Binary Mixture of Pharmaceutical Residual Solvents and Their Thermodynamic Investigation

Article Information

Md Sydur Rahman1,*, Muhammad Habibullah2

1Graduate Student, Department of Chemistry, Mississippi State University, USA

2Professor, Department of Chemistry, University of Chittagong, Bangladesh

*Corresponding author: Md Sydur Rahman, Graduate Student, Department of Chemistry, Mississippi State University, USA

Received: 12 June 2022; Accepted: 16 June 2022; Published: 22 June 2022

Citation: Md Sydur Rahman, Muhammad Habibullah. Binary Mixture of Pharmaceutical Residual Solvents and Their Thermodynamic Investigation. Journal of Pharmacy and Pharmacology Research 6 (2022): 62-79

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Abstract

Molecular interaction of pharmaceutical residual solvents mixture (2-Butanol with m-Xylene) were studied through deep investigation on thermodynamic properties (Enthalpy, Entropy, Free energy) over the entire range of composition at temperature of 298.15 K to 323.15 K and at atmospheric pressure. Results are interpreted and reported in the light of solvation process which is referred to as the transition of molecules from their own environment. Next, the excess thermodynamic properties were calculated, and these excess properties were fitted by the Redlich–Kister polynomial equation. The calculated excess properties are discussed in terms of molecular interactions between 2-Butanol and m-Xylene.

Keywords

Residual solvent; Thermodynamic property; Binary mixture; 2-Butanol; m-Xylene

Residual solvent articles; Thermodynamic property articles; Binary mixture articles; 2-Butanol articles; m-Xylene articles

Article Details

1. Introduction

The pharmaceutical industry is one of the largest users of organic solvents per amount of the final product [1-3]. Organic solvents are constantly present in the pharmaceutical production processes and the properties of binary liquid mixtures are of interest to pharmacist, medicinal scientists, condensed-matter theorists, experimental chemists, and physicists etc. An understanding of the intermolecular forces which give rise to the diverse phenomena observed experimentally is important for both practical and applications-oriented reasons. In chemical process industries, materials are normally handled in fluid form and therefore, the physical, chemical, and transport properties of fluids draw attention. Thermodynamic investigation of liquid mixtures consisting of polar and nonpolar components is of considerable importance in understanding the intermolecular interaction between the component molecules and in processing product formulation in several industrial and technological purposes. Residual solvents testing become one of the important parts of quality control in pharmaceuticals [4, 5].

Residual solvents in pharmaceutical products are defined as organic volatile compounds that are used or produced in the manufacturing of drug substances or excipients, or in the preparation of drug products. Among the residual solvents 2-Butanol (or 2-Bu-OH) and xylene are very significant in the view of pharmaceutical importance [6, 7]. 2-Bu-OH is an organic polar compound normally found as an equal mixture of the two stereoisomers, a racemic mixture of (R)-(−)-2-Bu-OH and (S)-(+)-2-Bu-OH. This secondary alcohol is a flammable, colorless liquid that is soluble in water and completely miscible with polar organic solvents such as ethers and other alcohols [8, 9]. Xylene is used in medical technology, dentistry and in industry as a solvent and in the manufacture of pesticides, chemical and pharmaceutical products [10, 11]. m-Xylene (or m-Xln), the most important type of xylene, is an aromatic hydrocarbon, based on benzene with two methyl substituents where “m” stands for meta, meaning the two methyl substituents are at location 1 and 3 on the aromatic ring. 

The practical importance of liquid mixtures rather than single component liquid systems, has gained much importance in assessing the nature of molecular interactions and in investigating the physico-chemical behaviors of such systems [12, 13, 14]. The systematic survey of literature shows that there is no systematic study specially on thermodynamic properties present in the binary mixture containing 2-Bu-OH and m-Xln with highly intensive observation of every specific proportion. In view of this importance, it is of interest to study the thermodynamic properties in order to understand the interaction behavior in their binary mixtures of various proportions with the variation of temperature. From the experimental values of density and viscosity, thermodynamic properties and their excess thermodynamic properties have been estimated at 298.15 K to 323.15 K. The result of excess properties viz: excess enthalpy of activation (DH#E), excess entropy of activation (DS#E) and excess free energy of activation (DG#E) were fitted to the Redlich-Kister equation [15] and plotted by graphical presentation.

