Chapter 6 Acoustic Non-linearity Parameter B/A of Binary Liquid Mixtures-I1

6.1 Introduction

The study of acoustic non-linearity parameter B/A in five binary liquid

mixtures at two different temperatures using Tong and Dong theory has formed

the subject matter of Chapter 5. This chapter (Chapter 6) deals with the

evaluation of B/A in seven binary liquid mixtures using four different theories

and making use of the ultrasonic velocity values at high pressures reported in the

literature [l-51. The variation of B/A with mole fraction of one component was

studied. Also, the excess parameters viz., excess B/A and excess adiabatic

compressibility were computed and were made use of in explaining the molecular

interactions existing in the liquid mixtures. Seghal [6] has reported a set of

relations involving the parameter BIA for the determination of the molecular

properties such as internal pressure, cohesive energy, effective Van der Waal's

constants, distance of closest approach of molecules, diffusion coefficient and

rotational correlation time of pure liquids. In the present work, these relations

applicable to pure liquids were extended to the case of binary liquid mixtures.

The molecular properties of five binary liquid mixtures at room temperature, those

of one binary liquid mixture at two temperatures and one binary liquid mixture at

three different temperatures were studied.

The binary liquid mixture systems chosen for the present study and the

high-pressure ultrasonic velocities of which are reported in the literature[l-51 are

1. Benzene + Aniline

2. Chlorobenzene + Aniline

3. Cblorobenzene + Bromobenzene

4. Toluene + o-Xylene

5. Toluene + Aniline

6. Benzonitrile + Nitrobenzene

7. Benzene + Nitrobenzene

6.2 Theory

In the first method to calculate BIA, Beyer's thermodynamic equation [7]

was used. This equation is

where C is the sound velocity, p the density, P the coefficient of thermal

expansion, T the absolute temperature and C, the specific heat at constant

pressure. The factors are the variations of sound velocity with

pressure and temperature respectively. The contribution of the second term in

equation[l] to BIA is very small and hence it is neglected. The values of - (FIT for the systems benzene + aniline, benzene + nitrobenzene, chlorobenzene +

aniline and chlorobenzene + bromobenzene are obtained from the literature[l-31.

For the other three systems (21, was calculated as follows

Nomura et al. [8] have derived a relation between ultrasonic speed C and

isothermal compressibility KT as

Integration of equation[6.2] between the limits of atmospheric

pressure(0.1 MPa) and any higher pressure p gives

In KT[p] = l n K ~ [o. 1 MPa] -2 in C[p] + 2 In [O. 1MPaI-

KT [p-0. I MPa] ------------------ (6.3)

Isothermal compressibility at different pressures of binary mixtures was

calculated using equation 6.3. A graph of I & @ ) against pressure p was drawn, which

was a stmight line and h m the slope the value of [aK f ' lap] was calculated.

Substituting the value of [aK r' 113 p] in equation 6.2 ( a ~ I ap)T was calculated.

In the second method to determine BIA, Tong Dong equation [9] for

evaluation of B/A values of pure liquids was extended to binary liquid mixtures [lo].

The details of Tong Dong theory is given in Section 5.2 of Chapter 5. The

temperature and pressure coefficients of sound velocity were theoretically

calculated using Tong and Dong method [ I 11 as follows.

The symbols have same meaning as that in Section 5.2 of Chapter 5.

These values were substituted in equation 1 together with other thermo dynamical

parameters for binary mixtures to get B/A values. This is the third method.

Haurmi Endo [12] obtained the following equation for calculating B/A

values of pure liquids using adiabatic compressibility, Ks.

Knowing isothermal compressibility K=(p) at different pressures kom

equation 6.5, adiabatic compressibility at different pressures Ks@) can be obtained

using the equation = y . The ratio of specific heat y was obtained by

using the method of Khanwalkar [13]. y is assumed to be a constant with change in

pressure. A graph of I&@)-' against pressure p was plotted which was a straight line

and kom the slope of the graph - was obtained.

The excess non-lineanity parameter, (B/A)~ for binary liquid mixtures is given

by [lo1

(B/A)~ = (BIA),,, - (B/A),d ------------------ (6.7)

where (BIA),,, is the non-linearity parameter of the mixture and is that

obtained from the ideal mixture relation

(B/A)id=x~ (B/A)t + xz(B/A)2 ------------------ (6.8)

where X I and x2 are respectively the mole fractions of the first and second liquids .

