International Journal of Applied Chemistry. ISSN 097-79 Volume, Number (07) pp. 54-55 Research India Publications http://www.ripublication.com Refractive Properties of Liquid Binary Mixture at Temperature Range T=98.5-.5 K Vikas.S.Gangwar, Gyan Prakash, Sandeep K. Singh and Ashish K. Singh* Department of Chemistry, V.S.S.D.College, Kanpur-0800., India. Abstract Densities and refractive indices were measured for the binary liquid mixtures formed by benzyl alcohol with benzene at (T=98.5, 0.5, 08.5 and.5) K and atmospheric pressure over the whole concentration range. Lorenz-Lorenz mixing rule, Ramaswamy and Anbananthan models and model devised by Gelenski were used to study the associational behaviour and molar refractivity of two weakly interacting liquids. These results have been discussed to study the type of mixing behaviour between the molecules. The measured data were fitted to the Redlich-Kister polynomial relation to estimate the binary coefficients and standard errors. Furthermore, McAllister multi body interaction model is used to correlate the binary refractive index with the experimental findings. Keywords: Binary liquid, refractive index, Lorenz-Lorenz, molar refractivity, theoretical models, Redlich-Kister. INTRODUCTION Refractive index at different temperatures of liquid mixtures is an important step for their structure and characterization. Along with other thermodynamic data, refractive index values are also useful in engineering calculations. Refractive index is useful in many practical purposes such as, to assess purity of substances, to calculate the molecular electronic polarizibility [], to estimate the boiling point with Meissner s [] method or to estimate the other thermodynamic properties. In recent past, several workers [-7] have applied various mixing rules in binary and ternary liquid mixtures.
544 Vikas.S.Gangwar, Gyan Prakash, Sandeep K. Singh and Ashish K. Singh The studied systems have industrial utility; the mixing behaviour of benzyle alcohol are interesting due to presence of hydroxyl group coupled with benzene. In this work, we present the experimental data on density and refractive index of binary liquid mixtures for benzyl alcohol with benzene at (T=98.5, 0.5 08.5and.5) K and atmospheric pressure over the entire composition range. These data were analyzed in terms of Lorenz-Lorenz mixing rule [8], model of Ramaswami and Anbananthan [9] and model suggested by Gelenski [0]. Models [9, 0] (associated) are based on the association constant as an adjustable parameter where as model [8] (non-associated) is based on the additivity of liquids. From these experimental data, deviation in molar refraction (R) have been studied and fitted to a Redlich-Kister type polynomial equation [] to derive binary coefficients and estimated the standard errors. McAllister multi body interaction model [] has also been used to study the nature of interactions involved in liquid mixture.. EXPERIMENTAL SECTION. Materials High purity and AR grade samples of benzyl alcohol and benzene used in this experiment were obtained from Merck Co. Inc., Germany and purified by distillation in which the middle fraction was collected. The liquids were stored in dark bottles over 0.4nm molecular sieves to reduce water content and were partially degassed with a vacuum pump. The purity of each compound was checked by gas chromatography and the results indicated that the mole fraction purity was higher than 0.99. All the materials were used without further purification. The purity of chemicals used was confirmed by comparing the densities and viscosities with those reported in the literature as shown in table. Table Comparision of Density and Refractive index with literature date for pure components at 98.5, 0.5, 08.5 and.5 K Compound T/K V/ cm mole - exp /g.cm * lit / g.cm nexp *nlit Benzene 98.5 89.96 0.87 0.876.4984.4979 0.5 89.966 0.8680 0.868.494.49486 08.5 90.706 0.865 -.480 -.5 9.9 0.8575 0.8576.4785 - Benzyl alcohol 98.5 0.80.04.04.578.587 0.5 04.4.076.076.56-08.5 05.4509.07 -.540 -.5 07.9780.066 -.57 - * Ref.8
