Refractive indices of binary liquid mixtures of squalane with benzene, cyclohexane and hexane at to K

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1 Indian Journal of Pure & Applied Physics Vol. 39, December 200 I, pp Refractive indices of binary liquid mixtures of squalane with benzene, cyclohexane and hexane at to K Subhash C Bhatia, Neelima Tripathi & Gyan P Dubey Department of Chemistry. Kurukshetra University,Kurukshetra Received 9 May 200 I; revised I October 200 I; accepted 28 October 200 I Densities, p, at K and refrac ti ve indi ces, n, at , , and K have been measured for the binary liquid mixtures of squalane with benzene, cyclohexane and hexane over the whole mole fraction range. From refractive index data, the refractive index deviations, L1n. at different temperatlll es have been calculated and fitted to the Redlich-Kister polynomial equation to estimate the adjustable parameters and the standard deviations. Further, theoretical prediction of refractive indi ces of these binary liquid mixtures at K have been made using various mi xing rules. Results obtained have been di scussed in tenlls of average percentage deviations. 1 Introduction This paper is a part of our systematic programme of studies on the thermodynamic properties of binary liquid mixtures with molecules of significantly different sizes and flow behaviour 1 In this paper, experimentally measured values of densities, p, at K and refractive indices, n, at , , and K and at atmospheric pressure, for the binary mixtures of squalane with benzene, cyclohexane and hexane are reported. Using these experimental data refractive index deviations, L1n, have been calculated at different temperatures and the results obtained have been correlated with composition using the Redlich Kister polynomial equation 2. Out of these binary liquid mixtures, densities and refractive indices at K for the system squalane+benzene have been reported earlier 1 Refractive index measurements in binary liquid mixtures have been made by several workers'- 6. In this paper refractive indices of binary liquid mixtures have been computed theoretically using Lorentz-Lorenz (L-L), Gladstone-Dale, (G-D), Wiener (W), Heller (H) and Arago-Biot (A-B) relations 7. The validity of these mixing rules for various binary and multi-component liquid mixtures 8-10 have been tested by severa I wor k ers an d. tt was concluded that these theoretical mixing rules are interrelated in a simple quantitative manner and perform well within the experimental error. These theoretically calculated values have been compared with the experimental data at S K and the results have been discussed in terms of average percentage deviations (APD). 2 Experimental Details 2.1 Materials Benzene, cyclohexane and hexane were Ranbaxy products and squalane was obtained from Acros Organics with stated purity > 99%. All the reagents except squalane were used after purification by fractional distillation. The experimentally measured values of densities at K and refractive indices at temperatures to 3 I 3. I 5 K of all the pure components are given in Table I. 2.2 Apparatus and Procedure Densities were measured at K and the temperature was maintained constant by a thermostatically controlled water bath. The densiti es of all the pure components and their binary mixtures were measured by a bi-capillary pycnometer with a bulb of I 2 em' and a capillary of an internal diameter of about I mm. Calibration of the pycnometer was done by de-ionized double-distilled water with g em ' as its density at 298. I 5 K. Details of its calibration and operationa l procedure have been described in our previous papers I. II _ The pycnometer, filled with the desired liquid was kept in a transparent glass-walled water bath with a thermal stability of ±0.0 I C, as checked by means

2 BHATIA e t a!.: BINARY LIQUID MIXTURES 777 of a calibrated thermometer. The relative error in the density measurement was within± g cm- 3. Refractive indices were measured at the temperature range to K with a thermostated Abbe refractometer (Erma, A-302 A) with an error of less than ± unit. Calibration of the instrument was done by measuring the refractive indices of doubl y di sti lled water, toluene and carbon tetrachloride at known temperatures 11 Water was circul ated into the pri sm of the refractometer by using a circulation pump, connected from a constant temperature water bath. The sample mixtures were directl y injected into the prism assembly of the instrument by means of an ai rti ght hypodermic syri nge. When the liquid attained the constant temperature, the refractive index values were noted. An average of three to four measurements were taken for a sample mixture. 3 Results and Discussion The experimental densities at K and refractive indices at to K for the three binary liquid mixtures are given in Tab le 2. The experimental refracti ve index data have been used to evaluate refractive index deviati on,.1n. using the equation : L1n = Lx;n;... ( I) where x; is the mole fraction of the /h component, n,, is the refractive index of the binary mi xture and n ; is for the i 1 h component (i = I or 2). For each mixture, the refractive index deviation was fitted with Redlich-Kister equation of the form : k Lin= X 1X2 I A; (x1-x2f 1... (2) i=l c <J L... J o.o x, Fig I - Refractive index deviation 1'111 for squalane ( I ) + benzene (2) (o): + cyclohexane (2) (1'1): and + hexane (2) (0 ) at K. T he curves have been drawn from Eq. (2) where k is the number of estimated parameters and A; are the polynomial coeffi cients obtai ned by fitting the equation to the experimental result with a leastsquares regression method. The standard deviation. cr, was defined as:... (3) where N is the number of measurements. The parameters of Eq. (2) and the standard deviations. cr, are compiled in Table 3. The values of refracti ve index deviations varying with the mole fraction of the first component for the investigated binary mixtures at K are presented in Fig. I. The L1n values for Table I -Properti es of pure liquid components Liquid p/g em ' at K 11 at K nat K 11at K 11 at K cxptl lit exptl Benzene Cyclo hexane lit " exptl lit exptl lit exptl lit !\ Hexane " 1.373zi 4 Squalane