(BiA)l and (B/A)* are the B/A values of the first and second pure liquids

respectively.

The various molecular parameters of binary liquid mixtures were

calculated using Sehgal's relations given below

Internal pressure n,= pc2 ( B I A + ~ )

MC2 Cohesive energy M = (6.10)

(BIA+l)

pc2v,2 Van der Waal's Constants a = -

(BiA+l)

Distance of closest approach of molecules

Difision coefficient

Correlation time T' = - ( B I A + 1) ----- (6.15) I where M is the molecular weight of the binary mixture calculated by ideal mixture

relation. M = XIMI+X~MZ in which XI and xz are the mole W o n s and MI, Mz are the

molecular weight of the first and second pure liquid respectively. VI is the molar

volume given by Vl = where p is the density of the mixture, k is the Boltzman's P

constant, R the universal gas constant and .q is the viscosity of the mixture. The

viscosity of the mixture was calculated by using the equation[l4] qx = x , ~ , f : + x , ~ , f:

where qland qz are the viscosities of the two pure liquids. The above molecular

parameters given in equations 6.9-6.15 were determined by substituting molecular

weight, density, viscosity, molar volume and BJA values ofbinary liquid mixtures.

6.3 Results and Discussions

The non-linearity parameter BIA of seven binary liquid mixtures

calculated using the four different methods are given in table 6.1.

It is seen that (table 6.1) BIA values of all the mixtures calculated using

the second and fourth methods agree with the values obtained by using Beyer's

method (equation 6.1) which is considered to be the most accurate one [I 53.

Table 6.1 Mole fraction (x) of second component, adiabatic compressibility ( K ) and non-linearity parameter (BIA) of binary mixtures determined using Beyer(a), Tong Dong(b), Tong Dong & Beyer(c) and Haurmi Endo(d) methods

Benzene + Nitrobenzene at 293.15K

512.0 10.81 13.97 17.60 460.2 10.84 16.22 20.00 420.7 10.53 14.66 18.04 383.8 10.44 14.74 17.97

Benzene + Nitrobenzene at 303.15K

7126 11.54 10.79 13.81 617.0 10.99 11.73 14.64 574.4 10.78 12.31 14.88 487.5 10.63 13.62 15.64 449.2 10.59 12.65 15.03 405.0 10.54 12.98 15.22

Benzene + Nitrobenzene at 313.15K 769.3 11.69 9.80 12.34 665.9 10.93 10.54 12.98 59 1.5 10.71 10.98 13.35 519.4 10.78 12.22 14.59 475.7 10.63 11.57 13.81 429.6 10.85 11.64 13.82

Benzene + Aniline at 298.15K 675.4 11.60 11.43 14.47 615.8 11.34 11.87 14.68 562.5 11.25 12.18 14.79 511.9 10.85 12.6 15.06 471.1 10.86 12.97 15.31 431.7 9.94 13.28 15.53 404.5 10.66 13.47 15.64 368.1 10.63 13.63 15.64

Cblorobenzene + Aniline at 298.15K 5h4.4 11.45 12.98 16.13 512.1 11.02 12.92 15.58 490.6 11.23 12.96 15.45 462.3 11.18 13.02 15.36 430.7 11.20 13.14 15.36 405.1 10.53 13.31 15.43 368.1 10.63 13.63 15.64

Chlorobenzene + Bromobenzene at 303.15K 733.6 11.19 12.09 14.66 706.3 11.22 11.88 14.36 685.0 11.13 11.68 14.08 665.8 11.05 11.63 13.94 655.0 11.19 11.66 13.91 644.3 11.21 11.75 13.94

Benwnitrile + Nitrobenzene at 298.1 5K 498.16 11.37 12.74 479.43 11.50 12.97 473.58 11.55 13.04 470.30 11.57 13.08 468.50 11.59 13.12 463.11 11.64 13.20 457.69 11.69 13.27 451.93 11.92 13.36 446.25 11.79 13.44 440.51 11.85 13.52 435.04 11.90 13.61 432.36 11.93 13.65 430.66 12.02 13.61 419.85 12.08 13.85 410.28 12.21 14.04 392.72 12.47 14.41

