Eugene D. Olsen, Robert J. Martin1 and Joseph E. AhnelI2
University of South Florida Tampa, Florida 33620
Rapidly Assembled, Linear AC Conductance or Resistance Recorder
M a n y advantages accrue to the automatic, continuous recording of solution conductance or resistance. Kinetics experiments become more convenient and applicable over a greater range of conditions than are possible manually ( I ) , titrations are facilitated, and flowing streams can be continuously monitored. Recently, Malmstadt-Enke instrumentation laboratories became available,a making it easier for students to learn practical electronics while building various pieces of apparatus. The accompanying text by Malmstadt, Enke, and Toren (3)contains an abundance of measuring devices that can be built as experiments, but there is no equipment or experiment for measuring the resistance or conductance of electrolyte solutions. This paper describes an ac resistance or conductance breadboard-type instrument that can be built in less than an hour by a beginning electronics student entirely from equipment and parts supplied by a Malmstadt-Enke instrumentation laboratory. The instrument is capable of conveniently measuring resistance over the range of 0.1 ohm to 1 megohm, and conductance over the range of 0.1 micromhos to 100 K micromhos, with each measuring mode linear to within 3% of full scale. Results are read out continuously on a meter, or recorder, or both. The use of the instrument for automatic conductometric titrations is illustrated, and applications to other experiments are suggested. Theory
The conventional means of measuring the conductance or resistance of electrolytic solutions employs a Wheatstoue bridge (3). Attempts were made in this laboratory to obtain recorder readout from a Wheatstone bridge circuit by using the slidewire of aservo recorder to automatically balance the unknown cell resistance, somewhat similar to the approaches of DeVerdier and Sjoberg (4), and James, Martin, and Randall (5). However, although the resistance function was reasonably linear, the conductance readout
Presented, in part, to the Division of Chemical Education at the Southeastern Regional Meeting of the American Chemical Society, Tallahassee, Florida, December, 1968. A mimeographed set of experimental directions, including complete directions for assembling this breadboard instrument and suggest,ions for several experiments, is available on request of the first author. 'Present address: Martin-Marietta Corp., Orlando, Florida. Present address: Chemistry Department, The Johns Hopkins University, Baltimore, Maryland 21218. 'Heath Company, Benton Harbor, Michigan 49023, Catalog Number EU-100A.
542 / Journol of Chemicol Education
could not be made linear over wide ranges, In addition, the recorder tended to "hunt" when measuring high resistances, probably because of distortion in the amplifier stages, and tended to become sluggish at low resistances, probably because of the diminishing signal power to the recorder as the measured resistance decreased. To eliminate the problems of a servo-balanced Wheatstone bridge circuit, an all-electronic non-bridge circuit was designed, .based on a simple application of Ohm's law. Figure 1 gives a block diagram of the instrument in the resistance-measuring mode. To
1
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Figure 1.
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Block diagram of rerirtonce-measuring instrument.
measure the resistance (r,) of a solution, a constant current ac source ( I ) is used, and the voltage drop across the unknown solution (e,) is measured on a meter or recorder after linear amplification. Thus, by Ohm's law, e, = Ir,, and the final voltage after amplification (en.*) is directly proportional to the resistance of the solution (e,.& = Ae,), where A = the voltage gain of the amplifier. The constant current ( I ) is obtained by using a constant voltage ac source (E), and making the range resistor ( R ) large in comparison to the unknown resistance (7,). Thus, for the series circuit of Figure 1, E = i ( R r,), where i is a variable current, but since r, is much smaller than R, i E / R = a constant ( I ) . Therefore, the voltage drop (e,) is directly proportional to r,, and after linear amplificat,ion, this ac voltage (em%)1s easily and accurately measured with a VTVM. If the VTVM contains output jacks across the meter movement, as does the Heath model EUW-24, then this signal can be
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Figure 2.
Circuit for measuring conductance.
