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Measurement and Modeling of Solubility of para-tert-Butylbenzoic Acid in Pure and Mixed Organic Solvents at Different Temperatures Vineet Aniya,†,‡ Debiparna De,† Abdul Muqeet Mohammed,† Prathap K. Thella,†,‡ and Bankupalli Satyavathi*,†,‡ †

Chemical Engineering Division, CSIR, Indian Institute of Chemical Technology, Hyderabad, Telangana 500007, India Academy of Scientific and Innovative Research (AcSIR), CSIR -Indian Institute of Chemical Technology Campus, Hyderabad, Telangana 500007, India

‡

ABSTRACT: The solid−liquid phase equilibrium of para-tertbutylbenzoic acid in methanol, ethanol acetic acid, propan2-ol, hexane, toluene, 1-octanol, para-tert-butyltoluene, methyl 4-tert-butylbenzoate, and binary (methanol + methyl 4-tertbutylbenzoate) mixed solvent have been determined experimentally within the temperature range of 293.15−333.15 K at atmospheric pressure using a static equilibrium method. The solubility of para-tert-butylbenzoic acid increased with the increase in temperature for the pure solvents, while in the case of methanol + methyl 4-tert-butylbenzoate a maximum solubility effect is achieved at 0.6115 solute-free mole fraction of methanol. The experimental solubility data in pure and binary solvent system were correlated by the modified Apelbat equation, the λh (Buchowski) equation, and the NRTL model, among which the modified Apelbat equation provided better agreement than those with the other models. Furthermore, to understand the nature of interactions involved in a solute−solvent system, the dissolution thermodynamic properties, including enthalpy, entropy, and Gibbs free energy, were determined. This experimental data will be an aid for the design and optimization of the separation and purification processes involving para-tert-butylbenzoic acid.

1. INTRODUCTION para-tert-Butylbenzoic acid is one of the tert-alkylaromatic hydrocarbons (molecular formula, C11H14O2; CAS Reg. No. 98-73-7) that plays an important role to make specialty resins, as an intermediate in pharmaceuticals and cosmetics, a modifier of alkyd resin, in intermediates for organic synthesis, lubricant additive agent, a fixative for fragrances, welding flux, and dye stuff. It is also the starting material for preparing a polycondensate and useful as a nucleating additive in plastic films and fibers. Further, it is also used for the production of antioxidants in metal cutting emulsions, as rust inhibitors in resin coatings and lubricating oil, and as a thermal stabilizer.1 Synthesis methods of para-tert-butylbenzoic acid involve the nitric acid oxidation method, solvent-free liquid-phase oxidation method, acetate solvent catalytic oxidation method, microwave radiation method, and potassium permanganate oxidation method. The most common process involves the liquid-phase air oxidation of 4-tert-butyltoluene with cobalt acetate as a catalyst, acetic acid as a solvent, and sodium bromide as an initiator. The precursor, 4-tert-butyltoluene, is produced by the alkylation of toluene with a tertiary alcohol, halide, or olefin.2 The crude product obtained from the oxidation process is flash-vaporized to remove the excess of solvent, and thereafter para-tert-butylbenzoic acid is isolated by the crystallization process. Moreover, the crystallization process has several advantages (low energyconsuming and low equipment investment) as compared to distillation that requires high energy consumption and high investment process.3 In the development and design of an © XXXX American Chemical Society

optimized crystallization process, the solubility data of the components involved are very crucial. It is also a prerequisite to understanding the thermodynamic behavior of solutions. In this context, to the best of the authors’ present knowledge, the solubility data of para-tert-butylbenzoic acid for these particular pure and mixed organic solvents has not yet been reported in the literature and are therefore investigated in the present study. In this work, the solid−liquid equilibrium (SLE) data of paratert-butylbenzoic acid in pure organic solvents (methanol, ethanol, acetic acid, propan-2-ol, hexane, toluene, 1-octanol, paratert-butyltoluene, and methyl 4-tert-butylbenzoate) and a binary mixture (methanol + methyl 4-tert-butylbenzoate) were measured in the temperature range of 293.15−333.15 K by a static method at the local atmospheric pressure.4 The solubility in the stated solvents finds an application in processing the reaction mixture and product from the oxidation of para-tert-butyltoluene and esterification of para-tert-butylbenzoic acid. The obtained experimental solubility data were correlated by using the modified Apelblat equation,5 λh equation,6,7 and the nonrandom two-liquid (NRTL) model. The solubility data in the tested solvents were used further to calculate the dissolution thermodynamic properties such as dissolution enthalpy, entropy, and the Gibbs free energy. Received: November 19, 2016 Accepted: March 6, 2017

A

DOI: 10.1021/acs.jced.6b00965 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Properties and Sources of Materials Used chemical (IUPAC name) para-tert butylbenzoic acid methanol ethanol acetic acid propan-2-ol hexane toluene 1-octanol para-tert butyl toluene methyl 4-tert butylbenzoate

CAS Registry Number

source

molar mass (g·mol−1)

initial mass purity

98-73-7

Sigma-Aldrich, India

178.23

0.99

67-56-1 64-17-5 64-19-7 67-63-0 110-54-3 108-88-3 111-87-5 98-51-1

S. D. Fine, India Merck, Germany S. D. Fine, India Finar, India S. D. Fine, India Finar, India Sigma-Aldrich, India Molychem, India

32.04 46.06 60.05 60.10 86.17 92.14 130.22 148.24

26537-19-9

Sigma-Aldrich, India

192.25

purification method

final mass purity analysis

T (K)

density (g·cm−3)

a

none

0.99

GC

0.995 0.998 0.995 0.998 0.995 0.998 0.99 >0.95

none none none none none none vacuum distillation vacuum distillation

0.995 0.998 0.995 0.998 0.995 0.998 0.990 0.995

GC GC GC GC GC GC GC GC

293 298 293 298 298 293 293 293

0.79103,b 0.79104c 0.78501,d 0.78492e 1.04928f 0.78126,c 0.78130g 0.65610h 0.86681,i 0.86687j 0.82550,k 0.82499l 0.86079,i 0.86120m

0.99

vacuum distillation

0.995

GC

293

1.0113n

a j

GC: gas chromatography. bReference 8. cReference 9. dReference 10. eReference 11. fReference 12. gReference 13. hReference 14. iReference 15. Reference 16. kReference 17. lReference 18. mReference 19. nReference 20

2.4. Analysis. The saturation concentration of para-tertbutylbenzoic acid was analyzed by a gas chromatograph (GC-2010, Shimadzu Corporation) equipped with a flame ionization detector (FID). A ZB-5 column (30 m × 0.53 mm × 1.5 μm) was used with a temperature-programmed analysis. Column temperature: 353 K maintain 0 min, 10 K·min−1 heating for 12 min, 473 K maintain 0 min, 10 K·min−1 heating for 8 min, 553 K maintain 2 min; injection mode, split ratio 50/1; injector temperature, 493 K and detector temperature, 523 K; carrier gas, helium; velocity of the carrier gas 87.1 mL/min, injected volume 0.2 μL liquid sample.