3 778 INDIAN 1 PURE & APPL PHYS, VOL 39,DECEMB E R 200 I Table 2-Experimental values of densities (p) at K and refractive indices (n) at and K for bin ary liquid mixtures p/g em ' nat nat nat nat at K K K K K Squalane( I )+Benzene(2) I I I I I Squalane( I )+Cyclohexane(2) Squalane( I )+Hexane(2) I.4349 I.430 I I.4468 I I.4472 I the mixture squalane +benzene show nggative trend unlike the other two systems where L1n values are positive over the entire mole fraction range, which is evident from the APD values presented in Table 4. Table 3-Parameters and standard deviations. 0'. of Eqs (2) and (3) for binary mixtures at to K for Lin 77K A 2 A 3 A 4 Squalane( I )+Benzene(2) Squalane( I )+Cyclohexane(2 l I Squalane( I )+Hexane(2) OS l Further, refractive indices of all the three binary mi xtures at K are computed using theoretical mixing rules. The widely used Lorentz-Lorenz (L L) relation is represented as: ( +- 2_1] ( 2 =2A>;.;- -IJ n ; n; (4) where, J; is the volume fraction of the i' 11 component obtaine,.d by the relation, J; = w; Pulp;, where p; is the de~sity of the i' 11 component, Pm is the density of the mixture and w; is the weight frac{ion of the i' 11 component. w; = M;X/LM;X;, where M; is the molecular weight of the i'h component. Eq. ( 4) can be written in an alternative form as: w1 W2 l l n~, ( - I ~ ( n ~ - I ( ni - I n,~, +2 )Pm = nl p:+ ni +2 -P2-... (5) Gladstone-Dale (G-D) equation has been represented by the equation: ".(6) In terms of density, Eq. (6) may be wri tten as:

4 BHATIA eta!. : BINARY LIQUID MIXTURES 779 Mixture Table 4-Average percentage deviations (A PD) for various theoretical mixing rules at K APD Squalane + benzene Squalane + cyclohexane Squalane +hexane L-L G w H A-B (7) Wiener's (W) equation is a relatively simple deviation of Lorentz-Lorenz equation:... (8) Heller's (H) equation in limiting form as applied to dilute solutions is: where m = n-/n 1... (9) Arago-Biot (A-B) relation for the evaluation of refractive index of the binary mixture assumes volume additivity as:... ( I 0) Refractive indices of the liquid mixtures have been calculated theoretically using all the abovementioned mixing rules. The results have been analysed in terms of average percentage deviations and are presented in Table 4. All the mtxmg rules provide excellent agreement for all the three binary liquid mixtures. An examination of Table 4 reveals that the values of average percentage deviation (APO) follow the sequence (squalane+benzene) > (squalane+hexane) > (squalane+cyclohexane). The average percentage deviation calculated from the mixing rules give approximately the same value, 0.49, for the binary liquid mixtures of squalane and benzene, and the value 0.30 for squalane and hexane system. The APO values obtained for the binary mixture of squalane and cyclohexane show better agreement than that for the other two liquid mixtures. For this mixture, L-L relation gives the maximum value of APO, whereas G-0 and A-B relations given minimum value of APO, It is interesting to note that the simplified form of the L-L equation [Eq. (5)], in which volume changes on mixing are neglected, perform well at low and at very high concentrations 7. The values of refractive indices calculated using G-0 and A-B relations are found to be identical when volume additivity is assumed. Heller's equation is applicable to dilute solutions and is simply a limiting form of the Wiener's equation. Also the values of APD obtained from Wiener's and Heller's relations are very close for all the three binary liquid mixtures. 4 Conclusion It can be concluded that the five theoretical mixing rules are interrelated and perform well within the limits of experimental error. For the squalane and cyclohexane mixture, G-0 and A-B relations perform well, and for the other two systems all the mixing rules provide approximately similar results. The APO value for the above systems ranges from to Acknowledgement One of the authors, (NT) is thankful to Council of Scientific and Industrial Research, New De lhi, for the financial assistance in the form of Research Associate. References Lal K. Tripathi N & Duhey G P,.I Cltem Eng Dat (2000) Pal A, Dass G & Kumar A..I Chem Eng Data, 44 ( 1999) 2. 3 Penas A, Calvo E. Pintos M. Amigo A & Bravo R..I Cltem Eng Data. 45 (2000) Pal A & Kumar A,.I Chem Eng Data. 43 ( 1998) Aminabhavi T M & Banerjee K..I Cltem Eng Data. 43 ( 1998) Lorenzi L D. Fermeglia M & Torriano G..I Cltem Eng Data, 43 ( 1998) 183.

5 780 INDIAN J PURE & APPL PHYS, VOL 39,DECEMBER 200 I 7 Heller W. 1 Phys Chem. 69 ( 1965) Lal K, Tripathi N & Dubey G P. Indian.I Pure & Appl Phys, 38 (2000) Pandey J D, Shukla A K, Shukla R K & Rai R D. Indian.I Chem, 27 A ( 1988) 336. I 0 Pandey J D, Shukla A K. Gupta S & Pandey S. Fluid Phase Equil, 103 (1995) 285. II Pandey J D, Tripathi N & Dubey G P. Acu.l"lica -A cta Acustica. 84 ( 1998) Riddick J A. Bunger W B & Sakano T. Or~?an i c solvent.r: Techniques of chemistry ed. Vol I (John Wiley & Sons. New York) TRC, Therm odynamic tables. Hydrocarbon Thermodynamic Research Centre: The Texas A & M University System, College Station. Texas Aucejo A. Bu rgued M C. Munoz R & Marques J L,.I Chem Eng Data. 40 ( 1995) 14 1.