P
fed directly to a millivolt recorder as shown in Figure 1. The way in which the resistance ( R ) serves as the range resistor of the instrument will be detailed shortly. To linearly measure the conductance (G) of an unknown solution [where G = l / r , ] , it is only necessary to interchange the positions of the range resistor ( R ) and the unknown solution resistance (r,), as shown in Figure 2. Now, if the range resistance (R) is made significantly smaller than the solution resistance (r,), then 'the voltage (e,) will be directly proportional to the conductance (G), which can be shown as follows. For the circuit of Figure 2, E = i,(r, R ) , but if R is much smaller than r,, then i, = E/r,, and since e, = i,R, then by substitution, e, = (ER/r,) = (k/r,) = kG, where E R = k = a constant. As will be shown in the next section, the voltage source (E) is 3.2 V ac, 60 Hz, as obtained from a center tapped filament transformer. The range resistors ( R ) are selected in the resistance-measuring function to be ten times the full-scale solution resistance, and in the conductance-measuring function to be one-tenth the full-scale solution resistance. Thus, in both resistance and conductance measuring modes, the full-scale voltage (e,) is about 0.32 V ac, and the amplifier gain ( A ) is adjusted in the calibration step to have a gain of about 30, thus making the full-scale output voltage (e,,) exactly 10.0 V ac, which is measured on the 15 V ac range of the VTVM. The dc voltage across the Heath Model EUW-24 meter movement is 250 mV full-scale, which is conveniently measured with the Heath model EU-20A servo recorder.
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Construction and Operation of Breadboard Instrument
Figure 3 gives a complete circuit diagram of the instrument. The circuit is showu with the range resistors and cell connected so as to measure the conductance of the cell. To measure the resistance of the cell, it, is merely necessary to interchange the positions of the cell and range resistors, and recalibrate the gain by means of the 1megohm potentiometer. To assemble the instrument, the triode amplifier, enclosed in a dotted box in Figure 3, is first constructed on an experimental chassis (Heath model EUW-13) as follows. First, a solderless 9-pin tube socket and a 1 megohm potentiometer control are mounted to the experimental chassis with the screws and nuts provided. Next, a 12AX7 vecuum tube is installed, and the filament is wired with spring-clip connecting wires. (From Figure 3 note that the filament of the tube is wired by (a) eon-
neeting together pins 4 and 5 of the tube, (b) connecting pin 4 or 5 to one green filament wire (coming from the octal power connector on the chassis), and (e) connecting pin 9 to the other green filament wire.) The two resistors m d two capacitors are then connected to the chassis with spring clips, and spring clip connecting wires are used to connect dl remaining parts of the amplifier as shown in Figure 3. To prepare the power supply, conneot a 1.5 milliampere meter (Heath Model EUW-18, with a 100 ohm resistor shunt) in the appropriately marked output terminals of a power supply (Heath model EUW-15), set the divider-regulator switch to "Regulator," and adjust the regulator voltage control to give +300 V dc. With the high voltage of the power supply turned off, use s. power cable with octal connectors to conneot the power supply to the experimental chassis. To connect the read-out system, set the vacuum tube voltmeter (Heath model EUW-24) to the 15 V ac range, and connect the VTVM probes to read between ground (black banana jack of chassis), m d the center pin of the 1 megohm potentiometer (red output banana jack). Readings can be made directly from the VTVM, or if desired, the readings o m he simdtrsneously recorded by connecting the output terminsls of the VTVlM (marked "Meter Terminals") to the input terminals of a. servo recorder (Heath model EUW-20A) set to the 250 mV range. Calibration of the circuit is best made by using two decade resistance boxes (Heath model EUW-3-80], one serving as the normal range decade and the other in place of the cell, for cdibration. Figure 3 shows how these components are hooked into the circuit. Banana plug patch cords can he used for all connections except for the 3.2 V ac signal, which is best connected with a hybrid patch cord from pin 9 of the tube to one side of the cell. The decade rsnge resistsnce settings for various conductance and resistance ranges are shown in Tables 1 and 2. Other intermediate values of resistances are possible, hut interniediate '
Table
1.
Settings of Decade Range Resistances for Various Conductance Ranges
Resistance corresponding to full-scale conductance
Decade range resist~nce (ohms)
Table 2.