2. EXPERIMENTAL SECTION 2.1. Materials. para-tert-Butylbenzoic acid (99%, analytical grade) used in the present study was purchased from SigmaAldrich, India and used as such without further purification. The details of the organic solvents used in the present work are listed in Table 1.8−20 2.2. Measurement of Melting Properties of para-tertButylbenzoic Acid. The fusion temperature (Tm) of para-tertbutylbenzoic acid has previously been reported in the literature.21 The fusion enthalpy is required to correlate the experimental solubility data, and therefore a differential scanning calorimeter (DSC) of PerkinElmer (Pyris-Diamond) is used to measure the melting temperature and fusion enthalpy of para-tert-butylbenzoic acid. The DSC instrument was precalibrated using indium as a reference material. The calibration was carried out using with 4.2 mg of sample and a heating rate of 5 K min−1. The melting properties of para-tert-butylbenzoic acid were measured within the temperature range 298−573 K under a nitrogen atmosphere. The standard uncertainties for temperature and fusion enthalpy were estimated to be 0.5 K and 240 J·mol−1, respectively. 2.3. Solubility Measurement. The solubility of para-tertbutylbenzoic acid in pure methanol, ethanol, acetic acid, propan-2-ol, hexane, toluene, 1-octanol, para-tert-butyltoluene, and methyl 4-tert-butylbenzoate and the binary system containing methanol + methyl 4-tert-butylbenzoate from 293.15 to 333.15 K were performed using static equilibrium method.4 The experiments were performed in a shaking incubator (LSI-4018R, Daihan LabTech, India) with a temperature accuracy within ±0.1 K. The experiments were started by gravimetrically weighing 50 g of solvents in Teflon-coated glass-stoppered Erlenmeyer flasks using a Shimadzu balance (AUX 220), capable of recording weights with an accuracy of ±0.0001 g to which an excess of para-tert-butylbenzoic acid was added. The solutions were agitated in the shaker continuously for 6 h at tested temperature to make sure the equilibrium is achieved. The precipitated para-tert-butylbenzoic acid crystals were further allowed to settle for another 8 h at the same conditions. The clear supernatant after settling was withdrawn using a glass syringe maintained at a higher temperature than the solution and mounted with a micron filter at the tip. These samples were further diluted using methanol as an internal standard. The experiments were repeated thrice, and the average values were used to calculate the mole fraction solubility.

3. RESULTS AND DISCUSSION 3.1. Pure Component Properties. The DSC thermogram of para-tert-butylbenzoic acid is shown in Figure 1. It is observed

Figure 1. DSC thermogram of para-tert-butylbenzoic acid.

from the DSC analysis that the fusion temperature (Tm) and the fusion enthalpy (ΔHfus) of para-tert-butylbenzoic acid are 439.06 K and 100.25 J·g−1 or 17.867 kJ mol−1, respectively. The Tm value obtained in this work was slightly higher than the values given in the literature (436.7 K),21 although it was within the range of experimental limits. The difference is attributed to sample purity, synthesis technique, and experimental conditions maintained. The intensity and sharpness of the peak indicate the B



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Table 2. Experimental (xexp) and Predicted (xcal) Mole Fraction Solubility of para-tert Butylbenzoic Acid in Different Solvents in the Temperature Range from T = 293.15−333.15 K at 94.9 kPaa λ equation

modified Apelbat equation T (K)

