ultrasonic absorption in binary liauid mixtures -...

Ultrasonic Absorption in Binary Liauid Mixtures

4.1 Introduction

Study of propagation of ultrasonic waves and their absorption and

dispersion forms one of the most important methods of investigation of properties

of matter in all the three states. It is well known that ultrasonic wave velocity in a

medium provides valuable information about the physical properties of the

medium. Similarly, study of absorption of ultrasonic waves in a medium provides

important information about various inter- and intra-molecular processes such as

relaxation of the medium or the existence of isomeric states or the exchange of

energy between various molecular degrees of freedom, etc.

In recent years, the measurement of ultrasonic absorption has been

extensively applied in understanding various loss mechanisms and distribution of

relaxation processes present in both pure and binary liquid systems [I-71.

Narayana and Swamy [81 studied ultrasonic relaxation in undecanoic acid and

showed that a single relaxation mechanism is present and that it is due to rotational

isomerism existing between cis and trans configurations of the acid molecules.

Ultrasonic absorption studies by Mishra and Samal [9] in binary mixtures of carbon

disulphlde with methyl iodide showed that in addition to vibrational relaxation, a new

dissipative process works for producing ultrasonic energy absorption in these

mixtures. Miecznik [lo] discussed the ultrasonic absorption behaviour of aqueous

solutions of n-ethyl acetamide over a frequency range of 10-100MHz and

concluded that the relaxation mechanism is associated with the formation and

disintegration of mixed molecular complexes. This chapter (Chapter 4) of the

thesis deals with the experimental study of ultrasonic absorption in a few binary

mixtures at different temperatures.

The literature survey shows that ultrasonic absorption studies have been

made in a large number of binary liquid mixtures of associated [ll-191 and

unassociated [20-2.51 liquids. But similar reports on binary mixtures of associated

and unassociated liquids are very limited [22,26]. A study of binary mixtures of

this type is of importance from the viewpoint of energy exchange during

molecular collisions between same and different types of molecules. This chapter

deals with the study of ultrasonic absorption in binary mixtures of nitrobenzene,

chlorobenzene, bromobenzene, toluene and benzene with methyl ethyl ketone as a

common component. Of these liquids, methyl ethyl ketone is an associated liquid

and all others are unassociated liquids.

The binary liquid systems chosen for the present study are

1. Methyl Ethyl Ketone (MEK) + Nitrobenzene

2. Methyl Ethyl Ketone (MEK) + Chlorobenzene

3. Methyl Ethyl Ketone (MEK) + Bromobenzene

4. Methyl Ethyl Ketone (MEK) + Toluene

5. Methyl Ethyl Ketone (MEK) + Benzene

4.2 Experimental

The liquids benzene, toluene, chlorobenzene and bromobenzene used for

the present investigations were of SRL AR grade, where as nitrobenzene and

methyl ethyl ketone were of Merck Synthesis grade. The liquids were used as

supplied. The liquid mixtures of different compositions were prepared by mixing

calculated volumes of each component. The liquid cell (described in Section 2.3

of Chapter 2) was filled with the sample. A quartz crystal of resonant frequency

2MHz was attached to the liquid cell. The quartz crystal was coupled to Matec

ultrasonic measuring system(described in Section 2.2.2 of Chapter 2) and the echo

pattern was obtained on the screen of the cathode ray oscilloscope. The echoes in

the echo pattern had an exponentially decreasing amplitude. For determining the

absorption, the heights of two successive echoes were measured for two different

positions of the reflector. From these echo amplitudes, ultrasonic absorption was

calculated using equation 2.9 of Chapter 2. The experiment was performed at

four different temperatures of 30, 40, 50 and 60°c, each temperature being kept

constant with 0 .5 '~ . In order to avoid temperature gradient and the resulting

turbulence in the liquid, the liquid was continuously stirred and measurements were

taken during the cooling process after all the disturbances in the liquid died out.

4.3 Theory

The binary mixtures chosen for the present study were mixtures of an

associated and an unassociated liquid. Several theories are available in the

literature for the estimation of ultrasonic absorption in binary mixtures of

associated [17,18,27,28] liquids as well as unassociated liquids [23,29,30]. As far

as the author knows, no such theory is available for the cases of binary mixtures

consisting of associated and unassociated liquids. Hunter et al. [25] has showed

that the plot of a/ f (a-absorption coefficient and f the frequency of ultrasonic

wave) against concentration of one of the components of a binary mixture is a

straight line running between the absorption of two liquids in their pure state, if

there were no molecular interaction between the two liquids in the binary mixture.