2. Experimental details

2-Bu-OH and m-Xln used in this research study were purchased from Sigma Aldrich Chemicals Company. According to the manufacturer, the purities of these compounds were >99%. The water used in all experimental work was double distilled in quality. The binary mixtures of 2-Bu-OH and m-Xln were prepared by using an analytical electrical balance with a precision of ± o.1 µg and later were converted to different composition of the mixture using dilution method. Special care was taken to prevent evaporation and the introduction of moisture into the experimental samples.

Density of all binary mixtures including pure solvents was measured using an oscillation densimeter (Anton Paar DSA 5000). To measure the viscosity Stabinger viscometer (svm-3000-stabinger-viscometer) was used. The temperature was previously set up by 298.15-323.15 K. The measurement was accomplished by the descending of the temperature in the viscometer. In both machinery processes the temperature was automatically controlled with an uncertainty of ±0.01 K.

3. Theoretical aspects

3.1 Calculation of different thermodynamic parameters for viscous flow:

Fluidity of liquid follows some mechanisms as liquid is considered as a combination of layers and so it flows as a rate process. To treat the viscosity as a rate process it is assumed that the motion of liquid layers involves the passage of a molecule from one equilibrium position to another in the same layer. To do so, it is necessary that a suitable ‘hole’ or site should be available, and the production of such a ‘hole’ requires the expenditure of energy, since work must be done in pushing back other molecules. The jump of the moving molecules from one equilibrium position to the next may thus be regarded as equivalent to the passage of the system over a potential barrier. Eyring and his co-workers using absolute reaction rate theory and partition functions, correlated viscosity [16] as follows:

image

Where, DG# is the free energy of activation per mole for viscous flow, h the Planck’s constant (=6.6262 x 10-34 J.sec), N the Avogadro number (= 6.023 x 1023 mol-1), R the molar gas constant (= 8.3145 JK-1mol-1) T the absolute temperature in Kelvin scale and h is the observed viscosity in mPa.s. According to the definition of DG# eq. (1) reduces to

image

Where, DH# is the enthalpy of activation per mole and  DS# the entropy of activation per mole for viscous flow.

The plot of image gives a straight line with slope, DH#/ R and intercept, -DS#/R assuming that DH# and DS# be almost independent of temperature. Therefore, DH# and DS# can easily be calculated from the slope and intercept of eq. (3) as,

image

The free energy of activation, DG#, for viscous flow has been calculated by using the simple thermodynamic relation,

image

3.2 Calculation of different excess thermodynamic parameters for viscous flow

The excess free energy of activation (DG#E), excess enthalpy of activation (DH#E) and excess entropy of activation (DS#E) for viscous flow were calculated by using the following relations,

image

Where, the subscripts 1 and 2 represent the pure components of the mixture.

The experimentally obtained values of excess properties for a system were fitted by the least square method using Redlich-Kister Eq. (13) of the form:

image

4. Results and discussion

4.1 Density and Viscosity of the binary mixture

The density and viscosity values of binary mixture as a function of the mole fraction of 2-Bu-OH(x1) respectively at temperatures (298.15 to 323.15) K can be known by Figure (1-2). The plotting displays the trend of changing these properties. The changes of the properties are evaluated for the changes of each proportion of the mixture component along with the variation of temperatures.

fortune-biomass-feedstock

Figure 1: Density trend analysis of the binary mixture

fortune-biomass-feedstock

Figure 2: Viscosity trend analysis of the binary mixture

From Figure 2 it can be observed that viscosity of the binary mixture of 2-Bu-OH + m-Xln increases in very disciplined way with the increasing proportion of 2-Bu-OH but decreases almost linearly with temperature rises. Here the nonpolar m-Xln is low viscous liquid and when it interacts with the polar one it breaks the intermolecular network of the 2-Bu-OH which was built due to a lot of H-bond as well as polar-polar interaction. Thus, there was an induction of polarity occurred in m-Xln and become induced dipole and attached to the polar 2-Bu-OH. Thus, the liquid mixture becomes more viscous. From Figure 2 it can be seen that the rising of viscosity first increases slowly but when the polar proportion is higher it rises sharply upward.