xexp

xcal

RD × 102

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 RAD

0.0561 0.0622 0.0685 0.0749 0.0811 0.0882 0.0951 0.1026 0.1092

0.0562 0.0622 0.0684 0.0748 0.0814 0.0882 0.0952 0.1022 0.1094

0.121 0.054 0.227 0.139 0.393 0.058 0.089 0.404 0.177 0.185

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 RAD

0.0721 0.0882 0.1032 0.1215 0.1399 0.1583 0.1765 0.1943 0.2115

0.0723 0.0875 0.1040 0.1215 0.1397 0.1582 0.1766 0.1945 0.2115

0.238 0.783 0.749 0.009 0.174 0.094 0.027 0.071 0.025 0.241

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 RAD

0.0320 0.0377 0.0469 0.0583 0.0725 0.0855 0.0987 0.1123 0.1252

0.0308 0.0390 0.0484 0.0590 0.0708 0.0838 0.0976 0.1122 0.1274

3.688 3.502 3.047 1.178 2.334 2.076 1.089 0.026 1.728 2.074

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 RAD

0.0991 0.1165 0.1338 0.1504 0.1669 0.1832 0.1992 0.2148 0.2298

0.1026 0.1179 0.1339 0.1502 0.1668 0.1832 0.1994 0.2149 0.2297

3.507 1.173 0.084 0.101 0.074 0.018 0.083 0.063 0.077 0.575

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 RAD

0.0244 0.0294 0.0345 0.0399 0.0453 0.0508 0.0554 0.0619 0.0663

0.0245 0.0293 0.0344 0.0398 0.0453 0.0508 0.0562 0.0614 0.0662

0.440 0.316 0.320 0.241 0.054 0.002 1.381 0.761 0.133 0.405

293.15 298.15 303.15 308.15

0.0315 0.0385 0.0466 0.0538

0.0316 0.0385 0.0460 0.0541

0.365 0.070 1.202 0.487

NRTL model

xcal

RD × 102

xcal

RD × 102

0.0577 0.0628 0.0682 0.0740 0.0803 0.0871 0.0944 0.1024 0.1110

2.856 0.950 0.457 1.140 0.952 1.199 0.672 0.261 1.642 1.125

0.0492 0.0557 0.0627 0.0703 0.0785 0.0874 0.0970 0.1073 0.1184

12.271 10.501 8.555 6.186 3.199 0.859 2.029 4.561 8.431 6.288

0.0782 0.0905 0.1041 0.1191 0.1357 0.1537 0.1734 0.1947 0.2176

8.448 2.601 0.856 1.947 3.044 2.900 1.778 0.171 2.867 2.735

0.0889 0.0999 0.1120 0.1249 0.1388 0.1538 0.1699 0.1871 0.2056

23.217 13.323 8.500 2.793 0.790 2.860 3.767 3.716 2.824 6.866

0.0320 0.0377 0.0469 0.0583 0.0725 0.0855 0.0987 0.1123 0.1252

5.569 8.511 4.526 0.365 4.307 4.351 2.851 0.468 3.422 3.245

0.0354 0.0412 0.0487 0.0578 0.0691 0.0815 0.0957 0.1119 0.1297

10.455 9.433 3.718 0.919 4.776 4.667 3.000 0.328 3.588 4.543

0.1065 0.1190 0.1324 0.1468 0.1624 0.1790 0.1968 0.2157 0.2359

7.495 2.068 1.039 2.373 2.727 2.298 1.211 0.456 2.656 2.480

0.1034 0.1163 0.1302 0.1453 0.1615 0.1790 0.1977 0.2178 0.2393

4.396 0.230 2.672 3.417 3.233 2.299 0.726 1.420 4.103 2.499

0.0282 0.0316 0.0353 0.0394 0.0439 0.0489 0.0544 0.0603 0.0669

17.933 9.560 4.142 0.531 1.495 2.330 0.637 1.220 2.118 4.441

0.0267 0.0304 0.0345 0.0390 0.0439 0.0493 0.0550 0.0614 0.0682

9.551 3.511 0.104 2.262 3.123 3.025 0.726 0.675 2.839 2.869

0.0348 0.0401 0.0462 0.0529

10.354 4.209 0.870 1.664

0.0376 0.0427 0.0485 0.0547

19.237 10.934 4.056 1.703

Methanol

Ethanol

Acetic Acid

Propan-2-ol

Hexane

Toluene

C



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Table 2. continued λ equation

modified Apelbat equation T (K)

xexp

xcal

RD × 102

NRTL model

xcal

RD × 102

xcal

RD × 102

0.0604 0.0688 0.0780 0.0883 0.0997

2.856 2.714 2.729 0.508 3.572 3.275

0.0616 0.0692 0.0774 0.0863 0.0959

0.926 2.173 3.502 2.744 0.374 5.072

5.412 2.947 1.437 0.385 0.378 0.524 0.645 0.164 0.797 1.410

0.0932 0.1044 0.1165 0.1293 0.1432 0.1580 0.1736 0.1902 0.2078

10.755 9.296 7.265 5.903 2.901 0.327 1.992 4.738 7.797 5.664

13.221 7.407 0.409 2.567 2.854 2.941 2.163 1.222 2.818 3.956

0.0222 0.0253 0.0288 0.0327 0.0370 0.0417 0.0468 0.0525 0.0585

21.180 13.476 4.140 0.652 0.919 2.230 2.703 3.010 0.682 5.443

7.085 2.248 1.331 0.980 2.103 2.056 1.396 0.150 2.340 2.188

0.0604 0.0689 0.0784 0.0887 0.1001 0.1126 0.1263 0.1412 0.1573

7.789 2.756 0.929 0.817 2.003 2.035 1.450 0.289 2.012 2.231

Toluene

a

313.15 318.15 323.15 328.15 333.15 RAD

0.0622 0.0707 0.0802 0.0888 0.0962

0.0625 0.0711 0.0798 0.0883 0.0965

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 RAD

0.1045 0.1151 0.1256 0.1374 0.1475 0.1585 0.1702 0.1816 0.1928

0.1046 0.1150 0.1257 0.1367 0.1478 0.1590 0.1702 0.1815 0.1927

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 RAD

0.0183 0.0223 0.0277 0.0325 0.0373 0.0426 0.0481 0.0541 0.0589

0.0183 0.0226 0.0272 0.0323 0.0375 0.0430 0.0484 0.0537 0.0588

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 RAD

0.0560 0.0671 0.0791 0.0894 0.1021 0.1150 0.1282 0.1416 0.1542

0.0564 0.0668 0.0781 0.0900 0.1025 0.1153 0.1283 0.1413 0.1540

0.487 0.642 0.511 0.478 0.284 0.503

1-Octanol 0.118 0.1101 0.083 0.1185 0.100 0.1274 0.533 0.1369 0.187 0.1469 0.309 0.1577 0.029 0.1691 0.060 0.1813 0.075 0.1943 0.166 para-tert-Butyltoluene 0.089 0.0207 1.144 0.0240 1.713 0.0276 0.767 0.0317 0.625 0.0362 0.843 0.0413 0.629 0.0471 0.677 0.0534 0.129 0.0606 0.735 Methyl 4-tert-Butylbenzoate 0.637 0.0600 0.375 0.0686 1.323 0.0780 0.685 0.0885 0.314 0.1000 0.295 0.1126 0.107 0.1264 0.242 0.1414 0.088 0.1578 0.452

Standard uncertainties u in temperature are u(T) = 0.05 K, u(P) = 0.20 kPa, and u(x)= 0.0101.

increasing temperature, but the increment is different for each pure solvent. At all of the investigated temperatures, the mole fraction solubility of methyl para-tert-butylbenzoic acid is highest in propan-2-ol (except 293.15 K) and lowest in para-tert-butyltoluene. Figure 2a and b further demonstrates that the solubility values of para-tert-butylbenzoic acid in the selected solvents. The solubility order in different solvents at 303.15 K follows the order as propan-2-ol >1-octanol > ethanol > methyl 4-tert-butylbenzoate > methanol > acetic acid > toluene > hexane > para-tertbutyltoluene. However, in terms of the mass fraction, the solubility of para-tert-butylbenzoic acid was found to be highest in ethanol and lowest in para-tert-butyltoluene. This difference is likely to be attributed to the large difference in the molecular weight of para-tert-butylbenzoic acid and other solvents. These results are also consistent with the analysis of their molecular structures and space conformations.22 The solubility of para-tert-butylbenzoic acid in the mixed solvent system of methanol + methyl 4-tert-butylbenzoate for changing mole fraction (solute-free basis) at different

highly crystalline nature of the compound. The fusion enthalpy (ΔHfus) obtained in the present study is very close to the value reported in the literature (17.9 kJ mol−1). The thermodynamic correlation used for the estimation of fusion entropy (ΔSfus) is represented in eq 1. ΔSfus =

ΔHfus Tm

(1)

The entropy of fusion for para-tert-butylbenzoic acid was thus obtained as 40.693 J·mol−1·K−1. 3.2. Experimental SLE Data. The measured mole fraction solubility of para-tert-butylbenzoic acid in methanol, ethanol, acetic acid, propan-2-ol, hexane, toluene, 1-octanol, para-tertbutyltoluene, and methyl 4-tert-butylbenzoate within the temperature range of 293.15−333.15 K have been tabulated in Table 2 and shown graphically in Figure 2. It can be clearly seen from the figure that the solubility of para-tert butylbenzoic acid in different solvents is a function of temperature and increases with D