Benzonihile + Nitrobenzene at 303.15K 513.03 11.40 12.05 493.13 1 1.44 12.24 487.01 11.45 12.3 483.62 11.46 12.33 481.76 11.46 12.36 476.63 11.47 12.41 470.85 11.48 12.48 464.73 11.49 12.54 459.45 11.51 12.57 453.74 11.52 12.65 447.44 11.53 12.73 444.66 11.54 12.76 442.71 11.54 12.78 432.69 11.56 12.91 422.13 11.58 13.05 403.87 11.63 13.30

Toluene + Aniline at 303.15K 705.21 11.99 11.67 632.62 11.74 11.61 567.50 11.54 11.37 502.20 11.42 10.99 441.03 11.36 10.53 384.03 10.52 10.04

Toluene + o-Xyline at 303.15K 705.21 12.01 11.67 696.80 12.00 11.90 682.73 12.01 12.17 672.34 12.00 12.45 660.34 11.99 12.76 649.24 11.98 13.1 1

Hence Tong Dong and Haurmi Endo methods may be considered to be more

accurate compared to the third method for the determination of B/A of binary

liquid mixtures. The large deviation of B/A values obtained using the third

approach, which is based on both Tong Dong and Beyer methods, from the values

obtained using Beyer equation (equation 1) might be resulting from the

inaccuracy of the expressions used for calculating temperature and pressure

coefficients of sound velocity (equations 6.4 and 6.5).

In benzene + aniline and benzene + nitrobenzene systems, as the mole

fractions of benzene decreases, density and sound velocity increases and hence

adiabatic compressibility decreases (table 6.1). It is found that the BIA values at

all temperatures decrease as the mole &tion of benzene is decreased. In

chlorobenzene + Aniline system also. the B/A values and adiabatic compressibility

shows a decreasing tendency as the mole fraction of chlorobenzene is decreased.

But in chlorobenzene t bromobenzene system, the variation of B/A and

compressibility with mole fraction of chlorobenzene is very small. In toluene +

aniline and toluene -t o-xylene systems, as the mole fraction of toluene is

decreased, the density and sound velocity increase and hence compressibility

decreases. It may be inferred that compressibility and BIA exhibit the same type

of variation with changes in mole fraction of one of the components of the liquid

mixtures. Therefore, just like compressibility, BIA may be considered as quantity

that determines the hardness of a liquid [12].

But in benzonitrle + nitrobenzene system, a contradictoxy observation was

observed. In this system, BIA and compressibility showed an opposite behaviour i.e.,

BIA increases while compressibility decreases with the decrease in the mole fraction of

nitrobemme. This may be explained on the basis of molecular interaction between

unlike molecules as follows.

The dipole moment of benzonitrile is 4.1 8 Debey and that of nitrobenzene is

4.22 Debey. So, a benmnitrile + nitrobenzene system is higbly polar in nature.

Therefore a strong dipole-dipole interaction is present in this system. Due to this

interaction the molecules are tightly packed and this system is an approximate

example of hard sphere binary liquid mixtures [12]. In the case of binary

mixtures of hard spheres in which the molecular diameters differ by a small

amount (molecular radius of benzonitrile is 2.129 A and that of nitrobenzene is

2.131 A), Harumi Endo [12] pointed that B/A is closely connected with the degree

of packing of hard spheres or hardness of the bulk of the liquid system. In the

present system, as the mole fraction of nitrobenzene increases, the degree of

packing increases and hence BIA increases. But the compressibility, which is

inversely depending on density and ultrasonic velocity decreases since, both

density and ultrasonic velocity increase with mole fraction of nitrobenzene.

The variation of the excess non-linearity parameter ( B I A ) ~ and the excess

compressibility I&E vs mole fraction of second component are shown in figures

6.1 and 6.2. It is seen that the variations of ( B I A ) ~ follow the same trend as that of

K:. The excess compressibility is reported to be a quantity which is proportional

to the strength of interaction between unlike molecules [16].

