Robert D. Rapp Albright College Reading, Pennsylvania I9604 and James E. Sturm Lehigh University Bethlehem, Pennsylvania 18015
Dipole Moments A physical-organic experiment
M a n y experiments in undergraduate chemistry courses tend to be restricted to a narrow area of chemistry and fail to demonstrate adequately the interdependence of the various disciplines of chemistry. To impart a good general understanding of the fundamentals of the major areas of chemistry is the object of undergraduate training in chemistry. This objective may be greatly fostered by means of experiments which cross traditional educational lines. I n consideration of these aims, an experiment involving dipole moment measurements was designed for the physical chemistry laboratory. Dipole moment measurements are well suited to demonstrate the application of physical methods to the solution of organic structural problems. Modern applications of this parameter are to be found in both inorganic (I) and organic (2,s)areas. A critical discussion of the determination and types of instrumentation has recently appeared (4). The experiment described here applies dipole moment measurements to a study of the conformation 2-chlorocyclohexanone. This study should make an otherwise abstract concept in organic chemistry a reality while generating a degree of proficiency in physical instrumentation. 2-Chlorocyclohexanonc primarily exists in two chair conformers, one in which the halogen is axial and the other in which the halogen is equatorial. The conversion of one conformer to the other may be readily visualized from framework models. I t is the equilibrium existing between these conformers at 25' which is to be investigated. If the dipole moment of pure conformer I is different from that of pure conformer 11, the dipole moment of an equilibrium mixture will be somewhere between the two extremes depending upon the composition of the mixture. As part of this experiment, the student will be required to estimate the dipole moment of the equatorial and axial conformers by a series of calculations. These calculations consist of the vector addition of the bond moments for each conformer. This portion of the experiment will illustrate the vector nature of the dipole moment and also establish the concept of conformers. The meaning of equatorial and axial substituents in a chair form of the cyclohexane ring will also be clearly established. Calculations
For the purposes of the calculations, the molecule may be placed on a Cartesian coordinate system and the bond moments resolved into x, y, and z components. These components are addcd and the new rc-
sultaut corresponding to the molecular moment calculated. I n the estimation of such moments, only bonds having significant moments are considered. I n 2-chlorocyclohexanone, these bonds are the carbony1 and the carbon-chlorine bond. The small moments associated with the carbon-hydrogen bonds are assumed to cancel as is usually done in such calculations (5). The geometry of the molecule is used to obtain the direction of the individual bond moments under consideration. The method of calculation will be illustrated for the equatorial conformer. This method although somewhat cumbersome for relatively simple molecules is readily adopted to the machine calculation of atomic coordinates in more complex systems. The justification for this more tedious procedure is greater general applicability.' The axial conformer can be calculated in a similar fashion. As part of the directions for the experiment, the one conformer moment may he calculated by way of illustration, and the student may be allowed to calculate the moment of the other conformer. The orientation of the molecule in the Cartesian coordinate system will be that shown in Figure 1 for the equatorial conformer. I n this coordinate system, the xy plane is defined by atoms 1, 5, and 6. I n order to arrive at the coordinates of the chlorine atom, the position of this atom will be described first in a coordinate system designated by a subscript 2 as in Figure 2. This system which simplifies the geometric calculations has the xz axis directed along the Cs-Ce bond and an ray, plane defined by Cn, Cs, and Ce with the origin at Cs. Normal tetrahedral geometry will be assumed with the exception of carbon six and it should he noted that the x2y2 plane bisectsLClCH. The geometric parameters needed in the subsequent calculations have been obtained from cyclohexanone (6) and chlorocyclohexane. The C1-C-H angle was assumed to be equal to the Cs-C,C1 angle and the dihedral angle was taken to he the normal dihedral angle. The C-C1 bond length was that used by Allinger, Freiburg, Czaja, and LeBel (7). These parameters are given below where d is bond distance in angstrom units and w is the dihedral angle about the CsCe bond. 0 = L ClCH = LCsCaCl = 109.5';
dc.c
=
1.54
' A reviewer has suggested a simpler approach in which the molecnle is viewed along the CrCa bond (Fig. 1). The bond moments for the earbonyl and C-CI bond each are resolved into two components, one along the C& bond and one perpendicular to the CrCs bond. The dipole moment of the moleculemay then be obtained by a vector addition of these four components.