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temperatures is summarized in Table 3. The measured solubility of para-tert-butylbenzoic acid for a particular mole fraction was found to increase with increasing temperature and presented in Figure 3a and b. Furthermore, Figure 4 shows the dependence of temperature on the solubility of para-tert-butylbenzoic acid in mixed solvents with varying mole fractions of methanol, on the solute-free basis at each temperature. It is evident that the solubility of para-tert-butylbenzoic acid in methanol + methyl 4-tert-butylbenzoate binary mixture increases as the methanol mole fraction varies from 0 to 0.6115 and subsequently decreases. This phenomenon is often referred to as the maximum solubility effect. The Scatchard−Hildebrand theory suggests that, when a solute (solid) is solubilized in a mixed solvent, the curve plotted between solubility and solvent composition (solute-free) passes through a maximum.23 It can also be concluded from Figure 4 that at each equilibrium temperature the binary system of methanol + methyl 4-tert-butylbenzoate solvent mixtures with a mole fraction of methanol at 0.6115 exhibited the highest dissolving capacity for para-tert-butylbenzoic acid. 3.3. Modeling of SLE Data. The modeling of experimental solid−liquid equilibrium data in this work is described by modified Apelblat equation,5 λh equation,6,7 and NRTL model.24 These equations provide the relationship (regressed parameters) between the solubility (mole fraction) with temperature for paratert-butylbenzoic acid in the different investigated organic solvents. Further, in order to evaluate the quality of the regressed parameters, the deviation between the experimental and that predicted by the models have been expressed in terms of their root-mean-square deviation (RMSD), relative deviation (RD), and relative average deviation (RAD) as follows: ⎡ ∑N (ZM − Z )2 ⎤0.5 i i ⎥ RMSD = ⎢ i = 1 ⎢⎣ ⎥⎦ k

Figure 2. Mole fraction solubility of para-tert-butylbenzoic acid in pure organic solvents. Experimental solubility: (a) 1-octanol (■), methanol (●), methyl 4-tert-butylbenzoate (▲), toluene (▼), hexane (◀), (b)-propan-2ol (□), ethanol (○), acetic acid (△), and para-tert butyl toluene (▽). Solid lines (−) are calculated data by the modified Apelblat model.

RD =

(2)

ZMi − Zi ZMi

(3)

Table 3. Experimental (xexp) and Predicted (xcal) Mole Fraction Solubility of para-tert-Butylbenzoic Acid in the Binary Mixture of Methanol + Methyl 4-tert-Butylbenzoate in the Temperature Range of 293.15−333.15 K at 94.9 kPaa λh equation

modified Apelbat equation T/K

xexp

xcal

RD × 102

xcal x′ = 0.2014

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 RAD

0.1012 0.1102 0.1219 0.1348 0.1484 0.1684 0.1884 0.2104 0.2330

0.1007 0.1106 0.1220 0.1351 0.1500 0.1672 0.1868 0.2093 0.2350

0.488 0.365 0.065 0.194 1.084 0.704 0.864 0.548 0.892 0.578

293.15 298.15 303.15 308.15 313.15 318.15

0.1034 0.1127 0.1248 0.1374 0.1515 0.1711

0.1029 0.1131 0.1247 0.1379 0.1530 0.1701

0.438 0.342 0.095 0.386 0.981 0.551

NRTL model

RD × 102

xcal

RD × 102

b

0.0923 0.1051 0.1192 0.1346 0.1513 0.1694 0.1888 0.2097 0.2321

8.767 4.586 2.206 0.150 1.938 0.597 0.215 0.330 0.365 2.128

0.0953 0.1079 0.1217 0.1367 0.1529 0.1705 0.1893 0.2095 0.2310

5.779 2.083 0.200 1.383 3.027 1.263 0.488 0.433 0.835 1.721

0.0986 0.1113 0.1250 0.1399 0.1560 0.1733

4.595 1.271 0.169 1.838 2.959 1.270

0.0954 0.1081 0.1220 0.1373 0.1539 0.1720

7.747 4.089 2.188 0.047 1.589 0.529

x′ = 0.3126

E



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Table 3. continued λh equation

