Barua, A K

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UNLIKE MOLECULAR INTERACTIONS FROM VISCOSITY AND INTER-DIFFUSIONA. K. BAEUAI ndian Association for the Cultivation of Science Calcutta-32{Heceived for publication, April 20, 1059),ABSTRACT. Forco constants for mihko molecular interactions for the systems 11^—CH4, Ha—COa.Ha—N^, H.j—He, Nj —O^H* for the Lonnard-Jonoa (12 : 6), model have been doiormmed by combining the data on inter-diffusion cooflfioient and viscosity of gas mix­tures. To test the appropriateness of the force constants thus dotormined, the available ox- ])orimBnial data have been compared with the values of the viscosity, mter-diffusion and thermal diffusion onloulatod by utilising these force constants and satisfactory agreement has boon obtained. From the available data it appears that the force constants, heroin deter­mined, give better agreement than those obtained from the usual combination rules.I N T R O D U C T I O NConsiderable amount, of informal-ion has been obtained for the like molecular interactions on the Leniiard-Jones (12 : 6) and the exp-six potentials from the experimental viscosity and second virial coefficient data. Some other properties such as, self-diffusion (ISrivastava and Madan, 1962); thermal diffusion (Srivastava and Madan, 1953); thermal conductivity (Saxena, 1955a; Srivastava 1957a) liave also been utilised. Unfortunately, information regarding the unlike mole­cular interactions has so far been very meagre. This is mainly due to the non­availability of suitable experimental data having sufficient accuracy and tempera­ture range.The most suitable property for determining unlike interactions is the inter- diffusion coefficient l)i2 for, it depends, to a first approximation, only on the unlike jutcraotions. Usually the range of temperature for these measurements is small so that it is not possible in practice to determine accurately the unlike interactions solely from inter-diffusion data. This lead Srivastava and Madan (1963) to utilise the extensive thermal diffusion data for this purpose and the method has been subsequently employed by several workers (Saxena, 1965b; Srivastava and Sri­vastava, 1957; Srivastava 1957b). Recently several workers (Strehlow, 1963; Bunde, 1955c; Rumpel, 1955, Srivastava and Srivastava, 1959; Srivastava, 1959) have tried to extend the temperature range of measurement of and have utihsed their data to determine unlike interactions on the Lennard-Jones (12:6) model. Srivastava and Srivastava (1969) have suggested a method in which the data on mter-diffusion coefficient and the viscosity of gas mixtures are292212 2 2 A. K, Baruacombined to determuio tlie force parameters for the unlike interactions. The arlvantage of this method is that it can be used even when the mter-diffusion coeffi- (dont 18 known at a single temperature provided it is sufficiently accurate. In this paper the accurate mter-diffusion data available in the literature have been combined with the data on viscosity of gas mixtures to determine unlike inter­actions on the Lennard-Jones (12 : G) model.D E T E K M I N A T J O N  OF  T H E  P A R A M E T E R S  The Lennard-J ones (12 : G) potential may be written as( 1)w'hero ^(r) is the potential energy between two molecules separated by a distance r, (T is the value of r for which 0(r) =  0, e is the deiith of the potential well. Un­fortunately, the thei>ry is not sufficiently develojied to give the unlike interaction parameters in terms of like ones and it is usual to employ some empirical combi­nation rules for this purpose. The set of rules, hitherto most successful, is the following :—o'la =  1/2K+0-2)*-12 =  (^ 1 •( 2)(3)Relations (2) and (II) are scmi-empincal and at best only approximate; it is there­fore always desirable to determine and from the experimental data by Slidable methods.The (ioefficient of iiiter-diffusion of two gases 1 and 2 may bo written, to the first approximation, in the form0.Q02G28|r3(Jf ,4 (4)wherii 7^ 13 is the mutual diffusion coefficient in cm^/soc, p the pressure in atmos­phere, is a reduced ciollision integral tabulated by Hirschfolder, Curtissand Bird (1964), and =  hTje^^. M-^ , arc the molecular weights and T is the tomporaturo in °K.The viscosity of a binary gas mixture, fo a first approximation is givenlayr,, 1 — 1- H-1 7Wll»Jl XT I T7* -Aj7 -T yq (5)where X ,=vi4 -V25  \ Tf^ \ ! ^13 \ I ^i?