Mole fraction of second component

Figure 6.1 Excess compressibility vs mole fraction of second component in the binary mixture

Mole fraction of second component

Figure 6.2 Excess BIA vs mole fraction of second components in the binary mixtures

According to Fort and Moore [17], a negative excess compressibility is an

indication of strong molecular interaction in the liquid mixtures while a positive

value indicates a weak interaction attributable to dispersion forces. Also, the

magnitude of the excess function depends on the relative strength of interaction [17].

The types of interactions between components of different mixtures are charge transfer,

hydrogen bonding dipole induceddipole and dipoledipole interactions. The origin of

molecular interactions existing in different binary liquid mixtures in the present study is

explained as follows.

In benzene + nitrobenzene system, due to the electron withdrawing nature

of NO2 group in nitrobenzene, a slight positive charge is developed in the benzene

ring and due to the resonance effect, this positive charge is delocalised which can

interact with the x electron cloud of the other benzene ring as shown below.

Also, the positive charge in nitrogen can interact with the n electron cloud

of other benzene rings resulting in a dipole-induced dipole interaction which may

be considered to be strong. This conclusion supports the results in figures 6.1 and 6.2.

In benzene + aniline system, the unshaded electron pair of nitrogen in aniline can

interact with the delocalised n orbitals of the benzene ring due to resonance. As a

result a slight positive charge is developed in the nitrogen of aniline which can

interact with the x electron of benzene as shown below.

This interaction is a sort of dipole-induced-dipole interaction which is

expected to be strong and which again supports the results shown in figures 6.1

ant1 6.2.

In chlorobenzene + aniline system, (BIA)~ and K S ~ have positive values

which indicates relatively weaker molecular interaction [I71 existing in the liquid

mixture.

Also, due to resonance effect, a slight positive charge is developed in the

nitrogen atom of aniline and the C1 atom of chlorobenzene. This causes a

repulsive interaction, which is very weak (figures 6.1 and 6.2).

In chlorobenzene + bromobenzene system also, (BIA)~ and K S ~ have

positive values. In this system, due to resonance effect, a small positive charge is

developed in the C1 atom of chlorobenzene and the Br atom of bromobenzene.

Due to these small positive charges, a weak repulsive interaction as represented

below may occur in the liquid mixture.

In benzonitrile + nitrobenzene system, the phenyl group of benzonitrile

can exhibit two phenomena-negative inductive effect and resonance [la, 191 Due

to the inductive effect, the nitrile carbon becomes more electron deficient which

facilitates molecular interaction between nitrile carbon of benzonitrile and the two

oxygens of nitrobenzene and between nitrile nitrogen of benzonitrile and nitrogen

of nitrobenzene shown below.

This is a sort of dipole-dipole interaction, which is expected to be strong.

On the other hand there is a resonance effect due to the delocalisation of electron

cloud in the phenyl group of benzonitrile [18]. Hence the electron density of

nitrile carbon can increase by delocalising the partial positive charge on the nitrile

carbon which should retard the molecular interaction between benzonitrile and

nitrobenzene. Thus these two phenomena have opposing effects. But fkom the

strong molecular interaction a seen in figures 6.1 and 6.2, it may be inferred that

negative inductive effect dominates over the resonance effect.

In toluene + aniline system, due to resonance effect, a positive charge is

developed in the nitrogen of aniline which can interact with the R electron cloud

of benzene ring in toluene as shown below. This is a kind of strong dipole-dipole

interaction which is expected to be strong.

In toluene + o-xylene system, due to positive inductive effect of the two

methyl substituents, there is an increase in the negative charge density in the

benzene ring of o-xylene compared to the charge density in the benzene ring of

toluene. Hence there is a possibility of repulsive interaction between the n electron

clouds of o-xylene and toluene as shown below. This repulsive interaction is a

sort of weak interaction between unlike molecules.

From the above discussion, it may be inferred that a negative value of

(BIA)~ indicates strong interaction and a positive value of (BIA)~ indicates a

relatively weak interaction between unlike molecules. This is in accordance with

the reported results [17] based on excess compressibility.

The molecular properties of the liquid mixtures calculated using BIA

values, are shown in table 6.2.