Settings of Decode Range Resistances for Various Resistance Ranges
Decade range resistance setting (ohms) 999 K 100 K 10 X 1000 100 10
I- - - - --
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Figure 3. Circuit diagram of instrument in conductance-measuring mode. Key: Range resistors = Heath model EUW-30, decode resistonce box; VTVM = Heath model EUW-24, vocvum tube voltmeter on 15 V oc range; Recorder = Heath model EUW-20, on 250 mV range.
Full scale conductance (micromhos)
Full scale resistance (ohms) 100 K 10 K 1000 100 10 1.0
ranges are normally unnecessary, and make reading the chart more inwnvenient. An exception is in conduetometric titrw tions where optimal expansion of the conductance scale is desirable, as illustrated later. In each table, the top row represents the survey rmge that would generally be used for the first measurement of a totally unknown system (thus, in Table 1, a 1.0 ohm range resistor setting would read out any conductance from zero to IUUK rnirn,mhu.i), wherem going h w t r urrw.iive rows in Tnb1e.i 1 and 2 represent* inrreaai~.glysen.' -111vc ' measurementv (thus, in Table 1, x lOOK ohm mnee resistor settiw would read o& an$ conductaice from zero to 1.0 micromhos). -1n the case of resistance measurements, a precision (lyo) 10 megohm resistor could be wed to extend the resistances measurable to 1 megohm. If a second decade box is not available for calibration, spring clip precision (1%) resiston could be used, or if f10% accuracy can be tolerated, a resistance substitution box (Heath model EUW-28) could he used. I n calibrating the instrument, Volume 47, Number 7, July 1970
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care should be taken to avoid shorting the 3.2 V tsc signal voltage directly onto the grid (pin 7 ) of the tube (see Fig. 3), which would overload the tube. Thus, in calibrating the instrument in the conductance made, the calibration resistance (inserted in place of the cell in Fig. 3) should not be allowed to go to zero ohms (shorted), snd in the case of resistance meamrements, the range decade should not be allowed to go to zero ohms. To calibrate the instrument after inserting the appropriate range and calibration resistors, the gain of the amplifier is adjusted with the 1 megohm potentiometer control until full scale resistance or conductance gives an output voltage ( e , d on the VTVM of 10.0 V ac, and then the recorder is made to read full scale with the "Vernier Sensii,ivity Control" on the recorder. In the case of condnctance measurements, the zero end of the scale is cdihrated by opening the cell circuit or increasing the calibration resistance to effectively infinite resistance, and then setting the zero on the VTVM with the "Zero Adjust" of the VTVM, followed by setting the recorder zero with the recorder "Zero Position." For accuracy on the 3y0 (of full scale) error level, one intermediate range can be calibrated, and recalibration is usually unnecessary far all other ranges except the most sensitive, dthough the accuracy can be improved slightly by recalibration of each range as it is used.
Figure 4.
Picture of instrument in operation.
