Evaluation of excess Gibbs energy of mixing in the binary mixtures of tri-n-butyl phosphate in nonpolar solvents using dielectric probe

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1 Indian Jownal of Pure & Applied Physi.:s Vol. 37, February 1999, pp , Evaluation of excess Gibbs energy of mixing in the binary mixtures of tri-n-butyl phosphate in nonpolar solvents using dielectric probe S K Ray, B Mohanty, S Tripathy* & G S Roy P G Department of Physics, Ravenshaw College, Cuttack *B J F3 College, Bhubaneswar Received 9 September 1998; accepted 21 December 1998 Excess Gibbs energy of mixing has been evaluated in the binary mi xtures of tri-n-butyl phosphate(tbp) in nonpolar solvents viz. benzene, carbon tetrachloride, p-xylene, n-heptane, cyclohexane and n-hexane. The (L'lGAIl)maxuna is in the order, benzene < carbontetrachloride < p-xylene < n-heptane < cyclohexape< n-hexane. TBP has maximum interaction in case of aromatic compound with benzene and least interaction with cycl)hexane. In the case of aliphati c compounds the interaction is highest in the mixture of TBP + CCI 4 and lowest in TBP +n-hexane.., 1 Introduction Thennodynamic functions like Gibbs energy, molar polarization, entropy and enthalpy are used by many workers I S in investigating the orientation of molecular dipoles in binary and ternary mixture in polar-polar and polar-nonpolar liquids Kolling 6, Payne and Theordou 7 have suggested that the excess functions are more useful than the thennodynamics functions in interpreting the molecular interaction in such binary mixtures. Here we have utilised the concept of mixibility in the binary mixture The mixibi lity between the two liquids in a mixture is maximum when the molecular interaction between them IS more. So the excess Gibbs energy of mixing can be defined as the deviation of Gibbs energy of mixmg of a real mixture from that of ideal mixturc. If the interaction between the t\\"o liquids in a rea l mixture is less, mixibility is less. the deviation from ideal mixture IS more hence the excess Gibbs energy of ml.'(i ng of the system is more R So \\"e have considered the excess the rnlodyn;llnics funct ions like the excess Gibbs energy of mixing for ll1terpreting the nature of. interaction in the binary mixture of polar and nonpolar liquids The equation fo r excess Gibbs energy of mixmg deri ved by us has the no\ elty of separately estimating the excess Gibbs energy due to the 1l1tcraction bet\\"een polar-polar molecules (.6G llr ). polar-induced nonpolar molecules (.6G AB ) and induced nonpolar-induced nonpolar molecules (.6G AA ) in the binary mixture where A and B correspond to nonpolar and polar liquid respectively. Though Haske1l 9 has developed a method for estimation of excess Gibbs energy of mixing in the binary mixtures of polar and nonpolar liquids, it has the limitations of not taking into account the short range interaction between the ;molecules in the mixture. So we have made a comparative study of the results obtained using our proposed equation and Haskell's equation in the binary mixture of acetic acid+carbon tetrachloride and n butanol + carbon tetrachloride. It is found lo that the resu lts obtained from our proposed equation presents a better picture on the orientation of molecular dipoles in these binary mixtures. Further we have observed that molecular interaction in a bll1ary mixture can be explained \-\ ith the help of.0.c;,'\13 (excess Gibbs energy of mixing due to interaction between polar and nonpolar molecules) m a better \\ ay than that of.0.gtotal..0.c. I13 and.0.c BIJ (Ref. II ) I.0.ClOtal= total excess Gibbs energy of mixmg,.0.g",;,.= excess Gibbs energy of mi:xing due to interaction bet\\"een induced nonpolar molecules in the mixture and.0.gf)u=excess Gibbs energy of mixing due to interaction bet \\cen polar molecules 111 the mi xtu rcl Here \\ e havc selected TBP as a polar liquid

2 128 INDIAN J PURE APPL PHYS. VOL 37, FEBRUARY 1999 in view of its utility as an important commercial extractant in the atomic energy industry for separation of plutonium and uranium from fission-products and other nuclides 12 2 Theory Kirkwood l3 correlation factor g is a shape dependent correlation function that takes into account the short range interactions between the neighbouring molecules. The value of g is greater than unity in case of associated liquid and is less than unity for nonassociated liquid l4 The reason for the difference in the value of g for the two categories of liquids is attributed to the fact that the molecular dipoles in the first category have parallel orientation (a - multimers) resulting in reinforcement of angular correlation, whereas the molecular dipoles in the second category have anti parallel orientation (p - multimer) which results in destruction of angular correlation. The expression for Kirkwood correlation factor in the binary mixture of polar and nonpolar liquids is. b 13 given y ( 2[; +& )2 m oob where A refers to nonpolar liquid and B refers to polar liquid; V",, Vn and V d"note the molar volume of nonpolar liquid, polar liquid and mixture respectively; EA and Em represent the dielectric constant of the nonpolar liquid and mixture respectively; Eoco is the square of the refractive index of the polar liquid; /lgj3 is the gas phase dipole moment of the polar liquid; N is the Avogadro constant; k is Boltzmann constant; Eo is the vacuum permittivity and T is the tcmperature in Kelvin. From the above expression, we have observed that gm increases as the mole fmction of the polar solute decreas'es in the solution. Tripathy et ar IS while studying the dielectric properties of alcohols and amines in extremely dilute solutions, have shown that gm increases in case of alcohols and decreases In case of amines as the mole fraction of polar solute decreases in the solution. Later, Roy et ar 16 have also observed that gm increases in the binary mixtures of TBP + tetrachloromethane, TBP+ n-hexane, TBP+n-heptane, TBP+ benzene and decreases in TBP + p-xylene, TBP+carbon disulphide, TBP+cyclohexane when the mole fraction of polar solute decreases in the solution. Thus the evaluation of gm does not properly reflect the nature of molecular interaction in these binary mixtures. It is reported l7 that when a binary mixture is formed, the expected properties such as thermodynamic parameter, dielectric properties and refractive index do not vary linearly. So the deviation of these parameters from the linear behaviour tenned as excess parameters is considered to be very important to study the nature of cluster formation (ie orientation of molecular dipoles) in the mixtures 6. 7 So we have defined a new parameter 8g, excess correlation factor utilizi ng the concept of Davis and Douheret 18.(2) In the binary mixture of polar and nonpolar liquids, the nonpolar molecules are slightly polarized So the effective dipole moment as well as the gas phase dipole moment of nonpolar liquid is negligibly small. Using the definition of correlation factor by Kirkwood and Osterl 9, the correlation factor g AA for the nonpolar liquid in the environment of polar liquid can be written as 2 f.1. eji 1 gm= I 1m -- = I4l ~o,2 ""'g where /-left is the effective dipole moment and I4l is the gas phase dipole moment So the nonpolar molecules in the environment of polar liquids 20 lack of correlation because of \vhich the correlation factor is one. Combining Eqs (2 ) and (3). the expression for the excess correlation factor can be written as Evaluation of excess Gibbs energy of mixing IS also an important method m the interpretation of liquid structure. Though theoretical treatment suggested by (3) (4)

3 RAY e/ ar. GIBBS ENERGY OF BINARY MIXTURES 129 Longuet-Higgins 23 is found useful in the interpretation of liquid structure involving weak interactions, yet it has its own limitations of not being applicable to hydrogen-bonded system. The reason for this may be attributed to the indistinguishability of the long range from short range forces. So the experimental measurement of excess Gibbs energy of mixing based on the evaluation of dielectric constant and other parameters is found more useful for this purpose. Winkelmann and Quitzsch 24 have extended their dielectric theory to estimate the excess Gibbs energy of mixing of binary mixture of polar liquids separately due to interactions between similar molecules and dissimilar molecules. From Winkelmann and Quitzsh (WQ) expression for the binary mixture of polar liquids, Swain and Roy2 have developed an equation for excess Gibbs energy of mixing for the binary mixture of polar and nonpolar liquids which can be written as t..gwq =- :(UjIJ- U;J )[ X IJ ~!/J ({ X H ( ~ Bn- l) + I} The expression in the curly bracket of Eq. (5) on simpli fication reduces to g,ucai (Ref 21,25) Hence the expression for dipolar excess Gibbs energy of mixing refers to an ideal condition only, which is revealed from the experimental observations".4 as (t..g W Q)maxlma occurs at equimolar concentrations Hence we have substituted 8g in place of g llu in Eq(5) and the expression for excess Gibbs energy of mixing bcc0i11cs X. 2 :\::() MiAI! =- ~ (R jlj- R;3 )[ X IJ ~!B ({ X n(t..g - 1) + 1 }] The terms in the curly bracket on expansion becomes X11gm+X ",\-X"ngllll(Ref 25) Thus Eq. (6) can be expressed as (5) (6) (7) t..g BB = - ~ (RjB - R~ )( X ~ gbb ~ ~B ) t..g!v\, t..g nn, t..g Al3 denote the excess Gibbs energy of mixing due to the interaction between induced nonpolar- induced nonpolar molecules, polarpolar molecules, polar-1i1duced nonpolar molecules in the binary mixture of polar and nonpolar liquids. The negative sign of t..g!v\ in Eq.