CHAPTER 3 ULTRASONIC STUDY OF MOLECULAR INTERACTIONS...

34

CHAPTER 3

ULTRASONIC STUDY OF MOLECULAR INTERACTIONS

OF BINARY LIQUID MIXTURES

3.1 INTRODUCTION

Considerable scientific and practical interest has been stimulated by

the investigation of inorganic liquids by ultrasonic measurements. A liquid is

of cohesive nature. Important physicochemical properties of solutions such as

adiabatic compressibility, viscosity, internal pressure, relaxation time etc may

be computed from ultrasonic velocity and density data. The extent to which

the cohesive forces are disturbed depends on the nature of the solute and

solute-solvent interactions. When an electrolyte is dissolved in a solvent, the

cations and anions from the crystal go into the solutions.

Basically, a binary mixture is formed by the replacement of like

contacts in the pure liquids. Ultrasound velocity measurements have been

extensively applied to assess the molecular interactions in pure and binary

liquid mixtures. Ultrasonic velocities of binary mixtures can be calculated

theoretically from Jacobsons free length theory, Schaaff’s collision factor

theory and empirical relations of Nomoto. The extent of deviation from the

theoretical values can be used to access molecular interactions in liquid

mixtures. In the binary mixtures containing non-polar liquids there can be

only induced dipole-induced dipole interactions, which arise due to polarity

aspects. The forces of attraction due to induced dipole-induced dipole are

very weak.

35

In this chapter, ultrasonic velocity, density and viscosity measurements have been employed to access the interactions existing between the molecules of the components in three binary liquid mixtures. The systems chosen are:

a. ammonium chloride : ammonium sulphate b. ammonium oxalate : ammonium formate c. zinc sulphate : zinc nitrate

The experimental values of ultrasonic velocity, density and viscosity for above three systems are discussed.

3.2 DENSITY (ρ) Density of mixed salts solution of binary mixture of ammonium chloride: ammonium sulphate, ammonium oxalate: ammonium formate and zinc sulphate: zinc nitrate were measured in different concentration at 303 K. As the number of particles increases, the density is also increases. Density increases with increasing the concentration due to the presence of ions or particles. The density of a mixed salt solution is increased with the increase in composition of ammonium sulphate, whereas they decrease with ammonium chloride (Kalidass et al., 1999). The measured density values of ammonium chloride and ammonium sulphate solution are given in Table 3.1. But, the density of a solution is found to be increases with increase in the concentration of ammonium oxalate and it is found to be maximum at 90:10 with a mole fraction of 0.8181, whereas they decrease with the increase in concentration of ammonium formate. It may be decreasing with further increase the concentration of ammonium oxalate. Similarly, a non-linear variation is found with the increase the concentration of zinc nitrate. The density of mixed salt solution shows a sharp increase which confirms the structural rearrangement of molecules (Ali et al., 2002).

36

Table 3.1 Experimental values of ultrasonic velocity (U), density (), acoustic impedance (Z), adiabatic compressibility (ad), intermolecular free length (Lf), molar sound velocity (R) and molar compressibility (W) of ammonium sulphate and ammonium chloride mixed salt solution in different concentrations at 303 K

Composition of ammonium chloride +

ammonium sulphate

Mole fraction (X1 ) of

(NH4)2 SO4

Velocity(U) ms-1

Density ()

kgm-3

Acoustic impedance

(Z) × 106

kg m-2s-1

Adiabatic compressibility

(ad )× 10-10

kg-1 ms2

Intermolecular free length

(Lf )x 10-10

m

Molar sound velocity

(R)

m3mol-1(ms-1)1/3

Molar compressibility

(W)

m3mol-1Pa1/7

100 : 00 0.0000 1542 1018 1.569 4.133 0.0129 0.607 1.150

90 : 10 0.0526 1550 1022 1.584 4.073 0.0128 0.653 1.238

80 : 20 0.1111 1568 1028 1.611 3.958 0.0126 0.703 1.334

70 : 30 0.1764 1579 1032 1.632 3.886 0.0125 0.760 1.443

60 : 40 0.2500 1590 1039 1.652 3.808 0.0124 0.822 1.560

50 :50 0.3333 1600 1043 1.669 3.744 0.0123 0.894 1.697

40 : 60 0.4285 1557 1049 1.634 3.931 0.0126 0.963 1.833

30 : 70 0.5385 1595 1055 1.683 3.726 0.0122 1.061 2.019

20 : 80 0.6666 1610 1060 1.707 3.639 0.0121 1.171 2.228

10 : 90 0.8181 1617 1066 1.723 3.588 0.0120 1.297 2.470

00 : 100 1 1625 1071 1.734 3.538 0.0119 1.451 2.764

37

3.3 VELOCITY (U)

A plot of ultrasonic velocity against mole fraction of ammonium

sulphate in different concentration at 303 K is shown in Figure 3.1. The

variation of ultrasonic velocity in a solution depends upon the increase or

decrease of intermolecular free length (Lf) after mixing the component.