modified Apelbat equation T/K

xexp

xcal

RD × 102

xcal

NRTL model

RD × 102

xcal

RD × 102

x′ = 0.3126 323.15 328.15 333.15 RAD

0.1917 0.2130 0.2356

0.1897 0.2121 0.2376

1.034 0.437 0.857 0.569

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 RAD

0.1133 0.1236 0.1358 0.1486 0.1631 0.1805 0.1982 0.2183 0.2383

0.1131 0.1238 0.1358 0.1490 0.1636 0.1798 0.1977 0.2175 0.2394

0.242 0.172 0.004 0.266 0.322 0.397 0.228 0.349 0.432 0.268

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 RAD

0.1321 0.1413 0.1518 0.1647 0.1775 0.1921 0.2089 0.2276 0.2456

0.1318 0.1415 0.1523 0.1643 0.1776 0.1923 0.2086 0.2266 0.2465

0.209 0.133 0.327 0.224 0.066 0.133 0.157 0.427 0.365 0.227

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 RAD

0.1322 0.1431 0.1551 0.1681 0.1821 0.1972 0.2133 0.2304 0.2486

0.1321 0.1432 0.1552 0.1682 0.1821 0.1970 0.2131 0.2303 0.2488

0.103 0.063 0.099 0.053 0.018 0.074 0.085 0.035 0.001 0.059

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 RAD

0.1266 0.1367 0.1481 0.1613 0.1738 0.1893 0.2064 0.2243 0.2418

0.1264 0.1369 0.1483 0.1609 0.1745 0.1894 0.2057 0.2234 0.2427

0.148 0.108 0.144 0.253 0.418 0.086 0.350 0.399 0.397 0.256

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 RAD

0.0959 0.1079 0.1207 0.1349 0.1455 0.1578 0.1716 0.1867 0.2034

0.0964 0.1080 0.1201 0.1327 0.1458 0.1593 0.1731 0.1872 0.2015

0.573 0.061 0.475 1.581 0.223 0.969 0.916 0.281 0.924 0.667

0.1918 0.2117 0.2330

0.060 0.608 1.106 1.542

0.1916 0.2126 0.2353

0.082 0.180 0.127 1.842

0.1106 0.1229 0.1361 0.1502 0.1653 0.1815 0.1988 0.2172 0.2368

2.389 0.608 0.206 1.073 1.377 0.562 0.332 0.473 0.646 0.852

0.1084 0.1216 0.1356 0.1505 0.1663 0.1826 0.1998 0.2175 0.2360

4.350 1.657 0.134 1.308 1.963 1.157 0.837 0.350 0.977 1.415

0.1262 0.1381 0.1507 0.1641 0.1784 0.1936 0.2097 0.2268 0.2449

4.421 2.312 0.759 0.350 0.511 0.785 0.364 0.348 0.284 1.126

0.1212 0.1351 0.1497 0.1647 0.1806 0.1968 0.2130 0.2293 0.2464

8.247 4.418 1.392 0.019 1.751 2.469 1.977 0.777 0.323 2.375

0.1312 0.1429 0.1554 0.1686 0.1827 0.1976 0.2134 0.2302 0.2479

0.783 0.155 0.198 0.337 0.329 0.229 0.077 0.097 0.266 0.275

0.1248 0.1386 0.1530 0.1681 0.1837 0.1998 0.2162 0.2329 0.2497

5.625 3.180 1.306 0.031 0.888 1.318 1.364 1.060 0.446 1.691

0.1246 0.1362 0.1486 0.1618 0.1758 0.1906 0.2064 0.2232 0.2409

1.522 0.353 0.323 0.307 1.125 0.713 0.004 0.512 0.344 0.578

0.1174 0.1309 0.1450 0.1597 0.1754 0.1913 0.2074 0.2240 0.2415

7.235 4.292 2.101 0.964 0.943 1.062 0.491 0.116 0.123 1.925

0.0987 0.1089 0.1198 0.1316 0.1442 0.1576 0.1721 0.1875 0.2040

2.952 0.915 0.687 2.437 0.923 −0.096 0.291 0.436 0.322 0.985

0.0926 0.1039 0.1161 0.1291 0.1433 0.1584 0.1744 0.1913 0.2090

3.398 3.704 3.813 4.314 1.515 0.401 1.665 2.470 2.781 2.673

x′ = 0.4002

x′ = 0.5065

x′ = 0.6115

x′ = 0.7036

x′ = 0.8122

a

Standard uncertainties u in temperature are u(T) = 0.05 K, u(P) = 0.20 kPa, and u(x)= 0.0101. bx′: Solute free mole fraction of methanol. F



Article

Figure 4. Mole fraction solubility of para-tert-butylbenzoic acid in the methanol + methyl 4-tert-butylbenzoate binary mixed solvent system against the mole fraction of methanol (x′) on solute-free basis at different temperatures: 293.15 K (■), 298.15 (□) 303.15 K (●), 308.15 K (○), 313.15 K (▲), 318.15 K (△), 323.15 K (▼), 328.15 K (▽), 333.15 K (▶).

on the fusion enthalpy. The values of parameters are obtained by correlating the experimental solubility data of para-tertbutylbenzoic acid at the different temperature and are reported in Table 4 and Table 5 for the pure solvents and the mixed solvent system, respectively. The computed solubility of para-tertbutylbenzoic acid in different solvents on the basis of the regressed parameters, along with the relative average deviation (RAD) and relative deviation (RD) are listed in Table 2 and Table 3. The computed solubility values with the modified Apelblat equation agree very well with the experimental ones and can be clearly seen in Figure 2 and Figure 3. The RMSD values obtained were no greater than 1.39 × 10−3 for pure solvents and 1.24 × 10−3 for the binary solvent system. Thereby, the experimental solubility of para-tert-butylbenzoic acid in the selected pure and mixed solvents at different temperatures can be correlated by the modified Apelblat equation. 3.3.2. λh Equation. Buchowski et al. proposed the nonactivity coefficient two-parameter λh equation that are used to correlate the SLE data.6

Figure 3. Mole fraction solubility of para-tert-butylbenzoic acid in the methanol + methyl 4-tert-butylbenzoate binary mixed solvent system. Experimental solubility: solute-free mole fraction of methanol (x′): (a) 0.2014 (■), 0.3126 (●), 0.4002 (▲), 0.5065 (▼), (b) 0.6115 (□), 0.7036 (○), 0.8122 (△). Solid lines (−) calculated data by the modified Apelblat model.

RAD =

1 N

i=1

∑ N

ZMi − Zi ZMi

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

(4)

where Zi is a regressed property value (mole fraction solubility) based on different models, ZMi is the corresponding experimental solubility value of from the data set, and N is the number of data points. 3.3.1. Modified Apelbat Equation. The dependence of the mole fraction solubility of para-tert-butylbenzoic acid upon temperature in the studied solvents is correlated by the modified Apelblat equation5 which is expressed as eq 5 ln x = A +

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

(6)

where Tm is the melting point of para-tert-butylbenzoic acid and λ and h are two model parameters. The value of λ reveals the nonideality of the solution, which is considered as the association number of solute molecules in the associating system, and h provides the excess mixing enthalpy of solution. Table 4 and Table 5 report the regressed values of λ and h, for the pure solvent and mixed solvent, respectively, along with their RMSD values. The RMSD with the λh equation was found to give larger deviations for both the pure solvents and mixed solvent system as compared to that of the modified Apelblat equation. In the pure solvent system, propan-2-ol exhibited the largest RMSD of 4.19 × 10−3, while for the binary solvent system it was observed to be 3.68 × 10−3 with the methanol solute-free mole fraction being 0.2014. However, the RAD values are not more than 4.4%. As a result, the λh equation can also be used to correlate the

(5)

where x (mole fraction) is the solubility of methyl para-tertbutylbenzoic acid in the organic solvents at experimental temperature T in Kelvin and A, B, and C are adjustable parameters. The variation in the solution activity coefficient is reflected by A and B values, while the value of C responses to the effect of temperature G



Article

Table 4. Parameters of the Different Models Used To Correlate Solubility Data of para-tert-Butylbenzoic Acid in Different Solvents λh equation

modified Apelbat equation

NRTL equation

solvent

A

B

C

RMSD × 102

λ

h

RMSD × 102

τ12

τ21

α

RMSD × 102

methanol ethanol acetic acid propan-2-ol hexane toluene 1-octanol para-tert-butyltoluene methyl 4-tert-butylbenzoate

57.82 295.58 263.99 194.13 287.87 296.50 71.25 325.67 213.39

−4178.95 −16012.13 −15299.05 −10749.85 −15543.93 −16180.29 −4658.98 −17660.58 −12078.81