4.2 Thermodynamic properties measurement

The three types of very important thermodynamic properties viz. entropy, enthalpy and free energy were very intensively studied for the binary mixture of polar + nonpolar compound. There excess values were also calculated and fitted in Redlich-kister fitting equation. Figure 3 shows the plot of enthalpy of activation ΔH# for the transport process vs. mole fraction of alcohol for the system over the whole range of composition (0 to 1). It is noticed that for the binary system ΔH# value (Table 1) continues to increase on addition of alcohol and eventually reach the value of pure 2-Bu-OH because H-bonded liquids, like 2-Bu-OH always require higher enthalpy for activation than that of the other low polar or nonpolar liquids. The excess enthalpies of the binary mixtures of aromatic hydrocarbons with 2-Bu-OH are graphically represented by the Figure 4. The excess enthalpy of activation for viscous flow (ΔH#E) show the negative values extended over a considerable region of concentrations.

Table 1: Experimental data for Enthalpy of activation of the binary mixture

Mole fraction of

Enthalpy (Expt.)

DH#

kJmol-1

Enthalpy (Theor.)

DH¹id

kJmol-1

Excess Enthalpy

DH#E

kJmol-1

Fitting

Value

DH#E*

kJmol-1

2-Bu-OH (x1)

m-Xln (x2)

0.0000

1.0000

8.2473

8.2473

0.0000

0.0000

0.0500

0.9500

8.8447

9.1483

-0.3036

-0.4519

0.1007

0.8994

8.7808

10.0609

-1.2802

-0.9986

0.1499

0.8501

9.4970

10.9482

-1.4512

-1.5620

0.1998

0.8002

9.8594

11.8470

-1.9876

-2.1274

0.2496

0.7504

10.1993

12.7449

-2.5456

-2.6618

0.2998

0.7002

10.1118

13.6486

-3.5367

-3.1529

0.3498

0.6502

11.0383

14.5502

-3.5119

-3.5863

0.3996

0.6004

11.5978

15.4470

-3.8493

-3.9553

0.4498

0.5502

12.1391

16.3519

-4.2128

-4.2609

0.4993

0.5007

12.7254

17.2432

-4.5178

-4.4925

0.5490

0.4510

13.4728

18.1394

-4.6666

-4.6509

0.5997

0.4003

14.3952

19.0534

-4.6582

-4.7280

0.6493

0.3507

15.0475

19.9470

-4.8995

-4.7104

0.7026

0.2974

16.3868

20.9079

-4.5211

-4.5723

0.7497

0.2503

17.4724

21.7567

-4.2843

-4.3289

0.8001

0.1999

18.9108

22.6649

-3.7542

-3.9175

0.8483

0.1518

19.9537

23.5317

-3.5780

-3.3499

0.9009

0.0991

22.0578

24.4800

-2.4222

-2.4915

0.9503

0.0497

23.9739

25.3712

-1.3973

-1.4104

1.0000

0.0000

26.2660

26.2660

0.0000

0.0000

Enthalpy, Excess Enthalpy and Fitting value of Excess enthalpy of activation for different molar ratios are listed in the table.

fortune-biomass-feedstock

Figure 3: Enthalpy curve for different mole fractions

fortune-biomass-feedstock

Figure 4: Excess enthalpy curve for different mole fractions

Figure 5 is for the plots of entropy of activation ΔS# for the viscous flow vs. mole fraction of alcohol for this binary system. The corresponding data are listed in Table 2. The typical nature of the small and negative (ΔS#) value of alcohol indicates that during the viscous flow of initial H-bonded order breaks down to form the activated complex of little ordered structure. On the other hand, negative (ΔS#) value for the aromatic hydrocarbons revealed that during the flow process the activated complex formed, are much more ordered.

