Determination and Correlation of Solubilities of Lauric Acid in Eight

Aug 14, 2014 - ABSTRACT: The solubilities of lauric acid in methanol, ethanol, propanol, n-butanol, n-pentanol, n-hexanol, isobutanol, and isoamylol...
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Determination and Correlation of Solubilities of Lauric Acid in Eight Alcohols Zhi-Hong Yang, Zuo-Xiang Zeng,* Li Sun, Wei-Lan Xue,* and Nan Chen Institute of Chemical Engineering, East China University of Science and Technology, Shanghai 200237, People’s Republic of China ABSTRACT: The solubilities of lauric acid in methanol, ethanol, propanol, n-butanol, n-pentanol, n-hexanol, isobutanol, and isoamylol were measured by synthetic method in the temperature ranging from (276.17 to 306.12) K. Results of these measurements were correlated by the modified Apelblat equation, the λh equation and activity coefficient models (NRTL and UNIQUAC). It was found that the modified Apelblat equation and the λh equation gave better correlation results. The thermodynamic properties of the solution process, including the Gibbs energy, enthalpy, and entropy were calculated by the van’t Hoff analysis.

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INTRODUCTION Lauric acid (CAS registry no. 143-07-7) is a fatty acid obtained from oils and fats as coconut oil and palm kernel oil by hydrolysis at high temperature and pressure.1,2 It is a raw material used as soaps, food, fiber materials, and other surface active agents.3,4 Besides, lauric acids with other saturated fatty acids have been used as metal-working lubricants to reduce friction between the moving chip and the contact surface of any cutting tool.5 Also, glycerol monolaurate produced from lauric acid is known to the pharmaceutical industry for its good antimicrobial properties.6,7 The esterification of lauric acid with short chain alcohols (1− 6 carbon atoms) is very important due to their industrial application, and esters produced from the esterification are mostly used as solvents, plasticizers, synthetic food odorants and scents, as well as precursors for various pharmaceuticals, agrochemicals and other compounds.8,9 For example, methyl laurate is used for chemical pruning of fieldgrown crops. It causes necrosis of the terminal bud and thus release axillary buds from apical dominance.10 Isoamyl laurate is used as a flavor in beer and wines.11 The solubility of lauric acid in the alcohols is closely related to the esterification and the purification of reaction mixture. Solubility data of lauric acid in some solvents were reported a long time ago. Harry et al. determined the solubility of lauric acid in methyl alcohol at low temperatures from 243 K up to 263 K.12 Ralston et al. determined the lauric acid solubility in ethanol from 273 K up to 313 K.13 Maeda et al. determined its solubility in ethanol at four temperatures in the study of the acid precipitation using water as antisolvent.14 Emilio et al. determined the lauric acid solubility in 2-propanol and propanol at the temperature from 279.0 K up to 315.3 K.6 However, it was found that no experimental solubility data of lauric acid in other alcohols were available in the literature, so an additional study is needed. In this work, the solubilities of lauric acid in methanol, ethanol, propanol, n-butanol, n-hexanol, n-pentanol, isobutanol, © 2014 American Chemical Society

and isoamylol were measured in the temperature range of (276.17−306.12) K. The experimental solubility data are correlated by Buchwski-Ksiazaczak λh equation, Apelblat equation, and activity coefficient models (NRTL and UNIQUAC).