Refractive Properties of Liquid Binary Mixture at Temperature Range 545. Apparatus and Procedure Before each series of experiments, we calibrated the instrument at atmospheric pressure with doubly distilled water. The calibration was accepted if the measurements were within ± 7.9.0-4 g.cm - of the published values. The densities of the pure components and their mixtures were measured with the bi capillary pyknometer The uncertainty in the density measurements was better than ± 7.9.0-4 g.cm - and reproducible to ± 5.0-4 g.cm- The liquid mixtures were prepared by mass in a air tight stopped bottle using a electronic balance model SHIMADZUAX-00 accurate to within ±0.mg.The average uncertainty in the composition of the mixtures was estimated to be less than ±0.000.All molar quantities were based on the IUPAC relative atomic mass table. Refractive index for sodium D-line was measured using a thermostatically controlled Abbe refractometer (Agato T, Japan). Calibration of the instrument was performed with double distilled water. A minimum of three readings were taken for each composition and the average valuwas considered in all calculations. Refractive index data are accurate to ± 0.000 units.. THEORETICAL Ramswami and Anbananthan [9] proposed the model based on the assumption of linearity of acoustic impedance with the mole fraction of components. Further Glinski [0] assumed that when solute is added to solvent, the molecules interact according to the equilibrium as; A+B = AB () and the association constant Kas can be defined as; K as [ AB] [ A][ B] () where A is amount of solvent and B is amount of solute in the liquid mixture. By applying the condition of linearity with composition obs = xa na + xab nab () where xa, xab, na and nab are the mole fraction of A, mole fraction of associate AB, refractive index of A and refractive index of associate AB respectively. The component AB can not be obtained in its pure form. Following simplifications have been made, firstly, concentration term should be replaced by activities for concentrated solution and second, there are also molecules of non associated components in the liquid mixture. The eq () takes the form, nobs = [xa na + xb nb + xab nab] (4) On changing both the adjustable parameters Kas and nab gradually, one can get
546 Vikas.S.Gangwar, Gyan Prakash, Sandeep K. Singh and Ashish K. Singh different values of the sum of squares of deviations, S = (nobs - ncal) (8) The minimum value of S can be obtained theoretically by a pair of the fitted parameters. But we found that for some Kas and nas, the value of S is high and changes rapidly, and for others, it is low and changes slowly when changing the fitted parameters. In such case, the value of nab should not be much lower than the lowest observed refractive index of the system or much higher than the highest one. Quantitatively, it should be reasonable to accept the pair of adjustable parameters Kas and nab which has the physical sense and which reproduces the experimental refractive indices satisfactorily. Gelenski [0] suggested that experimental results with significantly good accuracy can be produced from the following equation as: n n n n n (9) cal where ncal is the calculated refractive index,, are the volume fraction of component and and n n are the refractive index of pure components. Lorentz-Lorenz (L-L) relation has widest application during the evaluation of refractive indices of mixture and density of pure components as well as density of the mixture and represented in terms of specific refraction as: n n m m n n n n here nm, n, n are the refractive indices of mixture and pure components,, respectively and, are the volume fractions of pure components. (0) 4. RESULTS AND DISCUSSION Table presents the comparison of experimental densities and refractive index of benzene, and benzyl alcohol with literature values at 98.5, 0.5, 08.5 and.5 K. Coefficients of the Redlich- Kister polynomials and their standard deviations (σ) are presented in Table. Parematers of McAllister three body and four body interaction model and standard deviations for refractive indices are presented in Table. Table 4 presents the comparison of average refractive index deviation ( nav) and percent average deviation (% nav) obtained from Lorenz-Lorenz mixing rule, Ramaswami and Anbananthan model and model suggested by Gelenski. Mixing data were recorded in Table 5.
