Prediction of Ultrasonic Velocity in Binary Mixtures of a Nuclear Extractant and Monocarboxylic Acids using Several Theoretical Models

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1 Predcton of ltrasonc Velocty n Bnary Mxtures of a Nuclear Extractant and Monocarboxylc Acds usng Several Theoretcal Models R. K. Mshra 1, B. Dala 1*, N. Swan 2 and S.K. Dash 3 1 BSH, Gandh Insttute of Engneerng and Technology (GIET), Gunupur, Odsha, Inda College of Basc Scence and Humantes, O..A.T, Bhubaneswar Odsha, Inda DESM, Regonal Insttute of Educaton (NCERT), Bhubaneswar, Odsha, Inda *correspondng author: , , (Fax) bswajt_dala@redffmal.com Abstract The ultrasonc veloctes, of pure nuclear extractant,.e. d (2-ethyl hexyl) phosphorc acd (DEHPA) and three monocarboxylc acds vz. acetc acd, proponc acd and n-butyrc acd and ther bnary mxtures over whole mole fracton range of DEHPA ( ) have been expermentally measured at K under atmospherc pressure. The theoretcal values of ultrasonc velocty of the bnary mxture have been calculated usng several theoretcal models such as s relaton (N), Impedance dependence relaton () and Danuusso model (D). Theoretcal values of ultrasonc velocty were compared wth expermental values and the relatve merts of these models were dscussed. Keywords: DEHPA, Bnary mxtures, ltrasonc velocty, Theoretcal models of ultrasonc velocty. I. INTRODCTION ltrasonc nvestgaton s one of the sgnfcant technques used for studyng the nature as well as degree of molecular nteracton between the lke and unlke molecules of the components n varous polar/apolar lqud mxtures, nvestgated by several researchers [1-4]. The study nfers the physcochemcal behavour of lqud mxtures whch s useful n the feld of petrochemcal, pharmaceutcal and nuclear energy ndustres. The ultrasonc veloctes for all bnary mxtures were evaluated theoretcally as a functon of composton usng s relaton, Impedance dependence relaton and model [5-8]. II. EXPERIMENTAL SECTION All the chemcals used n ths nvestgaton are of Analytcal Reagent grade and were obtaned from E- Merck Chemcals Ltd. Inda. These chemcals were used wthout further purfcaton. Our procedures of measurements have been descrbed earler [9]. III. RESLTS AND DISCSSIONS The values of ultrasonc veloctes, of pure d (2- ethyl hexyl) phosphorc acd (DEHPA) and three monocarboxylc acds vz. acetc acd, proponc acd and n-butyrc acd and ther bnary mxtures wth DEHPA as a common component were measured expermentally at K under atmospherc pressure. The expermental value of ultrasonc veloctes n lqud mxtures were compared wth those values calculated usng varous theoretcal models, vz. s relaton, Impedance dependence relaton and model [5-8, 10] and are presented n Table 1. Such an evaluaton offers a smple method to nvestgate molecular nteractons besdes verfyng the applcablty of varous propertes of lqud mxtures [5-8, 10]. sng the respectve models, ultrasonc velocty such as N, and D were estmated (Table 1) by the followng relatons and models as gven by x R x V 3 (1) N x Z x (2) D m M eff x M where x,, ρ, Z, (3) R V m 1/ 3, V m and M are mole fracton, ultrasonc velocty, densty, acoustc mpedance, molecular sound velocty, molar volume and molecular weght of th component of the mxture respectvely and M eff = x M s the effectve molecular weght of the mxture. The root mean square devaton relatve (RMSD) between the ISSN: Page 304

2 expermental and theoretcal values of ultrasonc velocty was calculated. The value of RMSD s used to estmate the relatve merts of the theoretcal relatons exp ) exp RMSD = ( 1 ) ( p th (4) where p s the number of expermental data ponts. TABLE I Expermental and theoretcal values of ultrasonc velocty (SI nt) of bnary mxtures of acetc acd, proponc acd and n-butyrc acd wth DEHPA ( ) Mole fracton Expt N D acetc acd + DEHPA proponc acd + DEHPA ISSN: Page 305