According to Eyring and Kinchaid (1938), velocity increases if the

intermolecular free length decreases and vice-versa as a result of mixing

component. It is seen that, the ultrasonic velocity increases initially with the

increase of concentration of ammonium sulphate. It attains a maximum at a

concentration of 50:50 with a mole fraction of 0.3333 (Table 3.1). The

increase in the concentration of ammonium sulphate weakens the molecular

forces and hence the abrupt change in velocity is obtained. This non-linear

variation of velocity with increase in concentration indicates the complex

formation between the constituents of the mixture (Manisha Gupta and Shukla

1996).

While in the case of ammonium oxalate and ammonium formate

salt solution, when the concentration is increased, the plots are linear up to the

concentration of 80:20 (Figure 3.2). At the composition of 90:10, the

ultrasonic velocity decreases with increase the concentration. It is observed

that, the mixed salt solution shows a critical characteristics at a mole fraction

of 0.8181. The positive or negative slop indicating the existence of very weak

intermolecular attractions in these systems and there is little deviation from

ideal behavior. This may be due to induced dipole-induced dipole type. The

abrupt variation in velocity at the concentration of 90:10 indicates the

formation of complex (Ali and Nain 1994; Tabhane and Patki 1985).

38

Similarly, the ultrasonic velocity decreases with the increase of

concentration of zinc nitrate. It attains a minimum at a mole fraction of

0.6928. The increase in the concentration of zinc nitrate weakens the

molecular forces and hence the abrupt change in velocity is obtained at a mole

fraction of 0.7945 (Figure 3.3). This non-linear variation of velocity with

increase in concentration indicates critical characteristics at a particular

composition (Muraliji et al., 2002a,b).

0.0 0.2 0.4 0.6 0.8 1.0

1540

1560

1580

1600

1620

1640

U (m

/s)

Mole fraction of Ammonium Sulphate

( (NH4 )SO4)2+(NH4)Cl2

Figure 3.1 Variation of ultrasonic velocity with mole fraction of

ammonium sulphate of a mixed salt solution at 303 K

Ultr

ason

ic v

eloc

ity (U

) ms-1

Mole fraction of ammonium sulphate

39

0.0 0.2 0.4 0.6 0.8

1550

1555

1560

1565

1570

1575

Ultr

ason

ic v

eloc

ity (U

) ms-1

Mole fraction of ammonium oxalate

(NH 4)2C 2O 4+HC OO NH 4

Figure 3.2 Variation of ultrasonic velocity with mole fraction

of ammonium oxalate of a mixed salt solution at 303 K

0.0 0.2 0.4 0.6 0.8 1.01570

1575

1580

1585

1590

1595

1600

1605

ultra

soni

c ve

loci

ty(U

) ms-1

mole fraction of zinc Nitrate

ZnSO4+Zn(NO3)

Figure 3.3 Variation of ultrasonic velocity with a mole fraction

of zinc nitrate of a mixed salt solution at 303 K

Ultr

ason

ic v

eloc

ity (U

) ms-1

Mole fraction of zinc nitrate

Ultr

ason

ic v

eloc

ity (U

) ms-1


40

3.4 INTER MOLECULAR FREE LENGTH (Lf)

Intermolecular free length in binary liquid mixtures can be used to

access the attraction between the component molecules. Increase in

concentration leads to decrease in gap between two species and it is referred

as intermolecular free length. On the basis of sound propagation in liquid

(Karthikeyan and Palaniappan 2005) the increase in free length after mixing,

decreases the sound velocity. The intermolecular free length has an inverse

behavior of ultrasonic velocity. The intermolecular free length is found to be a

predominant factor in determining the nature of sound velocity variation in

liquid mixtures (Karthikeyan and Palaniappan 2005; Eyring and Kinchaid

1938). Table 3.1 shows the values of intermolecular free length of ammonium

sulphate and ammonium chloride solution. It shows that the decrease of

intermolecular free length with the increase of concentration of ammonium

sulphate and reaches minimum value (Figure 3.4). The value of

intermolecular free length in a binary mixture depends on concentration. It is

observed that, a sudden increase in length with decrease in velocity at a mole

fraction of 0.4285 of ammonium sulphate. This indicates that there is a

significant interaction present between the solute molecules due to which

structural arrangement molecules are considerably affected (Ishwara Bhat and

Shree Varaprasad 2003).

In the mixed solution of ammonium oxalate and ammonium

formate, intermolecular free length decreases with increase the concentration

of ammonium oxalate and reaches a minimum (Figure 3.5). An increase in

intermolecular free length produces a decrease in velocity. This indicates that,

there is a significant interaction between solute molecules. Thus, the structural

arrangements are considerably affected (Manisha Gupta and Shukla 1996;

Karunanidhi et al., 1999). A sudden change in free length at a given

concentration may be due to weakening of intermolecular attraction.