Refractive Properties of Liquid Binary Mixture at Temperature Range 547 Table Coefficients of the Redlich-Kister Equation and Standard Deviations ( ) for Molar Refractivity of Binary Liquid Mixtures at Various Temperatures benzene+benzylalcohol T A0 A A A x0 4 R 98.5 0.0578 0.068 0.0545-0.4 0.59 0.5 0.0578 0.057-0.0058-0.4 8.94 08.5 0.0498 0.09 0.04569-0.55 54.8.5 0.06 0.09000 0.07498-0.64 4.6 Table Parameters of McAllister Three body and Four body Interaction Model and Standard Deviations () for Refractive index of Binary Liquid Mixtures at Various Temperatures benzene + benzylalcohol 98.5.5848.59 8.7.59790.5560.5459 7.5 n 0.5.58057.569.65.569.5875.5006.46 08.5.59904.5744 8.5.54.50575.5906.44.5.546.5466 5.8.595.5606.5976 4.89 Table 4 Comparison of Average and Average Percent Refractive Index Deviation (nav,% nav ) computed from all the models at Various Temperatures benzene + benzylalcohol Temperature Kas n ab nav x0 4 (eq.4) nav x0 4 (eq.0) nav x0 4 (eq.9) % %nav %nav nav(eq.0) (eq.4) (eq.9) 98.5 0.0005.579 69.090 65.09 64.8058 0.4 0.46 0.4 0.5 0.0006.559 6.9600 56.449 56.6 0.7 0.40 0.7 08.5 0.0007.555 08.580 00.458 0.05 0.66 0.7 0.66.5 0.0009.540 8.9990 8.8 9.049 0.78 0.85 0.78
548 Vikas.S.Gangwar, Gyan Prakash, Sandeep K. Singh and Ashish K. Singh Table 5 Volume fraction (Ф), Experimental Densities (), Observed Molar Refractivity (RExp), Theoretical Molar Refractivity(RTheo) and Percent Refractive Index Deviation (% n) obtained from different Models for Binary Liquid Mixtures at various temperatures. benzene + benzylalcohol T=98.5K /g.cc n exp R exp R Eq.0 R Eq.4 R Eq.9 % n Eq.0 % n Eq.4 % n 0.54.0008.599.487.079.009.087 0.87 0.6 0.86 0.909 0.995.589 0.0699 9.7905 9.766 9.797 0.770 0.446 0.75 0.49 0.985.57 9.490 8.8579 8.866 8.859 0.409 0.447 0.400 0.54 0.960.56 8.7457 8.47 8.804 8.4 0.469 0.59 0.467 0.64 0.9445.500 8.4655 7.8876 7.8590 7.8889 0.8 0.868 0.84 0.70 0.96.545 8.089 7.656 7.60 7.667 0.5647 0.5998 0.56 0.799 0.900.50 7.8759 7.58 7.55 7.57 0.49 0.508 0.499 0.8677 0.895.5099 7.06 7.0057 6.996 7.006 0.496 0.4587 0.487 0.966 0.880.50 6.7500 6.749 6.746 6.7495 0.00 0.009 0.0006 Eq.9 T=0.5K /g.cc n exp R exp R Eq.0 R Eq.4 R Eq.9 % n % n % n Eq.0 Eq.4 Eq.9 0.546 0.9998.578.78 0.9700 0.948 0.9705 0.649 0.9 0.64 0.95 0.9874.57 0.65 9.864 9.86 9.8650 0.999 0.445 0.988 0.46 0.9754.56 9.4 8.998 8.90 8.9407 0.544 0.5646 0.5 0.5 0.9564.545 8.77 8.77 8.407 8.780 0.556 0.60 0.55 0.60 0.954.50 8.8 7.9994 7.9660 8.000 0.98 0.4454 0.970 0.76 0.900.5099 8.505 8.678 8.87 8.686 0.5076 0.548 0.5065 0.794 0.8897.50 8.8 7.6680 7.6454 7.6686 0.690 0.670 0.68 0.8680 0.8845.4989 7.080 7.085 7.0700 7.0857-0.0074 0.047-0.0080 0.968 0.8789.4965 6.5 6.589 6.575 6.58-0.074-0.060-0.077
Refractive Properties of Liquid Binary Mixture at Temperature Range 549 T=08.5K /g.cc n exp R exp R Eq.0 R Eq.4 R Eq.9 % n % n % n Eq.0 Eq.4 Eq.9 0.54 0.9875.570.5.8.0.5 0.686 0.4079 0.690 0.909 0.9756.565 0.505 0.0465 0.0005 0.046 0.60 0.6640 0.609 0.49 0.96.55 9.66 9.079 9.075 9.0787 0.756 0.86 0.757 0.54 0.946.500 8.978 8.56 8.4700 8.5 0.687 0.6996 0.695 0.64 0.954.5099 8.5775 7.990 7.9456 7.994 0.85 0.8809 0.859 0.7 0.899.5089 8.550 7.85 7.85 7.858 0.94 0.9807 0.948 0.790 0.8745.5099 8.597 7.7670 7.747 7.7666.488.94.49 0.8677 0.8645.4998 7.7490 7.06 7.86 7.04 0.69 0.660 0.695 0.966 0.8566.4900 6.908 6.846 6.85 6.845 0.07 0.67 0.09 T=.5K /g.cc n exp R exp R Eq.0 R Eq.4 R Eq.9 % n % n % n Eq.0 Eq.4 Eq.9 0.57 0.9745.550.876.5.485.5 0.980 0.448 0.994 0.869 0.968.54 0.67 0.05 0.06 0.88 0.65 0.797 0.654 0.408 0.95.5 9.9 9.696 9.04 9.676 0.8608 0.9504 0.865 0.576 0.954.50 9.06 8.54 8.476 8.54 0.9046 0.9954 0.907 0.668 0.90.5098 9.0499 8.404 8.78 8.85.086.90. 