/2«!?_/ U ^  i/2 \ ^ 1  /JMolecular Interactions from Viscosity, etc. 2231.\  4M^M^ }/-^12 J_ Vn \ _ l 1\ 712 f  JM]: ):ci, rrg are the mole fractions, 7/^ , r/g are the viscosities and JUfg fh® molecular weights of the components 1 and 2  respectively, is the viscosity of a liypotheti- (!al gas having the molecular weight 2^f,ilfg/(71fi+irg). A^*  is a function of the collision integrals and is tompBratiire dependent. Jt has been tabulated by Hirschfelder, Curtiss and Bird (lt)54). Solving Eq.(4) and 5^ ) to eliminate <rig we obtain.A *  ^ i f  1 ■' 0^ i s  .( ^ )  + 1 -> h] + 1 )!>;.„,*-... (6)with _  266.93 7),g0.002628 ilf^ ' Jig f x io - ’Thus by knowing D^ g, and rj,^  at the same temperature T°K, .djg* may bedetermined. I"rom the tables the value of corresponding to this value of .412* can be read and hence c^ g/jt may be calculated from the relation =  Once the value Ci2/k is fixed, or^ g can bo dotormmed from Eq. (4). If 4)^2 data are available at several temperatures, the corresponding values of o-^ g are determined and the mean taken.The force parameters trig, 1^2/^ obtained for the systems Hg-CHj, Hy-COg, Ilg-Ng, Hg-Ho and N2-C 2H 4 have been recorded in table 1  In the table are also given for the sake of comparison the values calculated from the combination rules. I t  will be seen from Table I that the values of trig determined from the experimental data are always lower than those given by the. combination rule. This is to be expected as the combination rule given by Eqn. (2 ) is expected to hold for rigid spheres only. I t  may also be observed that except in the case of N2~CgH4, the values obtained foi 6'i2/& are always higher than those obtained from the combination rule. ' '  ....................224 A . K . B a r u aTABLE IForce Parameters on the Leniiard-Jones (12:6) Model•1Oas PairFrom D i 2 and From combination ruloHRof. for data<Jj2 A 0’i2 A D i 2H 2—CH4 3.346 71.31 3.425 67.54 (Boyd,1951)(Hirsehfoldor,1949)H .—CO2 3 429 83.37 3.482 79.54N2- C 2H 4 3.883 135.60 3.957 137.00 >> »Ha—Na 3.283 58.41 3.325 55.20 (Bunde,1955)(Ittorbeekj et  al, 1947)H 2—Ho 2.747 21.31 2.772 20 70 (Rumpel, 1955)(Hirsohfeldor,1949)C O M P A R I S O N  W I T H  E X P E R I M E N TTn order to test the reliability of the force parameters thus determined it is necessary to sec how far they reproduce the experimental data over a wide range of temperature. In table IT are shovm the experimontiil and the calculated values of for the systems for which data are available at more than one temperature. values have also been calculated from the combination rules. I t  will bo seen from table IT, that the force parameters determined m the pre^nt paper represent the experimental better than the combination rules,and this is very marked in the case of H^-He.TABLE IIExperimental and the calculated values of For / / 2-N 2 and Hg-HcGas Pair T°KD ]2 in cma/sec.Expt. Calo. from force para­meters obtainedCalc, from combinatiion rules298.2 0.7385 0.7714 0.7603H 2- N 3 328.2 0.9079 0.9074 0.8966'"358.2 1.062 1.053 1.016298.2 1.550 1.539 1 665H 2—He 328.2 1.843 1.805 1.940358.2 2.080 2.092 2.232Molecular Interactions from Viscosity, etc. 225Jn table III  are shown the experimental and the calculated values of the viscosity of gas mixtures, for differojit gas pairs.In table IV are shown the calculated and the experimental values of the thermal diffusion factor kj, for the gas pairs for which data are availableTABLE IIIExperimental and calculated values of x 10’ (in gm/cm.sec)Gas Pair % ol ligUtor ICxpt. Calc, from Calc, fromoonsiituent force jiara- combinationmctoi’Hobtainedrulep28.08 1099 1107 1093293 48.56 1098 1108 109260.22 1080 1092 108192.23 955 960 94428 08 1337 1339 133048.56 1328 1327 1320373 60 22 1306 1307 1290H 3--C H 492.23 1132 11.30 112128.08 1602 1601 1.59148.55 1587 1574 1576473 60 22 1551 1551 1.54002,23 1338 1329 132128.08 1718 1722 170548 55 1699 1695 1683623 00 22 1662 1663 165092.23 1423 1413 141119.93 1601 1504 1502300 41.29 1606 1510 151278.50 1370 1372 137419.93 1945 1953 1945400 41.29 1933 1038 1930Ha—CO278 50, 1713 1721 171819.93 2358 2350 2346500 41.29 2321 2318 230778.50 2026 2023 201119 93 2542 2549 2528550 41.29 2506 2515 248178.50 2173 2175 2160226 A. K .  