41

0.0 0.2 0.4 0.6 0.8 1.00.0118

0.0120

0.0122

0.0124

0.0126

0.0128

0.0130

L f x 1

0-10 m


((NH4)2SO4)2+NH4Cl2

Figure 3.4 Variation of intermolecular free length with mole fraction of

ammonium sulphate of a mixed salt solution

0.0 0.2 0.4 0.6 0.8 1.0

0.01255

0.01260

0.01265

0.01270

0.01275

0.01280

Lf A

Mole fraction of Ammonium oxalate

Amm.oxalate+Amm.formate


ammonium oxalate of a mixed salt solution

Inte

rmol

ecul

ar fr

ee le

ngth

(Lf )

x 1

0-10 m


Inte

rmol

ecul

ar fr

ee le

ngth

(Lf )

x 1

0-10 m


(NH4)2C2O4 + HCOO NH4

42

Similarly, it is seen that the concentration of zinc nitrate increases

the intermolecular length and sudden decrease at a mole fraction of 0.7945 of

zinc nitrate (Figure 3.6). It indicates that there is a significant presence in

between the molecules due to the dipole induced dipole or dipole-dipole

interaction leads structural rearrangement as described earlier (Nikam et al.,

2004; Rama Rao et al., 2004). It may be pointed out here that the free length

values at a given concentration in different systems can be used to compare

the induced ionic-ionic interactions in the above three systems investigated.

3.5 ADIABATIC COMPRESSIBILITY (βad)

Adiabatic compressibility (βad) values were calculated for three

mixed salt solution. Adiabatic compressibility is inversely proportional to U2

and the trend in adiabatic compressibility with concentration is the reverse of

the trend in U with concentration in all the three system.

The adiabatic compressibility decreases with increases in

concentration. This is an ideal trend. In the mixed ammonium chloride and

ammonium sulphate salt solution, the compressibility decreases with increase

in concentration of ammonium sulphate (Table 3.1). And it attains sudden

increases at a mole fraction of 0.4285 of ammonium sulphate (Figure 3.7). It

means, ion-solvent interaction increases at a given composition (Varma and

Surendar Kumar 2000; Kalidass et al., 1999).

43

0.0 0.2 0.4 0.6 0.8 1.0

0.1150

0.1155

0.1160

0.1165

0.1170

0.1175

0.1180

0.1185

L f A

Mole fraction of Zinc Nitrate

ZnSO4+Zn(NO

3)2


zinc nitrate of a mixed salt solution

0.0 0.2 0.4 0.6 0.8 1.0

3.5

3.6

3.7

3.8

3.9

4.0

4.1

4.2

x1

0-10 kg

m-2S

-1


(NH4)2SO

4+NH

4)Cl

2

Figure 3.7 Variation of adiabatic compressibility with mole fraction of


Inte

rmol

ecul

ar fr

ee le

ngth

(Lf )

x 1

0-10 m


Adi

abat

ic c

ompr

essi

bilit

y (

ad )

x 10

-10 k

g-1 m

s2


(NH4)2SO4 + (NH4)Cl2

44

Every solvent has a limit for compression called the limiting a

compressibility value. The compressibility of a solvent is higher than that of

a solution and it decreases with increases in concentration. In the mixed

solution of ammonium oxalate and ammonium formate, the compressibility

decreases with increase in concentration of ammonium oxalate solution

(Figure 3.8). At a mole fraction of 0.8181 of ammonium oxalate, it is found to

increases. That means ion-solvent interaction increases (Ravinder Reddy and

Linga Reddy 1999). Similar non-linear variation of compressibility is also

occurs in the zinc nitrate and zinc sulphate salt solution (Figure 3.9). It shows

that the reverse effect as that of impedance (Nikam et al., 2004). The

variations of adiabatic compressibility with concentration indicate that the

strength of induced ionic-ionic interactions concentration is dependent.

0.0 0.2 0.4 0.6 0.8 1.03.92

3.94

3.96

3.98

4.00

4.02

4.04

4.06

4.08

4.10

adx1

0-10 k

g-1m

s2

Mole fraction Ammonium oxalate


Figure 3.8 Variation of adiabatic compressibility with mole fraction of


Adi

abat

ic c

ompr

essi

bilit

y (

ad )

x 10

-10 k

g-1 m

s2


(NH4)2C2O4 + HCOONH4

45

0.0 0.2 0.4 0.6 0.8 1.03.28

3.30

3.32

3.34

3.36

3.38

3.40

3.42

3.44

3.46

3.48

3.50

ad

x 10

-10 k

g -1m

s2


Zn(NO3)2+ZnSO4

Figure 3.9 Variation of adiabatic compressibility with mole fraction of zinc nitrate of a mixed salt solution

3.6 ACOUSTIC IMPEDANCE (Z)

The variation of acoustic impedance and mole fraction of ammonium sulphate is shown in Table 3.1. In the aqueous solution of ammonium sulphate and ammonium chloride, acoustic impedance increases with increase the concentration of ammonium sulphate suggesting that the ion-solvent interaction increases till the mole fraction of 0.3333. But it decreases at mole fraction of 0.4285. And again it is increases with concentration. It may be due to the complex formation in the solution and this may be on the basis of the interaction between solute and solvent molecules (Ravindra Natha Reddy and Ramamurthy 1995). As the concentration of ammonium oxalate increases, acoustic impedance increases, whereas compressibility decreases and it is shown in Table 3.2. The usual behavior of the linear increase of acoustic impedance is noticed in the solution. This behavior of linear variation is observed till the

