Solubility Determination and Thermodynamic Models for 2

May 27, 2015 - The thermodynamic properties of the standard dissolution enthalpy, standard entropy, and the standard mole Gibbs free energy were evalu...
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Solubility Determination and Thermodynamic Models for 2‑Methylnaphthalene in Different Solvents from T = (278.15 to 303.15) K Fang Zhang, Yaocun Tang, Long Wang, Li Xu, and Guoji Liu* School of Chemical Engineering and Energy, Zhengzhou University, Zhengzhou 450001, People’s Republic of China ABSTRACT: The solubility of 2-methylnaphthalene in different organic solvents was experimentally studied by the equilibrium method at temperatures from (278.15 to 303.15) K under atmospheric pressure. The solubility of 2methylnaphthalene in all solvents increased with the increasing temperature. The solubility data were correlated with four thermodynamic models including the van’t Hoff equation, modified Apelblat equation, λh equation, and Wilson model. It was found that the calculated solubility with modified Apelblat equation provided a good agreement with the experimental values for the solubility behavior of 2-methylnaphthalene. The thermodynamic properties of the standard dissolution enthalpy, standard entropy, and the standard mole Gibbs free energy were evaluated based on the van’t Hoff analysis. The values of enthalpy of dissolution are positive, which indicate that the dissolution process of 2methylnaphthalene in different organic solvents is endothermic.

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including the van’t Hoff equation,17 modified Apelblat equation,18 the Buchowski−Ksiaz̨ ċ zak λh equation,19 and the Wilson equation.20 Furthermore, the thermodynamic properties including the standard enthalpy, standard entropy, and standard Gibbs free energy in the dissolution process of 2methylnaphthalene were calculated based on the van’t Hoff equation.

INTRODUCTION As an important chemical raw material, 2-methylnaphthalene is widely used in the production of vitamin K3 and organic dyes. More important, it is also utilized in the roles of surfactant, water reducer, dispersant, and so on.1 However, during the preparation process of 2-methylnaphthalene, the crude product always contains indole, quinoline, and some other nitrogencontaining compounds. The boiling points of these compounds are very close which means it is not easy to separate 2methylnaphthalene with a high purity from the mixture by distillation. At present, some methods for the separation of 2methylnaphthalene have been proposed.2−8 Solvent crystallization is an important method for purifying the 2methylnaphthalene from the crude products in these separation processes.9−11 The solvent crystallization process has an advantage of low energy consumption and high purity. The process strongly relies on accurate solubility data in commonly used solvents which play an important role for understanding the solid−liquid phase equilibrium. Therefore, determination of the solubility of 2-methylnaphthalene in solvents is necessary for the design of a separation process. To the best of our present knowledge, the solubility data for 2-methylnaphthalene in n-heptane, ethylene glycol, and dimethyl sulfoxide (DMSO) are reported in previously published literature.12 However, the solubility data of 2-methylnaphthalene in other organic solvents is rarely available in open works. In our study, the solubilities of 2-methylnaphthalene in ethylene glycol, ethanol, acetone, 1,4dioxane, isopropanol, butyl acetate, n-butyl alcohol, n-heptane, and n-hexane were determined experimentally from (278.15 to 303.15) K using an analytical stirred flask by the equilibrium method.13−16 The experimental solubility data of 2-methylnaphthalene were correlated by thermodynamic models, © 2015 American Chemical Society

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EXPERIMENTAL SECTION Chemicals. 2-Methylnaphthalene (0.98 in mass fraction) was purchased from Aladdin. The crude 2-methylnaphthalene was recrystallized three times in ethanol; its purity was higher than 0.999 in mass fraction, which was confirmed by GC (type, Tian Mei 7890, Shanghai). All of the reagents, including ethylene glycol, ethanol, acetone, 1,4-dioxane, isopropanol, butyl acetate, n-butyl alcohol, n-heptane, and n-hexane, were analytical grade with mass fractions higher than 0.995. The detailed description of these chemicals is presented in Table 1. Solubility Measurement. The solubility data were measured by the equilibrium method in a specially designed 50 mL doubled jacketed glass vessel. The saturated solutions of 2-methylnaphthalene were obtained by adding excess 2methylnaphtalene with 20 mL solvents. The mixed solutions were fully agitated by magnetic stirring for over 24 h to make sure the solution attained equilibrium. Agitation was stopped, and the slurry was kept still for 2 h to settle the unsolved particles before sampling. The upper clear solution was withdrawn and analyzed until the composition of the liquid

