Barua, A K

Pal, Arun K

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VISCO SITY OF POLAR-NONPOLAR GAS MIXTURESARUN K. PAL AND A. K. BARUAI ndian  Association fob thb OoltiItation of Science, Calcutta-32. I ndia{IteceAved May 31, 1967)ABSTRACT. Viscosity of ammonia-nitEogon and sulphur dioxide-hydrogen gas mixtures has been measured over a temperature range firom 30*’ to 200"C and at pressures below 10 cm. Hg. by using a precision osciUating disc visootoeter. The results have been utilised to obtain informations on unlike interactions and also to generate inter-diffusion coeffloients of these RVBtemB.I N T R O D U C T I O NIt has been shown by a number of workers (Weissman el nl. I»62; Weisstnan, 19t)4; Srivastava, 1961 and Hirsclifelder e/ a/. 19603 that on the basis of the Chapman-Enskog theory it is possible to determine unliki' interactions from viscosity of gas mixtures. The combination rules generally used to calculate unlike interactions (Hirschfelder e,t fiJ. 1954) being uncertain, only information obtained from experimental data are reliable. Viscosity, to th(‘ first approxima­tion, is not affected significantly by inelastic collisions (Monchick et al, 1963). Thus, this property can be used with confidence for obtaining information on the spherical part of the iutennoleeular potential of polyatomic gases as well.In this paper we have reported the results of our measurements of the viscosity of the polar-nonpolar gas mixtures, ammonia-nitrogen and sulphur dioxide- hydrogen over a temperature range from 30'’—200°C and at pressures below 10 cm. Hg. Attempts have been made to derive information on unlike interactions from these data.E X P E R I M E N T A LThe precision all-metal oscillating-disc viscometer together with its acces­sories used in our measurements has been described in detail in earlier papers (Kestin et al, 1959; Kestin d  al, 1963: Pal et al, 1967a and Pal et al. 1967b). The working formulae and method of preparation of gas mixtures have also been described (Pal et al, 1967a, 1967b).The gases ammonia and sulphur dioxide were prepared by standard labora­tory procedures (Pal et al, 1967a). Hydrogen and Nitrogen used for calibration were supplied by the Indian Oxygen Co.. Ltd. (purity 99.95%). The overall accuracy of our viscosity data for the mixtures should be within 1 %. The visco­sity data obtained by us are given in tables I and I I . It may be mentioned here that for pure ammonia the viscosity values obtained by us are on the average 2%65713714 Artm K. Pal and A. K. Barualower than those reported earlier (Pal et al, 1967a). Mass spectrometric analysis showed that the previously used ammonia gas contained small percentage of air as impurity which can easily explain the discrepancy. However, the general conclusions drawn (Pal et ai, 1967a) regarding ammonia n^main unaltered. With the present data for ammonia the agreement with the earlier data (Carmichaels et al, 1963 and Iwasaki et al, 1964) become excellent (within 1%) over the whole temperature range.The only previous data for the systems ammonia-nitrogen and sulphur dio­xide-hydrogen are those of Trautz et al, (1931). As the experimental temperatures are different it is not possible to compare our experimental data with the earlier ones. However, in the range wheri  ^ comparison is possible by interpolation the agreement of our data with those of Trautz et al, (1931) is within 2% which should be considered as satisfactory in vicM' of the uncertainties in the earlier experi­mental methodsCOMPARISON WITH THEORYThe viscosity of a binary gas mixture can he expressed as (Hirschfelder et al, 1054),\nmix] 1 ~h ZfiX ~ ,+  T \ ... (1)whereX , -  *1* +  2*1*. ^ * * .Vi. VzM , ] 1 { M ,+ M ,)^  \1 1 IM , \m J - \  4M 1M 2 ^1 1 1 ] 4-V i V z ' Vz( l iH h l ] -n z ’where iCj are the mole fractions of the components 1 and 2, M i, M 2 being thecorresponding masses. 7/12 is the viscosity of a hypothetical gas ofand A ^ i2 ratio of collision integrals which is a very slowly varying function of temperature.I t  is possible to represent polar-nonpolar interaction as interaction between two nonpolar molecules. Consequently, wc have used Lennard-Jones (12:6)Viscosity of Oas Mixtures 715potential for our oaloulations. The combination rulea f„r polar-nonpolar inter- aotionB can be written as (Hirschfelder et al, 1964),.. (2a) .. (2b)where the subscript n  and p  stand for iiompolar and polar component respectively, f is given by... (3)where a„ is the polarizability of the nonpolar molecule in cubic angstroms. The force parameters for the nonpolar gases were taken as those determined from viscosity data (Hirschfelder ef nl. 1954) and for the polar components the values of <Tp and €p as obtained on the 12-6-3 model (Monchick et. al, 1961) were used. The values of ijnUx a t different temperatures as obtained from eqn. (1) are shown in column 4 of Tables T and IT. It may be seen that the agreement between the ex­perimental and the calculated values of is excellent (within 1%).Recently. Chakraborty and Gray (1965) have measured the viscosity of a muuber of polar-nonpolar gas