Adi

abat

ic c

ompr

essi

bilit

y (

ad )

x 10

-10 k

g-1 m

s2


46

mole fraction of 0.6666. The value of impedance is suddenly decreases at a mole fraction of 0.8181. The variation of acoustic impedance shows dips at a given concentration again support the existence of molecular interaction. The decrease in impedance with increase in concentration can be explained on the basis of interaction between ion-solvent, which increases the intermolecular free length (Madhu Rastogi et al., 2002). Similarly, in the mixed solution of zinc sulphate and zinc nitrate, the acoustic impedance decreases with increases in the concentration of zinc nitrate, till the mole fraction of 0.6928. The variation of impedance is shown in Table 3.3. The sudden increase in impedance at a mole fraction of 0.7945 of zinc nitrate may be due to the critical characteristics in the solution and this may be on the basis of the interaction between solute and solvent complex (Ravinder Reddy and Linga Reddy 1999). 3.7 VISCOSITY (η)

Viscosity depends mainly on the availability of bulky or less mobile entities of salt solution. The viscosity is related to normal forces in the liquids. The variation of viscosity of ammonium sulphate and ammonium chloride mixed salt solution at 303 K is shown in Figure 3.10. The changes in density and viscosity can be correlated to hydrophilic (Hydrogen bond forming or structure making) or hydrophobic (Hydrogen bond disrupting or structure breaking) character of solute. The viscosity is gradually increases and suddenly decreases with the increase concentration of ammonium sulphate. A dip is shown at a mole fraction of 0.8181 of ammonium sulphate and again it increases. Similarly, in the case of ammonium oxalate and ammonium formate solution, the values of viscosity increases and attains the maximum values of 0.25 and 0.6666 mole fraction of ammonium oxalate (Figure 3.11) and then decreases with further increase in concentration which indicates the weakening of intermolecular interaction between the component molecules (Prasad 2003).

47

Table 3.2 Experimental values of density (), ultrasonic velocity (U), adiabatic compressibility (ad), acoustic

impedance (Z), free length (Lf), molar volume (V), molar sound velocity (R), molar compressibility (W)

and molar volume (V) of ammonium oxalate and ammonium formate in different concentrations at 303 K

Composition of ammonium

chloride + ammonium

sulphate

Mole fraction of

ammonium oxalate (X1)

Ultrasonic

velocity(U) ms-1

Density

() kg m-3


ad ×10-10

kg-1 ms2

Acoustic impedance

(Z)

kg m-2s-1

Intermolecular

Free length(Lf) ×10-10m

Molar sound

velocity

(R)

m3 mol-1

(ms-1)1/3


(W)

m3 mol-1Pa1/7

Molar volume

(V) m3 mol-1

100 : 00 0.000 1551 1018 4.085 1578562 0.01280 0.717 1.360 0.0619

90 : 10 0.053 1555 1018 4.064 1582634 0.01277 0.755 1.430 0.0651

80 : 20 0.111 1554 1020 4.062 1584713 0.01276 0.793 1.503 0.0685

70 : 30 0.177 1554 1020 4.059 1585243 0.01276 0.838 1.589 0.0724

60 : 40 0.250 1557 1021 4.040 1589697 0.01273 0.889 1.685 0.0767

50 :50 0.333 1559 1022 4.027 1593145 0.01271 0.946 1.793 0.0816

40 : 60 0.429 1563 1023 4.003 1598540 0.01267 1.012 1.918 0.0872

30 : 70 0.539 1574 1025 3.938 1613350 0.01257 1.088 2.063 0.0935

20 : 80 0.667 1575 1025 3.935 1613965 0.01256 1.177 2.231 0.1012

10 : 90 0.818 1556 1026 4.025 1596538 0.01271 1.275 2.419 0.1101

00 : 100 1.000 1567 1025 3.972 1606513 0.01262 1.405 2.665 0.1210

48

Table 3.3 Experimental values of ultrasonic velocity (U), density (), specific acoustic impedance (Z), adiabatic

compressibility (ad), intermolecular free length (Lf), viscosity () of zinc sulphate and zinc nitrate at

different concentration at 303 K

Composition of zinc

sulphate + zinc nitrate

Mole fraction

of

(ZnSO4)

Mole fraction of

(Zn(NO3)2)

(X1)

Ultrasonic velocity (U)

ms-1

Density (ρ)

kgm-3

Acoustic impedance

(Z)

kgm-2s-1


( βad) × 10-10

kg-1ms2

Intermolecular

free length

(Lf ) × 10-10 m

Viscosity

(η)×10-3

Nsm-2

90 : 10 0.903 0.0970 1604 1176 1886737 3.304 0.1151 1.597

80 : 20 0.8054 0.1946 1600 1170 1871200 3.340 0.1157 1.529

70 : 30 0.7071 0.2929 1597 1168 1864961 3.358 0.1160 1.497

60 : 40 0.6081 0.3919 1595 1166 1859930 3.371 0.1163 1.427

50 : 50 0.5085 0.4915 1590 1164 1851396 3.397 0.1167 1.562

40 :60 0.4082 0.5918 1585 1163 1843228 3.422 0.1172 1.603

30 : 70 0.3072 0.6928 1573 1161 1826285 3.481 0.1182 1.621

20 : 80 0.2055 0.7945 1581 1164 1840932 3.436 0.1174 1.631

10 : 90 0.1031 0.8969 1577 1159 1828248 3.468 0.1170 1.632

49

0.0 0.2 0.4 0.6 0.8 1.0

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

(Vis

cosi

ty) 1

0-3N

sm-2


(NH4)(SO

4)

