edited by JOE RICH Blackhawk Christian School FORWayne, IN
Inventory Control An Inexpensive and Easily Constructed Device for Quantitative Conductivity Experiments Timothy R. Rettlch' Illinois Wesleyan University Blaamington, IL 61702 Rubln Battlno State University Dayton. OH 45435 Recently, several articles," have appeared in this Journal showing qualitative and semiquantitative conductivity demonstrations. While solution conductivity is a good illustration of many chemical properties, traditional conductivity experiments are prohibitively expensive for a general chemistry lab experiment. The conductivity bridgelelectrode system we present in this paper has advantages over commercial models. The low cost and easilv replaced electrodes make this system practical for use i n a general chernistrv lab, while its accuracy and wide applicability permit its usein or quantitative chemisiry experiments. Theconductivity bridwshown in the figure, takesadvantage of a low-cost, hFgh-impedance digital multimeter (DMM). The student uses the DMM t o measure the potential between points x and y (V,) and the potential between points y and z (V,). The voltage across the electrodes (V,) is related to the resistance of the solution by
Wright
(2)
R(so1ution) = - R(resistor)
sion depths. Cell constants for all of the electrodes prepared this way were between 1and 2 cm-'. The table lists the suggested parts and approximate cost of the equipment for the conductivity meter. For the electrodes, a rubber stopper, paraffin, and graphite rods are needed. The graphite rods we used (Fisher #04-677-5) are sold in a bulk quantity from which 200 to 300 electrodes can be made for a total price of $55. This is the most expensive
Figure 1. me conductivity brldgelelecbodesystem. (1)
Note that the resistance is indirectly calculated from the ac circuit in the figure, as opposed to dc resistance measurement, which would lead t o polarization problems. Also, note that precision resistors need not be used; the exact resistance of an inexpensive resistor need only be measured directly. A varietv"~of resistors should be made available in order t o maintain an appropriate number of significant figures on the DMM.We use a set of four: 100.1000.10.000. and 100,000 $2. Incorporation of the resistors into interchangeable d i a l banana ~.l u-e.sas . shown in the fieure,. areatlv facilitates chaming ranges. The circuit in the figure is mounted on a % X 4x 6-in. plate of Plexiglas or hardboard, with %in.-high feet made from dowels. The range resistors are stored on this plate in holes drilled at one edae. Connections from the binding posts t o the power suppliare made under the plate. Any 6 2 4 - V ac isolation transformer can be used. Those made for model railroad trains and slot cars are widely available. The electrodes shown in the fieure are simple graphite rods, about 6 mm in diameter and TO to 15 cm long. They are held in place by a two-hole rubber stopper (size 8 or 9) as suggested by W i l l i a m ~The . ~ lower half of each rod is dipped in molten paraffin. which is allowed to harden. The bottom surface is scraped clean with a knife-this insures a ronstant surface area for the electrodes, and permits variable immer-
Components of the Conductlvlty Meter
a
~~
DMM: Soar Ccrp. Model ME 540 w equivalent
T: Aurora Toy transformer Madel Al-B (24 V ac)
or PaRs Express $120-170 or equivalent
~~~~~
~
Author to whom correspondence should be sent. Vie, E. J. Chem. Educ. 1987, 64, 550. Gadek, F. J . J. Chem. Educ. 1987, 64,628. 'Russo, T . J. Chem. Educ. 1986,63.981-982. Williams, H. P. J. Chem. Educ. 1985,62,799 See any handbook or physical chemistry laboratow manual. 168
Journal of Chemical Education
Cnst
Itam
. 4 Dual Banana Plugs: Parts Express if090470
Dual Bindlna" Post: Parts Ex~ress.. 61090-475 2 Blndino Posts: 61090-485 . - . -.- Parts Exoress .. ~
~
4
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~~~
.ow-P~e~i~ion Assone0 RBS stols-15$
each a less
Paraffin
Figure 2. Schematic diagram of the apparatus.