B a ru aTABLE II I  (contd.)Gas Pair TOR % of lighter Expt. Calc, from Calc, fromconstituent force para­ combinationmetersobtainedrules84.0 1251 1254 125055.9 1560 1663 1567Ha—Na 291.1 38 0 1660 1661 166524.1 1677 1675 167913 4 1742 1745 176255 20 1317 1319 1322293 00.69 1252 1258 126569.18 1166 1172 117665 20 1551 1550 1660373 60.69 1478 1481 1486Ha—Ho69 18 1383 1379 138855 20 1817 1818 1793473 60 69 1728 1737 171469.18 1619 1617 159855 20 1939 1942 1895523 00.09 1852 1857 181969.18 1732 1735 169423.79 1169 1174 1172300 43.05 1308 1312 130275 95 1574 1576 157323.79 1491 1496 1490400 43.05 1655 1658 1651Na—C.H#75.95 1956 1954 195023.79 1788 1788 1778500 43.05 1963 1974 196275.95 2292 2297 228523.79 1921 1927 1908550 43.05 2108 2117 209275 95 2453 2469 2439A glance at the Table TTI hIiowh that the agreemejit between the experim enttal and the calculated values of is very satisfactory. In general the same degree of agreement is obtained with the force parameters determined in the paper and with those determined from combination rules. But at least in some cases the former gives better agreement.Molecular Interactions from Viscosity, etc. 227Agreement in the case of thermal diffusion factor is only approximate. However, generally the agreement is better than that obtained with the usual (oinbination rules. A part of the disagreement between the experimental and i,lnj calculated values of kj, may be attributed to comparatively large inaccuracy m the experimental determination of kj,.TABLE IVExperimental and calculaled values of thermal diffusion factoi* kj,kn, X loadas Pair % oflightor const ituontT°K Expi. Calc, from forcG para- motors obtainedCalo from combination rulesRef. for dataHa—CO 2 633003706. H9 8.998 13 8 898.39 (Bastick al, 1939)9 6029.4 3.9.6 4.07 3.9742.0 143 6.21 6.23 6.01Ila—Na77.6 4.84 4 ff2 1^.44■ (Ibba fit al, 1926)29 4 5 48 6 74 6 9042.0 264 7 40 7.39 7.3777 5 6 63 7.04 6.36HI 35S 1.79 2 0.6 2.31 (Murphey, 1947)60 4.81 3 9460 4.42 3.8870 330 3 50 3.3880 2 84 2 6290 1.32 1.44A C K N O W L E D G M E N T S3.743.563 08 (Heath, 19412.311.29The author is grateful to Prof. B. N. Srivastava, D.Sc., F.N.I., for suggesting the problem and for his valuable guidance throughout the progress of the work.R E F E R E N C E SBastick, R. E., Heath, H- R. and Ibbs, T. L., 1939, Proc. Boy. Soc. {Lond), A178, 643. Boyd, C. A. et al„ 1951, J. GJiem. Phya. 19, 548.Bunde, R. E., 1955, Univ. of Wisconsin, CM-850, 8 Aug.228 A. K, BarmHeath, H. n., Ibha T. L. and Wild, N. E., 1941, Prm. Roy. Soc. (lend), A178, 880.Hirachfeldor, J.O., Bird' R. B. and Spotz, E. L., 1949, Chem Rev. 44, 206.Hii’BChfoldor, J. 0., CuriiHH, C. F. and Bird, R. 13., 1954, Molecular Theory of Gaaea and Liquida, John Wiley & Sons, Inc,, Now York.Ibbs, T, L , drew, K. E. and Hirst, A. A., 1926, Proo. Roy. Soc. {Lond), A41, 456, Itlnrbnok, A. van, Paomol, 0. van, Liordo, Mibs I. Von, 1947, Physiva 13, 38. Murpboy, B. P., 1947, PhyB. Rev. 72, H34.Rumpel, W. F., 1955, Univ. of Wisconsin, CM—851, 1 Aug.Saxona, S. C., 1955a, hid, J. Phys.t 29, 587.Saxona, S. C., 195,5b, Ind. J. Phya., 29, 131.Srivnstava, B. N. and Madan, M, P., 1952, Phil. Mag. 63, 968.SrivaBt-ava, B. N. and Madan M. P., 1953, J. Chcm. Phys., 21, 807,Hrmisiavn, B. N, and Srivnsiava, K. P., 1957, Phyaica, 23, 103.Snvastava, B. N and SrivaHtava, K. P., 1969, J. Chem. Phya., (in pross) Srjvastava, K. P., 1957a, Ivd. J. Pfiya., 81, 404.Srivastava, K. P., 1957b, J. Chem. Phya., 26, 579.Snvaatuva, K. P., 1959, Physical (in press)Strohlow, R. A., 1953, .7. Chem. Phys., 21, 2101.

Unlike Molecular Interactions from Viscosity and Inter-Diffusion

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Unlike Molecular Interactions from Viscosity and Inter-Diffusion

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