2+(NH

4)CL

2

Figure 3.10 Variation of viscosity with mole fraction of ammonium

sulphate of a mixed salt solution at 303 K

0.0 0.2 0.4 0.6 0.8 1.01.13

1.14

1.15

1.16

1.17

1.18

1.19

x 1

0-3N

sm-2

mole fraction of ammonium oxalate

amm oxalate + amm formate

Figure 3.11 Variation of viscosity with mole fraction of ammonium

oxalate of a mixed salt solution at 303 K

Visc

osity

() x

10-3

Nsm

-2

Visc

osity

() x

10-3

Nsm

-2


50

Similarly the variation of viscosity with the concentration of zinc

nitrate is shown in Figure 3.12. The viscosity decreases with the increase in

the concentration of zinc nitrate reaches its minimum at a mole fraction of

0.3919 and increases on further increase in concentration of nitrate, which is

due to the less cohesive force between them (Subramanyam Naidu and

Ravindra Prasad 2004). From the observed viscosity values, it is confirmed

that, viscosity is more sensitive to structural changes because of

solvent-solute interactions (Rajkotia and Parsania 1998).

0.0 0.2 0.4 0.6 0.8 1.01.40

1.45

1.50

1.55

1.60

1.65

x10

-3 N

sm-2

Mole fraction of Zinc nitrate

ZnSo4+Zn(NO3)2

Figure 3.12 Variation of viscosity with mole fraction of Zinc nitrate of a

mixed salt solution at 303 K

3.8 INTERNAL PRESSURE (i)

Internal pressure in binary mixtures can used to assess the

intermolecular attraction between the components. Internal pressure is a

energy volume co-efficient and is a measure of the attractions and repulsions

Vis

cosi

ty (

) x 1

0-3 N

sm-2

51

of the molecules in the liquid systems. Its measurements are significant in the

evaluation of thermodynamic properties of liquid because it is closely related

to ultrasonic velocity, viscosity and compressibility in the liquid phase. The

internal pressure values reflect the net cohesive/adhesive forces available in

the medium. Such forces will drastically change if mole fraction of

components is changed (Figure 3.13).

0.0 0.2 0.4 0.6 0.8 1.0

1000

1200

1400

1600

1800

2000

2200

2400

2600

Pre

ssur

e(P

a) x

102

mole fraction of ammonium sulphate

NH4Cl2+NH4SO4

Figure 3.13 Variation of internal pressure with mole fraction of


The internal pressure is linearly decreasing with concentration of

ammonium oxalate which shows that the attractive force increases

(Figure 3.14) (Sabesan et al., 1980). A decrease in internal pressure with

concentration confirms that the presence of solvent-solute interactions (Raj

Kotia et al., 1999). Similarly, the same linear variation is observed in the case

of ammonium sulphate and ammonium chloride salt solution (Tables 3.4-3.6).

Inte

rnal

pre

ssur

e (

i) x

102

Pa


52

Table 3.4 Computed values of mole fraction, molar volume (V), available volume (Va), attenuation (α), relaxation time (), internal pressure (πi), viscosity (η) and free volume (Vf) of mixed salt solution of ammonium chloride and ammonium sulphate solution in different concentrations

Composition of Ammonium Chloride +

Ammonium Sulphate

Mole fraction (X1) of

ammonium sulphate

Molar

volume (V) m3mol-1

Available volume (Va)

m3mol-1

Attenuation

(α)

Np m-1

Relaxation

time ()

10-13 sec

Pressure (πi) 102 ×Pa

Viscosity

(η)

10-3 NSm-2

Free volume(Vf)

10-3

m3

100 : 00 0.000 0.053 0.051 0.0292 5.708 2562 1.036 2.536

90 : 10 0.053 0.056 0.055 0.0295 5.748 2434 1.059 2.767

80 : 20 0.111 0.061 0.059 0.0287 5.714 2252 1.083 3.047

70 : 30 0.176 0.065 0.064 0.0286 5.730 2070 1.106 3.369

60 : 40 0.250 0.070 0.070 0.0280 5.651 1888 1.113 3.814

50 :50 0.333 0.076 0.076 0.0330 6.696 1874 1.341 3.311

40 : 60 0.429 0.083 0.081 0.0374 7.385 1760 1.409 3.378

30 : 70 0.539 0.091 0.091 0.0370 7.487 1616 1.507 3.648

20 : 80 0.667 0.010 0.101 0.0396 8.083 1511 1.666 3.699

10 : 90 0.818 0.111 0.112 0.0280 5.755 1135 1.203 7.118

00 : 100 1.000 0.123 0.125 0.0319 6.564 1069 1.392 6.840

53

Table 3.5 Experimental values of viscosity (), relaxation time () , internal pressure (i), available value (Va), free volume (Vf) and attenuation () of ammonium oxalate and ammonium formate in different concentrations at 303 K

Composition of ammonium formate +

ammonium oxalate

Mole fraction of

ammonium oxalate

(X1)

Mole fraction of

ammonium formate

(X2)