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EXPERIMENTAL SECTION Lauric acid (mass fraction ≥ 98.0 %) was purchased from Shanghai Lingfeng Chemical Reagent Co., Ltd. of China. It was crystallized three times from acetone. Its purity checked by gas chromatography (8700 PerkinElmer) was 0.999 mass fraction.15 The methanol, ethanol, propanol, n-butanol, n-pentanol, n-hexanol, isobutanol, and isoamylol (purchased from Shanghai Chemistry Reagent Company, China) used for experiments were analytical reagent grade. Their mass fraction purities were better than 99.5 %. The solubility of a solid in a solvent is generally determined by two static methods: analytical method16,17 and synthetic method.18−20 In this work, the synthetic method was used to determine the equilibrium of the solid−liquid system. The apparatus and the procedure were similar to those described in the literature.21−23 The experimental apparatus includes a glass solid−liquid equilibrium vessel surrounded by water jackets, a laser detecting system, a temperature controlling system and a magnetic stirring system. The glass cell is about 150 cm3 volume with a to-and-fro magnetic stirrer. Laser beam go through the glass vessel, and the power of laser is converted into electrical signal and detected by galvanometer. A short description of the experiment is given as follows: A predetermined mass of solvent (about 20 g ± 0.001 g) was added to a glass vessel with a magnetic stirrer and a mercury thermometer with the precision of ± 0.05 K. The temperature Received: March 7, 2014 Accepted: July 28, 2014 Published: August 14, 2014 2725

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Table 1. Experimental and Calculated Solubilities of Lauric Acid in in Methanol, Ethanol, Propanol, n-Butanol, n-Pentanol, nHexanol, Isobutanol, and Isoamylol at Temperature T and Pressure p = 0.1 MPaa γ1

(x1exp -x1cal)/x1exp T/K

x1exp

Apeblat

λh

276.17 279.16 282.16 285.15 288.15 291.14 294.14 297.13 300.13 303.12 306.12

0.0318 0.0419 0.0555 0.0723 0.0942 0.1231 0.1607 0.2077 0.2643 0.3411 0.4328

0.0126 0.0048 0.0054 −0.0028 −0.0074 −0.0041 0.0025 0.0043 −0.0057 0.0035 −0.0009 0.0049

0.0189 0.0095 0.0072 −0.0028 −0.0085 −0.0049 0.0019 0.0039 −0.0057 0.0038 −0.0007 0.0062

0.0422 0.0554 0.0739 0.0924 0.1186 0.1508 0.1938 0.2436 0.3053 0.3857 0.4825

−0.0213 −0.0090 0.0230 −0.0043 −0.0017 −0.0040 0.0072 0.0012 −0.0052 0.0010 0.0002 0.0065

0.0095 0.0126 0.0352 0.0022 −0.0008 −0.0073 0.0021 −0.0045 −0.0092 0.0005 0.0052 0.0081

0.0540 0.0685 0.0859 0.1083 0.1352 0.1685 0.2103 0.2611 0.3189 0.3992 0.4882

−0.0037 0.0015 −0.0023 0.0028 0.0000 −0.0006 0.0024 0.0038 −0.0094 0.0055 −0.0010 0.0028

0.0130 0.0117 0.0023 0.0037 −0.0015 −0.0036 −0.0005 0.0015 −0.0107 0.0058 0.0008 0.0050

0.0646 0.0801 0.0999 0.123 0.1509 0.1882 0.2293 0.2833 0.3377 0.4179 0.5101

−0.0077 −0.0062 0.0010 −0.0008 −0.0053 0.0096 0.0022 0.0113 −0.0145 0.0002 0.0020 0.0053

0.0170 0.0075 0.0080 0.0000 −0.0080 0.0048 −0.0031 0.0071 −0.0166 0.0007 0.0057 0.0071

0.0742 0.0907 0.1126 0.1372 0.1668

0.0054 −0.0033 0.0062 0.0015 −0.0042

0.0175 0.0044 0.0098 0.0015 −0.0060

ARD 276.17 279.16 282.16 285.15 288.15 291.14 294.14 297.13 300.13 303.12 306.12 ARD 276.17 279.16 282.16 285.15 288.15 291.14 294.14 297.13 300.13 303.12 306.12 ARD 276.17 279.16 282.16 285.15 288.15 291.14 294.14 297.13 300.13 303.12 306.12 ARD 276.17 279.16 282.16 285.15 288.15

