A Simple Device for Conductivity Experiments Mohammad H. Ghatee Shiraz University, Shiraz, Iran 71454
Conductance measurements are among the most reliable techniques in physical and electroanalytical chemistry, but accurate and meaningful measurements of electrolytic conductance require attention to the design of electrodes, cells, and the measuring circuitry. The details of all experimental techniques of conductance measurement are almost impossible to be considered in undergraduate courses, but the introduction of some basic ~racticala s ~ e c t sof electrode Drocesses and measuring clrcunry would strcngthcn the insight toward the sublect. We have madc devircs that allow students in ohvsiral chemistry laboratories to carry out an experiment& Set up to measure conductance of solutions. A stabilized power supply, a sinusoidal oscillator, a Wheatstone bridge, and a null detector are the main components of the set up ( I ) . A conductivity device has been designed by Havrilla (2) that uses a CMOS 555 Timer to produce approximately 1000 Hz of pulsed current. The pulse is applied to two electrodes in a solution, and the current through the solution is assumed to be a measure of conductance. We recognized several noticeable points in this method. First, the 555 Timer pulls its output through a n active pull-up resistor (e.g., transistor in series with a diode) that could, in the cutoff region of the diode, keep the output impedance coustant. When a load on the output pulls the transistor iuto cutoff, the output impedance adjusts itself so much that the timer output can retain a constant voltage. This coustancy in voltage is good enough when one is concerned only with high and low logic in driving TTL circuits. We checked on the circuit in reference 2, and found, in a similar experiment with distilled water, that the output voltage of the 555 Timer dropped by 8.7%. If the external divider (2) drives the active pull-up resistor iuto the cutoff region, one still has to be concerned with the change in current due to the voltage drop. Second, because the duty cycle1(3) of the Timer (as it could be designed) is less than 0.5, the pulses subject the charge carriers to an uneven field in each cycle. Third, the timer output is coupled to an external differentiator circuit to make a bipolar current pulse. The output waveform of the differentiator does not vary steadily in each cycle. On the other hand, the charging and discharging time constants of the capacitor (eqs 1 and 2, respectively) are different:
where, R,is the resistance of the 10 pF capacitor and R, is the resistance of the solution. The resistances of the voltage divider are 100 and 10. The value ofRc is estimated by extrapolation to be about 50 R (4). For a typical solution withR, about 400 R, z&a:dr is about 1.5. This makes the waveform even more unsymmetrical in a cycle. Thus, some i n a m a c i e s occur with the pulsed current method. A simple device for conductivity experiments that 'The duty cycle of the 555 Timer is equal to the ratio of the time period of the successive high and low voltages of the output waveform of the timer. Practically, duly cycle can be calculated from the relationship Rd(Ra+ 2Rb),where 4 and R, are the eaernal adjustable resistors (6).
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Journal of Chemical Education
Figure 1. Schematic circuit diagram ofthe conductivity device,
operates at a highly constant voltage is that of an oscillator with a sinusoidal bipolar waveform. Figure 1shows the schematic circuit diagram of the sinusoidal oscillator that uses +9 and -9 V DC to run a 741 Operational Amplifier. The positive feedback loops maintain the frequency of the oscillator at approximately 1000 Hz (5).At the present time, the electrodes are standard conductivity electrodes (coated with platinum black and a cell constant of 0.75 cm-'1. A digital multimeter (DMM), the Hioki 3200, is used in series with one of the electrodes to measure the current, and a second meter, the Uni Volt DT-830, to measure the voltage across the electrodes (see Fig. 2 1. We designed two different circuits. In one, we grounded the output leadofthe 741 through one diode. In the second, we grounded the output through two diodes in series. Therefore, the voltage at point VOmt would be about the nominal cutoffvoltage of a diode for the first arrangement (e.g., 0.6 V) and about twice as much for the second arrangement. This method allows us to see the effect of the
(fromthe oscillator)
JUniG q Volt
Hioki
Conudctivity Electrodes Figure 2. Experimental set up for measurement of the current and voltage.
