A Modified Resonance Apparatus for the Determination of Sielectric Constants Talna H. Chao Chemistry Board of Study, Division of Natural Sciences, SUNY Purchase, Purchase, NY 10577 This report describes a modified resonance apparatus used in our physical chemistry lab for the determination of dielectric constants of liquids. The standard resonance apparatus as described by Shoemaker et al.' uses a fixed-frequency oscillator and ;precision condenser, whereas in our setup a variable radio frequency (rf) signal generator and a digital frequency meter are used, and therefore the rf frequency instead of the capacitance of a condenser is varied in order to bring about resonance. Ours is aconvenient alternative to the standard apparatus. For each samnle. since the resonance freauencv is read from the frequerky meter, the capacitance caibe caiculated. At resonance. the followine eauation describes the relationship between' the capacitAce'(c, in Farads), the resonance frequency V, in Hertz) and the inductance (L, in Henries):
FREQUENCV METER
~.........-----.-....... RF FREQUENCV GENERATOR
The block diagram of the modified resonance apparatus. The dielectric constant 6 of a sample can be found by a measurement of the capacitance of a dielectric capacitor in the sample of interest (C I,) vs. air (Cab),since r = C,,./ C.i,. (The dielectric constant of air is 1.0005 a t 25 "C and 1 atm, which is very close to the value 1.0000 in vacuum.). Our apparatus consists of an oscilloscope (Tektronix 5103N). a variable-frequency low-output impedance (50 Q) rf signal generator ( ~ a v e t e k swee~/func&ongenerator Model 180), a digital frequency meter (Data Precision 57401, and a resonance-circuit. T h e rf signal generator also powers the resonance circuit, which consists of an induction coil L, a ~arallelcombination of canacitors-the sensine-canacitor of . ihe dielectric constant ceil (C,,a) and the coarse capacitor (C,.,.). The figure shows the hlock diagram of the apparatus. The dielectric constant cell consists of a radio variable capacitor (0 to 50 pF) fixed to a ceramic plate and follows the design of Shoemaker et al.' The oscilloscope is used for the detection of the voltage minimum across the sensing resistor (30 a) placed in series with the inductorlcapacitor (Ll C,,.,). At the voltage minimum, the resonance frequency is readfrom the digitai frequency meter. The capacitance of the cell in the liquid sample (C,u(liquid)) can be found a t a fixed mesh setting. This is found by taking the difference in the capacitance of the circuitry including and excluding the dielectric cell. For this purpose, the total circuit capacitance (C,i,.it) including cables but not the dielectric cell was first determined after the cables were connected to the LIC,, c i r ~ u i t r yThe . ~ cables were then soldered to the sensing canacitor ( C , d and with the sensing capacitor immersedin the mediumof interest the total capacitance (Ctotal)could be determined.3
,.,,
'
Shoemaker, D. P.: Garland. C. W.: Stelnfeld, J. I.; Nibler, J. W. Experiments in Physical Chemistry, 4th ed.; McGraw-Hill: New York, 19il.
Equation 2 can be used for the actual calculation of 6. Since only the direct readings of frequency (n are used, a knowledge of the value of L is therefore not nece~sary.~ The table summarizes the results we obtained for m-xylene, dichloromethane, propanol, and toluene. The samples (Aldrich, >99% purity) were all dried with anhydrous Na2S04 before use. The precision of our results, of course, is limited by the ability to locate the voltage minimum visually, which corresponds to an error in the frequency readings MHz for all the samples. The of approximately f2 X limits of error in the calculated dielectric constants due to DleleCtrlc Constants Obtained for Pure Llauld Samoles fmld
Gm?
Sample
(MHz)
(pF)
air propanoi toluene dichloromethane mxylene
1.444 0.936 1.371 1.130
77.4 184.1 85.4 126.2
1.373
85.8
(e~periment)~
e
(literature)"
1.0005 (25 OC) 19.4 i 0.7 (25 'C) 20.1 (25 OC) 2.45 i 0.11 (25 "C) 2.38 (25 "C) 9.41 i 0.46 (20 "C) 9.08 (20 OC)
-
2.44 i 0.11 (20 'C)
2.24 (20 '6)
,
Our values: f,,,o.n = 1.500 MHz: C,,,,.= 71.6 pF. The dear- of meshlna" should not be chanoed - from that used for air. The values of I,.,.,and C, .,., need to oe determined only once at the beginnng of the experiment. H. = 68 2 % pF L '1.57 X 'For our setup: C.,
-
then
-
.
calculated usiw h e standard procedure for propaition of srrw and h(frequency) = 2 X MHz. d V a l v a ~were laLen horn me CRC Handbwk.
Volume 65
Number 9 September 1988
837
the errors in the frequency readings are also listed in the table. The experimental values are in very good agreement with the literature va1ues.s Our setup can also be used for an alternative experimental ~rocedureas described hv Shoemaker e t al.'. which involves the determination of thecapacitance of the "ariahle capacitor set a t the maximum and then a t the minimum Dosition; and the difference is used in the calculation. The fixed plate procedure eliminates the possible errors associated with the reproducibility of the settings, but it also introduces a different source of error since a small part of the cell capacity
838
Journal of Chemical Education
remains unchanged for different mediums. We tried both procedures and found little difference in the quality of our data. Ack"wledgment
The author would like to thank Walter Sallstrom for helpful discussions and the assembly of the ao~aratus. .. s Handbook of Chemlshy and Physlcs, 57th ed.: The RubberCo.: Cleveland, OH, 19761977; E-56.
Chemical