mixtures over the temperature range from 25°C to 80®C. They found tha t for those systems generally the agreement between the experimental and the calculated values of to be not quite satisfactory. It is difficult to say whether this discrepancy is due to some particular feature of the systems sttidied or due to experimental uncertainties.U N L I K E  I N T E R A C T I O N  F R O M  M I X T U R E  V I S C O S I T YDATAIt has been shown by a number of workers (Weissman 9t al, 1902; Weissman 1904, and Srivastava, 1961) that it is possible to determine imlike interactions from viscosity of gas mixtun^s. Eqn. (1) can be solved for in the following manner (Srivastava, 1961)Via y /6 * — 4flC2a .. (4)whereTABLE 1Viscosity and inter-diffusion coefficient of NHg-Na gas m ixtures a tdifferent tem peratures716 Arun K. Pal and A. K. Baruamole frac- TJX 10'' X 10*^  (9^ 12) (p^ia)T ‘»C tion of N H 3 (gem ^aeo"‘ )^ (g.cm~^seo*^) (om*8eo“ )^ (cm*90c~'1.0000 102.81 —0.7904 119.44 120.460.6709 136.17t4 0.6027 141.60 142.21 0.210 0.2170.4020 148.61 —0.2007 167.85 165.210.0000 176.06 —1.0000 113.72 —0.7700 136.40 134.890.687C 161.71 —64 0.6021 168.06 167.61 0.267 0.2600.4003 167.03 —0.2007 179.37 179.420.0000 191.30 —1.0000 130.76 - —0.7700 154.96 164.620.6876 170.10100 0.6021 177.34 177.26 0.222 0.2220.4003 186.08 -0.2007 198.92 198.810.0000 210.10160too1.0000 149.28 —0.7603 176.11 176.020.6920 190,030.4928 179.01 198.210.3986 203.76 —0.2262 216.72 217.800.0000 230.6 —1.0000 167.98 —0.7603 196.72 197.700.6920 207.86 —0.4928 216.20 217.910.3986 2 2 2 .11 —0.2252 236.25 238.520.0000 252.250.41S 0.41S0.607 0.610Viscosity of Oas MixturesTABLE IIViscosity and inter-diffusion data of gas mixturo at differenttemperatures717T^C30100160mole frew;- t) x 10'^  tion of SOa (gm.cm*^300B6C‘ )^ sec*"^ )1.0000 133.01 _0.8219 134.45 136.400.5957 135.01 —0.4919 136.75 140.710.4069 137.01 — '0.2005 136.41 139.330.0000 90.00timu X lOT („D,a)) (pUjj,)(gin.cm '’ (cm*.«oc“‘) (cm“.sec“>)1.0000 144.020.7866 145.46 148.420,6975 147.210.4863 148.46 1.50 050.4000 148.010.2006 147.12 149.760.0000 95.60 —1.0000 168.90 —0.7866 168.06 172.620.5975 167.950.4863 166.91 174.830.4000 165.95 —0.2005 162.89 167.310.0000 104.70 -  -1.0000 192.20 —0.8110 192.03 195.240.6024 192.50 —0.6023 192.52 198.480.4018 192.53 -0.2000 177.88 186.000.0000 115.601.0000 211.50 —0.8110 214.11 214.230.6024 214.99 --0.5023 216.40 216.210.4018 213.370.2000 194.72 200.300,0000 122.60 —0.600 0.6100.706 0.7010.884 0.8761, 105 1.0861.8i0 1.30671S Arun K. Pal and A. K. Barua- “'•■ (t J ) ] + ’ ■ ■ •{ ^ ’ + 1 ^ ) -1C - -  2*1*4 VmhI t is possible to (leteriniao the tinlike interaction parameters, and e,j, from the temperature dependence of i/ig. can also be used to generate pDy, from the relation (Hirschfelder et al, 1954),p D 12 ’ ■ 4 (6)p  being the pressure in atmosphere. By substituting the values of *4 ♦ as obtained by using force parameters calculated from the combination rules pDi^ values can be obtainf*d. It may be pointed out that this calculation of is equivalent to obtaining unlike interaction parameters. It is possible to measure the viscosity of gas mixtures much more preciselj^ than the diffusion coeflScients. Consequently, this method of obtaining from the mixture viscosity data should be inoit^  reliable than the actual measurements of this property by the existing techniques.In column 6 of tables 1 and Tl are also shown the calculated values of on the Chapman-Enskog theory by using the combination rules giviMi in eqns. (2a) and (2b). I t  may be seen that the agreement between the values of /),y thus obtained with those calculated from the mixture viscosity data is excellent. This probably shows the usefulness oi* the combination rules inspite of their semi-empirical nature.A C K N O W L E D G M E N TThe authors are grateful to Prof. B. N. Srivastava for his kind interest.R E P" E R E N C E SCarmiohaol, L. T., Reamer, H. H., and Sage, B. H., 1963, J .  Chem, Eng. Data, 8, 400.Chakraborty, P. K., and Gray, P„ 1966, Trans. Faraday Soc., 61, 2422.Hirschfelder, J . O., Taylor, M. H. and Kihara, T., 1960, Report WIS^OOR-29.Hirschfelder, J, O., Curtiss, C. F., and Bird, R. B., 1964, Molecnlar Theory of Gases and Liquids, John Wiley A Sons, Inc., New York.Iwasaki, H.. Kestin, J . and Nagashima, A., 1964, J. Chem. Fhyx,, 40, 2988.Kestin. J . iwid Leidenforst, W., 1959, Physica, 25, 1033.Kestin, J . and Mason, E. A., 1961, J. Ohstn. Phya., 85, 1676.Monchick, L., and Mason, E. A., 1961, J. Ghem. Phys., 35, 1676.Monchick, L., Yun, K. S. and Mason, E. A., 1963, Chem. Phys., 89, 654.Pal, A. K. and Barua, A. K., 1967a, Trans. Faraia^ Soc., 63, 841.- ------------------------------------, 1967b, J. Chem. Phys., 47, 216.Srivastava, I. B., 1961, Indian J . Phys., 85, 86.Trautz, M., and Heberlingh, R., 1931, Ann. Physik, 10, 156.Weissman, S., 1964, J. Ghem. Phys., 40, 3397.Weienman, 8. and Mason, E. A., 1962, J. Ghem. Phys., 87, 1289.

Viscosity of Polar-Nonpolar Gas Mixtures

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Viscosity of Polar-Nonpolar Gas Mixtures

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