NRTL methanol −0.2673 −0.1885 −0.1117 −0.0609 −0.0191 0.0146 0.0361 0.0400 0.0242 0.0067 −0.0252 0.0689 ethanol −0.2014 −0.1264 −0.0487 −0.0335 −0.0025 0.0146 0.0315 0.0267 0.0138 0.0008 −0.0189 0.0472 propanol −0.1185 −0.0774 −0.0489 −0.0185 0.0000 0.0131 0.0223 0.0234 0.0078 0.0043 −0.0172 0.0319 n-butanol −0.0774 −0.0549 −0.0280 −0.0138 −0.0040 0.0170 0.0161 0.0229 −0.0003 0.0005 −0.0110 0.0224 n-pentanol −0.0539 −0.0419 −0.0160 −0.0073 −0.0012 2726

UNIQUAC

NRTL

UNIQUAC

−0.4151 −0.2721 −0.1423 −0.0539 0.0138 0.0601 0.0809 0.0727 0.0371 −0.0038 −0.0541 0.1096

3.1339 3.0192 2.8940 2.7568 2.6039 2.4325 2.2407 2.0315 1.8121 1.5822 1.3698

2.8923 2.8829 2.8521 2.7922 2.6940 2.5485 2.3505 2.1074 1.8403 1.5660 1.3310

−0.2464 −0.1516 −0.0568 −0.0314 0.0067 0.0279 0.0444 0.0361 0.0167 −0.0036 −0.0294 0.0592

2.5085 2.4232 2.3273 2.2259 2.1114 1.9857 1.8453 1.6977 1.5433 1.3865 1.2425

2.4242 2.3753 2.3096 2.2311 2.1316 2.0127 1.8708 1.7150 1.5487 1.3801 1.2294

−0.1556 −0.0978 −0.0582 −0.0175 0.0074 0.0237 0.0333 0.0314 0.0110 0.0005 −0.0268 0.0421

2.1220 2.0651 2.0028 1.9336 1.8571 1.7720 1.6773 1.5740 1.4645 1.3458 1.2318

2.0568 2.0270 1.9874 1.9358 1.8714 1.7923 1.6974 1.5884 1.4699 1.3409 1.2198

−0.1053 −0.0712 −0.0350 −0.0130 0.0013 0.0250 0.0244 0.0286 0.0021 −0.0026 −0.0184 0.0297

1.8486 1.8078 1.7624 1.7123 1.6567 1.5938 1.5251 1.4482 1.3680 1.2787 1.1896

1.8042 1.7818 1.7518 1.7135 1.6660 1.6070 1.5382 1.4575 1.3713 1.2750 1.1807

−0.0714 −0.0518 −0.0195 −0.0058 0.0030

1.6502 1.6193 1.5845 1.5462 1.5035

1.6260 1.6066 1.5813 1.5500 1.5118

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Table 1. continued γ1

(x1exp -x1cal)/x1exp x1exp

T/K 291.14 294.14 297.13 300.13 303.12 306.12

−0.0025 −0.0065 0.0017 0.0117 −0.0090 0.0017 0.0043

−0.0049 −0.0093 −0.0003 0.0109 −0.0085 0.0036 0.0070

0.0827 0.0991 0.1219 0.1513 0.1834 0.2198 0.2655 0.3222 0.3898 0.4639 0.5495

0.0206 −0.0081 −0.0066 0.0086 0.0038 −0.0082 −0.0090 −0.0009 0.0072 0.0030 −0.0029 0.0063

0.0230 −0.0061 −0.0057 0.0093 0.0038 −0.0086 −0.0094 −0.0012 0.0069 0.003 −0.0027 0.0073

0.0659 0.0817 0.1021 0.1277 0.1576 0.1945 0.238 0.2889 0.3514 0.4224 0.5138

0.0015 −0.0086 −0.0069 0.0023 0.0006 0.0046 0.0038 −0.0007 0.0006 −0.0059 0.0027 0.0031

−0.0121 −0.0184 −0.0118 0.0000 0.0013 0.0072 0.0067 0.0028 0.0028 −0.0057 −0.0006 0.0063

0.0814 0.1001 0.1218 0.1497 0.1788 0.2168 0.2625 0.3147 0.3764 0.4463 0.5371

0.0037 0.0080 0.0049 0.0154 0.0000 0.0028 0.0065 0.0035 0.0005 −0.0081 0.0002 0.0043