−8.18 −42.88 −37.90 −28.12 −41.99 −43.09 −10.14 −47.43 −30.82

0.020 0.037 0.139 0.125 0.031 0.035 0.032 0.029 0.048

0.15 1.52 1.48 0.89 0.18 0.52 0.22 0.29 0.77

7472.66 1724.19 2273.66 2141.40 9818.81 4724.83 4130.32 8210.97 2970.46

0.101 0.387 0.275 0.419 0.181 0.205 0.240 0.134 0.137

5.79 2.68 0.55 1.63 3.92 2.99 7.68 3.10 1.22

−0.25 −0.77 1.49 −0.57 0.34 0.08 −0.81 0.61 0.28

0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30

0.541 0.857 0.306 0.478 0.131 0.290 0.894 0.185 0.227

Table 5. Parameters of the Different Models Used to Correlate Solubility Data of para-tert-Butylbenzoic Acid in the Binary Mixture of Methanol + Methyl 4-tert-Butylbenzoate λh equation

modified Apelbat equation

NRTL equation

x′

A

B

C

RMSD × 102

λ

h

RMSD × 102

τ12

τ21

τ13

τ31

τ23

τ32

α

RMSD × 102

0.2014 0.3126 0.4002 0.5065 0.6115 0.7036 0.8122

−167.27 −156.76 −93.00 −110.82 −49.02 −77.14 75.18

5893.73 5431.64 2662.27 3749.31 873.25 2133.78 −5103.08

25.50 23.93 14.39 16.90 7.75 11.93 −10.58

0.119 0.118 0.057 0.052 0.014 0.058 0.124

1.29 1.07 0.79 0.57 0.52 0.54 0.53

1810.60 1979.07 2246.80 2495.65 2554.32 2576.06 2976.16

0.368 0.267 0.151 0.096 0.054 0.116 0.162

−0.04 −0.07 −0.07 0.03 0.02 −0.01 0.14

0.20 −0.02 0.63 1.21 1.31 1.18 0.78

−0.26 −0.32 −0.59 −0.82 −0.85 −0.77 −0.69

0.63 0.69 0.38 0.11 0.06 0.09 0.39

0.03 0.05 0.06 0.05 0.06 0.06 0.02

0.09 0.11 0.18 0.19 0.02 0.18 0.15

0.30 0.30 0.30 0.30 0.30 0.30 0.30

0.285 0.333 0.249 0.489 0.342 0.392 0.406

obtained solubility data of para-tert-butylbenzoic acid for pure solvent and mixed solvent systems. 3.3.3. NRTL Model. Renon and co-workers proposed the NRTL model based on the concept local composition which otherwise is widely used in calculating and correlating the vapor− liquid phase equilibrium and SLE.24 For a component i, the expression of NRTL model describing the activity coefficient is given as eqs 7 and 8. 3

ln γi =

∑ j = 1 τjiGjiXj 3

∑k = 1 Gkixk

3

+

∑ j=1

whereas the largest RMSD for the methanol + methyl 4-tertbutylbenzoate binary solvent system was 4.89 × 10−3 at a solutefree mole fraction of 0.5065 of methanol. Moreover, from the RAD values (Table 2 and Table 3), it can be concluded that the NRTL model is not very reliable to be used to correlate the solubility of para-tert-butylbenzoic acid the nine pure solvents and the binary solvent system studied. Finally among the three models investigated, the calculated solubility based on modified Apelblat equation gave better correlation results than that of experimental ones as compared to the λh equation and the NRTL model. 3.4. Dissolution Thermodynamic Properties. The estimation of thermodynamic functions of solutions is a prerequisite for modeling SLE studies. The dissolution enthalpy (ΔdH°) vary according to interactions of solvent−solute, solvent−solvent, and solute−solute, whereas the entropy change (ΔdS°) is a function of the disorder degree or randomness of a system.23,25 Thus, in order to interpret the solubility of para-tert-butylbenzoic acid in different pure solvents and mixed solvent systems better, the thermodynamic functions of solutions were evaluated. As all of the systems under consideration were nonideal, the enthalpy of dissolution (ΔdH°)), the entropy of dissolution (ΔdS°), and the Gibbs free energy of dissolution (ΔGd) can be calculated as follows:26

3 ⎛ ∑ X τ G ⎞ ⎜τij − k = 1 K kj kj ⎟ 3 3 ∑k = 1 Gkjxk ⎜⎝ ∑k = 1 Gkjxk ⎟⎠

XjGij

(7)

Gij = exp( −αijτij),

τij = aij +

aij = aji = 0.3

bij T

,

τij ≠ τji , (8)

where T is the absolute temperature and γi is the activity coefficient of component i. Additionally, the SLE without solid−solid phase transition can be approximated by the following equation: ln γ1x = −

ΔHfus ⎛ 1 1 ⎞ ⎟ ⎜ − R ⎝T Tm ⎠

(9)

where x, Δfus, Tm, R, and T are the mole fraction solubility of the solute, fusion enthalpy, the melting point of the solute, the universal gas constant, and the absolute temperature of the solution, respectively. Equation 9 assumes that the enthalpy is independent of temperature. The activity coefficient that depends on the mole fraction and temperature of solution (eq 7) is used to solve eq 9 iteratively to obtain the modeled solubility results. The calculated solubility results are presented in Table 2 and Table 3 for the pure solvents and binary mixed solvent, respectively. Table 4 and Table 5 reports the interaction parameters and RMSD values for the NRTL model. The largest RMSD of 8.94 × 10−3 was obtained for the pure solvent 1-octanol,

Δd M ° = Δmix M id + ΔfusM + ME + (ΔMA + ΔMB) (10)

where M represents either H, S, or G. ΔmixMid is the mixing property of an ideal solution, ME is the excess property, ΔfusM is the thermodynamic property of fusion of the solute, ΔMA is the change of thermodynamic property of the heating process, and ΔMB is the change of thermodynamic property of the cooling process. However, as the values of thermodynamic functions of fusion of solute are much greater than the sum (ΔMA + ΔMB), it can be considered negligible. Furthermore, for the ideal state ΔmixHid = 0, whereas ΔGfus = 0 at the SLE state.27 All of the H



Article

Table 6. Dissolution Properties and Thermodynamic Functions of para-tert-Butylbenzoic Acid in Different Solventsa T (K)

a

ΔdH° (J mol−1)

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

19403.90 19455.63 19508.25 19561.74 19616.10 19671.34 19727.45 19784.44 19842.31

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

24482.77 24709.24 24939.53 25173.66 25411.62 25653.41 25899.03 26148.47 26401.75

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

18810.93 18842.27 18874.14 18906.54 18939.47 18972.93 19006.91 19041.43 19076.48

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

23185.12 23366.95 23551.85 23739.82 23930.87 24124.99 24322.19 24522.47 24725.82

293.15 298.15 303.15 308.15 313.15

19077.34 19117.84 19159.03 19200.90 19243.46

ΔdG° (J mol−1)