In the present study a1 f was found to vary nonlinearly with concentration of

one component (discussed detail in Section 4.4). The non-linear variation of a1 f

with concentration of one component supporn the presence of strong molecular

interactions existing in the present liquid mixture. Moreover, the variation of

a / f with concentration of one component in binary mixtures of associated liquids

is reported to show an absorption peak [12]. This absorption peak is amibuted to

the interaction between molecules of the two liquids, which results in the formation of

a compound structure or complexes in the liquid mixture [19]. Similar absorption

peaks are also observed in binary mixture of an associated and an unassociated liquid.

Sette [22] observed absorption peaks at intermediate concentrations in binary liquid

mixtures of ethyl alcohol + nitrobenzene and methyl alcohol + nitrobenzene.

The absence of ultrasonic absorption peaks in the present study (figures

4.1- 4.5) indicates that complex formations are absent in the present binary

systems. Also, the experimental variation of ale .with concentration of one

component in the present study is similar to that of ultrasonic absorption of two

unassociated liquids with strong inter molecular interaction reported in the

literature [25]. Hence, theories of ultrasonic absorption in binary mixture of

unassociated liquids were applied for the interpretation of results in the present

study of binary mixtures consisting of associated and unassociated liquids.

Pinkerton [29] was the first to give an equation connecting ultrasonic

absorption in liquid mixtures with concentration of one component. Bauer [30] h m an

analysis of vibrational specific heat and relaxation frequency gave a satisfactory

explanation of the variation of absorption in a binary mixture with concentration of

one component. Sette [23] modified some of the assumptions made by Bauer and

gave a more. accurate explanation of absorption in binary liquid mixtures. A brief

description of the theories of ultrasonic absorption is given below.

4.3.1 Pinkerton theory

In a binary mixture of liquids A and B, the equilibrium between energies

associated with internal and external degrees of fieedom is set up by collisions. It is

posslble to define four relaxation times. r,, r,, ,rA, andr,,. ru and r,, are

relaxation times for collision between similar molecules of type A and B

respectively, r,, is that for collision of exited B with de-exited A and z,,is for

collision of excited B with de excited A. If the absorption in A is much greater than

in B, Pinkerton assumed that r,, > r,, and r,, = r,, = r, . Let x denotes the

86

fraction of molecules of type B in the binary mixture and neglect differences in

molecular diameters. Then, in unit time, a fraction of (I-x) of A will collide with

molecules of the same kind and have relaxation time rM and a fraction x of B will

have relaxation timer,, . Then the number of molecules relaxing in a short time

At will be proportional to

where rAef is the effective relaxation time for molecules of type A.

Assume the condition that the maximum value of absorption per unit

length ,urn = ail where h the wavelength of ultrasonic wave in the medium is same

in both the pure liquids and the absorption is additive for the two molecular spices

in the mixture. Pinkerton [29] showed that

Substituting for rAea from equation (4.1) and using the condition a(x) = a, when

x = 0 and a(x) = a, whenx = 1, the final equation becomes

7 'A - AA - where ----lly a B TBE

4.3.2 Bauer theory

Some of the basic assumptions of Pinkerton 1291 are also considered in

Bauer theory. Let the liquid A be more strongly absorbing than the other liquid B.

Then A has much greater relaxation time than B so that an A molecule once

exited has a much smaller chance of de excitation than an excited B molecule.

For simplicity it will be assumed that only binary collisions need be considered

and collision between excited molecules may be neglected. Let A and A*

represent an unexcited and an excited A molecule, and similarly B and B*

represent an unexcited and an excited B molecule. Then (A*A) collision is much

less efficient than (B*B) collision because relaxation frequency of liquid A is

much smaller than that of liquid B. In a mixture of molecules of both species A and

B, there will be, in addition to (A*A) and (B*B) collisions, (A*B) and @*A)

collisions. (A*B) and (B*A) collisions have high de-excitation efficiency because it is

in general impossible for a quantum of vibrational energy to be transferred h m one

type of molecules to the other without loss of energy. Pinkerton [29] assumed that

(A*B) and @*A) collisions are as efficient in producing excitation and de-excitation as

@*B) collisions. Thus as the concentration of B molecules increases the net

efficiency of all collisions tends rapidly to the value corresponding to the liquid B

so that the absorption falls sharply.