−0.0074 −0.0020 −0.0041 0.0080 −0.0062 −0.0009 0.0046 0.0035 0.0016 −0.0063 0.0019 0.0043

ARD 276.17 279.16 282.16 285.15 288.15 291.14 294.14 297.13 300.13 303.12 306.12 ARD 276.17 279.16 282.16 285.15 288.15 291.14 294.14 297.13 300.13 303.12 306.12 ARD a

λh

0.2037 0.2467 0.3015 0.3685 0.4354 0.5298 ARD

276.17 279.16 282.16 285.15 288.15 291.14 294.14 297.13 300.13 303.12 306.12

Apeblat

NRTL n-pentanol 0.0079 0.0081 0.0139 0.0166 −0.0071 −0.0102 0.0167 n-hexanol −0.0351 −0.0424 −0.0238 0.0033 0.0082 0.0041 0.0053 0.0102 0.0113 0.0004 −0.0133 0.0143 isobutanol −0.0986 −0.0734 −0.0431 −0.0125 0.0038 0.0185 0.0227 0.0183 0.0122 −0.0045 −0.0146 0.0293 isoamylol −0.0577 −0.0350 −0.0222 0.0007 −0.0028 0.0078 0.0152 0.0137 0.0080 −0.0054 −0.0089 0.0161

UNIQUAC

NRTL

UNIQUAC

0.0137 0.0138 0.0176 0.0171 −0.0094 −0.0155 0.0217

1.4558 1.4031 1.3445 1.2805 1.2157 1.1472

1.4660 1.4127 1.3512 1.2827 1.2134 1.1415

−0.0435 −0.0464 −0.0246 0.0046 0.0109 0.0073 0.0083 0.0118 0.0113 −0.0015 −0.0162 0.0169

1.5085 1.4817 1.4518 1.4187 1.3823 1.3429 1.2993 1.2523 1.2022 1.1518 1.1026

1.4961 1.4755 1.4504 1.4207 1.3864 1.3475 1.3033 1.2545 1.2022 1.1498 1.0992

−0.1214 −0.0869 −0.0460 −0.0094 0.0108 0.0267 0.0303 0.0235 0.0134 −0.0078 −0.0224 0.0362

1.7763 1.7394 1.6980 1.6520 1.6009 1.5440 1.4807 1.4116 1.3360 1.2572 1.1757

1.7404 1.7199 1.6922 1.6564 1.6120 1.5578 1.4935 1.4201 1.3381 1.2526 1.1664

−0.0762 −0.0450 −0.0255 0.0027 0.0022 0.0143 0.0213 0.0178 0.0090 −0.0081 −0.0151 0.0216

1.4991 1.4788 1.4559 1.4298 1.4006 1.3673 1.3294 1.2872 1.2399 1.1889 1.1337

1.4739 1.4648 1.4512 1.4322 1.4077 1.3765 1.3381 1.2931 1.2415 1.1857 1.1267

Standard uncertainties u are u(T) = 0.05 K, ur(p) = 0.05, ur(x1) = 0.02.

of this system was controlled to be constant (fluctuates within ± 0.05 K) by a low temperature thermostat. A known mass of lauric acid was added into the vessel at a constant temperature and the mass of the lauric acid was determined by an analytical balance with an accuracy of ± 0.001 g. The dissolution of the solute was examined by the laser beam penetrating the vessel. The power of the laser that went through the sample increased as the solid decreased. When the last piece of solid disappeared, the laser power reached the largest value, otherwise the laser power could not reach the largest value. When the laser power

reached the largest value, the next portion of solid was introduced. The above process was repeated until the laser power could not reach the largest value for 2 h and the last increment was less than 0.01 g. The same experiment was conducted at least three times, and the mean value was used to calculate the mole fraction solubility. By repeating the above procedure at different temperatures, the solubility of lauric acid in alcohols was obtained. The estimated uncertainty of the experimental solubility values is less than 2 %, which results from the uncertainties in 2727

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Table 2. Model Parameters in Different Solvents λh