ΔdS° (J mol−1 K−1)

Methanol 1735.82 1699.97 1660.72 1620.39 1581.27 1532.59 1484.99 1430.21 1385.24 Ethanol 1785.59 1608.62 1447.16 1248.29 1051.16 857.18 668.02 485.49 311.48 Acetic Acid 736.06 697.65 628.07 542.73 437.16 343.47 250.09 154.89 64.95 Propan-2-ol 1009.95 829.61 655.07 489.50 327.58 169.96 17.35 −129.53 −269.99 Hexane 2575.33 2555.47 2533.83 2509.60 2484.29

ζH (%)

ζTS (%)

40.19 40.50 40.81 41.12 41.41 41.73 42.04 42.37 42.65

62.22 61.71 61.19 60.69 60.20 59.70 59.22 58.73 58.27

37.78 38.29 38.81 39.31 39.80 40.30 40.78 41.27 41.73

57.35 58.42 59.43 60.54 61.61 62.66 63.67 64.64 65.57

59.29 58.65 58.06 57.44 56.84 56.27 55.73 55.21 54.72

40.71 41.35 41.94 42.56 43.16 43.73 44.27 44.79 45.28

41.58 41.80 42.12 42.49 42.91 43.27 43.63 43.99 44.32

60.68 60.19 59.65 59.09 58.50 57.95 57.41 56.88 56.37

39.32 39.81 40.35 40.91 41.50 42.05 42.59 43.12 43.63

55.57 56.54 57.46 58.34 59.19 60.01 60.80 61.56 62.28

58.74 58.09 57.48 56.90 56.35 55.82 55.32 54.83 54.37

41.26 41.91 42.52 43.10 43.65 44.18 44.68 45.17 45.63

36.21 36.50 36.78 37.06 37.34

64.25 63.73 63.21 62.71 62.20

35.75 36.27 36.79 37.29 37.80

T (K)

ΔdH° (J mol−1)

318.15 323.15 328.15 333.15

19286.71 19330.64 19375.25 19420.55

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

20246.08 20326.79 20408.87 20492.31 20577.12 20663.29 20750.83 20839.73 20930.00

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

20400.76 20486.80 20574.29 20663.23 20753.63 20845.49 20938.79 21033.56 21129.78

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

19017.18 19055.61 19094.70 19134.43 19174.82 19215.85 19257.54 19299.87 19342.86

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

20761.70 20860.15 20960.27 21062.05 21165.50 21270.61 21377.38 21485.82 21595.93

ΔdG° (J mol−1)


Hexane 2457.96 37.61 2441.23 37.85 2403.10 38.15 2387.34 38.38 Toluene 2473.69 40.55 2422.88 40.99 2359.31 41.48 2306.58 41.91 2239.40 42.38 2171.05 42.84 2090.16 43.34 2021.13 43.78 1964.00 44.18 1-Octanol 622.29 47.39 534.68 47.86 448.27 48.32 350.09 48.81 266.75 49.24 175.35 49.69 77.89 50.14 −17.03 50.58 −110.34 51.01 para-tert-Butyltoluene 2691.23 35.61 2683.72 35.86 2658.26 36.15 2640.75 36.42 2623.13 36.68 2599.11 36.95 2572.39 37.22 2539.36 37.51 2520.26 37.75 Methyl 4-tert-Butylbenzoate 1296.03 46.32 1196.60 46.90 1088.16 47.49 999.31 48.00 886.26 48.58 774.22 49.14 659.86 49.70 544.59 50.25 438.84 50.76

ζH (%)

ζTS (%)

61.71 61.24 60.75 60.30

38.29 38.76 39.25 39.70

63.01 62.45 61.88 61.34 60.79 60.25 59.71 59.19 58.71

36.99 37.55 38.12 38.66 39.21 39.75 40.29 40.81 41.29

59.49 58.94 58.41 57.87 57.37 56.87 56.37 55.89 55.43

40.51 41.06 41.59 42.13 42.63 43.13 43.63 44.11 44.57

64.56 64.06 63.53 63.03 62.54 62.04 61.55 61.06 60.60

35.44 35.94 36.47 36.97 37.46 37.96 38.45 38.94 39.40

60.46 59.87 59.28 58.75 58.18 57.64 57.10 56.58 56.08

39.54 40.13 40.72 41.25 41.82 42.36 42.90 43.42 43.92

Combined standard uncertainties U are Uc(ΔdH) = 0.045ΔdH, Uc(ΔdG) = 0.05ΔdG and Uc(ΔdS) = 0.025ΔdS.

⎡ ∂GE /T ⎤ H E = − T 2⎢ ⎥ ⎣ ∂T ⎦

remaining thermodynamic functions for the dissolution of solute were evaluated using the following equations:27 n

Δmix Gid = RT (∏ xi ln xi) i=1

n

GE = RT (∏ xi ln γi)

(11)

i=1

n

Δmix S id = −R(∏ xi ln xi) i=1

(13)

SE = (12)

HE − GE T

(14)

(15)

The change in enthalpy, entropy, and Gibbs free energy for the dissolution process of para-tert-butylbenzoic acid in different pure solvents and mixed solvent systems has been reported in Table 6 and Table 7. It is evident from these tables that all of the

where xi represents the mole fractions of each component at the given temperature. The excess thermodynamic functions are further estimated using the following equations.28,29 I



Article

Table 7. Dissolution Properties and Thermodynamic Functions of para-tert-Butylbenzoic Acid in the Binary Mixture of Methanol + Methyl para-tert-Butyl Benzoatea T (K)

ΔdH° (J mol−1)

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

16911.73 16877.73 16843.15 16808.00 16772.28 16735.98 16699.10 16661.65 16623.63

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

17126.57 17099.96 17072.90 17045.39 17017.43 16989.03 16960.17 16930.86 16901.10

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

16679.70 16637.71 16595.02 16551.62 16507.51 16462.68 16417.15 16370.91 16323.96

293.15 298.15 303.15 308.15 313.15

16765.63 16726.61 16686.92 16646.58 16605.57

a

ΔdG° (J mol−1)


x′ = 0.2014 −2126.98 −2189.94 −2258.89 −2328.58 −2397.41 −2475.37 −2547.65 −2616.54 −2679.24 x′ = 0.3126 −2334.085 −2395.00 −2460.181 −2530.165 −2601.137 −2678.994 −2753.09 −2822.467 −2887.305 x′ = 0.4002 −2535.612 −2595.921 −2656.677 −2719.398 −2781.084 −2841.432 −2896.692 −2947.059 −2990.763 x′ = 0.5065 −2557.618 −2613.303 −2668.456 −2727.564 −2783.374