(7)indicates that excess Gibbs energy of mixing is due to the interaction between the induced nonpolar molecules in the environment of polar molecules in the solution I I 3 Experimental Details The dielectric constant measurements were carried out with a wavemeter-oscillator combination at 455 khz (Ref 14) at K The set up )Vas standardised with liquids of kno\\ti dielectric constant and the reproducibility of dielectric constant measurement at r.f range was ± which has been obtained by comparing literature data 27 The cell temperature was controlled with an electronically regulated thermostatic arrangement with temperature variation of ±O I K The refractive indices were measured at the regulated temperature with Pulfrich refractometer at sodium-d line. The chemicals used were of analytical reagent grade purified by standard procedure 28 and re-distilled before use (purity> 99.5 mass %)The reproducibility of the refractive index was ± The density measurement was done by a semi-microbalance with pyknometer of 25ml capacity placed in a separate thermometric bath precise up to ± 0.0 I K. The accuracy of measurement of density in this case was ± 2 x I 0 5g cm 3 4 Result and Discussion The experimental data of Ern, Eoom, gm, 8g, t..g w Q and t..g i\1l have been presented in Table I and variation of t..gi\b with the mole fraction of TBP at K has been displayed in Fig I. Here we have mj.de a comparative study between the results of the correlation. factor (gm ) and excess Gibbs energy of mixing (t..g w Q) obtained by Dash el a/ 3 with the results of excess correlation factor (8g) and t..g,'\b using

4 130 INDIAN J PURE APPL PHYS. VOL 37, FEBRUARY 1999 our proposed model (Eqs 4 and 6) in the binary mixtures of polar and nonpolar liquids. We have used the value of Em, Eoom' molar volume obtained from our experiment to evaluate 8g and t.g AIl W e have observed in Table I, the value gm increases with the increase of X B and gm approaches the value of correlation factor of pure polar liquid when X Il X B approaches unity Thus the variation of gm does not depict the actual picture of cluster fonnatlon of molecular dipoles in the binary mixtures. But the excess correlation factor changes its sign with the increase of mole fraction of polar solute which indicates the conversion of p-multimers (antiparallcl orientation of molecular dipoles) to ex-mu ltimers (parallel orientation of molecular dipoles). Here (t.gwq.)ma)(j ma occurs nearl y at cquimolar concentration, which reflects the nature of an ideal condition as discussed in theory. But t.gail depicts the nature of molecular aggregation in the binary mixture of polar and nonpolar liquids due to the interaction between polar with induced nonpolar molecules. Hence we have undertaken to evaluate 8g and t.g AIl using our proposed equation to study the molecular interaction in the binary mixtures of polar and nonpolar liquids. 'T 0 E..., (l) <.;) <l SO 30 10, '3 CYCLOHEXANE en-hexi\ne o n-heptane 6 C C Ll.! D-XYLENE BENZE NE (t.g AB )maxlma IS 111 the order earbontetrachloride < p-xylene evclohexane < n-hexane. of benzene < n-heptane TBP is a mildly associated liquid (g= \3) indicating the predominance of ex-multimers with parallel orientation of molecular dipoles. It IS observed 16 that TBP molecules can remain either 111 head tail IFig. 2(a) J or wood pile r(fig 2(b) Jarrangement The fonner results in forn1ation of ex - multimers and the latter favours the fonnation of p multimers When a sma ll amount of TBP is added to nonpolar solvents, there is a gradual conversion of ex - multimers to p- multimers which reduces the internal energy of the rr.ixture. Consequently, excess Gibbs energy of mixing (t.g,\il) increases. This process continues till the structure of TBP transfonns from head tail to wood pile structure in the solution In this process the voids of the nonpolar solvents are almost filled up by TBP molecules so that there is no furt her disorder in TBP molecules Excess TBP. because of its associated character. res ults in head-tail arrangement of its o\\n molecule i.e more number of ex-m ultimers are created for which excess Gibbs energy of mixing (t.g AIl ) decreases 2 (0) Wood - pile arrangement -p /"'" < < XB Fi g. 1- Variation of,\ GAil with mole Iraction oftijp ill non polar solvent at K 2 (b) Heacl- tail arrangement Fig. 2- I lead-tail and wood-pile arrangement of TIJI' molecules We have observed in Fig I that in a ll the binary mixtures, the excess Gibbs energy of mixing first increases. attall1s a maxima and thereafter decrease to zero when the mole fraction of solu te approaches unity. The liquids selected arc nonpolar aprotic (benzene. CCI 4, p-xylene, cyclohexane, dioxane, n -heptane) and polar aprotic (TBP). Therefore the interaction ir. the