Apeblat

a

NRTLa

UNIQUAC

system

a

b

c

λ

h

g12-g22

g21-g11

U12-U22

U21-U11

methanol ethanol propanol n-butanol n-pentanol n-hexanol isobutanol isoamylol

−23.71 −43.34 −85.01 −126.09 −72.03 11.53 18.38 −48.28

−5356.95 −3991.16 −1653.92 481.55 −1658.09 −5171.15 −5797.61 −2501.23

7.05 9.72 15.67 21.64 13.42 0.83 −0.02 9.75

0.96 1.07 0.92 0.91 0.93 1.00 0.91 0.88

7704.21 6539.75 6669.43 6327.63 5911.02 5409.24 6190.10 5845.34

997.41 772.23 1392.75 1603.46 1583.34 1109.13 1615.54 2082.26

2011.24 1679.31 782.08 296.15 27.73 147.56 188.98 −534.01

4010.04 2316.05 2043.96 1762.37 1486.14 1126.13 1737.69 1575.36

−740.27 −988.46 −1002.43 −963.64 −888.06 −726.22 −962.72 −969.71

Calculated with the third nonrandomness parameter α = 0.3.

liquid can be modeled by the following simplified thermodynamic equation:26,27

temperature measurements, measuring the weight and purity of the samples. To verify the reliability of the experimental apparatus, solubility of lauric acid in propanol was measured and compared with literature.6 Our results agreed with the data in literature, with an average solubility deviation of 2 %. So it has been proven that this experimental technique is reliable. The saturated mole fraction solubility of lauric acid (x1) in solvent is obtained from the following equation: x1 =

m1/M1 m1/M1 + m2 /M 2

ln x1γ1 =

(1)

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⎡ τ G 2 ⎤ τ12G12 21 21 ⎥ ln γ1 = x 2 2⎢ + (x 2 + x1G12)2 ⎦ ⎣ (x1 + x 2G21)2

RESULTS AND DISCUSSION Experimental solubilities of lauric acid in methanol, ethanol, propanol, n-butanol, n-pentanol, n-hexanol, isobutanol, and isoamylol from 276.17 to 306.12 K are listed in Table 1. The experimental solubilities data are correlated by the modified Apelblat equation, Buchwski-Ksiazaczak λh equation and activity coefficient models (NRTL and UNIQUAC). Modified Apelblat Equation. The relationship between solubility of lauric acid and temperature is correlated with the modified Apelblat equation24 b + c ln T T

(5)

where G12, G21, τ12, and τ21 are the model parameters. UNIQUAC Model. The UNIQUAC model is an extension of the quasi-chemical theory from Guggenheim30 for nonrandom mixtures containing components of different size. For each binary mixture the activity coefficient of this model has the form:31,32 ln γ1 = ln

ϕ1 x1

+

⎛ r ⎞ θ z q1 ln 1 + ϕ2⎜l1 − 1 l 2⎟ r2 ⎠ 2 ϕ1 ⎝

⎛ τ21 − q1 ln(θ1 + θ2τ21) + θ2q1⎜ ⎝ θ1 + θ2τ21

(2)

where a, b, and c are the empirical constants. The value of c represents the effect of temperature on the fusion enthalpy, as a deviation of heat capacity. The values of a and b reflect the variation in the solution activity coefficient and provide an indication of the effect of solution nonidealities on the solubility of solute. Buchwski−Ksiazaczak λh Equation. The Buchwski− Ksiazaczak λh equation was originally proposed by Buchowski et al.25 and is given as ⎛1 ⎛ 1 − x1 ⎞ 1 ⎞ ln⎜1 + λ ⎟ ⎟ = λh⎜ − x1 ⎠ Tm ⎠ ⎝T ⎝

(4)

where ΔfusHm is the enthalpy of fusion at the melting point. To calculate the solubility, melting temperature (Tm) and molar enthalpy of fusion of solute (ΔfusHm) are required. For lauric acid, Tm and ΔfusHm can be obtained from the literature.14 NRTL Model. The NRTL model proposed by Renon and Prausnitz28,29 contains three parameters per binary interaction, compared with the two parameters of the Wilson model, but is based on a similar local composition treatment. The activity coefficient of this model can be expressed as

where m1 represents the mass of solute and m2 represents the mass of solvents, respectively. M1 is the molecular mass of solute; M2 is the molecular mass of solvents, correspondingly.