Received: November 22, 2014 Accepted: May 14, 2015 Published: May 27, 2015 1699

DOI: 10.1021/je5010627 J. Chem. Eng. Data 2015, 60, 1699−1705

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Table 1. Properties of Solvents MW

MP

ΔfusH

mass fraction purity

purification method

K

(kJ·mol−1)

0.999 0.997 0.998 0.997 0.998 0.999 0.999 0.998 0.997 0.998

recrystallization

307.73c

11.966c

density

solvent

(g·mol−1)

(kg·m−3)

2-methylnaphthalene ethylene glycol n-butyl alcohol n-hexane acetone 1,4-dioxane isopropanol butyl acetate n-heptane ethanol

142.20 62.07 74.12 86.18 58.08 88.11 60.10 116.16 100.2 46.07

1.029a 1113.5b 809.5b 660.6b 784.5b 1033.7b 780.9b 882.5b 679.5b 789.3b

source Aladdin Sinopharm Chemical Reagent Co. Ltd. Tianjin Fengchuan Chemical Reagent Co. Ltd. Tianjin Kemiou Chemical Reagent Co. Ltd. Tianjin Kaitong Chemical Reagent Co. Ltd.

a

Taken from ref 21. The density values for 2-methylnaphthalene are given at 293 K. bTaken from ref 22. The density values for ethylene glycol, nbutyl alcohol, 1,4-dioxane, ethanol, and butyl acetate are given at 293 K, and for n-hexane, acetone, isopropanol, and n-heptane, at 298 K. cTaken from ref 23.

given solvents follow the order butyl acetate > n-heptane > 1,4−dioxane > n-hexane > acetone > n-butyl alcohol > ethanol > isopropanol > ethylene glycol. For 2-methylnaphthalene, at different temperatures, the solubility in ethylene glycol increases very slowly with increasing temperature. The solubility of 2-methylnaphthalene may be caused by the temperature, the nature of the solvent, the intermolecular interactions, hydrogen bonding interaction, and so on. The polarity of the solvent follows the order ethylene glycol > ethanol > acetone > 1,4-dioxane > isopropanol > butyl acetate > n-butyl alcohol > n-heptane > n-hexane.24 As shown in Figure 1, the solubility of 2-methylnaphthalene increases with decreasing polarity of the solvent. Solubility Modeling. To extend the application field for 2methylnaphthalene, four thermodynamic models were applied to make the correlation between the temperature and the solubility values in the selected pure solvents. van’t Hoff Model. According to the thermodynamic principles of the solid−liquid equilibrium, the van’t Hoff equation is a universal equation used to correlate mole fraction of a solute’s solubility with temperatures.17

phase did not vary. In general, it took about 9 h to reach equilibrium. Subsequently, 1−2 mL of equilibrium liquid phase with precision of 0.01 mL was withdrawn and quickly transferred into a preweighed glass vessel of 50 mL. The sample was immediately weighed in an analytical balance with a precision of 0.0001 g. The sample was then diluted to 50 mL with corresponding chromatographic grade solvent, and 0.4 μL was taken out to determine the concentration by GC. The desired temperature was maintained by circulating water inside and outside the jacket from a thermostat. A thermostatic water bath (type, DC4006, Shanghai Bilon Precision Instrument Co., Ltd.) was used to control the water temperature with the precision of 0.01 K. The actual temperature was determined by a mercury thermometer (precision, 0.01 K) inside the inner chamber of the vessel. An excess of 2-methylnaphthalene was added to the glass vessel to the next temperature value after the sample was taken out from the saturated solution at a certain temperature. The solubility in mole fraction of the solute (x) in different solvents is defined as follows: x=

mA /MA mA /MA + mB /MB

ln x = A +

where mA and mB are the masses of solute and solvents and MA and MB are the molecule weights of solute and solvents, respectively. GC Conditions. The type of capillary column used in the GC was an OV-17 column (3500 mm × 3 mm). The following conditions were used: temperatures, 473 K (injector) and 423 K (FID); carrier gas, N2, with flow rate of 2.2 mL·min−1; temperature program, from 373 K (10 min) to 513 K (12 min) at 12 K·min−1; injection mode, split; split ratio, 10:1; injection volume, 0.4 μL.

