Indian Journal of Chemical Technology Vol. 12, September. 2005, pp. 588-592 Notes An ultrasonic study of multicomponent liquid systems J D Pandey*, A K Singh & Ranjan Dey Department of Chemistry, University of Allahabad, Allahabad, 211 002, India Received 19 April 2004; revised received 27 May 2005; accepted 20 June 2005 A modified Flory theory has been employed for the computa- tion of ultrasonic velocity of four quaternary liquid mixtures at 298.15 K. Ultrasonic velocity of these four systems have also been computed using Van Dael ideal mixing relation, Nomoto relation and Collision factor theory. A comparative study has then been carried out as regards the merits and demerits of the em- ployed relations. Keywords: Quaternary liquid mixtures, ultrasonic velocity, Flory theory IPC Code: B01J19/10 Physicochemical behaviour and molecular interac- tions occurring in a variety of liquid mixtures and so- lutions can be studied with the aid of ultrasound ve- locity. There has been an increasing interest in the study of molecular interactions and a number of ex- perimental techniques have been used to investigate the interactions between the components of the binary liquid mixtures. Since data on sound velocity offers a convenient method for determining certain thermody- namical properties of liquids and liquids mixtures, which are not obtained by other methods, extensive work has been done 1-4 for investigating liquid state through analysis of ultrasonic propagation parameters and to correlate ultrasonic velocity with other physical and thermodynamic parameters. A number of work- ers 3,5,6 have carried out successive evaluation of ultra- sonic velocity theoretically by various empirical and semi-empirical relations and statistical mechanical theory proposed by Flory. Flory explored the statisti- cal theory starting from reduced equation of state and using comparatively simple partition functions suit- able for liquids. Extensive use of Flory theory has been made for computation of various excess thermo- dynamic functions 8,9 . Recently, Pandey et al. 5 have applied Flory theory in conjunction with Auerbach and Altenberg relation for computation of ultrasonic velocity. In the present investigation, for the first time, a modified Flory the- ory has been employed for computation of ultrasonic velocity of four quaternary liquid mixtures, viz. n- pentane + toluene + n-heptane + cyclohexane, n- pentane + n-hexane + benzene + toluene, n-pentane + n-hexane + cyclohexane + benzene and n-decane + n- hexane + cyclohexane + benzene at 298.15K. Ultra- sonic velocity for the aforementioned systems have also been computed via Van Dael ideal mixing rela- tion, Nomoto relation and Collision Factor Theory 3 . The necessary parameters for computation have been taken from literature 10,11 . Theoretical Ultrasonic velocity of quaternary liquid mixtures have been evaluated by using Flory's statistical the- ory, Van Dael empirical relation, Nomoto relation, and collision factor theory as given below. The expression of ultrasonic velocity is given by Flory theory as 2 / 1 mix mix , mix 1 ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ρ β = s U … (1) where β s,mix and ρ mix are the isentropic compressibility and density of the mixture, respectively. Both β s,mix and ρ mix are obtained by Flory theory, as described earlier 5 . In this method, computation of ultrasonic ve- locity requires the knowledge of various reduced and characteristic parameters of pure components, which can only be evaluated using the corresponding ther- mal expansion coefficient (α) and isothermal com- pressibility (β T ) data. Thermal expansion coefficient (α) and isothermal compressibility (β T ) of pure com- ponents are evaluated through the following equations 4 / 1 T ) 0191 . 0 ( β × = α … (2) 3 / 4 2 9 / 4 3 T 10 71 . 1 ρ × = β − U T …(3) where all the symbols have their usual meaning. _______________ *For correspondence (E-mail: drranjan@hotmail.com)