Alex Bonllla and Basil Vassos University of Puerto Rico ~ i ~ ~ i s d r00931 as.
II
A Novel Approach for Dipole Moment Laboratory Experiments A physical chemistry laboratory experiment
The determination of the dipole moment of polar molecules in solution has been a standard experiment in many physical chemistry laboratories, and is described in many laboratory texts.'.Z The experiment can be done by bridge methods or by beterodyne-beat approach.3 In both cases the cost of equipment used, while relatively large, was not considered as an important factor. Nowdays however, due to inflation and Department budget cuts this is not so any more. We propose a method of direct counting which has the advantage of low cost, simplicity, and precision; moreover its functioning is more easily understood by the students than that of the classical approach. Method
The experimental procedure and tbe sample used are the same as described in the Garland and Shoemaker text.' The basic difference between the standard technique and the proposed lies in the electronic equipment. Instead of the heterodyne beat-frequency oscillator system, we have designed and constructed the simpler one given in Fieure 1. The basic circuit is a one-transistor oscillator. The frequency of oscillation (I)is determined hy rhe total capacitance C?., formed by the cell, C , and the parasitic capacitance (",due to the leads, etc. The frequency of oscillation depends also on the inductance, L , of the coil by the relation f = 1/(2*V'm)
(1)
where (2) Cr=C+C' The cell was constructed followingthe Garland and Shoemaker design.' We used two different variable air capacitors, one of 200 pf and the other of 400 pf, both with about 14 pf residual capacitance when open. The transformer is a Heath unit from the Malmstadt-Enke electronics (No. 40-78); but most any R F transformer will do. The inductance of the transformer used was around 0.6 mH. An IN3904 transistor was used, but most any transistor can be used. The entire circuit was powered by a low price ($51) power
'Shoemaker, D. P., and Garland, C. W., "Experiments in Physical Chemistry," 2nd. Ed., MeGraw-Hill Book Co., New York, 1967, pp. 295-303. ZDaniels,F., et al., "Experimental Physical Chemistry," 7th. Ed., McCraw-Hill Book Co., New York, 1970, pp. 203-230. "hien, J. Y., J. CHEM. EDUC., 24,494 (1947).
130 1 Journal of ChemicalEducation
k
COUNTER
A Figure 1. Schematic of circuit used in dielectric constant experiment
supply of 15 V. We used a model902 of Analog Devices (P.O. Box 280, Norwood, Mass., 02062). The counter is a low cost Heathkit unit, type IB-1101. The unit can be bought already assembled or in kit form. The most inexpensive way ($290) is to buy i t in kit form and have a talented student assemble the unit. The counter offers a sensitivity of 50 mV rms and a frequency range of 1Hz to 100 MHz. Our frequency measurements were in the range of 0.6-1.2 MHz and the counter provided an accuracy of 0.001 MHz (4.1%). he circuit is constructed on a small vedorboard sheet (4% X 3% in.) inside a metal minibox (5 X 4 X 3 in.). he metal box served as an electrostatic shield and protective housing. All leads were made of RG-59 coaxial cable. The power supply was mounted on another metal box (6% X 5 X 2 in.). The cost of boxes, transistor, transformer, capacitors, resistances, and cable is a moderate $30, giving a total amount of about $370 for the entire electronic set-up.
Procedure The liquid sample is introduced in the cell, making sure that there are no air bubbles between the plates of the capacitor which is set fully open. When the sample reaches a constant temperature, the power supply is turned on and the circuit begins to oscillate. By eqn. (1) the frequency of oscillation can he expressed as (3) f = k/(v'G) where k is a constant for a given circuit. A frequency reading (fop,.) is taken at this open position, and then the cell is fully closed and another frequency reading is taken ( f , l d ) . The capacitance contributed by the cell only, C, is obtained for the difference between the open and closed capacitances since the parasitic capacitance, C', in taking this difference cancels out; thus
Figure 2. Dielectric mnhtant variation wkh mole fraction of chlorobenzene.
c = k2((1/f2.io8.d)- (l/pown)l (4) Clearly, C, depends on the dielectric constant of the medium (4 between the plates by C = (constant) < (5) where the constant depends on the geometry of the capacitor. To eliminate the two unknown conatants in eqns. (3) and (4), a pair of measurements are taken with air as the cell meSince the dium. These readings are (f,,,,),i, and (fdd).i,. dielectric constant of air can he taken as unity, it follows that the dielectric constant of the sample is given by
6
=
kz1 1
~
1
11
-
d
~
(6)
IEEi - K " I d r Experimental Resuns and Discussion Dielectric constants of chlorohenzene and orthodichlorohenzene solutions in benzene were measured in our physical chemistry lahoratory by using the described method. Tables 1and 2 show the experimental frequency measurements and dielectric constant calculated using eqn. (6). Figures 2 and 3 show the linear behavior of the dielectric constant ( r ) as a function of composition. Density measurements of these solutions were made following the Drocedure of Garland and Shoemaker' and usine our dielectiic constant data the dipole moments of chlor; henzene and orthodichlorohenzene were determined. For Table 1.
Dielectric Constant of Clorobenrens in Benzene st 25 OC Frequency (MHz)
Molar Fraction Xr.u.rl
7
Air (own)
Table 2.
Air (closed)
Sample (own)
Frequency (MHz)
Fraction
XC,H,CI,
Sample (closed)
~ielectric Constant
k)
k0.01
Dielectric Constant of Orthodichlorobenzene in Benzene at 25 "C
Molar Air (open)
Air (closed)
Sample (open)
Flgure 3. Dielectric wnstant variation with mole fraction of arihodichloroben-
zme.
.
Sample (closed)
DielectriC Constant
id
i 0.01
chlorohenzene, the dipole moment ohtained was 1.61 i 0.05 D and for orthodichlorohenzene 2.30 f 0.03 D. These values are in excellent agreement with the literature reported values. Acce~tedex~erimentald i ~ o l moments e rnnae from 1.5.5-1.60 D fo; chlorobenzene a n d i . 2 ~ 2 . 3 2D for okhodichlorohen~ene.~ I t is interesting also to compare the dielectric constants ohtained for pure henzene at 25'C. The dielectric constant of 2.29 was ohtained from highly purified benzene (Table 2). In contrast, for henzene dried only for 30 min with molecular sieve (8-12 mesh beads) the dielectric constant was 2.33 (Table 1). The latter result is perhaps more representative of teaching lahoratory conditions. The accepted c for henzene is 2.28, an excellent a g ~ e e m e n t . ~ The data on orthodichlorohenzene were taken with a 400-~f cell. It has been found that if theconductivity of thesolution is relativelv laree. the cirruit s t o ~ o e doscillatine in rhe fullv closed positionv(a limitation of the very simpc electronic; used). Thus for chlorohenzene a 200-~fcell was used. This is the recommended value for general use in these experiments. A too small variahle capacitor will diminish suhstantiallg the precision of the dielectric mnstnnt measurements. In conclusion, the simple circuit described makes the experiment simpler to perfnorm,faster, and with better accuracy. Moreover, i t proves to he economically attractive. Acknowledament The authors wish to thank Dr. Rafael Arce for helpful discussions and comments, to Ms. Ana Maria Pic6 for some of the measurements, to Mr. Raal Mdrquez for assembling the frequency counter kit, and to Mr. Humberto Luao for the compute; program used to calculate dipole moments. 'McCleUan, A. L., "Tables of Experimental Dipole Moments," W. H. Freeman and Ca., San Francisco, 1963. 5Handbook of Chemistry and Physics," Edited by the Chemical Rubber Co., 49th Ed. Volume 54, Number 2 February 1977 1 I31