B (T /K)

(1)

where x represents the mole fraction solubility of 2methylnaphlene; the parameters A and B can be acquired by regression of the solubility using multidimensional unconstrained nonlinear minimization. The objective function (OF) is expressed as ⎛ x cal − x exp ⎞2 OF = ∑ ⎜⎜ i cal i ⎟⎟ xi ⎠ i=1 ⎝ N

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RESULTS AND DISCUSSION Solubility Data. The mole fraction solubility data of 2methylthphalene in ethylene glycol, ethanol, acetone, 1,4dioxane, isopropanol, butyl acetate, n-heptane, n-butyl alcohol, and n-hexane in the temperature range from (278.15 to 303.15) K are listed in Table 2. The dependence of 2-methylthphalene solubility on temperature has been presented in Figure 1. The results suggest that the mole fraction solubility of 2methylnaphthalene increases with increasing temperature. The solubility of 2-methylnaphthalene in mole fraction in the

(2)

where N is the number of experimental points. The superscript “cal” stands for evaluated values, and “exp”, experimental values. The calculated solubility is listed in Table 2. The values of A and B, along with the relative deviation (RD) and root-meansquare deviations (RMSD) achieved are presented in Table 3. The RD and RMSD are defined as follows:

RD = 1700

xi − xical xi

(3) DOI: 10.1021/je5010627 J. Chem. Eng. Data 2015, 60, 1699−1705

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Table 2. Mole Fraction Solubility of 2-Methylnaphthalene in Different Organic Solvents with the Temperature Range from (278.15 to 303.15) K under 0.1 MPaa van’t Hoff model T K 278.25 283.25 288.35 293.25 298.35 303.25

λh equation

Apelblat

RD x 0.007418 0.008106 0.008642 0.009633 0.010245 0.01149

cal

x

0.007326 0.008040 0.008811 0.009592 0.01045 0.01131

av value

% 1.24 0.81 −1.95 0.43 −1.96 1.53

RD cal

x

%

Ethylene Glycol 0.007461 −0.57 0.008034 0.89 0.008718 −0.88 0.009483 1.56 0.01041 −1.55 0.01143 0.47

