Viscosity of Binary PolarGas Mixtures: CH3Cl–H2S and CH3Cl–SO2P. K. Bhattacharyya Citation: The Journal of Chemical Physics 53, 893 (1970); doi: 10.1063/1.1674154 View online: http://dx.doi.org/10.1063/1.1674154 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/53/3?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Reply to Comment on Viscosity of Binary PolarGas Mixtures J. Chem. Phys. 52, 2797 (1970); 10.1063/1.1673395 Viscosity of Binary PolarGas Mixtures J. Chem. Phys. 52, 2796 (1970); 10.1063/1.1673394 Viscosity of Binary PolarGas Mixtures J. Chem. Phys. 51, 828 (1969); 10.1063/1.1672075 Transport Properties of PolarGas Mixtures. I. Viscosities of Ammonia—Methylamine Mixtures J. Chem. Phys. 47, 2798 (1967); 10.1063/1.1712300 Transport Properties of PolarGas Mixtures J. Chem. Phys. 36, 2746 (1962); 10.1063/1.1732363

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THE JOURNAL OF CHEMICAL PHYSICS VOLUME 53, NUMBER 3 1 AUGUST 1970

Viscosity of Binary Polar-Gas Mixtures: CHaCI-H2S and CHaCl-S0 2

P. K. BHATTACHARYYA

Indian Association for the Cultivation of Science, Calcutta-32, India

(Received 29 January 1970)

Viscosities of the binary polar-gas mixtures, CHsCI-H2S and CHsCI-S02, have been measured in the temperature range from -35 to 35°C with an oscillating-disk viscometer. The data have been utilized to derive information on unlike polar-polar interactions. The results show the remarkable success of effectively spherically symmetric potentials and semiempirical combining rules in representing mixture viscosities of polar systems.

I. INTRODUCTION

In an earlier paperl viscosities of a number of polar gases in the temperature range from -50 to 35°C were reported. The results show the success of effectively spherically symmetric potentials in representing the viscosity of polar gases. For polar-gas mixtures an additional complicating factor is the estimation of the unlike interaction between the molecules. In the ab­sence of suitable experimental data this is generally done by a set of semiempirical combining rules. Vis­cosity, which is insensitive to inelastic collisions,2 is one of the most useful sources of information on inter­molecular forces in polyatomic gases. Accurate experi­mental data for polar-polar gas mixtures, particularly at lower temperatures where dipole-dipole forces are likely to be more important, are very scanty.

In this paper the viscosities of the binary mixtures CHaCI-H2S and CH3CI-S02 are reported in the tem­perature range from -35 to 35°C. The data have been utilized to derive information on unlike polar-polar interactions.

II. EXPERIMENTAL

The oscillating-disk viscometer and experimental pro­cedure have been described in detail elsewhere.l,3 The polar gases were prepared and dried by standard laboratory procedures. Each gas was further purified by fractionally distilling it in vacuo near its boiling point, with generous rejection of the head and tail portions.

composition range where S02 is in low concentration, but deviate by up to 1.5% in the other composition range.

m. COMPARISON WITH THEORY

The interaction between a pair of like polar molecules may be represented by the Stockmayer or 12-6--3 potential given by5

q,(r) = 4EC(o/r)lL (o/r) 6+ 0 (o/r) 3],

0= (J'2/4Eu3)~,

~= 2 coslh cos82- sinlh sin62 cosrp, (1)

where J' is the dipole moment, E and (T are, respectively, the potential well depth and collision diameter for o---tO, 81 and 62 are the angles the dipoles make with the line joining the centers of the molecules, and rp is the azimuthal angle. The interaction between two unlike polar molecules can be represented by Eq. (1) in terms of potential parameters approximated by the following combining rules5 :

(T12=!«(T1+(T2) , E12= (EIE2)112,

012= (0102)112[ «(T1(T2)112/ (T12]3, (2)

where the SUbscripts 1 and 2 stand for the pure com­ponents and 12 for the binary systems. To the first approximation, the Chapman-Enskog expression for the viscosity of a binary gas mixture can be written as6

(3) The binary gas mixtures were made in a gas-mixing with unit, and the compositions were calculated by the law

x~= (X12) + (2X1X2) + (X22) , of partial pressures. The pressure of the gas or gas mix­ture in the viscometer was kept well below its satura­tion pressure at the measured temperature and never exceeded 5 cm Hg.