Viscosity ()

10- 3 Nsm-2

Relaxation time ()

10 – 13 sec

Internal pressure (i) Pa

Available volume

(Va) m3 mol-1

Free volume (Vf) m3

Attenuation () 10-7 Np m-1

100 : 00 0.0000 1.0000 1.179 6.421 2313 0.0600 0.6128 0.1633

90 : 10 0.0526 0.9481 1.152 6.243 2155 0.0633 0.6609 0.1584

80 : 20 0.1111 0.8888 1.168 6.323 2045 0.0665 0.6862 0.1605

70 : 30 0.1765 0.8235 1.174 6.355 1920 0.0703 0.7216 0.1613

60 : 40 0.2500 0.7500 1.182 6.358 1799 0.0746 0.7618 0.1613

50 :50 0.3333 0.6666 1.143 6.137 1644 0.0795 0.8399 0.1553

40 : 60 0.4286 0.5714 1.158 6.179 1529 0.0851 0.8892 0.1560

30 : 70 0.5385 0.4615 1.146 6.019 1395 0.0920 0.9740 0.1509

20 : 80 0.6666 0.3333 1.173 6.156 1288 0.0995 1.0281 0.1542

10 : 90 0.8181 0.1818 1.134 6.086 1154 0.1070 1.1447 0.1543

00 : 100 1.0000 0.0000 1.146 6.071 1035 0.1185 1.2522 0.1528

54

Table 3.6 Computed values of molar volume (V), molar sound velocity (R), molar compressibility (W), available volume (Va), relaxation time (τ), attenuation constant and internal pressure in ZnSO4 and Zn (NO3)2 in different concentrations

Composition of zinc sulphate +

zinc nitrate

Mole fraction of

Zn(NO3)2

(X1)

Molar volume (V)

m3mol-1

Molar sound velocity

(R)

m3mol-1(ms-1)1/3


(W)

m3mol-1Pa1/7

Available volume(Va)

m3mol-1

Relaxation

time (τ)

10-13 sec

Attenuation

(α) 10-15

Nepm-1

Internal pressure

(i) 10-5

90 : 10 0.0970 0.2453 2.871 5.547 0.2459 7.034 2.754 1.393

80 : 20 0.1946 0.2475 2.895 5.589 0.2475 6.807 2.672 1.362

70 : 30 0.2929 0.2487 2.907 5.612 0.2482 6.701 2.635 1.346

60 : 40 0.3919 0.2499 2.920 5.636 0.2491 6.414 2.525 1.311

50 : 50 0.4915 0.2511 2.931 5.657 0.2496 7.074 2.794 1.372

40 :60 0.5918 0.2524 2.943 5.679 0.2500 7.316 2.898 1.391

30 : 70 0.6928 0.2536 2.949 5.693 0.2493 7.522 3.003 1.408

20 : 80 0.7945 0.2537 2.956 5.706 0.2507 7.472 2.968 1.397

10 : 90 0.8969 0.2557 2.976 5.743 0.2520 7.547 3.006 1.396

55

0.0 0.2 0.4 0.6 0.8 1.0

1000

1200

1400

1600

1800

2000

2200

2400

i a

tm

Mole fraction of Ammonium oxalate


Figure 3.14 Variation of internal pressure with mole fraction of


The variation of the internal pressure with the increase in the

concentration of zinc nitrate is shown in Figure 3.15. The primary effect of

dissolving zinc nitrate is lowers the compressibility of the solvent molecules.

The lowering of compressibility results in the increase of ultrasonic velocity

and hence pressure increases with concentration. With reference to the

Figure 3.15, the pressure decreases up to the mole fraction of 0.3919 and then

increases reaching the maximum at 0.6928 again decreases (Rajendran and

Marikani 1994). The internal pressure values are less in mixed solution

ammonium oxalate and ammonium formate systems suggesting the presence

of weak induced ionic-induced ionic interactions.

Inte

rnal

pre

ssur

e (

i) Pa



56

0.0 0.2 0.4 0.6 0.8 1.01.30

1.32

1.34

1.36

1.38

1.40

1.42

i 10-5


ZnSO4+Zn(NO3)2

Figure 3.15 Variation of internal pressure with mole fraction of zinc

nitrate of a mixed salt solution

3.9 MOLAR VOLUME (V)

A small quantity of ammonium sulphate is added to the mixed

solution (Table 3.4), ion-solvent interaction occurs resulting considerable

increase intermolecular spaces between the molecules as suggested by

Jacobson (Jacobson 1952). This contributes to increase in molar volume. It

is also noted that, an increase in molar volume decreases the intermolecular

interactions. This trend shows that bonding length decrease with the increase

in concentration and hence the intermolecular interaction decreases. Similar

trend occurs in the case of ammonium oxalate: ammonium formate and zinc

nitrate: zinc sulphate mixed salt solution. From the results it shows that the

complex has formed almost constant molar volume which indicating that

every molecules present in the complex has same molar volume (Viswanadha

Sastry et al., 2003).

