Prakash, Jai

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Indian J. Phya. 49, 84-86 (1976)On the evalution of dipole moment using Guggenheim'smethodJ a i  P k ak ashDepartment of Physics, University of Gorakhpur, Gorakhpur 273001 (Received 25 June 1974, revised 18 September 1974)Ouggouhoim’s method for the determination of dipole moment of a polar solute in a nonpolar solvent is widely \ised because it avoids the measurement of density of different dilute solutions. In the present note it has been shown that formula for Guggenheim’s method can also be derived from Debye equation on tine assumption that the dielectric constant of the solvent is equal to the square of its refrac­tive index.L  I n t ro du ctio nThe determination of dipolemoment of a polar solute in a nonpolar solvent through dielectric measurements gives a value in close agreement with the gaseous value. It is simply because of the fact that in siich a situation, the system is in a quasi "isolated state and the polar molecules arc well separated from each other such that the dipole-dipole interaction forces are absent. Various methods (Dobye 1929, Halvorstadt & Kumler 1942, Higasi 1943, Guggenheim 1949, Smith 1950, Guggenheim 1951) have been proposed for determining the dipole moment of a polar solute in a nonpolai* solvent. The method suggested by Guggenlieim (1951) is widely used (Murty 1957, Purcell & Singer 1965) because it avoids the measurement of density of different dilute solutions. However, it has recently boon shown by Bock k  Iwacha (1968) that for solute molecules, having a low dipolemoment value, Guggenheim’s method does not give rea,sonable results. Further, using partial quantity to dielectric polarization, Palit (1952) has estab­lished, that Guggenheim’s method is a special case of the more general Palit’s method. This discrepancy may be due to the fact that the Guggenheim’s method is derivable from Debye equation which is valid only for very dilute polar non­polar mixtures. The purpose of the present note is to show that the formula used in the Guggenheim’s method can be derived from the Debye equation under the assumption that the dielectric constant of the solvent is equal to the square of its refractive index.84UvaluaHdm of dipole moment 852 . M e t h o d  o f  C alotjlatiokThe dielectric behaviour of a polar solute in a nonpolar solvent can very well be represented with the help of Debye^s relation (Debye 1929) as(1)€oi8+2 w*Dia+2 “^  9*;T ’Avhere €q is the static dielectric constant, nj) is the refractive index measured at n frequency off from the dielectric dispersion region, n is the number of solute molecules per c.c., and fi is its dipolemoment. Suffix 12  represents the solution. The above expression can be rearranged as^  ^  21 MJcT . . .  (2)0^12 — ^ *D12(®012 ^ 2 )111 eq. (2), d is the density, is the weight fraction of the solute molecule and is its molecular weight. Eq, (2) could be used for determining the value of II if density of different dilute solutions are measured. Such measurements of density are avoided if wc use very dilute solutions as shown in the following jiaragraphs.I t can be seen that for infinitely dilute solution i.e., when 0 eq. (2)reduces to2 ' W»2"*^ 0 27 MJcT... (3)whore suffix 1 stands to represent the solvent. Eq. (3) is an equation of a straight liu(^  provided the measiu'ements are done at a fixed temperature. I t  suggests, therefore, that when X  is plotted against for different dilute solutions, it will I'ORult into a straight line, the slope of which at gives the value of //-.However, it has been pointed out by LeFevre (1950) that smoothing should be performed directly on the measured quantities such as €012 rather thanou any derived parameter. The value of X in terms of and will be( - )V dw, I =  f“'2—^0 L (6p i+ 2)*f dcpig \[ dW2 } 102—^02nDiTn^jy[+2)^^]. ... (4)\ OW2 /W2-4oJIf we assume at this stage that for solvent the static dielectric constant is equal square of its refractive index i.e., Cpj =  n^Dv combined with eq,(3) can be 'written as\ Debye ) ■ = 'N 4wH i(eoi+2)* • ( - )'2 / tt»2*->0 ... (5)86 Jai Prakashwhere\W2f Wi^o L \ OW2  I W2-^ 0 \ OW2  / tPa—>0 JThus the value of fi can be evaluated ^vith the help of eq. (5). I t  can be remarked hero that tho use of modified form of Debye equation avoids the measurement of density of different dilute solutions and needs only the density of solvent at experimental temperature. Eq. (5) is evidently representing the Guggenheim's equation manifesting tho fact that Guggenheim’s method can be derived from Debye equation following the assumption e(,i =A ck no w ledg m entThe author is thankful to Professor Nitish K. Sanyal for encouragements and to Professor S. Chandra for helpful discussions.R e f e r e n c e sBook E. & Iwaoha D. 1968 Canada J. Chem. 46, 523.Debye P. 1929 Polar Moleculea, Chemical Catalog Co. Inc., Now York, Guggenhoim E. A. 1949 Trnna. Farad. Soc. 45, 714.Guggonhoim E. A. 1951 Trans. Farad. Soc. 47, 573.Halveratadt I. F. & Kumlor W. D. 1942 J. Ayn. CJmm. Soc. 47, 2988. Higaai K. 1943 Bull. Inst. Phys. Ghem. Eos. Tokyo 22, 806.LeFovre R. J. W. 1950 Trans. Farad Soc. 46, 1.Murty C. R. K. 1957 Ind. J. Phys. 31, 266.Polit S. R. 1952 J. Am. Chom. Soc. 74, 3952.Purcell W. P. & Singer J. A. 1965 J. Phys. Ghcm. 69, 4097.Smith J. W. 1960 Trans. Farad. Soc. 46, 394.

On the Evalution of Dipole Moment using Guggenheim's Method

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On the Evalution of Dipole Moment using Guggenheim's Method

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