Computation of Thermoacoustic and Thermodynamic Properties of Aqueous Methyl Orange Solution from Density and Sonic Speed Data

J. D. Pandey1, Rupali Sethi1*, Subhash Chandra Shrivastava1, Vandna Pathak2 and S. K. Vishwakarma2

1 Deparment of Chemistry, University of Allahabad, Allahabad-211002, INDIA

2 Department of Chemistry, Mahatma Gandhi Chitrakoot Gramodaya Vishvavidyalaya, Chitrakoot, Satna-485331, INDIA

* Correspondence: E-mail: sethirupali.au@gmail.com

(Received 16 Jan, 2019; Accepted 11 Feb, 2019; Published 20 Feb, 2019 )

ABSTRACT: Density and ultrasonic speed data have been used to calculate a number of useful and important thermoacoustic and thermodynamic parameters such as thermal expansivities, a, isothermal compressibility, ßT, internal pressure, Pint, specific heat ratio, ?, surface tension, s, Pseudo-Grüneisen parameter, ?, non-linearity parameter, B/A, by empirical relations at T= (303, 308, 313 and 318) K temperatures in the range concentration from 0.05 to 1 molar. Solvation number, Sn , has been computed to support the conformational change in geometry of aqueous methyl orange solution. The calculated values highly support the change in orientation and abnormal behavior of methyl orange solution at varying concentrations and quite satisfactory results are obtained.

Keywords: Methyl orange; empirical relations; thermodynamic properties; ultrasonic speed; non-linearity parameter and internal pressure.

INTRODUCTION: The decolourization/fading of aqueous dye solutions by high intensity ultrasonic waves have been studied quite early by a number of workers. 1,2 The degradation of coloured chrome Azural S-Al complex has also been studied at 2MHz frequency of such high intensity ultrasonic waves.3 But the propagation of low amplitude ultrasonic waves in aqueous dye solutions has so, far, not been studied.

Hence the ultrasonic propagation parameters such as ultrasonic speed, absorption, relaxation etc could not be measured in such solutions. After an exhaustive literature survey we have come across two papers 4,5 dealing with the determination of ultrasonic speed, density, viscosity, surface tension of methyl orange4 and 4-methyl-7-hydroxycoumarin.5 The chemical structure of methyl orange is depicted in Figure 1. It is worthwhile to mention that these ultrasonic propagation parameters can be employed to determine a number of important and useful thermodynamic and transport properties of liquids and solutions.

img2

Figure 1: Structure of Methyl Orange.

With a proper theoretical formalism, the estimated properties will be helping in structural and physicochemical studies of system. In order to achieve such goal, we have for the first time, taken such studies for dye solutions. The structure and nature of, and interactions occurring in liquids and solutions can be investigated from density and ultrasonic speed data. The experimental techniques involved in the measurements of density and ultrasonic speed are very simple, quick and quite precise. Such data can be employed to estimate a number of useful and important thermodynamic properties of liquids and solutions. There is only one thermodynamic property which can be directly determined from density and ultrasonic speed data, which is the adiabatic (isentropic) compressibility, ßs given by:

img2

This property cannot be determined by any other method. In order to estimate other thermodynamic properties, some empirical relations based on dimensional analysis, have been developed during recent past. 6-11 In the present work we are using these equations for computing various thermodynamic and thermoacoustical properties of aqueous solutions of methyl orange. The experimental data of density (?) and ultrasonic speed (u) have been taken from the recent paper of Thanuja et al.4 The other paper5 has quite limited data and hence ignored.

THEORETICAL FORMULATION: Based on the dimensional analysis6-11 the following empirical relations between ?-u and thermodynamic properties have been deduced:

img2

One of the very important and useful parameter, known as pseudo-Grüneisen parameter (?), which has been studied by many workers 12-16 for investigating the internal structure and clustering phenomenon in liquids and solutions. Also, it is a dimensionless measure of change in entropy with volume or the thermal pressure and is usually investigated through the relations given below. Physical significance of this thermodynamic parameter has recently 13 been discussed and applied for liquids. This parameter is given by:

img2

The significance and importance of another thermodynamic parameter, called the Beyer’s acoustic non-linearity parameter (B/A), has been discussed by several workers during recent years.17-20

There are several methods of determination of B/A, but there are several limitations. In the present case of methyl orange solutions, the only possible three formulae can be employed. These are:

img2

RESULTS AND DISCUSSION: Computation of various thermodynamic and thermoacoustical properties of aqueous methyl orange solution have been done using the experimental data of density, ?, and ultrasonic speed, u, at four different temperatures 303, 308, 313 and 318K and varying concentrations (0.05 - 2.0) mole %. The experimental values of density and ultrasonic velocity were taken from the paper of Thanuja et al.4 The calculated values of a, ßT, Pint, ?, s and ? from empiricial equations (1) to (6) are recorded in Table 1.

