Theoretical Predictions of Viscosity of Binary and Ternary Liquid Mixtures at K

Transcription

1 Asan Journal of Chemstry Vol. 20, No. 6 (2008), Theoretcal Predctons of Vscosty of nary and Ternary Lqud Mxtures at K VIKASH SINGH, K.K. TIARI* and V.K. SINGH Department of Chemstry, Rastrya Post Graduate College Jamuha, Jaunpur , Inda E-mal: drkktwar@redffmal.com Vscostes of fve bnary [cyclohexane (1) + carbon tetrachlorde (2), benzene (1) + toluene (2), benzene (1) + cyclohexane (2), toluene (1) + carbon tetrachlorde (2) and toluene (1) + cyclohexane (2)] and three ternary lqud mxtures [carbon tetrachlorde (1) + cyclohexane (2) + benzene (3), toluene (1) + cyclohexane (2) + carbon tetrachlorde (3) and benzene (1) + cyclohexane (2) + toluene (3)] at K have been calculated usng renkel relaton, Kendall-Munroe relaton, ngham relaton, Arrhenus-Eyrng relaton, assljewa relaton, Sutherland-assljewa relaton and Croenauer- Rothfus-Kermore relaton. Valdty of these relatons has been checked by calculatng average percentage devatons between calculated values and expermental values obtaned from lterature. Sutherland-assljewa relaton gves maxmum devatons for all the systems n comparson to other methods employed. Other relatons gve comparatvely good results. Key ords: Vscosty, nary, Ternary, Lqud mxture, Transport propertes. INTRODUCTION Thermodynamc and transport propertes 1 of bnary and ternary lqud mxtures provde a lot of knowledge about molecular nteractons occurrng n lqud mxtures. However, vscosty s an mportant transport property 2 for process desgn n petroleum, petrochemcal, chemcal and other ndustres nvolvng flud transportaton, mxng, agtaton, fltraton, heat exchange and concentraton. Therefore, vscostes of bnary and multcomponent lqud mxtures have been determned usng expermental methods 3-10 and theoretcal methods by several workers. Varous lqud vscosty models (renkel, Kendall-Munroe, addtve, ngham, Hnd-Ubbelhode, etc.), proposed for bnary non-electrolytc solutons, have been extended 14 for predctng the vscosty of multcomponent lqud solutons. Although a number of predctve equatons are avalable for estmatng vscosty of

2 4174 Sngh et al. Asan J. Chem. multcomponent systems, few workers have used these relatons for the predcton of vscosty of lqud mxtures. Moreover, for computng the vscostes of mxture only the expermental values of vscosty and molecular weght of pure components along wth the densty of the mxture are requred. or the frst tme, as far as our knowledge s concerned, we are dong comparatve study of these relatons for the predcton of vscosty of bnary and ternary lqud mxtures. In ths paper, we are reportng the calculated values of vscosty of fve bnary [cyclohexane (1) + carbon tetrachlorde (2), benzene (1) + toluene (2), benzene (1) + cyclohexane (2), toluene (1) + carbon tetrachlorde (2) and toluene (1) + cyclohexane (2)] and three ternary lqud mxtures [carbon tetrachlorde (1) + cyclohexane (2) + benzene (3), toluene (1) + cyclohexane (2) + carbon tetrachlorde (3) and benzene (1) + cyclohexane (2) + toluene (3)] at K usng renkel 12 relaton, Kendall-Munroe 12 relaton, ngham 12 relaton, Arrhenus-Eyrng 12 relaton, assljewa 11 relaton, Sutherland-assljewa 3 relaton and Croenauer-Rothfus-Kermore 3 relaton. Valdty of these relatons has been checked by calculatng average percentage devatons (APD) between calculated and expermental values obtaned from lterature 15. THEORETICAL The vscosty of the bnary and ternary lqud mxtures, undertaken for the present study, has been calculated usng renkel relaton, Kendall- Munroe relaton, ngham relaton, Arrhenus-Eyrng relaton, assljewa relaton, Sutherland-assljewa relaton and Croenauer-Rothfus-Kermore relaton whch are outlned below. renkel relaton: 3 ln = = 1 Kendall-Munroe relaton: 3 x η + 2(x 1 x 2 ln η 12 + x 2 x 3 ln η 23 + x 3 x 1 ln η 31 ) + 3x 1 x 2 x 3 ln η 123 (1) ln = x lnη (2) = 1 ngham relaton: 3 = = 1 x η (3) Arrhenus-Eyrng relaton: 3 ln ( V m ) = x ln(ηv ) (4) = 1