ln x1 = a +

ΔfusHm ⎛ 1 1⎞ − ⎟ ⎜ R ⎝ Tm T⎠

−

⎞ τ12 ⎟ θ2 + θ1τ12 ⎠

(6)

Using model eqs 2−6, the solubilities of lauric acid in methanol, ethanol, propanol, n-butanol, n-pentanol, n-hexanol, isobutanol, and isoamylol were correlated, and the model parameters were optimized. The optimum algorithm applied in the parameter estimation program was the Nelder-Mead Simplex approach.33,34 Function f minsearch in the optimization toolbox of Matlab (Mathwork, MA) uses the Nelder-Mead Simplex approach and can be employed for the minimization of the objective function. Table 2 shows the optimized model parameters. The calculated values resulting from the modified Apelblat equation, Buchwski−Ksiazaczak λh equation and activity coefficient models (NRTL and UNIQUAC) and the comparisons between experimental data and calculated ones are shown in Figure 1 (in three alcohols: methanol, n-butanol, and

(3)

where λ and h are two adjustable parameters obtained from the solubility data and Tm is the melting temperature. The value of λ reflects the nonideality of the solution system, whereas h estimates the enthalpy of solution. Activity Coefficient Models. On the basis of the solid_liquid equilibrium criteria, the solubility of solute in 2728

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where N refers to the number of data points for each solvent, cal xexp 1,i is the experimental solubility value and x1,i is the calculated solubility value obtained from the models. From Table 1 and Figure 1, it was found that the solubilities of lauric acid in alcohols increase with increase of temperature, but the increment with temperature varies according to different solvents. The molar solubility decreases in the order methanol < ethanol < propanol < n-butanol < isobutanol < npentanol < isoamylol < n-hexanol at constant temperature. From Table 1, the overall ARDs of the four models are 0.47% (Apelblat), 0.64% (λh), 3.09% (NRTL), 4.21% (UNIQUAC) respectively. Therefore, the correlation goodness order of the models is the modified Apelblat equation > λh equation > NRTL model > UNIQUAC model. The experimental solubility and the correlation equations (Apelblat and λh) can be used as essential models in the esterification and purifying processes of lauric acid in industry.

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THERMODYNAMIC PROPERTIES FOR THE SOLUTION In this study, the thermodynamic functions in the process of solution of lauric acid are calculated on the basis of the solubility of lauric acid in different alcohols. The standard molar enthalpy of solution (ΔHosoln) is generally obtained from the slope of the ln x versus 1/T plot from eq 8, which is the van’t Hoff analysis and defined as ⎛ ∂ ln x1 ⎞ 0 ΔHsoln = −R ⎜ ⎟ ⎝ ∂(1/T ) ⎠

(8)

Over the limited temperature interval studied [(276.17 to 306.12) K], the heat capacity change of solution may be assumed to be constant; hence, the derived values of ΔHosoln would also be valid for the mean temperature, Tmean = 290.83 K. Equation 8 can also be written as ⎛ ⎞ ∂ ln x1 0 ΔHsoln = −R ⎜ ⎟ ⎝ ∂(1/T − 1/Tmean) ⎠

(9)

Figure 2 presents the plots of ln x1 against 10 (1/T − 1/ Tmean) for lauric acid in different solvents. From Figure 2, it is clear that the plots are linear, and the values of slope (k), intercept (d), and the correlation coefficient (r2) for the plots are listed in Table 3. So eq 9 can also be written as 4

0 ΔHsoln = −Rk

(10)

The standard molar Gibbs energy change for the solution process, ΔGosoln is calculated according to Krug et al.35 as o ΔGsoln = −RTmeand

The standard molar entropy change for the solution process, ΔSosoln is obtained as