0.707 0.8754.5076 9.7 8.658 8.6 8.64.676.405.698 0.7898 0.856.5089 9.5 8.0945 8.058 8.09.484.4959.440 0.8655 0.865.4887 8.6 7.965 7.9070 7.956 0.70 0.4 0.74 0.954 0.86.4865 7.89 7.68 7.6077 7.6 0.84 0.049 0.849 Ramaswami and Abananthan model has been extended and corrected for the prediction of refractive index of weak interacting binary mixtures which was originally derived for the prediction of acoustical impedance. The results of fittings obtained from the model were utilized properly. The basic doubt regarding this model except the assumption of linearity of refractive index with mole fraction is that these liquids have poor tendency to form dimmers. Calculations were performed using a computer program which allows easily both the adjustable parameters simultaneously or the parameters were changed, manually. We constructed the data sheet in a computer program, with association constant Kas and CAB as the fitted parameters (CAB is the refractive index in the pure component
550 Vikas.S.Gangwar, Gyan Prakash, Sandeep K. Singh and Ashish K. Singh AB means a hypothetical liquid having only the associate A-B. On changing these parameters, the equilibrium concentrations of species [A], [B] and [AB] will change and the refractive index can be computed. The difference between experimental and theoretical refractive index is used to obtain the sum of squares of deviations. It is assumed that in solution three associates are formed instead of two (pure A, pure B and AB). The values of refractive index in pure associate can be treated as a fitted one with the value of Kas. The mixing function, R was represented mathematically by the Redlich-Kister equation [] for correlating the experimental data as: p y x ( x ) A (x ) i i () i 0 where y refers to R, x is the mole fraction and Ai is the coefficients. The values of coefficients Ai were determined by a multiple regression analysis based on the least squares method and are summarized along with the standard deviations between the experimental and fitted values of the respective function in Table. The standard deviation is defined by. m / ( y exp y ) / ( ) i cal m p i () i where m is the number of experimental points and p is the number of adjustable parameters. For the case the values lie between.5 x 0-4 to 54.8 x 0-4 and the largest value corresponds to benzene + benzyl alcohol mixture at 08.5 K. Molar refractivity was obtained from refractive index data according to following expression: R= [n -/ n +] M/ ρ () where M is the mean molecular weight of the mixture and ρ is the mixture density. The molar refractivity deviation function has been calculated by the following expression: R= R- ФR- ФR (4) where Фand Ф are volume fraction Фi = ( xivi / xivi) was used [-5]. There is no general rule that states how to calculate a refractivity function. Konti et al [6] reported deviations in molar refractivity with volume fraction referring to the Lorenz- Lorenz mixing rules. McAllister multibody interaction model [] which is based on Eyring s theory of absolute reaction rates and for liquids the free energy of activation are additive on a number fraction and that interactions of like and unlike molecules. The three body model is defined as: ln n x ln n x x ln a x x ln b x ln n ln( x xm / M) x x ln( M / M) / ] x x ln[( M / M ) /] x ln( M / )] (5) M