The viscosity data obtained at different temperatures as a function of composition are shown in Column 3 of Tables I and II. The over-all accuracy of the data was estimated to be ±0.6%. In earlier publicationsl.3 our data for the pure components, H2S, S02, and CH3CI, have been compared with previous results. For the CHaCI-H2S mixtures there are no previous viscosity data. For the other system, CHaCI-S02, at 35°C where direct comparison is possible, our data are in excellent agreement with those of Chakraborti and Gray! in the

893

711 7]12 7]2

+ X22M2] , 7]2 M1

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894 P. K. BHATTACHARYYA

TABLE I. Experimental and calculated viscosities '1 for the binary system CHaCl-H2S at different temperatures.

Mole 1Jmix8

fraction 1Jexvtl (calc) of CHaCl (p.P) (p.P) %dev.

35 0.000 124.0 0.200 121.5 121.3 -0.2 0.389 118.8 118.9 0.1 0.597 115.8 116.5 0.6 0.776 114.0 114.5 0.4 1.000 112.2

5 0.000 113.1 0.200 110.2 110.2 0.0 0.389 107.4 107.8 0.4 0.597 104.6 105.5 0.9 0.776 103.0 103.7 0.7 1.000 101.8

-20 0.000 Hl3.11 0.200 100.5 100.8 0.3 0.389 97.8 98.5 0.7 0.597 95.8 96.3 0.5 0.776 94.0 94.7 0.7 1.000 93.0

-35 0.000 97.1 0.200 94.9 94.6 -0.3 0.389 92.3 92.6 0.3 0.597 90.5 90.7 0.2 0.776 88.6 89.3 0.8 1.000 87.8

a Calculated with the redetermined force parameters of H,S'.

where Xl and X2 are the mole fractions, 1]1 and TJ2 the viscosities, and M1 and M2 the molecular weights of components 1 and 2, respectively, TJ12 is the viscosity of a hypothetical gas of mass 2M1M21 (M1+ M 2), calcu­lated with the unlike-interaction parameters, and A12* is a ratio of collision integrals which is insensitive to the choice of potential parameters. For the calculation of TJmix from Eq. (3), the experimental values of TJ1 and 1/2 were used. The like-interaction force parameters for S02 and CRaCl were taken from Ref. 7, while for R2S those redetermined from the viscosity data of Bhattach­aryya et aU were used. The unlike interaction param­eters 0'12 and E12 were obtained from the combining rules given in Eq. (2) and 812 was approximated by using the more simplified expression (pp. 222-223 of Ref. 6)

(4)

The values of 1/mix thus obtained are shown in Column 4 of Tables I and II.

In the expression for 1/mix [Eq. (3) J, the quantity 1/12 is sensitively dependent on the unlike polar-polar interactions and can be obtained8 from experimental 1/mix values. 1/12 is also related to the diffusion coefficient

D12 by the expressions

PD12 = O.6TJ12[ (M1+ M2) I M1M2JA12* RT, (5)

where p is the pressure. As A12* is a very slowly varying function of reduced temperature T*, D12 can be ob­tained from Eq. (5) by utilizing A12* values calculated with Elk values given by the combining rules. The D12

values obtained from experimental 1/mix values and those calculated directly from the Chapman-Enskog expression6 using combination rules are shown in Col­umns 3 and 4, respectively, of Table III.

IV. DISCUSSION OF RESULTS

From Tables I and II, it is seen that for both systems the agreement between the experimental and calculated values of 1/mix is excellent and within experimental error. In fact, the agreement is much better than that obtained for polar-nonpolar gas mixtures.3 This has also been observed by Chakraborti and Gray.4.9

The PD12 values are more sensitively dependent on the unlike interactions than is the mixture viscosity. Of the two systems studied, only the diffusion coeffi­cient of the CRaCI-S02 system has been measured

TABLE II. Experimental and calculated viscosities '1 for the binary system CHaCl-S02 at different temperatures.

Mole fraction '1exptl '1mix (calc) of CHaC! (p.P) (p.P) %dev.