Figure 5 also reveals that with increase of concentration of alcohol, the negative value decreases for the binary system of 2-Bu-OH + m-Xln respectively. It indicates that during the flow process at the certain composition of mixtures, the molecular order of the activated and inactivated state for each of the mixtures is same. The excess entropy ΔS#E of activation for the system are shown (Figure 6) as a function of mole fraction of 2-Bu-OH. The plots of ΔS#E vs. mole fraction of 2-Bu-OH Figure 6 for the binary mixture show an almost similar trend at those of the excess enthalpy (ΔH#E). The curve has been found to be concave in nature. The negative excess entropy signifies that the species formed in the activated state are more ordered than what is to be expected to the additive law.

Table 2: Experimental data for Entropy of activation of the binary mixture

Mole fraction of

Entropy (Expt.)

DS#

Jmol-1 K-1

Entropy (Theor.)

DS#id

Jmol-1 K-1

Excess

Entropy DS#E

Jmol-1 K-1

Fitting

Value DS#E*

Jmol-1 K-1

2-Bu-OH (x1)

m-Xln (x2)

0.0000

1.0000

-53.7654

-53.7654

0.0000

0.0000

0.0500

0.9500

-51.7552

-51.3158

-0.4394

-0.9349

0.1007

0.8994

-71.7320

-48.8346

-3.2086

-2.2531

0.1499

0.8501

-49.7181

-46.4224

-3.2957

-3.6748

0.1998

0.8002

-48.6127

-43.9789

-4.6339

-5.1185

0.2496

0.7504

-47.6356

-41.5379

-6.0977

-6.4842

0.2998

0.7002

-48.1038

-39.0810

-9.0228

-7.7373

0.3498

0.6502

-45.2342

-36.6297

-8.6046

-8.8437

0.3996

0.6004

-43.6499

-34.1915

-9.4584

-9.7901

0.4498

0.5502

-42.1572

-31.7316

-10.4256

-10.5802

0.4993

0.5008

-40.5356

-29.3084

-11.2272

-11.1861

0.5490

0.4510

-38.5053

-26.8720

-11.6333

-11.6068

0.5997

0.4003

-35.9968

-24.3870

-11.6098

-11.8182

0.6493

0.3507

-34.4003

-21.9576

-12.4427

-11.7829

0.7026

0.2974

-30.6157

-19.3452

-11.2704

-11.4360

0.7497

0.2503

-27.6821

-17.0375

-10.6446

-10.8196

0.8001

0.1999

-23.8235

-14.5684

-9.2550

-9.7820

0.8483

0.1518

-21.3038

-12.2120

-9.0918

-8.3609

0.9009

0.0991

-15.6459

-9.6339

-6.0120

-6.2240

0.9503

0.0497

-10.7034

-7.2109

-3.4924

-3.5347

1.0000

0.0000

-4.7782

-4.7782

0.0000

0.0000

Entropy, Excess entropy and Fitting value of excess entropy of activation for different molar ratios are listed in the table.

fortune-biomass-feedstock

Figure 5: Entropy curve for different mole fractions

fortune-biomass-feedstock

Figure 6: Excess entropy curve for different mole fractions

Table (3-8) shows the variation of free energy of activation ΔG# for the viscous flow of the system as a function of 2-Bu-OH under the whole range of composition at temperature 298.15 K to 323.15 K and trend of changing this thermodynamic property are given by the Figure 7. The ΔG# values increase very slowly in the initial stage which is followed by a relatively greater rise with increasing concentration of 2-Bu-OH. The curves for ΔG# for the system are found to be smooth and similar. But a crossover of curves between temperature 298.15 K and 323.15 K is noticed in the system at higher mole fraction of 2-Bu-OH. It is also revealed from the Figure 7 that the nonpolar (m-Xln) rich region the ΔG# values increase slightly with the rise of temperature but at the alcohol rich region it is vice versa.