Results and Discussion
Figure 4 shows a picture of the assembled unit in operation. Starting from the left may he seen the power supply, with an optional milliammeter (for monitoring current in the plate circuit) resting on top of the power supply; in front of the power supply is the solution whose conductance is being measured; to the right of the solution is the triode amplifier, mounted on the aluminum chassis; to the right of the amplifier is the decade resistance box which supplies the range resistors; in back of the amplifier and resistance box is the VTVM, reading out the ac voltage which is proportional to the conductance; and on the far-right is the recorder, reading out the dc voltage across the meter of the VTVM. The conductance-resistance instrument described can be built in less than an hour by a beginning electronic student. The linearity and accuracy of the instrument, as checked against Heath model EUW-30 decade boxes, accurate to within 0.5%, was found to be within 3% of full scale on all ranges, and was usually within 2% of full scale. Some of the error is contributed by up to 1% recorder overshoot, which seemed to he a characteristic of the four different Heath recorders tried, and which resulted in readings up to 1% of fullscale high as the pen traveled downscale. Reproducibility of readings in one direction was always within 1% which means calibration corrections could be made 544
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if better than 3% accuracy were needed. After a ten minute warm-up of the ac power supply (tube filaments) the stability of the instrument is excellent, with less than 0.5y0 drift in an hour, and less than a ly0 drift over a several hour period. The sensitivity is such that a 1% change in conductance or resistance can clearly be seen on the recorder chart. The accuracy of the instrument for measuring solution ConduCtanCe~ was checked by comparing the conductance of four different concentrations of hydrochloric acid, ranging 0.05 M down to 5.0 X M, using both an Industrial Instruments model RC-16B2 conductivity bridge, accurate to l%, and the instrument herein described, using the same conductivity cell. I n the case of the 0.05 M hydrochloric acid, the agreement was better than 4y0,and the other three solutions agreed within 3%, which is consistent with the accuracy expected. The fact that linearity of the instrument turned out to he better than 3% (whereas the design theory described earlier would predict readings up to 10% low at full scale) is reasonable in view of the increasing convexity of the 12AX7 plate characteristic curves as the grid voltage becomes more positive (6). Thus, as the input voltage approaches full scale, the grid swings increasingly positive, causing a higher plate current per volt than obtained a t normal bias, and this positive voltage distortion compensates almost exactly for the otherwise low output voltages as full scale is approached. To investigate the effect of a more favorable ratio of range resistance (R) to full scale measured resistance (r), an extra stage of amplification was added to the circuit of Figure 3, in order to provide sufficient gain to set full scale resistance to 1/100 that of the range resistor. Linearity was no better than a t 1/10 ratios, but a 1/50 ratio improved linearity to within 2% of full scale, undoubtedly because at this gain setting the distortion was most precisely compensated. However, the linearity was not sufficiently improved to justify the added complexity to the beginning electronics student of adding the extra stage of amplification. The reliability of the linearity was checked by constructing the amplifier shown in Figure 3 from four different sets of electronic components, with all resulting instruments showing linearity within 3%.
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Applications Aufomation of Condudometric Titrotions
Although the continuously-recording conductometric apparatus described above greatly shortens the time and effort necessary to perform a conductometric titration with a manual buret, a simple means of automatic-titrant delivery was devised to fully automate the titrations. Procedure. The titrant delivery apparatus of Olsen and Adamo (7) was used, modifying only the buret and drop-counter systems. Although the Hempel distilling-column buret described earlier (7) could be used with high accuracy, it is usually sufficient for student conductometric experiments to use an ordinary 50ml buret, again using a capillary flow restrictor fastened to the buret tip to regulate the flow rate as desired. The capillary flow restrictor allows the buret stopcock to be turned on full, avoiding the problem of changing flow rate that comes with partially opened stopcocks
(8). By preparing a series of capillary flow restrictors as described earlier (7), a constant flow rate in the range 0.2 to 1.0 ml/min, and a constant drop size in the range 0.04 to 0.08 ml/drip, can be selected for a given titration. Since conductometric titrations require a titrant that is a t least ten times as concentrated as the solution being titrated (S), the titrant concentration and sample volume can be conveniently chosen to restrict the volume of titrant used per titration to about 1-2 ml, thus keeping the flow rate change negligible over the course of a titration, and obviating the necessity of a reservoir bottle to maintain a constant titrant height (7, 8). If a strong base is used as the titrant, the top of the buret should be closed off with an Ascarite absorption tube to avoid carbon dioxide error; and if strong bases are titrated, it is advisable to sweep the titration vessel with nitrogen to avoid carbon dioxide absorption, or alternately, the extent of carbon dioxide absorption can be studied from the curvature or double end points in the end point region. The addition of both phenolphthalein and methyl orange indicators during the course of the titration serves to delineate the carbonate error. As a means of positively marking the addition of each titrant increment on the recorder chart, a simple drop counter was devised as shown in Figure 5. With
Figure I Circuit for recording number of drops. Key: Recorder = Heath model EUW-20, on 250 mV range; Power supply = Heath model EUW-17, tronrirtor power supply set ot 10-15 V; Resistonce box = Heath model EUW-28, resistonce substitution box on about 47 K ohm.
about 47 kilohms on the resistance substitution box and about 10-15 V on the transistor power supply (about one-half the maximum voltage available), most titrant solutions will give a clearly discernible voltage pulse on the recorder as the solution momentarily "shorts" across the platinum wires. Both the magnitude and polarity of the voltage pulse can be controlled using the applied voltage as a course control and the 10 kilohm potentiometer control as a fine control. If the transistor power supply is not available, an adequate voltage pulse can be obtained by substituting a small 9 V transistor batter^.^ Other titration details, including a procedure for calibration of titrant increments and a convenient titration-vessel system, were described earlier (8). A chart speed of 1-in./min was used. 'For example, x Burgess madel 9E battery.