5 RA Y elol. GIBBS ENERGY OF BINARY MIXTURES 131 Table I - Yanation of I\g,UIJ [\GAIl oftl31' In Nonpo lar solvents at K XII r.m [ 'LoIn gm I\g TBP + bcn/cnc t'i(jw (2 J/lllOI G,\uJhnol Oll-l 24% () II O ~ <1 U.82 - U () o I X 1 XliS 2211 U () 25 OR I US - U () () I U U ~ U.06 BP + n-hcxanc U I I I U3 1 9U4 I U2 - U.UI U (, I 2U I 93U I I 107.U I 944 I 2U I I I I U TBP + CCI4 5U D I II U 1.21 U U I U X5 I U (, o U6 IUU U h P + n-hcptanc D IHO JO I n )- -D02 BP + p-xy lcnc l OM a IS ,f aa -D D (J J (,() J.OR X D X I+~... J.06 P + cyclohcxanc J D > Ul U J ) D U U.99 -D () ).14 17()

6 132 INDIAN] PURE APPL PHYS VOL 37, FEBRUARY 1999 binary mixture of such polar and nonpolar liquids is due to induction effect i.e. when a nonpolar solvent is added to a polar liquid, the possibility of polar solute inducing the polar effect in the nonpolar liquid thereby opens the channel of interaction between the two liquids. The strength of interaction depends upon the extent of induction of the nonpolar liquid by the polar liquid. Therefore we consider t.g,\b as available parameter for studying the molecular interaction in such binary mixtures. In the case of TBP + benzene binary mixture, TBP bemg a polar aprotic liquid induces certain amount of polarization in the benzene molecule which helps, interaction bet\\ een the positive end of TBP molecule with the induced negative end of benzene molecule or vice versa The relatively less interaction in the case of p-xylene + TBP mixture is probably due to steric hindrance offered by C CH3) group of the p-xylene. The negligible interaction in case of cyclohexane + TBP mixture is probably due to the absence of 1t-electron cloud in cyclohexane. In its absence, it is difficult on the part of TBP molecule to induce polarity in cyclohexane. The interaction in case of TBP + carbontetrachloride binary mixture is probably due to interaction between phosphoryl group of TBP with C1'5. of CCl 4.The small interaction in n hexane + TBP and n-heptane + TBP is due to the fact that TBP fails to induce reasonable polarity in such nonpolar liquid due to its long chain structure. In view of this, our proposition of the expression of excess Gibbs energy of mixing (t.g AB ) between polar and induced nonpolar molecules reflects the molecular interaction in a better way than that obtained through modified Winkelmann and Quitzsch equation (Eq. 5); Haskell 's equation lo and thus merits consideration. References Brandstadt E, George U & Kolbe A, J Mol Liq. 31 (1985) Swain B B & Roy G S, Jpn J Appl Phys. 25 (1 986) Dash S K, Chakrabarty V & Swain B 13, A-C-H Model Ch ern, 131 ( 1994) Tripathy S & Swain 13 B, Chern Papers, 45 ( 199 I ) Garabadu K& Swain B B, Phy s Chern Liq, 31 ( 1996) Kolling 0 W, Allal Chern, 59 (1987) Payne R & Theodorou J, J Phys Ch ern, 76 ( 1972) Ray S K & Roy G S, J fndianfnst Sci. 72 ( 1992) 487., 9 Haskell R W,.J Phys Chern, 73 ( 1969) Ray S K & Roy G S, Phys Chern Liq, 31 ( 1996) I I Ray S K & Roy G S, A-C-H Model Chern, 133 ( 1996) Naylor A & Eccles H, fnl Solvenl Ext Conf (Moscow). ( 1988) 3 I. 13 KirkwoodJG, J ChernPhys, 1(1939) Swain B B, Acla Chirn Hung, 117 (1984 ) Tripathy S, Dash S K, Garabadu K, el al. J Mol Liq. 55 ( 1993) Roy G S, Dash S K, Das J K, e/ al. Bol Soc Chil Quirn. 40 ( 1995) Subramanian \1, Bellubi B S & Sobhanadri S S, Pramana- J Phys,41 (1993)9. 18 Davis M I & Douheret G, Thermochim Acla. 104 ( 1986) Oster G & Kirkwood J G, J Chern Phys, II ( 194 3) Dumnuf D A & Miller W ]-1, Mol Ltq C,ySI, 60 (1980) 28 I. 21 Ray S K, Roy G S & Tripathy S, Cflem Papers, 50 (1 996) Ray S K, Tripathy S, Misra G S P & Roy G S, J Pure & Appl Phys, 5 (1993) Longuet-Higgins H C, Proc R Soc A, 205 ( 195 I) Winkelmalill J & Quitzsch K, Z Phy s Chem (Leipzig). 257 (1976) Ray S K, Roy G S & Tripathy S, Asian'! Phys, 3 (1994) Ray S K & Roy G S, Phys Chern Liq, 3 I (1996) Handbook of chemislry alld physics, CRC Press, Inc., Ohio, 60th Edition, ] Weissberger A, Technique of organic chemistry (Inter Science, New York), 7, 1955.