Figure 8 shows the variation of excess free energy ΔG#E of activation at 298.15 to 323.15 K over the whole composition range for this binary system (Table 3-8). In each case, the ΔG#E values are negative, but with the rise of temperature, the values are less negative, i.e., (δΔG#E/ΔT)p is positive. The general nature of the curves does not virtually change with the variation of temperature. The negative excess free energies indicate according to the Eyring image that the viscous flow of the solutions of the aromatic hydrocarbons in 2-Bu-OH is enhanced, causing the viscosity to decrease from the values expected ideally.

The free energy of activation is often regarded to be an energy barrier that a molecule must surmount in order to make a hole which is a necessary requirement for a molecule to flow through. The excess values throughout the whole concentration range are negative with minima falling around 0.6 mole fraction of 2-Bu-OH. The negative excess free energy indicates the reduction of energy barrier height and hence increases of viscous flow.

Table 3: Experimental data for Free energy of activation of the binary mixture at 298.15 K

Mole fraction of

Free Energy (Expt.)

DG#

kJmol-1

Free Energy

(Theor.)

DG#id

kJmol-1

Excess

Free Energy

DG# E kJmol-1

Fitting

Value

DG# E*

kJmol-1

2-Bu-OH (x1)

m-Xln (x2)

0.0000

1.0000

24.2774

24.2774

0.0000

0.0000

0.0500

0.9500

24.2755

24.4481

-0.1726

-0.1732

0.1007

0.8994

24.2974

24.6210

-0.3235

-0.3268

0.1499

0.8501

24.3205

24.7890

-0.4686

-0.4664

0.1998

0.8002

24.3533

24.9593

-0.6060

-0.6013

0.2496

0.7504

24.4018

25.1294

-0.7276

-0.7286

0.2998

0.7002

24.4540

25.3006

-0.8466

-0.8460

0.3498

0.6502

24.5249

25.4714

-0.9465

-0.9495

0.3996

0.6004

24.6120

25.6412

-1.0293

-1.0364

0.4498

0.5502

24.7083

25.8127

-1.1044

-1.1064

0.4993

0.5008

24.8111

25.9815

-1.1704

-1.1573

0.5490

0.4510

24.9531

26.1512

-1.1981

-1.1903

0.5997

0.4003

25.1277

26.3244

-1.1967

-1.2044

0.6493

0.3507

25.3040

26.4937

-1.1897

-1.1974

0.7026

0.2974

25.5149

26.6757

-1.1608

-1.1627

0.7497

0.2503

25.7259

26.8365

-1.1106

-1.1031

0.8001

0.1999

26.0137

27.0085

-0.9948

-1.0010

0.8483

0.1518

26.3054

27.1727

-0.8673

-0.8571

0.9009

0.0991

26.7226

27.3523

-0.6297

-0.6358

0.9503

0.0497

27.1651

27.5212

-0.3560

-0.3565

1.0000

0.0000

27.6907

27.6907

0.0000

0.0000

Free energy, Excess free energy, and Fitting value of excess free energy for different molar ratios at 298.15 K are listed in the table.

Table 4: Experimental data for Free energy of activation of the binary mixture at 303.15 K

Mole fraction of

Free Energy (Expt.)

DG#

kJmol-1

Free Energy

(Theor.)