Results. Figure 6 illustrates the automatically recorded conductometric titration of forty ml of 0.025 M HC1 with 0.85 M NaOH. The drop size, as determined by weighing duplicate 10 drop samples, was about 0.08 ml, and the cell constant of the platinum electrodes was about 0.70 cm-'. The end point is determined by extrapolating the straight line portions before and after the end point, with the location of the intersection indicating the drop within which the end point has occurred. Determination of the precise fraction of the drop to the end point is facilitated by the fact that the value of each increment and the flow rate are both constant, thus enabling the fractional distance to the intersection to be taken as the fraction of the drop to the end point (9). Thus, in Figure 6, the end point occurred a t 14.30 drops added. The average of seven such titrations had an error of +0.5% with a relative standard deviation of 0.6%. Other Applications. Continuous recording of solution conductance or resistance has not generally been available for student experiments and the instrument described should make possible a number of exercises not otherwise possible or convenient. As an example, an excellent experiment for measurement of reactions rates with an ac conductivity bridge has been described by Chessick and Patterson (I), but the instrument they described is accurate to only *5%, gives resistances instead of conductances, and being a manual instrument the conditions had to be carefully controlled in order to keep the reaction slow enough to be measurable. Continuous recording with the instrument described would give a plot of conductance versus time directly, and would permit faster reactions and higher temperatures to be conveniently studied. As another example, the instrument should be useful for continuously monitoring the conductivity of flowing streams, a technique which has been shown to be useful in certain chromatographic separations by a number of workers (4, 6, 10). It must he emphasized, however, that conductivity changes in excess of about 1% must occur to be detectable with this instrument. To observe smaller changes in conductivity, a more complex differential conductivity monitor is required (11).
NUMBPI OT TNRANI MOPS ADDED
Figure 6. Automaticdly recorded conductometric titrotion of 40 ml of 0.025 M HCI wilh 0.85 M NoOH. Legend: Dmp sire, 0.080 ml; Row rate, 0.60 ml/min; recorder speed, 1.0 inlmin; cell constant 0.70
cm-l.
Volume 47, Number 7, July 7 970
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Literature Cited (1) Cnas~cr.J. P.. AND PATTBB~ON, A,. JR., J. CHEW.EDDC.. ST, 242 (1960). (2) MALXBTADT, H. V., EN=., C. G.,A N D TOREN.E. C., In., "Ele~tronim for Scientists." W. A. Benjamin. Ino., New York. 1965. (3) WILLARD,H. H., MBRRIFT, L. L., Ja.,m o DEAN.J. A.. "Instrumental Mathoda of Analysis, 4th ed., D. Van Nostrand Go., Inc., New York. 1966.
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(4) DaVennme, C. H., A N D Braa~na,C. I.. Ado Chcm. Sand.. 8, 1161 (1954). (5) J~ues.A. T., MARTIN,A. J. P.,A N D RANDAT,',S. S.. BioChem. J.. 49. 293 (1951). (6) Reference (2). p. 593. (7) OLBEN.E. D., AND ADIMO.F. 8.. A n d . Chcm., 39, 8 1 (1967). (8) O ~ a m E. . D., J. C n m . Eoac.,48, 310 (1966). (9) OLBEN,E. D., A N D WALTON, R. D., J. CXEM.EDUC.,48, 659 (1966). (10) Wrcseom, R., 2. And. Cham.. 132, 401 (1951). (11) O w m , E. D.. m n MARTIN, R. J., ac~eptedforpublioation in Talonto.