The thermoacoustic non-linearity parameter, B/A, and the internal pressure, Pint, have been calculated from two different methods namely Hartmann-Balizer20 and Ballou 21 using equations (7), (8) and (9) are enlisted in Table 2.

Table 3 focuses on the calculated values of apparent molar volume ( ), apparent molar isentropic compressibility ( ) and most important of all the solvation number at all temperatures considered above using equations (10), (11) and (12).


Table 1: Estimated values of thermal expansivity (a), isothermal compressibility (ßT), internal pressure (Pint ), specific heat ratio (?), surface tension (s), pseudo-Grüneisen parameter (G) at T= (303, 308, 313 and 318) K.

Conc.

T

ax103

ßTx1017

Pint

?

s

?

(mole%)

K

K-1

atm-1

atm

Nm-1

0.05

303

0.9984

52.713

459214

1.308

43.411

1.018

308

0.9906

51.081

477068

1.2997

44.447

0.982

313

0.9875

50.436

488003

1.2908

44.872

0.941

318

0.9888

50.713

492935

1.2829

44.689

0.9

Ideal

303

1.0422

62.59

430265

1.3503

38.164

1.109

0.1

303

0.9867

50.275

476107

1.3084

44.98

1.031

308

0.9953

52.062

470596

1.3001

43.817

0.979

313

0.9644

45.879

525531

1.2928

48.176

0.97

318

0.9681

46.595

526869

1.2849

47.619

0.925

Ideal

303

1.0435

62.884

429762

1.3519

38.031

1.113

0.5

303

0.9641

45.832

510631

1.3088

48.212

1.057

308

0.9707

47.093

507678

1.3005

47.241

1.005

313

0.9942

51.817

478800

1.2916

43.972

0.937

318

0.9833

49.578

501684

1.2833

45.454

0.906

Ideal

303

1.0423

62.598

430253

1.3503

38.161

1.109

1

303

0.9899

50.922

472139

1.3092

44.551

1.031

308

0.9892

50.781

479764

1.3005

44.643

0.986

313

0.986

50.125

491172

1.292

45.081

0.946

318

0.9808

49.08

505804

1.2837

45.799

0.91

Ideal

303

1.0423

62.602

430271

1.3504

38.159

1.11

2

303

1.007

54.553

448914

1.31

42.308

1.016

308

0.9972

52.446

468868

1.3013

43.576

0.981

313

0.9901

50.983

485551

1.2928

44.511

0.945

318

0.9887

50.684

494356

1.2845

44.708

0.905

Ideal

303

1.0422

62.587

430271

1.3503

38.166

1.109

Table 2: Calculated values of non-linearity parameter (B/A) and internal pressure (Pint) at T= (303, 308, 313 and 318) K.

Conc.

T

B/A

Pint

B/A

Pint

(mole %)

K

Hartmann

atm

Ballou

atm

0.05

303

8.4763

265310

2.9302

639704

308

8.3869

274644

2.8206

674768

313

8.3653

276893

2.7942

683454

318

8.3935

272877

2.8288

669471

Ideal

303

8.6216

227192

3.1081

532109

0.1

303

8.3209

282901

2.7399

705066

308

8.444

267921

2.8906

650349

313

8.0524

315403

2.4111

837025

318

8.1097

306714

2.4813

802597

Ideal

303

8.6216

226396

3.1081

530245

0.5

303

8.0315

320369

2.3855

854642

308

8.125

306639

2.5

799451

313

8.444

267431

2.8906

649160

318

8.3177

281484

2.7359

702039

Ideal

303

8.6216

227171

3.1081

532063

1

303

8.3537

278499

2.7801

689139

308

8.3603

277218

2.7882

684990

313

8.334

279801

2.7559

695342

318

8.2821

285518

2.6923

717760

Ideal

303

8.6212

227177

3.1076

532116

2

303

8.5684

254285

3.0429

601818

308

8.4559

265869

2.9051

643772

313

8.3802

273904

2.8125

673908

318

8.3761

273878

2.8074

674445

Ideal

303

8.6216

227201

3.1081

532131

Table 3: Calculated values of apparent molar volume (?v) apparent molar isentropic compressibility (?ks) and solvation number (Sn).

Conc.