Table 6.2 Mole W o n of second component(x), internal pressure (xi), cohesive energy (AA) Van der Waal's constants (a & b) distance of closest approach (d) diffusion coefficient 0) and rotational correlation time (7') of binary mixtures

Benzene + Nitrobenzene at 293.15K -60.132 0.954 0.0687 3.791 -75.241 1.232 0.0748 3.900 -86.071 1.456 0.0791 3.974 -97.212 1.687 0.0826 4.031 -1 12.499 2.038 0.0876 4.1 11 -127.241 2.385 0.0916 4.173

Benzene + Nitrobenzene at 303.15K -56.584 0.905 0.0675 3.768 -69.697 1.147 0.0735 3.877 -8 1.936 1.395 0.0786 3.964 -90.640 1.581 0.0819 4.020

-106.274 1.935 0.0873 4.116 -121.032 2.275 0.0914 4.169

Benzene + Nitrobenzene at 3 13.15K -52.589 0.8490 0.06566 3.735 -65.886 1.0917 0.07248 3.859 -77.268 1.3220 0.07769 3.950 -88.761 1.5560 0.08171 4.017 -101.360 1.8520 0.08690 4.099 -112.677 2.1310 0.09090 4.163

Benzene + Aniline at 298.1513 -58.947 0.939 0.0680 3.785 -66.116 1.056 0.0708 3.829 -73.128 1.173 0.0728 3.866 -83.282 1.340 0.0751 3.906 -09.648 1.464 0.0766 3.931 -107.494 1.742 0.0790 3.972 -107.925 1.756 0.0793 3.978 -119.467 1.957 0.0809 4.004

Chlorobenzene + Aniline at 298.15K -79.699 1.488 0.0849 4.068 7.086E-09 -88.827 1.601 0.0841 4.055 4.158E-09 -90.550 1.606 0.0831 4.040 3.363E-09 -94.862 1.654 0.0826 4.031 2.747E-09 -100.294 1.715 0.0819 4.020 2.23OE-09 -1 11.457 1.872 0.0820 4.021 1.872E-09 -1 19.098 1.990 0.0823 4.027 1.491E-09

Chlorobenzene + Bromobenzene at 303.15K -79.554 1.490 0.0849 4.0685 7.67964E-09 -81.551 1.541 0.0861 4.087 7.343E-09 -84.766 1.615 0.0873 4.107 6.649E-09 -87.400 1.677 0.0884 4.124 6.205E-09 -89.050 1.719 0.0892 4.136 5.805E-09 -9 1.746 1.782 0.0901 4.150 5.434E-09

Benzonitrile + Nitrobenzene at 298.15K -9 1.44 1.72 0.088 4.11 4.28E-09 -93.95 1.77 0.088 4.12 4E-09 -94.75 1.78 0.088 4.12 3.91E-09 -95.21 1.79 0.088 4.12 3.87E-09 -95.45 1.80 0.088 4.12 3.83E-09 -96.20 1.81 0.088 4.12 3.75E-09 -96.94 1.82 0.088 4.12 3.67E-09 -96.40 1.81 0.088 4.12 3.59E-09 -98.57 1.85 0.089 4.13 , 3.52E-09 -99.41 1.87 0.089 4.13 3.44E-09 -100.21 1.88 0.089 4.13 3.37E-09 -100.63 1.89 0.089 4.13 3.34E-09 -100.35 1.89 0.089 4.13 3.3E-09 -102.39 1.92 0.089 4.14 3.17E-09 -103.75 I .95 0.089 4.14 3.04E-09 -106.22 1.99 0.090 4.14 2.81E-09

Benzonitrile 4- Nitrobenzene at 303.15K -89.14 1.68 0.087 4.1 1 4.87E-09 -92.40 1.74 0.088 4.12 4.56E-09 -93.46 1.76 0.088 4.12 4.47E-09 -94.05 1.77 0.088 4.12 4.43E-09 -94.40 1.78 0.088 4.12 4.38E-09 -95.33 1.80 0.088 4.12 4.29E-09 -96.42 1.82 0.088 4.12 4.21E-09 -97.55 1.84 0.089 4.13 4.12E-09 -98.54 1.86 0.089 4.13 4.04E-09 -99.71 1.88 0.089 4.13 3.96E-09 - 100.97 1.90 0.089 4.13 3.89E-09 -101.53 1.91 0.089 4.14 3.85E-09 -101.98 1.92 0.089 4.14 3.81E-09 -104.11 1.96 0.089 4.14 3.67E-09 -106.50 2.00 0.090 4.14 3.52E-09 - 1 10.89 2.08 0.090 4.15 3.27E-09