DG#id

kJmol-1

Excess

Free Energy

DG# E kJmol-1

Fitting

Value

DG# E*

kJmol-1

2-Bu-OH (x1)

m-Xln (x2)

0.0000

1.0000

24.5462

24.5462

0.0000

0.0000

0.0500

0.9500

24.5343

24.7047

-0.1704

-0.1685

0.1007

0.8994

24.5577

24.8651

-0.3075

-0.3156

0.1499

0.8501

24.5691

25.0212

-0.4521

-0.4480

0.1998

0.8002

24.5963

25.1792

-0.5829

-0.5757

0.2496

0.7504

24.6400

25.3371

-0.6971

-0.6961

0.2998

0.7002

24.6945

25.4960

-0.8015

-0.8074

0.3498

0.6502

24.7511

25.6545

-0.9035

-0.9053

0.3996

0.6004

24.8302

25.8122

-0.9820

-0.9874

0.4498

0.5502

24.9191

25.9713

-1.0523

-1.0535

0.4993

0.5008

25.0138

26.1280

-1.1142

-1.1014

0.5490

0.4510

25.1457

26.2856

-1.1399

-1.1323

0.5997

0.4003

25.3077

26.4463

-1.1387

-1.1453

0.6493

0.3507

25.4760

26.6035

-1.1275

-1.1385

0.7026

0.2974

25.6679

26.7724

-1.1045

-1.1055

0.7497

0.2503

25.8643

26.9217

-1.0574

-1.0490

0.8001

0.1999

26.1328

27.0814

-0.9485

-0.9520

0.8483

0.1518

26.4119

27.2338

-0.8218

-0.8153

0.9009

0.0991

26.8009

27.4005

-0.5997

-0.6046

0.9503

0.0497

27.2187

27.5572

-0.3385

-0.3388

1.0000

0.0000

27.7145

27.7145

0.0000

0.0000

Free energy, Excess free energy, and Fitting value of excess free energy for different molar ratios at 303.15 K are listed in the table.

Table 5: Experimental data of Free energy of activation of the binary mixture at 308.15 K

Mole fraction of

Free Energy (Expt.)

DG#

kJmol-1

Free Energy

(Theor.)

DG#id

kJmol-1

Excess

Free Energy

DG# E kJmol-1

Fitting

Value

DG# E*

kJmol-1

2-Bu-OH (x1)

m-Xln (x2)

0.0000

1.0000

24.8151

24.8151

0.0000

0.0000

0.0500

0.9500

24.7931

24.9613

-0.1682

-0.1639

0.1007

0.8994

24.8179

25.1093

-0.2914

-0.3043

0.1499

0.8501

24.8177

25.2533

-0.4356

-0.4297

0.1998

0.8002

24.8394

25.3991

-0.5597

-0.5502

0.2496

0.7504

24.8782

25.5448

-0.6666

-0.6637

0.2998

0.7002

24.9350

25.6914

-0.7564

-0.7687

0.3498

0.6502

24.9772

25.8377

-0.8604

-0.8611

0.3996

0.6004

25.0485

25.9832

-0.9347

-0.9385

0.4498

0.5502

25.1298

26.1300

-1.0001

-1.0006

0.4993

0.5008

25.2165

26.2746

-1.0581

-1.0455

0.5490

0.4510

25.3382

26.4200

-1.0818

-1.0743

0.5997

0.4003

25.4877

26.5683

-1.0806

-1.0863

0.6493

0.3507

25.6480

26.7132

-1.0653

-1.0796

0.7026

0.2974

25.8210

26.8691

-1.0481

-1.0483

0.7497

0.2503

26.0027

27.0069

-1.0042

-0.9949

0.8001

0.1999

26.2520

27.1542

-0.9022

-0.9031

0.8483

0.1518

26.5184

27.2948

-0.7764

-0.7735

0.9009

0.0991

26.8791

27.4487

-0.5696

-0.5735

0.9503

0.0497

27.2722

27.5933

-0.3211

-0.3212

1.0000

0.0000

27.7384

27.7384

0.0000

0.0000

Free energy, Excess free energy, and Fitting value of excess free energy for different molar ratios at 308.15 K are listed in the table.

Table 6: Experimental data of Free energy of activation of the binary mixture at 313.15 K

Mole fraction of

Free Energy (Expt.)