T

?v

?ks

Sn

Mol %

K

m3 mol-1

m2N-1

0.05

303

119.61

7245.4

-0.025

308

125.42

7362.3

-0.025

313

127.36

7429.4

-0.025

318

133.21

7472.7

-0.025

303

332.06

9685.7

-0.021

0.1

303

209.96

4074.9

-0.026

308

213.28

4354

-0.024

313

218.85

3827.9

-0.028

318

222.22

4041.5

-0.026

303

334.72

5740.8

-0.02

0.5

303

281.14

1574.7

-0.028

308

282.46

1771.1

-0.025

313

282.9

1823.8

-0.024

318

283.79

1756.3

-0.025

303

328.46

2359.3

-0.02

1

303

290.26

1477.9

-0.025

308

290.97

1464

-0.025

313

291.69

1455.6

-0.025

318

292.41

1436.6

-0.026

303

328.3

1939.5

-0.02

2

303

295.22

1396.9

-0.023

308

295.86

1353.6

-0.024

313

296.49

1342.2

-0.024

318

297.13

1345.5

-0.024

303

328.09

1729

-0.02

There is a sharp fall in density (?), ultrasonic speed (u), thermal expansivities (a), isothermal compressibility (ßT), internal pressure (Pint) owing to the stereochemistry of methyl orange. Methyl orange exhibits geometrical isomerism at N=N (azo group). The structure can be represented as Figure 2 syn (Z) and Figure 3 anti (E) 2D forms. Figure 4 and Figure 5 represents syn (Z) and anti (E) 3D form.

img2

Figure 2: Syn form (2D).

Here dark grey balls represents carbon atom, light grey are the hydrogen atoms, blue is nitrogen, yellow is sulphur atom and red balls are the oxygen atoms. At low concentration less molecules of methyl orange are available in water so it prefers the anti conformer where the two nitrogen atoms are more available for hydrogen bonding therefore denser. But as the methyl orange moiety increases equal number of molecules in syn as well as (in equilibrium) anti form exists. In syn form the lone pair on nitrogen is less available for hydrogen bonding due to steric hindrance and hence less density at higher mole fraction.

img2

Figure 3: Anti form (2D).

img2

Figure 4: Syn Form (3D).

img2

Figure 5: Anti Form (3D).

Increase in molar concentration decreases the values of a and ßT as they are inversely proportional to density, density increases in region of low concentration and low temperatures (303, 308K) and apparently increases in region of high concentration and temperatures (313 and 318K) due to breakdown of hydrogen bonds, releasing the dipoles of water leading to formation of intermolecular hydrogen bonds. Similarly Pint increases with concentration till 0.5 then decreases till 2 % showing close interaction between solute-solvent in region of low concentration, which apparently decreases abruptly with increase in solute volume or solute molecules in solvent leading to an increase in the volume of solution. At high concentration, the solute-solvent interactions present are dominated by solute-solute interaction. Similar is the trend with temperature in case of Pint.

Heat capacity ratio, ?, increases with concentration as the number of interacting molecule increases, the bulky group in methyl orange increases with concentration thereby more association with solvent (water) molecules and reverse trend is with temperature as rise in temperature keeps the molecules in excited state predominantly. With increase in concentration of methyl orange the ? value increases till 0.5 mol% then there is a sharp decrease from 1to 2 mol% indicating large clustering and more compact lattice structure during interaction till 0.5 mol% followed by sudden decrease, this abnormal behavior is due to sharp decrease in density due to sudden increase in the volume of the solution with the addition of methyl orange. The rise in temperature at each concentration decreases the value continuously predicting that as the temperature increases continuously the interaction between the solute and solvent decreases due to increased intermolecular distance and breaking or lengthening of hydrogen bonds prevalent between them.

The non-linearity parameter, B/A values as calculated by Hartmann and Ballou relations, show a marked decrease with concentration till 0.5% and apparent increase till 2% concentration indicative of more number of interacting molecules in the system. The temperature rise decreases the value of B/A at each concentration as the ultrasonic speed increases with increasing intermolecular distance and volume in the same order. Deviation from ideal behavior is noticed in solution with a concentration of 0.1%. At elevated temperature breaking of hydrogen bonds becomes more feasible.

Apparent molar volume and apparent molar compressibility are increasing with temperature as well as concentration. An attempt has also been made to deduce the values of , Sv, , Sk using Masson’s equations and . Here and measure the solute-solvent interaction, whereas S v and Sk the experimental slopes, measure the solute-solute interaction. Unfortunately, in the present case of methyl orange solution, the versus plots are found to be non-linear, hence cannot be used to determine , Sv, , Sk. In addition, the solvation number is negative indicates that the ion is likely to dissolve in solvent but with increasing temperature and concentration the negative value increases showing less interaction with water molecules.

CONCLUSION: A remarkable property of methyl orange dye has come into being owing to its sharp fall in density and ultrasonic speed at a high concentration due its stereochemistry. The change in conformation on varying concentration is responsible for its abnormal behavior. The solvation number parameter supports its uniqueness. The above is depicted well with the help of self explanatory diagrams drawn with the help of software, ACD LAB Chem Sketch for 2D conformation and Gauss View software for 3D conformation. The solvation number parameter supports the above explanation. This is a stepping milestone in our explanation of the interaction parameters with the help of software and its successful implementation justifying the uniqueness of methyl orange in solution chemistry.

ACKNOWLEDGEMENT: One of the author (SCS) is thanks to CSIR, New Delhi for the financial help. We are also thankful to Dr. Amrita Dwivedi for her assistance in using the softwares.

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