Figure 1. Experimental mole fraction solubility (x1) of lauric acid in different alcohols: ■, methanol; ●, n-butanol; ▲, n-hexanol; −, correlation results: (a) modified Apelblat equation; (b) λh equation; (c) NRTL model; (d) UNIQUAC model.

o o ⎞ ⎛ ΔHsoln − ΔGsoln o ΔSsoln =⎜ ⎟ Tmean ⎝ ⎠

N

∑ i=1

cal |x1,exp i − x1, i |

x1,exp i

(12)

With the aim to compare the relative contributions by enthalpy (% ζH) and by entropy (% ζTS) toward the solution process, eqs 13 and 14 were employed.36,37

n-hexanol). The average relative deviations (ARDs) defined by eq 7 and activity coefficients are also listed in Table 1 1 ARD = N

(11)

%ζH = 100

(7) 2729

o |ΔHsoln | o o |ΔHsoln| + |T ΔSsoln |

(13)

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temperature and increased with rising temperature, but the increment was different for each alcohol. The experimental data were fitted by the modified Apelblat equation, λh equation and the activity coefficient models (NRTL and UNIQUAC), the results showed that the overall ARDs of the four models are 0.47% (Apeblat), 0.64% (λh), 3.09% (NRTL), and 4.21% (UNIQUAC), respectively. The thermodynamic properties for the solution process including Gibbs energy, enthalpy, and entropy were obtained by the van’t Hoff analysis. The thermodynamic parameters values proved that the solution process of lauric acid in the alcohols is endothermic, and the contributor to the standard molar Gibbs energy of solution is the enthalpy during the dissolution. Moreover, the experimental solubilities in this work and the correlation equation (Apeblat and λh) can be used for the purification and reaction system related to lauric acid.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

Figure 2. Plots of ln x1 against 104 (1/T − 1/Tmean) for lauric acid in different solvents: ■, methanol; ○, ethanol; ▲, propanol; ☆, nbutanol; ●, n-pentanol; ★, n-hexanol; △, isobutanol; □, isoamylol; −, correlation results. o |T ΔSsoln | %ζTS = 100 o o |ΔHsoln| + |T ΔSsoln |

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REFERENCES

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(14)

According to eqs 10−14 and values of k and d in Table 3, the above thermodynamic functions relative to solution process of lauric acid in solvents at mean temperature are obtained and also listed in Table 3. From Table 3, it can be seen that the variation tendency of the dissolution enthalpy in different solvents is almost opposite to the trend of the solubility. The standard Gibbs free energy of solution is positive in all cases as is the enthalpy of solution, therefore the dissolution process of lauric acid in alcohols is always endothermic. Moreover, from Table 3 it follows that in all the mixtures the main contributor to the standard molar Gibbs energy of solution of lauric acid is the enthalpy (% ζH > 52 %).

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CONCLUSIONS The solubilities of lauric acid in eight pure alcohols were measured from 276.15 K up to 306.15 K by a synthetic experimental method. The solubility was a function of

Table 3. Values of k, d, and Thermodynamic Functions Relative to Solution Process of Lauric Acid in Solvents at Mean Temperature solvent

k

d

r2

ΔHosoln/ KJ·mol−1

ΔGosoln/ KJ·mol−1

ΔSosoln/J·mol−1·K−1

% ζH

% ζTS

methanol ethanol propanol n-butanol n-pentanol n-hexanol isobutanol isoamylol

−0.7386 −0.6839 −0.6212 −0.5823 −0.5552 −0.5395 −0.5802 −0.5307

−2.1131 −1.9085 −1.7948 −1.6903 −1.6019 −1.5254 −1.6639 −1.5425

0.9991 0.9983 0.9986 0.9974 0.9975 0.9977 0.9996 0.9991

61.41 56.86 51.65 48.41 46.16 44.86 48.24 44.12

5.109 4.615 4.340 4.087 3.873 3.688 4.023 3.730

193.58 179.63 162.66 152.40 145.40 141.55 152.04 138.89

52.17 52.12 52.19 52.20 52.19 52.14 52.18 52.21

47.83 47.89 47.81 47.80 47.81 47.86 47.82 47.79

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