Inte

rnal

pre

ssur

e (

i) x

10-5

Pa


57

3.10 MOLAR SOUND VELOCITIES (R) AND MOLAR

COMPRESSIBILITY (W)

Molar sound velocity is an additive function of the chemical bonds

in the molecule and it is useful in correlating molecular structure with

ultrasonic velocity. The linear variation in the Rao constant values with

concentration suggests that the interactions are concentration dependent. The

values of molar sound velocity and molar compressibility are computed of the

liquid mixtures given by Nomoto (Adgankar et al., 1988) is based on the

assumption of linearity of variation of the molecular sound velocity with mole

fractions and further on the additively of the molar volume in the liquid

mixtures. The values of R & W are indicating the linear variation for above

three mixed salts solution. Therefore, the values of velocities increase with

increasing the concentration (Gour et al., 1986). Thus, the linearity

considered here, can be attributed to the intermolecular interactions between

the component molecules of the mixtures.

3.11 AVAILABLE VOLUME (Va)

The available volume is increases with concentration of ammonium

sulphate and it shows a linear variation. But in the case of zinc sulphate and

zinc nitrate, it is observed as a non-linear variation. From the values, it is

inferred that the available volume is directly proportional to velocity. The

values show a sudden decrease at a concentration of 0.6928 which confirms

that the complex formed has less available volume (Ramanathan and

Ravichandran 2004). The same linear variation is also absorbed in the

ammonium oxalate and ammonium sulphate salt solution. Available volume

shows that the non-linear values indicating the structural variations at

molecular levels inside the liquid system (Muraliji et al., 2002a).

58

3.12 ATTENUATION (α)

The attenuation is increase with the concentration of ammonium

sulphate and it shows a sudden decrease at a mole fraction of 0.8181, while,

the variation of attenuation with the concentration of ammonium oxalate in

the mixed salt solution is non linear. It shows a non-linear variation.

Similarly, in the case of zinc nitrate and zinc sulphate salt solution, the

attenuation value decreases up to the concentration of 0.3919 again increases

reaching the maximum at the mole fraction of 0.6929 and again it decreases

(Tables 3.4-3.6). It confirms that the complex formed has high attenuation

value (Muraliji et al., 2002 a,b).

3.13 RELAXATION TIME (τ)

Acoustical relaxation time depends upon viscosity and

compressibility. Relaxation time of a system can be used to characterize the

intermolecular interactions. The values are calculated for three systems at

different concentration. Relaxation process leads to absorption of the waves,

which is related to structural changes in the liquids (Kannappan and

Rajendran 1992).

The relaxation time shows a non-linear variation. It shows a dips at

a mole fraction of 0.33 and 0.5385 with increase the concentration of

ammonium oxalate. Similarly, in the case of zinc nitrate and zinc sulphate

mixed salt solution, the relaxation time is decreases with concentration of

zinc nitrate. It is decreases up to the mole fraction of 0.3919 and above that it

increases. The variation of relaxation time reaches minimum and then

increases as the concentration of zinc nitrate. The increases of relaxation time

with concentration support the solute-solvent interactions (Muraliji et al.,

2002a) (Tables 3.5 and 3.6).

59

3.14 FREE VOLUME (Vf)

The free volume is the effective volume in which the molecules in

the liquid can move and obey perfect gas law. In the mixed solution of

ammonium sulphate and ammonium chloride, the free volume is increases

with concentration of ammonium sulphate. It sudden increases at two points

with a mole fraction of 0.25 and 0.8181 and hence a non-linear variations are

absorbed. It decreases on further increases in the concentration.

Similarly, in the study of ammonium oxalate and ammonium

formate solution, the increase in free volume with concentration indicates the

variations in cohesive forces of this liquid system with changes in solute

concentration. The change in size and shape of the molecules results in the

structural rearrangements of the molecules in the mixture. The structural

changes features are as a result of the reaction between like and unlike

molecules during the mixing of liquids.

In this case, free volume increases with increase in concentration

suggest that the packing of molecules becomes loose. The trend is found to

be opposite to that of internal pressure observation (Kannappan and

Rajendran 1992). But in the case of zinc nitrate and zinc sulphate salt solution

it shows a maximum at a mole fraction of 0.3919 and on again increasing

with concentration. Its value seems to be decreasing which shows that

cohesive force varies with the changes in the solute concentration

(Pauling 1960; Muraliji et al., 2002 c).

3.15 DISCUSSION

The two salts, ammonium sulphate and ammonium chloride, are

dissolved in water to form NH4++, SO4

- and Cl- ions. These ions are strongly

60

bonded with water molecules. NH4+ ion is always bonded with metal ion.

The ionic radii of SO4- and Cl- are 1.4 and 1.81 Å respectively (Pauling

1960). From the literature (Kavanau 1964) it can be seen that the relatively

small ion like SO4 induces higher order in the water structure. It is explained

that the observed non-linear increase in ultrasonic velocity and decrease in

ultrasonic absorption in the aqueous solutions of the ammonium salts based

on the flickering cluster model and Hall’s two state models for liquid water.

According to the Flicker cluster model, NH4+ ions have a structure breaking

property which results in the increase in closely packed structures of water

which in turn leads to an increase in cohesion. This causes increase in velocity

and decrease in compressibility (Subramaniam Naidu and Ravindra Prasad

1996). In the case of ammonium oxalate solution, the absorption is maximum

at a particular concentration because of oxalate ions (anions).