3 Vol. 20, No. 6 (2008) Vscosty of nary and Ternary Lqud Mxtures 4175 assljewa relaton: η m = η x 1+ A j x j Sutherland-assljewa relaton: η m = j xη A j x Croenauer-Rothfus-Kermore relaton: lnν m = x lnν j In eqns. 1-7,, V m, ν m, x, η, V and ν are respectvely the vscosty, molar volume and knematc vscosty of mxture and mole fracton, vscosty, molar volume and knematc vscosty of th component of lqud mxture. A j and A j are adjustable parameters called assljewa coeffcents nterpreted by Grey et al. 16 and Pandey et al. 17 as the rato of the effcences wth whch molecules j and mpede the transport of momentum by molecules. A j can be expressed as A 2 1/ 2 3/8 M 1 η j j = η j M (8) (5) (6) (7) RESULTS AND DISCUSSION The values of densty and vscosty of pure component taken from lterature 15 are recorded n Table-1. The values of vscosty of fve bnary [cyclohexane (1) + carbon tetrachlorde (2), benzene (1) + toluene (2), benzene (1) + cyclohexane (2), toluene (1) + carbon tetrachlorde (2) and toluene (1) + cyclohexane (2)] and three ternary lqud mxtures [carbon TALE-1 VALUES O DENSITY AND VISCOSITY O PURE LIQUIDS AT K Pure lqud ρ (10 3 kg m -3 ) η () enzene Toluene Cyclohexane Carbon tetrachlorde

4 TALE-2 CALCULATED VALUES O VISCOSITY O INARY LIQUID MIXTURES AT K USING RENKEL RELATION, KENDALL-MUNROE RELATION, INGHAM RELATION, ARRHENIUS-EYRING RELATION, ASSILJEA RELATION, SUTHERLAND-ASSILJEA RELATION AND CROENAUER-ROTHUS-KERMORE RELATION AND THEIR PERCENTAGE DEVIATIONS ROM EXPERIMENTAL VALUES x Cyclohexane (1) + Carbon tetrachlorde (2) enzene (1) + Toluene (2) Sngh et al. Asan J. Chem.

5 x enzene (1) + Cyclohexane (2) Vol. 20, No. 6 (2008) Vscosty of nary and Ternary Lqud Mxtures 4177

6 x Toluene (1) + Carbon tetrachlorde (2) Sngh et al. Asan J. Chem.

7 x Toluene (1) + Cyclohexane (2) = renkel relaton, = Kendall-Munroe relaton, = ngham relaton, = Arrhenus-Eyrng relaton, = assljewa relaton, = Sutherland-assljewa relaton, = Croenauer-Rothfus-Kermore relaton Vol. 20, No. 6 (2008) Vscosty of nary and Ternary Lqud Mxtures 4179

8 TALE-3 CALCULATED VALUES O VISCOSITY O TERNARY LIQUID MIXTURES AT K USING RENKEL RELATION, KENDALL-MUNROE RELATION, INGHAM RELATION, ARRHENIUS-EYRING RELATION, ASSILJEA RELATION, SUTHERLAND-ASSILJEA RELATION AND CROENAUER-ROTHUS-KERMORE RELATION AND THEIR PERCENTAGE DEVIATIONS ROM EXPERIMENTAL VALUES x 1 x Carbon tetrachlorde (1) + Cyclohexane (2) + enzene (3) Toluene (1) + Cyclohexane (2) + Carbon tetrachlorde (3) Sngh et al. Asan J. Chem.

9 x 1 x enzene (1) + Cyclohexane (2) + Toluene (3) Vol. 20, No. 6 (2008) Vscosty of nary and Ternary Lqud Mxtures 4181

10 x 1 x = renkel relaton, = Kendall-Munroe relaton, = ngham relaton, = Arrhenus-Eyrng relaton, = assljewa relaton, = Sutherland-assljewa relaton, = Croenauer-Rothfus-Kermore relaton Sngh et al. Asan J. Chem.

11 Vol. 20, No. 6 (2008) Vscosty of nary and Ternary Lqud Mxtures 4183 tetrachlorde (1) + cyclohexane (2) + benzene (3), toluene (1) + cyclohexane (2) + carbon tetrachlorde (3) and benzene (1) + cyclohexane (2) + toluene (3)] at K have been calculated usng eqns. 1-8 and are recorded n Tables 2 and 3, respectvely. Percentage devatons between calculated and expermental values are also reported n Tables 2 and 3. The values of densty of the mxture requred for the calculaton are taken from lterature 15. Valdty of aforementoned relatons has been checked by calculatng average percentage devatons (ADP) between calculated and expermental values obtaned from lterature 15 and recorded n Tables 4 and 5. TALE-4 AVERAGE PERCENTAGE DEVIATIONS ETEEN EXPERIMENTAL AND CALCULATED VALUES O VISCOSITY O INARY LIQUID MIXTURES AT K USING RENKEL RELATION, KENDALL- MUNROE RELATION, INGHAM RELATION, ARRHENIUS-EYRING RELATION, ASSILJEA RELATION, SUTHERLAND-ASSILJEA RELATION AND CROENAUER-ROTHUS-KERMORE RELATION nary lqud mxture Cyclohexane (1) + Carbon tetrachlorde (2) enzene (1) + Toluene (2) enzene (1) + Cyclohexane (2) Toluene (1) + Carbon tetrachlorde (2) Toluene (1) + Cyclohexane (2) = renkel relaton, = Kendall-Munroe relaton, = ngham relaton, = Arrhenus-Eyrng relaton, = assljewa relaton, = Sutherland- assljewa relaton, = Croenauer-Rothfus-Kermore relaton. TALE-5 AVERAGE PERCENTAGE DEVIATIONS ETEEN EXPERIMENTAL AND CALCULATED VALUES O VISCOSITY O TERNARY LIQUID MIXTURES AT K USING RENKEL RELATION, KENDALL- MUNROE RELATION, INGHAM RELATION, ARRHENIUS-EYRING RELATION, ASSILJEA RELATION, SUTHERLAND-ASSILJEA RELATION AND CROENAUER-ROTHUS-KERMORE RELATION Ternary lqud mxture Carbon tetrachlorde (1) + Cyclohexane (2) + enzene (3) Toluene (1) + Cyclohexane (2) + Carbon tetrachlorde (3) enzene (1) + Cyclohexane (2) + Toluene (3) = renkel relaton, = Kendall-Munroe relaton, = ngham relaton, = Arrhenus-Eyrng relaton, = assljewa relaton, = Sutherland- assljewa relaton, = Croenauer-Rothfus-Kermore relaton.

