Study of Conformational Equilibria by Dipole Moment ~easurements A Source of Experiments in Physical Organic Chemistry JoZo P. Conde and Joaquim J. Mwra-Ramos Departamento de Engenharia Qufmica, S e c ~ i de o Quimica-Fisica e Termodinhica, lnstituto Superior Tecnico, 1000 Lisboa, Portugal The determination of molecular dipole moments provides valuable information about the structure of molecules and has been used to determine rigid structures and to study problems such as rotational isomerism and conformational equilibria (1, 2). This method was one of the first nsed to study the internal rotation and to establish the existence of rotational isomerism. The study of these dynamic processes has pedagogic importance since it enables the understanding of one physical method which can be applied to other chemical prohlems which might involve concepts of organic, inorganic, and physical chemistry or chemical thermodynamics. The study of the rotational isomerism in snccinonitrile by dipole moment measurements (3)may be cited as an example of this kind of work. In this paper we discuss some problems related to the study of conformational equilibria by dipole moment measurements, and we illustrate with the conformational equilibrium of trans-1,2-dihromocyclohexane.The purpose of this experiment is to demonstrate the interdependence of the various areas of chemistry, and it may be used in undergraduate chemistry courses with different objectives, namely: 1) to determine the equilibrium constant and AG*, the standard Gihbs energy for the equilibrium, and to nnderstand the physical significance of the thermodynamic standard states; 2) to analyze the solvent effect on the eqnilibrinm. Although the necessary background knowledge on stereochemistry and conformational analvsis is eenerallv ..~rovided in the hisic organic chemistry couises, tge reading of some introductory texts on the subject ( 4 ) can be advantageous to the students. The method we use to estimate the dipole moments (5)is somewhat different from that currently used and it has certain advantages: 1) it only requires the determination of the dielectric constants of the solutions; 2) it allows the determination of the dipole moment from the Debye and from the Onsager equation using the same experimental data, 3) it gives the student a better appreciation of the theoretical models that are directly involved in the simple method described below. The exprrlmrnt requires mly a bur-hour period and has t n m succ~essfullvverf~mnedat the Phvsi~alChrm~strv[.ahoratory of the ~ n i i i t u t oSuperior ~ 6 c n i c o(University b f ~ i s bon). The Determination of the Dipole Moment The methods commonly nsed for the determination of the dipole moment of a polar molecule in an apolar solvent are based on the Debye theory of dielectrics (6, 7). This is the case with the most current methods of Halverstadt-Knmler (8) and of Guggenheim (9). As pointed out by Onsager (lo), the Dehye theory makes an incorrect treatment of the internal field and, as a consequence, leads to dipole moments which are solvent dependent, even in the case of rigid molecules (5).Both the Dehye and the Onsager theories are based
on the fundamental equation for the study of the dielectric properties of liquid mixtures (11): r - l -
-E =
4s
x
Nj[njEi
;
+A EdJ] 3kT
(1)
where k is the Boltzmmn constant. T the al~solutrtemperature. E thc rlecrric field strength, r the dielectriccnnstant or permittivity of the mixture, N the number of particles per unit ofyolume, ol the scalar polarizahility, fi the dipole moment, Ei the internal field, Ed the directing field, and the index j refers to the jth kind of particle. Equation 1 is valid in the linear domain where the polarization is proportional to the field and is a result of the basic electrostatic relationship, where D is the electric displacement and P is the total polarization. The right-hand side of eq 1 is thus the sum of induced polarization (first term) and orientation polarization (second term). The difference between the Dehye and the Onsager theories of dielectrics lies with the definitions of the internal field (Ei) and of the directing field (Ed). The Debye Theory According to Debye theory, Ed is identified with Ei and made equal to the so-called Lorentz field EL (the field in a virtual spherical cavity), defined as
Replacing Ei and Ed by ELin eq 1we obtain
which is the Dehye equation. For a mixture containing only apolar components (fij = 01, eq 2 takes the form 6-1 -=-