Consider the transition probabilities of (AA), (AB), (BA) and (BB) Bauer [29]

derived as expression for calculating absorption as

a C 1 where, F = 1 -4B- and Z = f: 1 fi . f: and f: are the vibrational

CA

relaxation frequencies, and CA and CB the vibrational specific heats of pure liquids

A and B. Also,

The vibrational specific heats Ci (CA or CB) can be calculated by using

Plank Einstein relation [31].

where vi is the vibrational frequency of the molecule for a given mode, R the

universal gas constant, k the Boltrman's constant, h the Plank's constant and T

the absolute temperature. The values of vi are taken from Herzberg [31]. In the

present case, the value of vi of methyl ethyl ketone is not available in Herzberg.

So, the method adopted by Rao and Suryanarayana [20] is used to determine vi.

First the ratio of principal specific heats y of the liquid for each temperature was

determined from the thermodynamic relation

y-i = C ~ ~ ~ T M / C ~ J .................... (4.6)

where C is the ultrasonic velocity ,B the cubical expansion coefficient, M the

molecular weight, Cp the specific heat at constant pressure, J the conversion

factor from calories to ergs which was taken as 4.18 x 10'. The parameters Cp

and p were taken from elsewhere [32]. Knowing y and Cp, the value of Cv was

calculated at each temperature. The vibrational specific heat C, (CA or Ce) was

then obtained by subtracting the contribution of the translational and rotational

degrees of freedom, namely 3R (here K=2).

The vibrational relaxation frequency f, for a liquid may be calculated

from the formula given by Lauhereau et ol. [33]

where C and a are the low frequency values of the ultrasonic velocity and

absorption of the liquid, Cp and Cv are its specific heats at constant pressure and

constant volume, and C, is the vibrational specific heat.

4.3.3. Bauer-Sette theory

Sette [23] modified some basic assumption of Bauer. According Sette

theory, unlike collisions (A*B) or (B*A) were more effective than like collisions

(A") or (B*B) and the four types of collisions were distinctly different.

Considering this, Sette modified Bauer relation as [23].

All the symbols except t' and u have the same meaning as in equation 4.4.

t . := 7,, IT, , andu = r,, ! r , , T,, and r , being the relaxation times for energy

transition due to A*B and B'A collisions According to Sette theory, the

90

parameters t' and u should be calculated using experimental values of the

absorption of the mixture at two different compositions that are rich in the

individual components.

4.4 Results and Discussion

The experimental results of a 1 f (ultrasonic absorption) in five binary

mixtures at four different temperatures are shown in figures 4.1-4.5 and the values

of a 1 f are given in table 4.1.

Figure 4.1

Mole fraction of MEK

ale vs mole fraction of MEK in the binary system Nitrobenzene at different temperatures

MEK +

Figure

~ ~~ - - -

I6O- ..~..~. ?J

VI 120-

E . .

u - 100- 0 H

X 80 - '"r

5

60 -

40 -

0.0 0.2 0.4 0.6 0.8 1 .O


a/P vs mole fraction of MEK in the binary system Bromobenzene at different temperatures

MEK

Figure


a/? vs mole fraction of MEK in the binary system Chlorobenzene at different temperatures

MEK +

0.0 0.2 0.4 0.6 0.8 1 .O


Figure 4.4 ale vs mole fraction of MEK in the binary system MEK + Benzene at different temperatures

4 , . , . , . , . , . , I 0.0 0.2 0.4 0.6 0.8 1 .O


Figure 4.5 ale vs mole fraction of MEK in the binary system MEK + Toluene at different temperatures

Table 4.1 Experimental values of Ultrasonic absorption(a/f2) in the binary liquid mixtures at different temperatures


X

a/? x 10" cm-' s2 :30°c 40°C

MEK + Nitrobenzene 74.58 81.85 70.16 79.44 67.39 72.31 60.97 67.45 54.96 61.73 50.69 55.25 48.19 5 1.39 44.41 49.61 4.3.10 48.70

MEK + Bromobenzene 138.00 144.50 121.69 133.75 116.62 124.19 110.36 117.69 106.93 114.04 88.98 94.23 67.14 75.76 60.46 68.14 43.10 48.70

MEK + Chlorobenzene 149.26 162.98 126.81 138.54 1 18.25 121.74 101.78 109.14 84.46 89.35 76.27 81.45 63.85 70.68 51.86 57.65 43.10 48.70

MEK + Benzene 1001.31 1087.85 402.17 461.73 219.81 242.44 188.17 201.17 163.81 180.41 121.45 139.33 86.17 92.73 52.31 58.64 4310 48.70

MEK + Toluene 86.57 90.57 75.89 82.13 70.54 77.61 67.34 71.51 63.58 68.25 59.36 63.64 55.87 60.72 51.71 54.91 43.10 48.70

In each plot, the variation of alp (a absorption coefficient and f the

frequency) with increase in the concentration of methyl ethyl ketone is non-linear.