DG#

kJmol-1

Free Energy

(Theor.)

DG#id

kJmol-1

Excess

Free Energy

DG# E kJmol-1

Fitting

Value

DG# E*

kJmol-1

2-Bu-OH (x1)

m-Xln (x2)

0.0000

1.0000

25.0839

25.0839

0.0000

0.0000

0.0500

0.9500

25.0518

25.2178

-0.1660

-0.1592

0.1007

0.8994

25.0781

25.3535

-0.2754

-0.2930

0.1499

0.8501

25.0663

25.4854

-0.4191

-0.4113

0.1998

0.8002

25.0825

25.6190

-0.5365

-0.5246

0.2496

0.7504

25.1164

25.7525

-0.6361

-0.6313

0.2998

0.7002

25.1755

25.8868

-0.7113

-0.7300

0.3498

0.6502

25.2034

26.0208

-0.8174

-0.8169

0.3996

0.6004

25.2667

26.1541

-0.8874

-0.8896

0.4498

0.5502

25.3406

26.2886

-0.9480

-0.9477

0.4993

0.5008

25.4191

26.4211

-1.0020

-0.9896

0.5490

0.4510

25.5307

26.5543

-1.0236

-1.0162

0.5997

0.4003

25.6676

26.6902

-1.0226

-1.0272

0.6493

0.3507

25.8200

26.8230

-1.0030

-1.0206

0.7026

0.2974

25.9741

26.9659

-0.9918

-0.9912

0.7497

0.2503

26.1411

27.0920

-0.9510

-0.9408

0.8001

0.1999

26.3711

27.2270

-0.8560

-0.8542

0.8483

0.1518

26.6250

27.3559

-0.7309

-0.7317

0.9009

0.0991

26.9573

27.4968

-0.5395

-0.5424

0.9503

0.0497

27.3257

27.6293

-0.3036

-0.3035

1.0000

0.0000

27.7623

27.7623

0.0000

0.0000

Free energy, Excess free energy, and Fitting value of excess free energy for different molar ratios at 313.15 K are listed in the table.

Table 7: Experimental data for Free energy of activation of the binary mixture at 318.15 K

Mole fraction of

Free Energy (Expt.)

DG#

kJmol-1

Free Energy

(Theor.)

DG#id

kJmol-1

Excess

Free Energy

DG# E kJmol-1

Fitting

Value

DG# E*

kJmol-1

2-Bu-OH (x1)

m-Xln (x2)

0.0000

1.0000

25.3527

25.3527

0.0000

0.0000

0.0500

0.9500

25.3106

25.4744

-0.1638

-0.1545

0.1007

0.8994

25.3383

25.5977

-0.2594

-0.2818

0.1499

0.8501

25.3149

25.7175

-0.4026

-0.3929

0.1998

0.8002

25.3255

25.8389

-0.5134

-0.4990

0.2496

0.7504

25.3546

25.9601

-0.6056

-0.5989

0.2998

0.7002

25.4160

26.0822

-0.6661

-0.6913

0.3498

0.6502

25.4296

26.2040

-0.7744

-0.7727

0.3996

0.6004

25.4850

26.3251

-0.8401

-0.8406

0.4498

0.5502

25.5514

26.4473

-0.8959

-0.8948

0.4993

0.5008

25.6218

26.5676

-0.9458

-0.9336

0.5490

0.4510

25.7232

26.6887

-0.9654

-0.9582

0.5997

0.4003

25.8476

26.8121

-0.9645

-0.9681

0.6493

0.3507

25.9920

26.9328

-0.9408

-0.9617

0.7026

0.2974

26.1272

27.0626

-0.9354

-0.9340

0.7497

0.2503

26.2795

27.1772

-0.8977

-0.8867

0.8001

0.1999

26.4902

27.2999

-0.8097

-0.8053

0.8483

0.1518

26.7315

27.4169

-0.6855

-0.6899

0.9009

0.0991

27.0355

27.5450

-0.5095

-0.5113

0.9503

0.0497

27.3792

27.6654

-0.2862

-0.2858

1.0000

0.0000

27.7862

27.7862

0.0000

0.0000

Free energy, Excess free energy, and Fitting value of excess free energy for different molar ratios at 318.15 K are listed in the table.