Toluene + Aniline at 303.15K 109,14:':! L -6283 1.26 0.084 4.06 124.08 -70.96 1.36 0.084 4.06 140.51 -78.62 1.45 0.084 4.05 160.29 -87.80 1.58 0.083 4.04 183.41 -98.40 1.71 0.083 4.04 226.13 -118.92 2.01 0.083 4.04

. . . Toluenc + o-Xyline at 303.15K 108.96 ' ' - 6 G 3 1.26 0.084 4.06 110.38 -65.99 1.34 0.088 4.1 1 112.62 "'L68.77 1.44 0.091 4.16 114.45 -71.33 1.54 0.094 4.21 116.59 '-74.12 1.65 0.097 4.26 118.70 -76.92 1.76 0.101 4.31

In all the seven systems, the internal pressure (n,) increases with increase in mole

fraction of one of the components. Internal pressure is the resultant of the forces

of attraction and of repulsion between molecules in a liquid medium, and is a

measure of.&&tbriti&~~f.;forces of dispersion, repulsion, ionic and dipolar

interactihns that contribute to the overall cohesion of the liquid. An increase in

the inr&al.pid&e- in all the seven liquid mixtures with increase in mole

fractionsbf one component shows that the resultant molecular interactions change

in such h way ak to increase the cohesion of the liquid mixtures. The magnitude

of the change in-internal pressure with increase in the mole fraction of

nitrobenzene' in benzene + nitrobenzene, aniline in benzene + aniline,

nitrobenzene in benzonitrile + nitrobenzene and aniline in toluene + aniline

systems is quite large compared to the corresponding changes in the other two

systems. This also points to the presence of strong interactions in benzene +

nitrobenzene, benzene + aniline, benzonitrile + nitrobenzene and toluene + aniline

systems.

Coheslve energy(AA) is the measure of the total molecular cohesion and it

represents the total strength or stiffness of the solvent structure [20:. In all the

seven binary liquid mixtures, the magnitude of the cohesive energy increases with

increase in the mole fractions of one component. The magnitude of the change in

cohesive energy, as the mole fractions of one component is increased, is much

larger in benzene + nitrobenzene, benzene + aniline, benzonitrile + nitrobenzene

and toluene + aniline systems compared to that for the other two systems The

study of variation cohesive energy with temperature in the case of benzene +

nitrobenzene systems show that as temperature increases the cohesive energy

decreases.

The effective Van der Waal's constants 'a' and 'b' represent respectively

a measure of the attractive forces between molecules md,the.effective volume of

a molecule. In the present study, the constants 'a' and 'b' increased with increase

in the mole fractlon of one component. The increase in the value of constant 'a'

indicates that the attractive forces in the binary liquid mixtures increase with the

increase in mole fractlon of one component. The variation in the values of the

distance of closest approach of molecules also have the same nature of variation

as those of a and b. It was found that as temperature increased the distance of

closest approach decreased.

It was found that diffusion coefficient (D) decreased with increase in the

mole fraction of one component in all the seven binary liquid systems (table 6.2)

but rotational correlation time (t') increased. The correlation time is the average

time between molecular collisions and is the length of time for which the

132

molecule can be considered to be in a particular state of motion [21]. In the

present study, the increase in correlation time with increase in the mole fraction of

one component lead to the conclusion that molecular motions in the liquid

mixtures were less rapid which indicated the presence of attractive forces between

unlike molecules.

6.4 Conclusion

Acoustic non-linearity parameter BIA in seven binary liquid mixtures was

cahxlated using four different methods. The variation of B/A with mole fraction

of one component is discussed. It is concluded that (B/A)~ is a useful parameter

to study molecular interpctions in binary liquid mixtures. Using BIA values of

binary mixtures, the characteristic molecular parameters were calculated and the

':.sr - variations of these parameters with increase in the mole fraction of one

component were studied.

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