12 4184 Sngh et al. Asan J. Chem. A perusal of Table-4 reveals that maxmum devatons are obtaned by usng Sutherland-assljewa relaton for the predcton of vscosty of bnary lqud mxtures under the present study whle other relatons gve comparatvely good results. The best results obtaned through utlzng renkel s relaton are due to the fact that t ncorporates all the possble major nteractons. Results obtaned by usng Kendall-Munroe relaton and ngham relaton are also good because these relatons were developed consderng the deal mxng of solutons. An nspecton of Table-5 suggests that Sutherland-assljewa relaton for the predcton of vscosty of ternary lqud mxtures gves maxmum devatons for all the systems n comparson to other methods employed for the calculaton. est results are obtaned by usng Arrhenus-Eyrng relaton for the computaton of vscosty of ternary lqud mxtures followed by Kendall-Munroe relaton. The trend of valdty of the presently used relatons s as follows: or bnary systems: renkel relaton > Kendall-Munroe relaton > ngham relaton > Arrhenus-Eyrng relaton > assljewa relaton > Croenauer-Rothfus-Kermore relaton > Sutherland-assljewa relaton. or ternary systems: Arrhenus-Eyrng relaton > Kendall-Munroe relaton > assljewa relaton > ngham relaton > Croenauer-Rothfus- Kermore relaton > renkel relaton > Sutherland-assljewa relaton. REERENCES 1. S. Varshney and M. Sngh, J. Indan Chem. Soc., 83, 233 (2006). 2. L. Lee and Y. Lee, lud Phase Equlb., 181, 47 (2001). 3. J.D. Pandey, S. Mukherjee, S.. Trpath, N.K. Son and A.K. Sharma, Indan J. Chem., 40A, 1214 (2001). 4. J.D. Pandey, S. Pandey, S. Gupta and A.K. Shukla, J. Soluton Chem., 23, 1049 (1994). 5. A.H. Nhaes and A.-.A. Asfour, J. Chem. Eng. Data, 50, 149 (2005). 6. I.-H. Peng and C.-H. Tu, J. Chem. Eng. Data, 47, 1457 (2002). 7. D. Gomez-Daz, J.C. Mejuto and J.M. Navaza, J. Chem. Eng. Data, 46, 720 (2001). 8. A. Al and A.K. Nan, Phys. Chem. Lq., 37, 161 (1999). 9. M.N. Roy,. Snha and V.K. Dakua, J. Chem. Eng. Data, 51, 590 (2006). 10. S.J. Tangeda and S. Nallan, J. Chem. Thermodyn., 38, 272 (2006). 11. J.D. Pandey, S. Mukherjee, M.K. Yadav and R. Dey, J. Indan Chem. Soc., 82, 39 (2005). 12. J.D. Pandey, V. Vyas, P. Jan, G.P. Dubey, N. Trpath and R. Dey, J. Mol. Lq., 81, 123 (1999). 13. J.D. Pandey, A.K. Shukla, Shkha and N. Trpath, J. Indan Chem. Soc., 73, 269 (1996). 14. J.D. Pandey, N. Agarwal, Shkha and K. Msra, Indan J. Chem., 29A, 113 (1990). 15. Shkha, Ph.D. Thess, Department of Chemstry, Unversty of Allahabad, Allahabad, Inda (1990). 16. P. Grey and C. Parknson, J. Chem. Soc. araday Trans. I, 1065 (1972). 17. J.D. Pandey and S.R. Prajapat, Proc. Natt. Acad. Sc. (Inda), 47A, 428 (1981). (Receved: 26 March 2007; Accepted: 21 ebruary 2008) AJC-6367