The Measurement of Current with the Described Conductivity Apparatus Equipped with a Sinusoidal Oscillator Circuit 1 Volts Conc. vl - Ea
Circuit 2 Volts
mA
I
I,,,
vl - Vza
-
mA
I
twr
0.050 0.006 2.00 2.02 0.029 3.82 3.91 0.025 0.005 1.64 1.65 0.024 3.18 3.24 2.45 0.0125 0.004 1.24 1.25 0.019 I 'V, and V Vare ~ the voltages across electrodes before and afler insening into
the solution,respectivelr
magnitude of voltage drop due to the conductance of the solutions (6)as a function of the applied voltage. The table shows the results of conductance measurements on some typical solutions. The currents measured were quite stable in 1 s. In all measurements, the DMM was set on the 20 mAscale. While measuring the currents and voltages, we monitored the output waveform of the oscillator on an oscilloscope, Tektronix 475. As was expected, the original output waveform had a diode clipping characteristic. We noticed that rising and falling edges of the oscillations, when applied to the electrodes, shifted appreciably inward in a symmetric way with respect to the original waveform, but the frequency did not change. Symmetrical shifting of the waveform shows that the total reactance of the oscillator has changed. We attribute the waveform shifts to coupling of the series capacitance of the solution medium and the parallel capacitance of the solution structure a t the electrode surfaces (7) with the integrator and differentiator loops of the oscillator. The table also shows the result of measurements with arrangements 1and 2. The voltage drops, (VI - Vz), due to the conductance of the solutions. For circuits 1and 2, V1 is 0.627V and 1.211V, respectively. The corrected currents, I,,, are the currents that could be developed if the voltage 2~here are diverse prices offered by suppliers
due to the conductance of the solution did not change. To calculate the corrected currents, we assumed that the conductivity is independent of applied voltage over small ranges of voltage. At a given concentration, from the corrected currents and the voltage drops of the two setups, one can see that the measurements with the first arrangement give current values that are almost independent of n ~ l i e dto the electrodes. This shows that the the voltaee a .. oscillator operates at highly constant voltage, and circuit 1 is nreferable to circuit 2. On the other hand, at low a m e n trations, both circuits produce results that are close to their uncorrected current values. Therefore, in practice, one need not to be concerned about the voltage drop, and the measured currents accurately correlate with the conductance of the solutions if they are to be compared with each other. This method is quite able to distinguish between different electrolvtes he.. KC1 and NaN04. The difference between condurtivity of substances wlth two ions i1.c.. NaUO.#,and three Ions 1i.e.. Na,SO,l is also indicative by &is megod. Because the cell constant in (2) was not reported, we could not compare the results directly. Using the conductivity device in (21, it takes a long time for current to stabilize (2). This, plus the facts already mentioned, may account for the incapability of the pulsed current method to establish a steady current in the solution. Our method is simple and accurate as well. The cost of one set is about $4.80,' excluding DMM's, a little less than the cost in (2). It can be used in physical chemistry laboratories when a sophisticated conductivity device is not available. It should be mentioned that there are standard experiments that can be fulfilled without knowing the absolute value of the conductance. An example is the calculation of the equilibrium constant of weak electrolytes in which dissociation constants are calculated from the ratio of eauivalent conductance a t a ziven concentration to the eq&alent conductance at infinite dilution (1).For the reason that the current. u s i w the described conductivity device, accurately co&atesto the conductance over an appreciable range of concentrations, this ratio can be substituted with the ratio of the corresponding currents. Acknowledgment The author would like to thank Farzad Shadkami for his help with this work and H. Firozabadi for reading the manuscript. Support from the personnel of the computer room and electronic workshop of the department of chemistry and physics are gratefully acknowledged. Literature Cited 1. Shoemaker, D . P e t al. E p e i m e n t s inPhyaieol Chemistry; McOraw-Hill: New York, 1981,4thed.,p 231. 2. Hamilla. J. W.J Chrm. Educ l631,68,80. 3.Schillik, D. L.;Belove. C . Eleefmnie Cilcuitn: Disciscfo and Ink#mfed;McGisciscw-Hill: New York, 1967, p 800. 4, Clifford, M. Xondbaok ofEledron2 lhbb8;Tab Books: BluePudge Summit,PA. 1972, p
75.
5. Millman, J.;Gmbe1.A.Miririrlmtmnics;McC~cc~ccw-Hill: New York, 1987. p 659. 6.Homplte, P ; Hill. W The An ofEledmn&; Cambridge University h s s : Inndon, 1980. pp 182-188. 7. Braunrtein, J.; Robbins, G D. J. Ckem. Edvc. 1812.52.5249.
Volume 70 Number 11 November 1993
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