1.32

Wilson model RD

cal

x

0.007417 0.008053 0.009115 0.01094 0.01500 0.027950

0.99

% 0.020 0.66 −5.48 −13.56 −4.41 −14.34

RD cal

x

0.004623 0.006059 0.008167 0.011299 0.017118 0.031172

6.41

% 3.70 25.30 5.50 −17.30 −6.1 −17.3 12.53

Ethanol 278.25 283.25 288.35 293.25 298.35 303.25

0.03893 0.05798 0.1089 0.1476 0.2874 0.4581

0.03427 0.05602 0.09842 0.1661 0.2810 0.4582

av value

11.94 3.38 9.62 −12.49 2.21 −0.01

0.03523 0.05678 0.09867 0.1656 0.2802 0.4587

9.50 2.07 9.39 −12.18 2.52 −0.12

6.61

0.03890 0.06422 0.1069 0.1757 0.3021 0.5373

5.96

0.051 −10.77 1.86 −19.00 −5.12 −17.29

0.04242 0.05627 0.07936 0.12425 0.33675 0.90319

9.02

−9 3 27.1 15.8 −17.2 −9.2 13.55

Acetone 278.45 283.25 288.35 293.25 298.35 303.25

0.2183 0.2864 0.3678 0.4841 0.5876 0.7413

0.2035 0.2787 0.3799 0.5063 0.6760 0.8843

av value

6.77 2.70 −3.28 −4.58 −15.05 −19.29

−2.18 −0.54 −0.80 3.11 −1.23 −0.14

0.2230 0.2880 0.3708 0.4691 0.5949 0.7423

8.61

0.1935 0.2778 0.3892 0.5203 0.6783 0.8439

1.33

11.37 3.00 −5.81 −7.46 −15.43 −13.84

0.2301 0.2775 0.3436 0.439 0.6182 0.8994

9.49

−5.4 3.1 6.6 9.3 −5.2 −21.3 8.48

1,4-Dioxane 278.25 283.25 288.35 293.25 298.35 303.25

0.4677 0.5081 0.5746 0.6499 0.7258 0.8168

0.4553 0.5152 0.5806 0.6516 0.7284 0.8113

av value 278.25 283.25 288.35 293.25 298.35 303.25

1.07 0.02763 0.05076 0.07695 0.1333 0.2334 0.4300

0.02099 0.03955 0.07476 0.1350 0.2445 0.4248

av value 278.15 283.15 288.15 293.15 298.15 303.15

24.05 22.08 2.85 −1.27 −4.77 1.21 9.37

0.6210 0.6731 0.7292 0.7868 0.8494 0.9506

0.6128 0.6707 0.7318 0.7962 0.8637 0.9344

av value 278.25 283.25

2.65 −1.40 −1.04 −0.25 −0.37 0.68

1.32 0.35 −0.37 −1.19 −1.68 1.70 1.10

0.05961 0.07943

0.03703 0.06882

37.87 13.35

0.4617 0.5154 0.5766 0.6464 0.7260 0.8168

1.29 −1.43 −0.35 0.54 −0.04 0.01

0.61 Isopropanol 0.02195 20.56 0.04048 20.26 0.07533 2.10 0.1349 −1.21 0.2438 −4.45 0.4249 1.17 8.29 Butyl Acetate 0.6188 0.35 0.6704 0.39 0.7277 0.20 0.7913 −0.57 0.8618 −1.46 0.9399 1.13 0.68 n-Butyl Alcohol 0.03850 35.41 0.07016 11.66 1701

0.4731 0.5150 0.5672 0.6338 0.7215 0.8419

−1.16 −1.36 1.29 2.48 0.58 −3.06

0.4675 0.5151 0.5713 0.6358 0.7213 0.8441

1.66 0.03150 0.04972 0.08060 0.1310 0.2283 0.4333

−13.97 2.04 −4.74 1.70 2.19 −0.78

1.37 0.03156 0.04247 0.06118 0.09982 0.36054 0.90684

4.24 0.6190 0.6725 0.7299 0.7916 0.8579 0.9294

0.32 0.08 −0.10 −0.61 −1.01 2.23

36.38 10.88

−14.2 16.3 20.5 25.1 −54.5 −11.9 23.75

0.62251 0.67151 0.7268 0.78648 0.85758 0.93568

0.73 0.03792 0.07084

0.1 −1.4 0.6 2.2 0.6 −3.3

0.62 0.67 0.72 0.78 0.84 0.95 0.76

0.06179 0.08123

−3.6 −2.3

DOI: 10.1021/je5010627 J. Chem. Eng. Data 2015, 60, 1699−1705

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Table 2. continued van’t Hoff model T