ζH (%)

ζTS (%)

44.87 44.90 44.95 44.99 45.04 45.10 45.15 45.18 45.19

56.25 55.77 55.28 54.80 54.32 53.84 53.37 52.91 52.47

43.75 44.23 44.72 45.20 45.68 46.16 46.63 47.09 47.53

46.31 46.33 46.37 46.42 46.47 46.54 46.59 46.63 46.65

55.79 55.32 54.84 54.37 53.90 53.43 52.97 52.53 52.10

44.21 44.68 45.16 45.63 46.10 46.57 47.03 47.47 47.90

45.47 45.45 45.44 45.43 45.42 45.40 45.36 45.30 45.23

55.58 55.11 54.64 54.18 53.72 53.27 52.83 52.41 52.00

44.42 44.89 45.36 45.82 46.28 46.73 47.17 47.59 48.00

45.84 45.81 45.78 45.77 45.74

55.51 55.05 54.59 54.14 53.69

44.49 44.95 45.41 45.86 46.31

T (K)

ΔdH° (J mol−1)

318.15 323.15 328.15 333.15

16563.90 16521.58 16478.59 16434.95

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

16954.69 16922.17 16889.10 16855.48 16821.31 16786.59 16751.31 16715.49 16679.12

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

17203.91 17179.96 17155.61 17130.85 17105.69 17080.12 17054.15 17027.77 17000.99

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

17676.56 17668.88 17661.06 17653.11 17645.04 17636.83 17628.49 17620.03 17611.43

ΔdG° (J mol−1)


x′ = 0.5065 −2836.826 −2886.417 −2929.984 −2967.068 x′ = 0.6115 −2388.202 −2445.096 −2500.535 −2561.098 −2619.307 −2674.23 −2724.885 −2770.237 −2809.18 x′ = 0.7036 −2152.06 −2207.44 −2262.49 −2327.50 −2388.03 −2449.43 −2507.58 −2560.19 −2606.22 x′ = 0.8122 −1553.874 −1613.78 −1672.318 −1742.957 −1805.715 −1871.39 −1938.357 −2005.098 −2070.852

ζH (%)

ζTS (%)

45.70 45.65 45.58 45.49

53.26 52.83 52.42 52.03

46.74 47.17 47.58 47.97

45.90 45.90 45.90 45.90 45.90 45.89 45.86 45.81 45.75

55.75 55.29 54.83 54.37 53.92 53.48 53.06 52.65 52.25

44.25 44.71 45.17 45.63 46.08 46.52 46.94 47.35 47.75

45.95 45.97 45.99 46.04 46.07 46.10 46.12 46.13 46.11

56.09 55.62 55.17 54.70 54.25 53.80 53.36 52.94 52.54

43.91 44.38 44.83 45.30 45.75 46.20 46.64 47.06 47.46

45.52 45.62 45.71 45.84 45.93 46.04 46.14 46.24 46.33

56.98 56.50 56.03 55.55 55.09 54.63 54.18 53.73 53.29

43.02 43.50 43.97 44.45 44.91 45.37 45.82 46.27 46.71

Combined standard uncertainties U are Uc(ΔdH) = 0.045ΔdH, Uc(ΔdG) = 0.05ΔdG and Uc(ΔdS) = 0.25ΔdS.

ΔdH° and ΔdS° values are positive, thereby indicating that the dissolution process is endothermic and entropy driven. It was further observed that the enthalpy values were slightly higher for the pure solvents than the binary system of methanol + methyl 4-tert butylbenzoate owing to more energy required to overcome the cohesive forces between the solute and pure solvent. This signifies a stronger temperature dependence of the solubility of para-tert-butylbenzoic acid in the pure solvents.4 The Gibbs free energy was observed to decrease with temperature indicating an increase in solubility. Accordingly, the lowest Gibbs free energy was obtained for the propan-2-ol system at 333.15 K due to the highest solubility of para-tert-butylbenzoic acid. Moreover, the relative contributions to Gibbs free energy by enthalpy and entropy have been calculated using the following equations: ζH % =

|Δd H | × 100 |Δd H | + |T Δd S|

(16)

ζTS% =

|T Δd S| × 100 |Δd H | + |T Δd S|

(17)

where, ζH and ζTS represent the relative contribution of enthalpy and entropy. The highest contribution for all the cases including pure and mixed solvents was attributed to dissolution enthalpy. However, the enthalpy contribution to Gibbs free energy was relatively larger for pure solvents than in the binary mixture investigated with the lowest ζH being 54.37% for the propan-2-ol system and 52.0% for the binary system of methanol + methyl para-tert-butylbenzoate at a methanol solute-free mole fraction of 0.4002.

4. CONCLUSIONS The present study investigates the solubility of para-tertbutylbenzoic acid in methanol, ethanol, acetic acid, propan-2ol, hexane, toluene, 1-octanol, para-tert-butyltoluene, methyl 4-tert-butylbenzoate, and the binary mixture of methanol + methyl 4-tert-butylbenzoate system at different temperatures from 293.15 to 333.15 K. Differential scanning calorimeter was used to evaluate the melting temperature and enthalpy of fusion for para-tert-butylbenzoic acid which was further used in the correlation the SLE data. The solubility of para-tert-butylbenzoic acid increased with the increase in temperature for the J



Article

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pure solvents with the maximum solubility being displayed in propan-2-ol and minimum solubility in para-tert-butyltoluene. The binary mixture of methanol + methyl 4-tert-butylbenzoate exhibited maximum solubility effect at 0.6115 solute-free mole fraction of methanol after which the solubility subsequently decreased. Among the modified Apelbat equation, the λh (Buchowski) equation, and the NRTL model that were used to correlate the experimental solubility data, the modified Apelbat equation gave an excellent goodness of fit as compared to the other models. Lastly, to enhance the design of systems involving para-tert-butylbenzoic acid, the dissolution thermodynamic functions of the solutions such as change in enthalpy, entropy, and Gibbs free energy were evaluated using certain correlations for the nonideal systems.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +91 040 27191399/3141; fax: +91 04027193626. E-mail address: [email protected]. ORCID

Vineet Aniya: 0000-0003-2446-2894 Bankupalli Satyavathi: 0000-0002-8495-317X Notes

The authors declare no competing financial interest.

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REFERENCES

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