Refractive Properties of Liquid Binary Mixture at Temperature Range 55 and the four body model is given by 4 ln n x ln n 4x x ln a 6x x ln b 4 M x x ln c x ln ln( x x M / )] 4x x M ln[( M / M ) / 4] 6x x ln( M / ) / ] 4x x M 4 ln[( M / M ) / 4] x ln( M / )] (6) where n is the refractive index of the mixture and x, n, M, x, n and M are the mole fractions, refractive index, and molecular weights of pure components and respectively; a, b and c are adjustable parameters that are characteristic of the system. In the above eqs. (5) and (6) the coefficient a., b and c have been calculated using the least squares procedure. The estimated parameters of the refractive index equations and the standard deviations,, between the calculated and experimental values are given in Table. It is observed that the four body model of the McAllister equation correlated the refractive index of the mixture to a significantly higher degree of accuracy for the systems than does the three body model. Furthermore, the values of the McAllister parameters have shown a decreasing tendency with rise in temperature. Generally, McAllister s models are adequate in correlation for those systems as evidenced by small deviations. With the increase of volume fraction (Ф), the values of refractive index obtained from all the models decrease at all temperatures except in few places. Results of molar refractivity computed from eq for the systems show regular trend except in few places as shown in Table 5. The minimum and maximum percent deviation (% nav) in refractive index are 0.00 at 98.5 K for benzene + benzyle alcohol respectively. The results of deviation in molar refraction, R, plotted as a function of Фi of benzene + benzyle alcohol mixtures at 98.5, 0.5, 08.5 and.5 K were displayed in the Figure. In all the cases, theoretical molar refractivity computed from all the models agree well within the experimental precision. The trend in all the figures is almost similar and negative. Molar refraction increases with molecular weight for all the systems. Density and refractive index depend on molecular weight and nature of solution and values decrease with increase of temperature as displayed in Table 5. Finally, it can be concluded that the expressions used for the interpolating the experimental data measured in this work gave good results as can be seen by inspecting the σ values obtained. All the models based on associated processes and non-associated processes give more reliable results and helpful in deducing the internal structure of associates through the fitted values of refractive index.
55 Vikas.S.Gangwar, Gyan Prakash, Sandeep K. Singh and Ashish K. Singh R T=98.5 K 0-0. 0 0. 0.4 0.6 0.8-0. -0. -0.4-0.5-0.6-0.7 Ф R T= 0.5 K 0. 0-0. 0 0. 0.4 0.6 0.8-0. -0. -0.4-0.5-0.6 Ф T=08.5 K T=.5 K R 0-0. 0 0. 0.4 0.6 0.8-0.4-0.6-0.8 - R 0 0-0. 0. 0.4 0.6 0.8-0.4-0.6-0.8 - Ф -. Ф Figure Plot of molar refractivity deviation, R, with volume fraction, Ф for Ф benzene+ (-Ф) benzylalcohol at 98.5, 0.5, 08.5 and.5 K: Lorenz- Lorenz mixing rule (Eq 0),, Ramaswami Anbananthan model (Eq. 4),, model devised by Gelenski (Eq.9) REFERENCES [] Kier, L.B., Hall, L.H., Molecular Connectivity in Chemistry and Drug Research, Sand Diego, Academic Press, (976) [] Rechsteiner, C.E., Boiling Point, in hand book of Chemical Property Estimation, Lyman, W.J., Reehl, W.F., Rosenblatt, D.H., (Eds.), American Chemical Society, Washington (990) [] Sharma, S., Patel, P.B., Patel, R.S., Vora, J.J., E.J. Chem. 4, 4-49 (007) [4] Mehra, R., Proc. Indian Acad. Sci. 5, 47-547 (00) [5] Fermeglia, M., Torriano, G., J. Chem. Eng. Data. 44, 965-969 (999) [6] Nayak, J.N., Aralaguppi, M.I., Toti, U.S., Amina Bhavi, T.M., J.Chem. Eng. Data. 48, 48-488 (00).
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554 Vikas.S.Gangwar, Gyan Prakash, Sandeep K. Singh and Ashish K. Singh