Theoretical Evaluation of Refractive Index in Binary Liquid Mixtures

The density and refractive index (RI) for four binary liquid mixtures : diethyl malonate + dimethylformamide (DEM+DMF), diethyl malonate + Hexane (DEM + HEX), diethyl malonate + tetrahydrofuran (DEM+ THF), diethyl malonate + 1,4-dioxane (DEM+DO) have been measured. The experimental values are compared with those calculated from Lorentz-Lorentz, Heller, Newton and Gladstone – Dale mixing rules.


Introduction
A literature survey shows that physicochemical properties of various liquid mixtures have been studied by several workers [1][2][3][4][5] .It has been reported that refractive index measurement in combination with density, boiling point, melting point and other analytical data are useful industrially 6 .Various empirical and semi-empirical relation have been used to predict refractive index in binary systems [7][8][9][10] .The validity of these mixing rules has been tested for some binary systems by few researchers 11,12 .

Experimental
All the solvents were of Analar grade and their purity was greater than 99%.The purity was checked by density and RI values of pure liquids with those reported in literature 13 .The values for pure liquids are given in Table 1.The mixtures were prepared (v/v) in air tight stoppered bottles to minimize evaporation losses.Densities and refractive index of all the mixtures were measured by pykuometer and Abbe's refractometer with an accuracy of ± 0.0001 gm and ± 0.0005 respectively.

Results and Discussion
The experimental refractive index and density of four binary mixtures are given in Table 2. From the following mixing rules, refractive index for all the mixtures was calculated: ) where n 12 is refractive index of the mixture, n 1 and n 2 are refractive indices of pure components 1 and 2 respectively.φ 1 and φ 2 are volume fractions of components 1 and 2 respectively and is given by : φ i = x i Vi/Σx i V i where x i and V i are the mole fraction and molar volume of i th constituent of binary mixture.

Heller relation (H):
It is based on light scattering equation of Debye and Rayleigh and is given by (n 12 -n 1 )/ n 1 = 3/2 φ 2 ( (n 2 /n 1 ) 2 -1)/((n 2 /n 1 ) 2 +2) 4. Gladstone -Dale equation : It is given by: where ρ 12 is the density of liquid mixture.ρ 1 , w 1 and ρ 2 , w 2 are the density and weight fraction of pure components 1 and 2 respectively.Using these four mixing rules of Lorentz-Lorentz, Newton, Heller and Gladstone -Dale, refractive index for all the binary liquid mixtures has been evaluated and are reported in Table 2.It is observed from Table 2 that the values of refractive index calculated by Lorentz-Lorentz, Heller and Newton mixing rules are almost same for all the four systems.However, slight variation is observed in theoretical values calculated by Gladstone-Dale equation.
The experimental values of refractive index are compared with the predicted results from the above mentioned mixing rules and the average % deviations were determined and are given in Table 3

Table - 1
. Refractive index of pure liquids at 303.15K.

Table 2 .
Experimental and Theoretical values of refractive index of binary liquid systems at .