88 19.90 22.26 8.57 16.55 22.16

ΔsolnG0 KJ·mol

ΔsolnS0

−1

16.42 18.28 10.42 12.70 9.24 4.55 9.04 12.24

Δsoln H 0 − Δsoln G 0 Thm

%ζTS =

|Δsoln H 0| |Δsoln H 0| + |ThmΔsoln S 0| |ThmΔsoln S 0| |Δsoln H 0| + |ThmΔsoln S 0|

ThmΔsolnS0 −1

KJ·mol−1

%ξH

%ξTS

2.38 −8.26 6.46 7.20 13.02 4.01 7.50 9.92

88.76 54.79 72.33 73.44 63.10 68.09 68.80 69.07

11.24 45.21 27.67 26.56 36.90 31.91 31.20 30.93

8.13 −27.07 21.17 23.56 41.64 13.06 24.46 32.77

CONCLUSION The solubilities of isatin in dichloromethane, toluene, acetone, ethyl acetate, 1,4-dioxane, DMF, THF, and acetonitrile have been measured from (278.15 to 333.15) K by a synthetic method, and it was found that they are functions of temperature and increase with the rise of temperature in all selected solvents. Ethyl acetate is thought to be the suitable solvent for the production of isatin in high purity. Four models including the ideal solution model, the modified Apelblat equation, λh equation, and Wilson equation based on solid−liquid phase equilibrium principles are used to correlate the solubility data of isatin in these solvents. The overall APDs of these models are less than 0.52%, showing good agreement with experimental data. The apparent standard enthalpy change of solution and entropy of isatin in different solvents are obtained with van’t Hoff plots, and the apparent standard Gibbs energy change of solution is calculated.

(14)

The relative contributions of enthalpy %ζH and entropy %ζTS to the solution process are calculated by following eqs 15 and 16:29 %ζH =

J·mol ·K

■

the solution processes (ΔsolnS0) can be obtained from the respective ΔsolnH0 and ΔsolnG0 at Thm using the Gibbs equation: Δsoln S 0 =

−1

× 100 (15)

× 100 (16)

All the standard thermodynamic functions, the relative contributions of the enthalpy and entropy for the isatin solution process in all the solvents, are collected in Table 4. The standard Gibbs energy of the solution is found to be positive in all cases, and hence, the solution process apparently is not spontaneous, which is similar to others reported elsewhere.16,17,30,31 The reason for this phenomenon has been explained in detail by others.16 It is necessary to mention that the solubility of isatin in these solvents apparently increases with the decrease of the values of standard Gibbs energy. Obviously, these results are in agreement with eq 13, which means that the lower the value of ΔsolnG0 is, the larger is the solubility of isatin. These results are also in line with the fact that the low ΔsolnG0 value is more favorable for dissolution. Furthermore, the ΔsolnG0 value follows the order of DMF < THF < 1,4-dioxane < acetone < acetonitrile < ethyl acetate < dichloromethane < toluene, which is exactly the opposite order of solubility of isatin in these solvents (DMF > THF > 1,4dioxane > acetone > acetonitrile > ethyl acetate > dichloromethane > toluene (see before)). Conclusion can be drawn that the standard Gibbs energy is the true reason for the different solubility behavior of isatin in these organic solvents. (DMF > THF > 1,4-dioxane > acetone > acetonitrile > ethyl acetate > dichloromethane > toluene.) The apparent enthalpy of solution is also positive in all cases, so is the apparent entropy of solution except in toluene. These results demonstrate that the dissolution process is always endothermic and entropy driven, which is in line with the phenomenon of increasing isatin solubility with increasing temperature. While in the case of isatin in toluene, the solution process is enthalpy driven. In addition, the main contributor to the positive standard molar Gibbs energy of isatin solution is the positive enthalpy (%ζ > 54.79 and even up to 88.76), which indicates energetic predominance on the dissolution process.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Fax: +86-379-65523821. Funding

Financial support from the Natural Science Foundation of Henan Province (No. 132300410319) and The Low Carbon Fatty Amine Engineering Research Centre of Zhejiang Province (2012E10033) is acknowledged. Notes

The authors declare no competing financial interest.

■

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H

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