3 n-butyrc acd + DEHPA In our earler study [10], the theoretcal results of ultrasonc velocty n bnary mxtures of MIBK wth DEHPA betokens that s relaton s more sutable n favour of expermental values of ultrasonc velocty. So s relaton makes accurate predcton of the ultrasonc velocty n that synergstc mxture havng hgher molecular volumes. In ths present work, we have the smlar analyss on another bnary mxtures of one extractant (DEHPA) + monocarboxylc acds over entre mole fracton range of DEHPA. The values of root mean square devaton are presented n Table 2 and the values are found low n all cases under study. ISSN: Page 306

4 Bnary system RMSD N D acetc acd (1) m s Fg. I. Expermental and theoretcal ultrasonc velocty of acetc acd + DEHPA. m s Fg. II. Expermental and theoretcal ultrasonc velocty of proponc acd + DEHPA m s Fg. III. Expermental and theoretcal ultrasonc velocty of n-butyrc acd + DEHPA TABLE II Root mean square devaton relatve (RMSD) to the predcted value of ultrasonc velocty by usng s relaton (N), Impedance dependence relaton () and model (D). proponc acd (1) n-butyrc acd (1) The applcablty of the theoretcal models wth the expermental value of ultrasonc velocty and the sutablty of these theores for all mxtures based on RMSD value s decreased as follows: D > N >. IV. CONCLSION Several theoretcal models have been correlated wth the expermental data of ultrasonc velocty and the relatve applcablty were studed n all bnary systems under nvestgaton. Theoretcal results of ultrasonc velocty such as N, and D n bnary mxtures of acds wth DEHPA nfers that model s more sutable n favour of expermental values of ultrasonc velocty. Thus, model makes accurate predcton of the ultrasonc velocty n the studed bnary mxtures. ACKNOWLEDGEMENT The authors are grateful to the Charman, Gandh Insttute of Engneerng and Technology (GIET), Gunupur and Prof (Dr) B.B. Swan, Ex-Professor, Khallkote College, Berhampur for ther contnuous support and valuable suggestons. REFERENCES 1. B. Dala, S.K. Dash, S. K. Sngh, N. Swan, and B.B. Swan, Physco-chemcal propertes of d-(2-ethylhexyl) phosphorc acd wth apolar solvents from ultrasonc studes, Phys. Chem. Lq. Vol. 50 (2), pp , D. R. Godhan, P. B. Dobarya, and A. M. Sanghan, Effect of temperature and solvents on ultrasonc velocty and thermodynamc parameters of 1, 3, 4-oxadazole dervatve solutons, J. Mol. Lq. Vol. 168, pp , S. S. Bttencourt, H. E. Hoga, R. B. Torres, J. V. H. Angelo, Thermodynamc and spectroscopc propertes of bnary mxtures of n-butylammonum butanoate onc lqud wth alcohols at T = ( ) K, J. Chem. Thermodynamcs Vol. 105, pp , S. K. Pradhan, S.K. Dash, L. Moharana, and B. B. Swan, ISSN: Page 307

5 Molecular nteracton parameters of bnary mxtures of dethyl ether and apolar solvents usng ultrasonc probe, Ind. J. Pure Appl. Phys., Vol. 50, pp , O., Emprcal formula for sound velocty n lqud mxtures, J. Phys. Soc. Jpn., Vol. 13, pp , D. Kumar, D. K. Rao, Study of molecular nteractons and ultrasonc velocty n mxtures of some alkanols wth aqueous propylene glycol, Ind. J. Pure Appl. Phys. Vol. 45, pp , G. V. Rama Rao, P. B. Sandhya Sr, A. V. Sarma and C. Rambabu, Comparatve Study of theoretcal ultrasonc veloctes of bnary mxtures of methanol and pyrdne at dfferent temperatures, Ind. J. Pure Appl. Phys. Vol. 45, pp , F., ltrasonc velocty and adabatc compressblty of lqud mxtures, Att della academa nazonale d lnce. Vol.10, pp , B. Dala, S. K. Dash, S. K. Sngh, N. Swan and B. B. Swan, ltrasonc and 31 P NMR nvestgatons of an acdc nuclear extractant wth some monosubsttuted benzenes J. Chem. Thermodyn. Vol. 93 pp , S.K. Dash, B. Dala, S. K. Sngh, N. Swan and B.B. Swan A comparatve study of expermental and theoretcal values of ultrasonc velocty n bnary mxtures of two nuclear extractants J. Pure Appl. ltrason. Vol. 36, pp 60-64, ISSN: Page 308