This non-linear variation of absorption with concentration of one component

strongly supports the presence of strong inter molecular interaction in all the five binary

liquid systems [25]. The values of ultrasonic absorption at 3 0 ' ~ determined using

Pinkerton, Bauer and Bauer-Sette theories along with experimental values are plotted in

figures 4.6 - 4.10.

-& J J M Pinkerton

A

40 ! I 0.0 0.2 0.4 0.6 0.8 1.0


Figure4.6 dP vs mole fraction of MEK in the binary system MEK + Nitrobenzene at 30 OC

I 1 0 0 0 2 0 4 0 6 0 8 1 0

-


Figure 4.7 a/? vs mole fraction of MEK in the binary system MEK + Bromobenzene at 30 OC

Figure


alfs vs mole fraction of MEK in the binary system Chlorobenzene at 3 0 ' ~

MEK +

:m. 'I- -*-*:I%*- *

0.0 0.2 0.4 0.6 0.8 1.0


Figure 4.9 ct/p vs mole fraction of MEK in the binary system MEK + Benzene at 30 OC


Figure 4.10 d? vs mole fraction of MEK in the binary system MEK + Toluene at 30 OC

From figures 4.6, 4.8 and 4.9 it is observed that Bauer-Sette theory is

satisfactory in the case of MEK + nitrobenzene, MEK + chlorobenzene and MEK +

benzene systems, but there is some disagreement between experimentally

determined absorption and absorption calculated using Bauer-Sette theory in the

binary mixture of MEK + bromobenzene (figure 4.7). In the case of MEK +

toluene, the parameters, t, u and Z appearing in equation 4.8 which were used to

calculate ultrason~c absorption according to Bauer Sette theory were negative.

Hence, ultrasonic absorption was not calculated theoretically using Bauer-Sette

theory in the case of MEK + toluene system.

Rao and Suryanarayana [20] applied Bauer-Sette theory for calculating

ultrasonic absorption in binary mixture of benzene and ethyl acetate. They found

that Bauer-Sette theory should not be applied to a binary system in which the

absorption of one or both of the components is predominantly due to rotational

isomeric relaxation process. The deviation of ultrasonic absorption calculated using

Bauer-Sette theory fiom experimentally determined absorption in the case of binary

systems exhibiting rotational isomerism is due to the fundamental assumption in the

Bauer-Sette theory. The basic assumption behind Bauer-Sette theory is that two

unassociated liquids forming a mixture are vibrationally relaxing and exchange

energy through binary collisions. But Comolly and de Groot [20] showed that the

molecules of a rotationally isomeric relaxing liquid do not get de-excited through a

collision process. It is reported that the contribution of vibrational relaxation to the

total absorption in the case ofrotational isomeric liquids is small [20].

In the present binary liquid systems, methyl ethyl ketone is a rotationally

isomeric liquid [34]. But the validity of Bauer-Sette theory in the case of MEK +

nitrobenzene, MEK + chlorobenzene and MEK + benzene systems pointed out that

even though MEK is a rotationaly isomeric liquid, vibrational relaxations are

predominant in above three binary systems. But in the case of MEK + bromobenzene,

rotational isomerism is more predominant than vibrational relaxation. Hence Bauer-

Sette theory is not satisfactory m the case of MEK + bromobenzene system.

4.5 Conclusion

Ultrasonic absorption in five binary liquid mixtures is determined

experimentally. In these binary liquid mixtures, methyl ethyl ketone(MEK) is a

common component and it is an associated liquid. Moreover, the absorption

process in methyl ethyl ketone is due to rotational isomeric relaxation. The other

components viz. nitrobenzene, chlorobenzene, bmmobenzene, toluene and benzene

are all unassociated liquids. In unassociated liquids, absorption is due to vibrational

relaxation. Bauer-Sette theory is satisfactory for the binary systems of MEK +

nitrobenzene, MEK + chlorobenzene and MEK + benzene. But this theory shows

appreciable deviation tiom experimental results in the case of MEK + bmmobenzene

system. This deviation is attributed to the fundamental assumption in the Bauer-

Sette theory regarding relaxation process.

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