RD xcal

x

K 288.35 293.25 298.35 303.25

λh equation

Apelblat

0.1304 0.2233 0.3705 0.6799

0.1267 0.2231 0.3942 0.6691

av value

% 2.88 0.10 −6.41 1.60

RD xcal

%

n-Butyl Alcohol 0.1274 2.30 0.2228 0.21 0.3931 −6.10 0.6695 1.54

10.37

Wilson model RD

xcal 0.1303 0.2283 0.3971 0.6540

9.54

RD

%

xcal

%

0.06 −2.23 −7.18 3.82

0.11344 0.17562 0.44502 0.90686

13.0 21.4 −20.1 −33.4

10.09

15.63

n-Heptane 278.15 283.15 288.15 293.15 298.15 303.15

0.5023 0.5786 0.6502 0.7262 0.8309 0.9065

0.5070 0.5752 0.6496 0.7307 0.8187 0.9138

av value

−0.94 0.60 0.09 −0.62 1.47 −0.81

−0.51 0.61 −0.12 −0.86 1.37 −0.60

0.5048 0.5751 0.6510 0.7325 0.8195 0.9119

0.76

0.5036 0.5747 0.6515 0.7335 0.8205 0.9121

0.68

−0.26 0.67 −0.19 −1.00 1.26 −0.62

0.50798 0.57041 0.64502 0.72962 0.83133 0.93159

0.67

0.50 0.57 0.65 0.72 0.83 0.90 0.70

n-Hexane 278.95 283.25 288.35 293.25 298.35 303.25

0.2827 0.3479 0.4428 0.5500 0.6427 0.8112

0.2812 0.3520 0.4391 0.5391 0.6627 0.8027

av value a

0.52 −1.20 0.83 1.98 −3.10 1.04

−0.40 −1.36 1.11 2.36 −2.90 0.79

0.2838 0.3526 0.4379 0.5370 0.6613 0.8047

1.45

0.2823 0.3526 0.4405 0.5437 0.6752 0.8305

1.49

0.14 −1.37 0.52 1.15 −5.06 −2.38

0.2921 0.3454 0.4173 0.5154 0.6805 0.9054

1.77

−3.3 0.7 5.8 6.3 −5.9 −11.6 5.60

The relative standard uncertainty is u(x) = 2%. The standard uncertainties u are u(T) = 0.01 K and u(p) = 2 kPa.

Modified Apelblat Equation. The solubility of 2methylnaphthalene with temperature is correlated with the modified Apelblat equation, which is a semiempirical equation based on solid−liquid phase equilibrium,18 and is expressed as ln(x) = A +

n

∑ i=1

(xical

⎤1/2

2⎥

− xi)

⎥⎦

(5)

where A, B, and C are the model parameters. The value of C reflects the effect of temperature on the fusion enthalpy. The experimental solubility data of 2-methylnaphalene were correlated with eq 5 using a nonlinear regression, and the calculated solubility are given in Table 2 and plotted in Figure 1. The regressed values of parameters A, B, and C together with the RD and RMSD are shown in Table 3. Table 3 and Figure 1 indicate that the calculated values by the modified Apelblat equation make a better agreement with the experimental values than those obtained from other models. The values of RMSD are not higher than 0.01. So the experimental solubility of 2-methylthphalene in the selected organic solvents at different temperatures can be correlated by the modified Apelblat equation. Buchowski−Ksiązċ zak λh Equation. Equation 6, originally proposed by Buchowski,19 is the expression for the λh equation. Parameters λ and hare parameters needed to correlate the experimental solubility data of 2-methylthphalene.

Figure 1. Solubility (x) of 2-methylnaphthalene with mole fraction in various solvents at different temperatures: ■, ethylene glycol; ●, ethanol; ▲, acetone; ▼, 1,4-dioxane; ◀, isopropanol; ▶, butyl acetate; ⧫, n-butyl alcohol; ☆, n-heptane; ★, n-hexane; , calculated values from modified Apelblat equation.

⎡1 RMSD = ⎢ ⎢⎣ n

B + C ln(T /K) (T /K)

(4)

xcal i

where n represents the number of experimental points, is the calculated solubility, and xi represents the experimental data of 2-methylthphalene. The value in Table 3 shows that the maximum value of RMSD calculated with the van’t Hoff model is 0.06974. In general the calculated solubility via the van’t Hoff model shows good accordance with the experiment value for the studied systems except for acetone and n-butyl alcohol.

⎛1 ⎡⎛ λ(1 − x) ⎞⎤ 1 ⎞ ln⎢⎜1 + ⎟⎥ = λ h ⎜ − ⎟ ⎠⎦ x Tm ⎠ ⎣⎝ ⎝T

(6)

where Tm is the melting point of 2-methylnaphthalene. The regressed values of λ and h and the RMSD values are given in 1702

DOI: 10.1021/je5010627 J. Chem. Eng. Data 2015, 60, 1699−1705

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Table 3. Parameters of the Equations for 2-Methylnaphthalene in Different Solventsa van’t Hoff model

a

solvent

A

ethylene glycol ethanol acetone 1,4-dioxane isopropanol butyl acetate n-butyl alcohol n-heptane n-hexane

0.350780 28.9840 16.2289 6.21912 32.7651 4.62522 31.8093 6.46455 11.4533

modified Apelblat equation

B −1465.55 −9026.08 −4958.70 −1948.71 −10195.6 −1422.71 −9768.02 −1987.05 −3539.85 λh equation

102RMSD

A

B

0.014 0.93 7.0 0.68 0.74 1.0 1.5 0.66 1.0

−189.16 −83.7281 −6.4430 −126.089 −105.503 −97.4026 −91.7945 46.5915 −56.5992

6804.79 −4036.84 −3208.71 3829.23 −4047.60 3028.07 −4277.75 −3739.50 −558.493

C 28.3927 16.8448 2.92693 19.8199 20.6481 15.2867 18.4616 −6.0110 10.1887 Wilson model