Volume 46, Number 12, December 1969
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851
Figure 2.
Final coordinate system of the equatorial conformer.
Figure 1.
The coordinates of the equatorial chlorine atom then are given by the followingrelations zn= dc.ol cos (180-8)
=
1.76 (0.3338) = 0.588
z, = dc.cl sin 8/2 = 1.76 (0.8166) = 1.437 H ~h= (d2c.c,
- zr2- zlB)l/a=
(0.688)'h = -0.830
k
The proper sign for y2 may be obtained from a consideration of the coordinate system. It is possible by means of appropriate rotations and or translations to proceed from one coordinate system to another. The coordinates above are expressed in terms of a new system in which the x axis is still directed along the CsC6 bond but the xy plane is defined by C1, Cs, and Cs and the origin is at C6. This requires a rotation about the x2 axis through w and translation of the origin by do-c along the x axis. The transformation equations are below XI
y,
z,
- z l + dc-c = 0.588 + 1.58 = 2.128 = y* ms w + zz sin w = - 1.659 d = l/n sin w + z, cas w = -0.001 A
It only remains to rotate this coordinate system through 4 about the zl axis to obtain the system shown in Figure 1. Hence z = z,eos 4 y = y1 cos 4
z =
2, =
+ y, sin 4 = -0.303 - z1 sin 4 H
=
-2.681
A 1
-0.001
The coordinates of the oxygen atom, Cs,and Cs may be obtained in a straightforward manner upon examination of Figure 1. The C=O bond distance from cyclohexanone is l.24 A and the coordinates of Cr are calculated as below z
=
Z =
(-0.30
- 0.80) (2.18) =
-1,36
1.76
The resultant moment for the equatorial conformer then becomes The dipole moment of the axial conformer may be obtained in a similar fashion. The coordinates for the axial conformer are given in Table 2. Using the same bond moments as for the equatorial conformer, a dipole moment of 2.55 D is obtained. Experimental The actual experimental directions are given for a Kahlsico model DM-1 dipolemeter and may require some slight revision to accommodate a. different instrument. Weigh into five 50.00-rnl tared volumetric flasks itpproximately 2.0, 1.5, 1.0, 0.5, and 0.2 g of 2-chlamcyclohexanone. The weightsshould be known to 0.0001 g. Fill the flasks to the mark with dry (dried over calcium hydride), freshly distilled benzene and reweigh. From the data ) each sample. calculate the weight fraction of the solute ( w ~for Fill the cell of the dipolemeter with dry benzene and allow the cell temperature to reach equilibrium (15 min). Determine the null point using the D2 range on the instrument. Take five
Table 1.
Eauotorial Conformer Coordinates
sin 4 = -1.54 (0.853) = -1.314
The coordinates of the atoms under consideration for the equatorial conformer are summarized in Table, 1. The x, y, and z components of each bond moment now may be calculated from the coordinates of the atoms and the bond moment. The bond moment for the carbonyl group in cyclohexanone is 3.08 D (8) and the moment of the carbon-chlorine bond in chlorocyclohexane is 2.18 D (9). The carbonyl bond moment is directed along the negative x axis and hence bas no
/
y or z component. The components of the carbon chlorine bond moment may be obtained from the cosine of the angle between the component desired and the direction of the bond. The cosine of this angle is defined by the difference in the coordinates of Cr and the chlorine atom divided by the bond distance. The cosine multiplied by the bond moment yields the component. This is illustrated below
do-c cos 4 = 1.54 (0.522) = 0.805 k
y = -dc.c
852
Initial mordinats ryrtom d the equ&xiol conformer.