Table 8: Experimental data for Free energy of activation of the binary mixture at 323.15 K

Mole fraction of

Free Energy (Expt.)

DG#

kJmol-1

Free Energy

(Theor.)

DG#id

kJmol-1

Excess

Free Energy

DG# E kJmol-1

Fitting

Value

DG# E*

kJmol-1

2-Bu-OH (x1)

m-Xln (x2)

0.0000

1.0000

25.6216

25.6216

0.0000

0.0000

0.0500

0.9500

25.5694

25.7310

-0.1616

-0.1498

0.1007

0.8994

25.5985

25.8418

-0.2433

-0.2705

0.1499

0.8501

25.5634

25.9496

-0.3862

-0.3745

0.1998

0.8002

25.5686

26.0588

-0.4902

-0.4734

0.2496

0.7504

25.5927

26.1678

-0.5751

-0.5665

0.2998

0.7002

25.6566

26.2776

-0.6210

-0.6526

0.3498

0.6502

25.6557

26.3871

-0.7314

-0.7284

0.3996

0.6004

25.7032

26.4960

-0.7928

-0.7917

0.4498

0.5502

25.7622

26.6059

-0.8438

-0.8419

0.4993

0.5008

25.8245

26.7142

-0.8897

-0.8777

0.5490

0.4510

25.9158

26.8230

-0.9073

-0.9002

0.5997

0.4003

26.0276

26.9341

-0.9065

-0.9090

0.6493

0.3507

26.1640

27.0426

-0.8786

-0.9028

0.7026

0.2974

26.2803

27.1593

-0.8791

-0.8768

0.7497

0.2503

26.4179

27.2624

-0.8445

-0.8326

0.8001

0.1999

26.6093

27.3727

-0.7634

-0.7564

0.8483

0.1518

26.8380

27.4780

-0.6400

-0.6480

0.9009

0.0991

27.1138

27.5932

-0.4794

-0.4802

0.9503

0.0497

27.4327

27.7014

-0.2687

-0.2681

1.0000

0.0000

27.8101

27.8101

0.0000

0.0000

Free energy, Excess free energy, and Fitting value of excess free energy for different molar ratios at 323.15 K are listed in the table.

fortune-biomass-feedstock

Figure 7: Free energy curves for different mole fractions at different temperatures

fortune-biomass-feedstock

Figure 8: Excess free energy curves for different mole fractions at different temperatures

5. Conclusion

Studies on thermodynamic properties along with their respective excess values in liquids and liquid mixtures is essential to understand the molecular interactions between unlike molecules, to develop new theoretical models [17] as well as engineering applications in pharmaceutical process industries. An understanding of the thermodynamic properties of 2-Bu-OH and m-Xln and their binary system have been measured at temperatures (298.15 to 323.15) K and in atmospheric pressure. Excess thermodynamic properties of binary mixture solvents were calculated and fitted with the Redlich–Kister equation. Thermodynamic properties derived from viscosity and its related parameters are also important in designing industrial equipments with better precision [18]. In these mixtures, the predominance of physical effect may arise due to dipole-induced dipole interaction resulting in disruption in the favorable orientation due to breaking of self-network built by H-bond among the polar molecules and rising dispersion force of nonpolar liquid. The observed excess thermodynamic values in all the mixture indicate the significant interaction between the unlike molecules.

Acknowledgement

This work was the partial fulfillment of academic degree of Master of Science in Chemistry supported by department of Chemistry of University of Chittagong. Teachers and students of this department supported in many ways during this research work to make it successful.

Abbreviations

2-Bu-OH = 2-Butanol

m-Xln = m-Xylene (or meta-Xylene)

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