102RMSD 0.010 0.91 0.72 0.42 0.68 0.71 1.4 0.60 1.0

solvent

λ

h

102RMSD

λ12

λ21

102RMSD

ethylene glycol ethanol acetone 1,4-dioxane isopropanol butyl acetate n-butyl alcohol n-heptane n-hexane

−0.00619660 0.49385 1.97129 −0.30035 0.29150 0.62517 1.15756 1.28137 0.81817

830543 15212.9 3270.75 3920.90 22979.3 1505.86 8559.42 1843.44 4003.18

0.70 3.5 5.4 64 21 78 2.9 71 1.6

1079.75 469.071 −9.45334 −311.997 636.030 −316.165 389.882 −244.519 −30.7725

5953.27 852.879 822.697 1222.42 756.402 605.240 6484.32 6544.73 6268.76

3.2 18 20 12 18 10 26 15 20

Standard uncertainties u are u(A) = u(B) = u(C) = 0.010, u(λ) = u(h) = 0.013, and u(λ12) = u(λ21) = 0.012.

The mean relative deviation (ARD%) plots for the solubility of 2-methylnaphthalene in different solvents with the four models are shown in Figure 2. It can be seen that the threeparameter Apelblat equation gives a lower mean relative deviation than the other three models.

Table 3. Table 3 shows that the maximum RMSD is 0.776 with the λh equation, with a higher value than that of the modified Apelblat equation. Wilson Equation. The relationship between the solubility of 2-methylnaphthalene in solvent and temperature can be expressed as follows:20 ln(xiγi) =

ΔHm ⎛ 1 1⎞ − ⎟ ⎜ R ⎝ Tm Ti ⎠

(7)

where ΔHm is the fusion enthalpy of 2-methylnaphthalene at the melting temperature Tm. The Wilson equation is expressed as eq 8, which is an expression of activity coefficient. ln γi = 1 − ln(∑ Λijxj) − j

∑ k

Λkixk ∑j Λkjxj

(8)

where Λij is the interaction parameter and can be calculated by Λij =

⎛ λij − λii ⎞ Vj ⎛ Δλij ⎞ exp⎜ − exp⎜ − ⎟= ⎟ Vi RT ⎠ Vi ⎝ ⎝ RT ⎠

Vj

Figure 2. Mean relative deviation (ARD%) plots for the solubility of 2methylnaphthalene in different solvents with the four models.

(9)

Vi is the molar volume of liquid component i. Δλij is the energy parameter (J·mol−1) of interaction between the components i and j, which are adjustable parameters, and has relevance with temperature. The two parameters could be obtained by regression from the experimental solubility data. The melting point and the fusion enthalpy were reported in previous publications for 2-methylnaphalene,23 which were 307.73 K and 11.966 kJ·mol−1. The calculated solubility and the regressed values of parameters Δλij are presented in Tables 2 and 3, respectively. From Table 3, we can see that the average value of RMSD calculated with the Wilson model is a little higher than those with the modified Apelblat equation and Δλh equation.

Thermodynamic Properties for the Solution. The standard thermodynamic properties could provide important information about the dissolution of compounds in a solvent. ° ) and standard The standard dissolution enthalpy (ΔHsol ° ) can be calculated from the van’t dissolution entropy (ΔSsol Hoff equation. The functions in the dissolution process of 2methylnaphthalene are calculated according to the solubility of 2-methylnaphthalene in different organic solvents. The standard molar enthalpy of dissolution (ΔH°sol) is generally acquired from eq 10:25 1703

DOI: 10.1021/je5010627 J. Chem. Eng. Data 2015, 60, 1699−1705

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

dissolution enthalpy in nine kinds of solvents is almost opposite to the change of the solubility. It can be inferred from ΔH°sol > 0 that the dissolution process is endothermic. The values of enthalpy are higher than those of entropy, which suggests that more energy is needed to overcome the force between the solute and the solvent in the dissolution process.26,27 ΔS°sol was positive for all the organic solvents, which demonstrated that the force for the dissolution process was entropy-driven. Equations 13 and 14 are employed to calculate enthalpy (%ζH) and entropy (%ζTS).16,28−30