35 0.000 130.9 0.203 127.0 127.5 0.4 0.395 123.3 124.1 0.6 0.603 119.7 120.2 0.4 0.811 115.9 116.1 0.2 1.000 112.2

5 0.000 120.2 0.203 115.9 116.3 0.3 0.395 112.1 112.7 0.5 0.603 108.5 108.9 0.4 0.811 104.4 105.2 0.8 1.000 101.8

-20 0.000 110.8 0.203 106.0 106.7 0.7 0.395 102.7 103.1 0.4 0.603 98.8 99.4 0.6 0.811 95.3 95.5 0.6 1.000 93.0

-35 0.000 104.6 0.203 100.5 100.6 0.1 0.395 97.0 97.2 0.2 0.603 93.5 93.7 0.2 0.811 90.0 90.5 0.6 1.000 87.8

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VISCOSITY OF BINARY POLAR-GAS MIXTURES 895

previously, by Chakraborti and Gray.lO Their results at 35°C, where comparison is possible by interpolation, are in excellent agreement with our data from viscosity measurements. Furthermore, it is found that our ex­perimental 17mix values at 35°C are in better agree­ment throughout the composition range with those (Fig. 2 of Ref. 10) calculated from the diffusion co­efficient by Chakraborti and Graylo than with those authors' experimental results.' It is seen from Columns 3 and 4 of Table III that for PD12 the agreement be­tween the values generated from mixture viscosities and those obtained directly from Chapman-Enskog theory using combining rules is excellent for both the systems under investigation. This shows that, as ob­served previouslyl for pure polar gases, an effectively spherically symmetric potential function together with the semiempirical combining rules can represent the viscosity of polar gas mixtures satisfactorily. Another interesting feature is the remarkable success of the combining rules for polar-polar interaction compared to those for polar-nonpolar interaction. The reason for the relative success of the combining rules for polar­polar interaction compared to those for polar-nonpolar

TABLE III. Experimental and calculated values of PD,. at differ­ent temperatures for the system CHaCI-H2S and CHaCl-SO •.

Temp. pD,. (exptl) pD12 (calc) System (0C) (atrn·crn2/sec) (atrn·cm2/sec)

CHaCI-H2S 35 0.0944 0.0958 5 0.0772 0.0778

-20 0.0638 0.0643 -35 0.0565 0.0569

CHaCI-S02 35 0.0715 0.0721 (0.0713)-

5 0.0576 0.0585 -20 0.0474 0.0483 -35 0.0424 0.0427

a From diffusion experiments of Chakrahorti and Gray.1O

interaction has been discussed by Rowlinson and Townleyll and Chakraborti and Gray.'

V. CONCLUSIONS

The mixture viscosity data reported in this paper show the success of Chapman-Enskog theory and the comparatively simple combining rules for polar-polar interactions in representing viscosity and diffusion co­efficients. However, both the properties are relatively insensitive to the inelastic collisions which are likely to be important in dipole-dipole interaction.l2 Transport properties like thermal conductivity and thermal diffusion which are sensitive to the inelastic collisions2 may provide interesting information in this respect.

ACKNOWLEDGMENTS

The author is grateful to Dr. A. K. Barua for sug­gesting the problem and to Professor B. N. Srivastava for his kind interE'st in this work. He is indebted to Dr. A. K. Ghosh for experimental advice. The author is thankful to the C.s.I.R. (India) for financial assist­ance in the form of a Senior Research Fellowship.

1 P. K. Bhattacharyya, A. K. Ghosh, and A. K. Barua, J. Phys. B 3,526 (1970).

2 L. Monchick, K. S. Yun, and E. A. Mason, J. Chern. Phys. 39,654 (1963).

3 P. K. Bhattacharyya and A. K. Ghosh, J. Chern. Phys. 52, 2719 (1970).

• P. K. Chakraborti and P. Gray, Trans. Faraday Soc. 62, 1769 (1966).

6 E. A. Mason and L. Monchick, J. Chern. Phys. 36, 2746 (1962).

6 J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids (Wiley, New York, 1964), p. 530.

7 L. Monchick and E. A. Mason, J. Chern. Phys. 35, 1676 (1961).

s I. B. Srivastava, Indian J. Phys. 35, 86 (1961). 9 P. K. Chakaraborti and P. Gray, Trans. Faraday Soc. 61,

2422 (1965). 10 P. K. Chakraborti and P. Gray, Trans. Faraday Soc. 62,

3331 (1966). 11 J. S. Rowlinson and J. R. Townley, Trans. Faraday Soc. 49,

20 (1953). 12 R. J. Cross, Jr., E. A. Gislason, and D. R. Herschbach, J.

Chern. Phys. 45, 3582 (1966).

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