The increase in structural order of water may result in more

cohesion at higher concentration and hence leads to decrease in

compressibility. The decrease in compressibility results an increase in

velocity. Such a possibility doesn’t exist in this case. But, from the velocity

curve, it is observed that there is a sudden decrease in velocity at a

composition of 60:40. From this, it concluded that, some complex molecules

may be formed. The above conclusion is similar to the one drawn by

Ragouramane and Srinivasa Rao (1998).

A similar effect is also observed in solutions of aqueous urinal

chloride, nitrate, strontium iodide, lead acetate, lead nitrate, cadmium bromide

and iodide (Kavanau 1964).

The ammonium oxalate and ammonium formate are freely soluble

in water. As a result of hydration, oxalate ion can form much unequal

distribution of water, by which regions with more density of water and less

61

density of water can be form. The region in which the oxalate ion is present

is to have higher density of water that those in which oxalate ions are absent.

This property is more important for oxalate ions than the formate ions.

Hence, as a result of introducing the oxalate ion, in the beginning, there is

increase in ultrasonic velocity. But at 0.1111 mole fraction of ammonium

oxalate; the value is less implying uniform distribution. But above this value,

gradual increases in the mole fraction of oxalate increases the velocity up to

the mole fraction of 0.6666. Hence, at mole fraction of 0.8181 implies, there

might be uniform distribution of oxalate ions and formate ions through the

matrix in order to have sudden drop in velocity. Pure ammonium oxalate at

mole fraction of 1.000, exhibits velocity is higher than ammonium format at a

mole fraction of 1.00. Since, ammonium oxalate yields 3 moles of ion per

mole. It can yield more heterogeneity in the distribution of water than

ammonium formates which scan furnish two moles of ions. It is to be said

that, multicharged “anions” in aqueous solution can show higher velocity,

than non-negative ion. When the negative charges are closes, the associated

solvent molecules are to be closer. It leads to the formation of higher and less

dense regions in water.

Similarly, the ultrasonic velocity of the solution derived from zinc

sulphate and zinc nitrate decreases with increasing the mole fraction of zinc

nitrate up to 0.6928. Since, zinc sulphate can furnish only 2 ions whereas

zinc nitrate can furnish 3 ions. Ultrasonic velocity is expected to be largely

influenced by the addition of zinc nitrate. Each ion, either Zn++, SO4= or NO3

-

can better organize solvents around them. The ultrasonic velocity is to

decrease with increase in the concentration of any ionic spaces. At the mole

fraction of zinc nitrate 0.7945, there is a increase in velocity. It illustrates,

organization of zinc nitrate themselves rejecting more water of hydration. But

at a mole fraction of 0.8969, there is a decrease in velocity. Hence, at this

mole fraction, the organized ions at 0.7945 must segregate. So this study

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illustrates that the complete dissolution of zinc nitrate up to the mole fraction

of 0.6928. But association of ions begins at mole fraction of 0.7945.

Suppression of association begins at mole fraction of 0.8969.

This suppression could be possible by charging individual neutral

ionic clusters. The density of mixture also decreases with increasing the mole

fraction of zinc nitrate up to 0.6928. So this clearly supports complete

dissolution of zinc nitrate, thus weakening the force between free water

molecules by adding zinc nitrate. At the mole fraction of 0.7945, since there

is a association of ions partly rejecting water at hydration, the density

increases. In other words, they release the water and enhance the hydrogen

bonding interaction. The density of the solution is decreased at the mole

fraction of 0.8969, since the association is suppressed by charging neutral

clusters. The water is to be taken for salvation. Hence, there may be weak

hydrogen bonding interaction in the water thus reducing its density. The data

and free length also supports the above view. With increase of mole fraction

of zinc nitrate, there is decreasing the hydrogen bonding interaction in water.

Hence, the free length is increases up to the mole fraction of 0.6928 of zinc

nitrate but at 0.7945, water is released, so there is more hydrogen bonding

interaction. This results in decrease in free length.

The viscosity of the solution increases with increase in the mole

fraction of zinc nitrate up to 0.6928. Since, water is being used more and

more for hydration. The free water has reduced hydrogen bonding

interaction. Hence, a decrease in viscosity is absorbed.

3.16 CONCLUSION

The ultrasonic study of 1N mixed salts solution of ammonium

sulphate and ammonium chloride, ammonium oxalate and ammonium

63

formate and zinc sulphate and zinc nitrate solution have been carried out. It

shows that the process of ion association and complex formation at the

concentration of 60:40. The same complex indications are absorbed at a mole

fraction of 0.0526 and 0.8181 of ammonium oxalate and at a mole fraction of

0.7945 of zinc nitrate salt solution.

Ultrasonic investigations on three binary liquid systems reveals

that, the liquid mixtures containing inorganic salts solutions exist some

complex formations at a particular concentration. This is due to induced

dipole-induced dipole attraction in the ammonium binary mixtures. While in

the case of zinc solutions, the compounds have weak intermolecular

attractions. These conclusions are supported by the trend in the acoustical

parameters and molecular interaction parameters.

CHAPTER 3 ULTRASONIC STUDY OF MOLECULAR INTERACTIONS...

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