(10)

The heat capacity change of solution can be assumed to be constant over the limited temperature interval studied at (278.15 to 303.15) K. The enthalpy of solution independent of temperature results from the vanishing of the heat capacity change. Hence, the values of ΔHsol would also be calculated for the mean temperature, Tmean = 290.53 K. The ΔGsol ° is calculated by (11)

%ξH =

(13)

“Intercept” stands for the intercept of the plot of ln x versus (1/ T − 1/Tmean). The standard molar entropy, ΔSsol ° , is calculated by

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

%ξTS =

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

(14)

° = −RTmean × intercept ΔGsol

° − ΔGsol ° ΔHsol ° = ΔSsol Tmean

The calculated %ζH and %ζTShave also been presented in Table 4 which showed that the values of %ζH were greater than those of %ζTS; the standard enthalpy was the main contributor to the standard Gibbs energy during the dissolution of 2methylnaphthane in the studied solvents.

(12)

Figure 3 presents the plot of ln x against (1/T − 1/Tmean) for 2-methylnaphthalene in different solvents at studied temper-

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CONCLUSION The solubility behavior of 2-methylnaphthalene in nine pure solvents, ethylene glycol, ethanol, acetone, 1,4-dioxane, isopropanol, butyl acetate, n-butyl alcohol, n-heptane, and nhexane, were determined experimentally by the equilibrium methods at different temperatures. The solubility data show a dependence on temperature which is found to increase with temperature in the following order: butyl acetate > n-heptane > 1, 4−dioxane > n-hexane > acetone > n-butyl alcohol > ethanol > isopropanol > ethylene glycol. Four models are utilized to correlate the solubility values of 2-methylnaphthalene in nine organic solvents. It turned out that the modified Apelblat equation could give better satisfactory correlation results with the experimental solubility data than those obtained by other models. Furthermore, the thermodynamic properties in the selected solvents were calculated with the values of standard molar enthalpy, and molar Gibbs energy changes are positive in the dissolution. The results indicated that the process was endothermic. The solubility data and correlation results are essential and would possess potential application for the purification process of 2-methylnaphthalene in industrial scale and for further theoretical studies.

Figure 3. Plots of ln x against 104(1/T − 1/Tmean) for 2methylnaphthalene in different solvents: ■, ethylene glycol; ●, ethanol; ▲, acetone; ▼, 1,4-dioxane; ◀, isopropanol; ▶, butyl acetate ; ⧫, n-butyl alcohol; ☆, n-heptane; ★, n-hexane.

atures. We can see from Figure 3 that the plots are linear, and the values of ΔH°sol, ΔS°sol, and the change of ΔG°sol are listed in Table 4. Results show that the change tendency of the

Table 4. Thermodynamic Functions Relative to the Dissolution Process of 2-Methylnaphthalene in Solvents at Mean Temperaturea

a

ΔHsol °

ΔGsol °

ΔSsol °

ζH

ζTS

solvent

(kJ·mol−1)

(kJ·mol−1)

(J·mol−1·K−1)

%

%

ethylene glycol ethanol acetone 1,4-dioxane isopropanol butyl acetate n-butyl alcohol n-heptane n-hexane

11.98 71.39 34.24 15.93 75.63 11.61 69.20 16.63 29.35

11.32 4.89 2.11 1.16 5.34 0.64 4.06 0.89 1.73

2.26 228.90 110.58 50.83 241.93 37.75 224.18 54.19 95.06

95.00 52.79 52.67 52.98 52.90 52.51 52.59 52.46 52.60

5.00 47.21 47.33 47.02 47.10 47.49 47.41 47.54 47.40

Standard uncertainties u are u(T) = 0.01 K, u(ΔHsol ° ) = u(ΔGsol ° ) = 0.1 kJ·mol−1, u(ΔSsol ° ) = 0.1 J·mol−1·K−1. 1704

DOI: 10.1021/je5010627 J. Chem. Eng. Data 2015, 60, 1699−1705

Journal of Chemical & Engineering Data

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Article

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The authors declare no competing financial interest.

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DOI: 10.1021/je5010627 J. Chem. Eng. Data 2015, 60, 1699−1705