Journol of Chemical Education
Table 2. stom
Axial Conformer Coordinates
z (1)
v
(A)
z
(A,
oonseeutive null readings checking t,he zero point between each reading. After draining the solvent from the cell, dry the cell by drawing dry air through the cell. Determine the refractive index of the hensene (n,). Mix the samples prepared above and determine the null readings (&) on the dipolemeter and the refractive indices (nn) for each sample. Wash the cell with honsene and dry hetween samples. Five readings should be taken for each sample as described above. All the physical measurements should be made a t 25'. From a value of 2.2727 for the dielectric constant of benzene (8,) a t 25' and the change in dielectric constant per scale division (A&/As) calculate the dielectric constants of the samples me* sured. Plot na4 - n12versus weight fraction of sohtte and determine the slopeof the curve (a,). Plot 6,s - 6, versusweight fraction of the solute and determine the slope of the curve (as). Using a value for the density of henzene (dl) a t 25" of 0.87370 and 8. molecular weight of 132.59 for 2-ehloroevclohexanone, calculate the dipole moment of the compound fro& the relation below. The symbols have the following meaning
K = Boltzmann constant = 1.381 X lo-? erg degree-', T = absolute temperature, M1 = molecular weight of solute, and N = Avogadro's number = 6.023 X loa3mole-'. The treatment of experimental data, and calculation of the dipole moment is esseutidlv that of Gueeenheim (10). The value of 8, was that
benzene a t 25". Having the experimental dipole moment of 2-chlorocycloheuanolie and the calrulated moments of the axial and equatorial conformers, the mole fraction of each conformer in the equilibrium mixture a t 25" should be determined. The value observed is a root mean square of the conformer contributions as shown by the relation below (Id). The subscripts a and e refer to axial and equatorial conformers while N is the male fraction.
rr4
=
+ N.rreZ
NarroP
The students should obtain a value of 0.548 for the mole frac-
tion of the equatorial conformer. Using 2-chloro4-1-butylcyclohexanone, Allinger and coworkers (7) obtained experimental values of 3.17 D and 4.29 D for the equatorial and axial conformers, respectively. With these dipole moment values, the mole fractions are 0.556 for the axial ronformer and 0.444 for the equatorial conformer. Conclusion
Considering the differences between the reported dipole moment for the pure conformers and the calculated moments, the students should present a critical evaluation of the assumptions made in the calculation of the dipole moment,s of the pure conformers. The assumption which contributes most to the discrepancy is that the bond moments are the same for both conformers. This will he reflected not only in a change in bond moment but also in a slight change in bond length. Literature Cited
(1) TOYODA, K., A N D PERSON,W. B., J. Am. Chem. Soe., 88, 1629 (1966). I). D., A N D GILMAN, T. S., J . Am. Chem. Soe., 85, (2) TANNBR, 2892 (1963). (3) GILMAN, T. S., J . Am. Chem. Sac., 88, 1861 (1966). H. B., J . Chem. Educ., 43,66 (1966). (4) THOMPSON, (5) WILCOX,JR., C. F.,J. Am. Chem. Soc., 82,414 (1960). (6) BOWEN,H. J. M., A N D SUTTON,L. E., "Tables of Interatomic Distances in Molecules and Ions," The Chemical Society, London, 1958, M132s. L. A,, CZAJA,R. F., A N D (7) ALLINGIIR,N. L., FBKIBERG, LISBEL,N. A., J. Am. Chem. Sac., 82,5876 (1960). (8) MCCLI:LLAN,A. L., "Tables of Experimental Dipole iMoments," W. H. Freeman and Co., San Franoisco, Calif., 1963, p. 208. (9) ROGERS,M. T., A N D PANISH,M. B., J . Am. Chem. Soc., 77, 4230 (1955). E. A,, Twns. Faraday Soe., 45, 714 (1949). (10) GZTGGENHEIM, A. F., A N D ~LOSSINI, F. I)., J . Res. Nall. BZL.St., (11) FORZIATI, 43,473 (1949). N. L., ALLINGER, J., AND LEBEL,N. A,, J . Am. (12) ALLING~IR, Chem. Sac., 82,2926 (1960).
Volume
46, Number 7 2, December 7 969 / 853