$55.00 $20.00 $1.25 $2.95 $1.00 $6.00 '30.60
item in the entire system, yet it costs considerably less than one traditional glass dip cell. A wide variety of experiments can be performed with this system. General chemistry experiments equivalent to the "light bulb demonstration^"^ can easily be run by measuring the resistance of distilled water, tap water, sugar solutions, salt solutions, etc. We have analyzed a wide variety of commercial oroducts includine vineear. bleach, and soft drinks with numerical results f i r comparison purposes. More quantitative experiments require the determination of a cell constant, C, using a KC1 solution of known conductivity, K,G with ionic strength similar to that of the solution being tested. Conductivity of unknown solutions can then be calculated from the resistance via x =
CIR
(2)
Strong acids and strong bases can be titrated conductimetrically without the frustration of missed end points. V, and V, readings are taken for every few milliliters of t ~ t r a n t added. The experimental conductivity is calculated by eqs 1 and 2, and then corrected for dilution by ~(corrected)= experimental) where Vo is the initial volume and Vt is the volume of titrant added. The corrected conductivity is plotted versus volume of titrant, resulting in linesegmentsofoppositeslopes.Their intersection clearlv marks the end~oint. ' even if relativelv far removed from an ictual data poi&. Weak versus strong acid-base titrations may also be done conductimetrically. Although the intersecting line segments may both have positive slopes, the intersection (i.e., endpoint) is clearly distinguishable. Samples of acetic acid, vinegar, glycine, salicylic acid, and piperidine were titrated with less than a 2% inaccuracy. The titrations of some weak polyprotic acids such as oxalic acid and citric acid clearly show separate endpoints for the first and subsequently ionized protons. Tartaric and phosphoric acidsdo not show an endpoint for the first proton, but clearly indicate a subsequent endpoint with less than a 2% inaccuracy. Advanced experiments in physical chemistry may involve molar conductivity, A, defined by
A graph of molar conductivity versus concentration of strong electrolyte showed typical behavior, i.e., increasing A with decreasing concentration. The expected high curvature a t very low concentrations increases the uncertainty in determining A' via extraoolation to zero concentration. Still. our system yielded valies with less than 5% inaccuracy dompared to literature values.
Another experiment, which can be conducted a t either an introductory or advanced level, is the determination of the dissociation constant for a weak acid or base. When the product of molar conductivity times the molarity versus the reciprocal molar conductivity is plotted, a line results with a slope of (Kd)(Ao)2and an intercept of -(Kd)(Ao). The value of experimental slopes we measured are generally quite good (less than 5%inaccuracv). Given a value for A'. KAcan be computed from only th;slope. The more elegant and selfcontained aporoach would be to calculate the dissociation constant vii -
K, = (inter~ept)~Islope (5) However, when Kd is small the intercept is quite near the origin and is susceptible to large percentage uncer, acid does not workwell, hut chloroacetainty. ~ e n c eacetic tic acid, salicylic acid, and the first constant for phosphoric acid were determined with less than 890 inaccuracv. The value for piperidine was somewhat worse (15%inaccuracy). Precautions. As with any electrical device used by students, precautions and supervision should be exercised to avoid the danger of accidental shock. All transformers should be tested for leaks to ground hefore use. Students should be reminded not to touch any of the exposed bridge elements while the power is on. However, they may safely move the insulated probes and range switches of the DMM. The use of isolation transformers A d connecting leads under the panel will help t o minimize the danger. Accuracy Limits. For highly accurate determination of Ao values, other factors need t o be included. Temperatures should be routinelv monitored in order to determine aonropriate literature values since conductivity changes about 2 8 oer OC. The conductivitv of water itself must be taken into account. If strong elec&olytes are measured over a wide concentration range, the electrodes may show a small change, e.g., 0.2% per mM, in cell constant. This can he corrected by measuring the apparent cell constant a t various KC1 concentrations. Our experience has shown that under these circumstances the apparent cell constant increases linearly with concentration. The fitting equation for the apparent cell constant C, is related to the concentration M, and to the cell constant a t zero concentration, Co,by
..
C=aM+C"
(6)
Again, theaM term isa small correction and is not necessary for conductimetric titrations of strong or weak acids and bases, nor for the determination of the dissociation constant of weak electrolytes. Acknowledgment
The late David J. Karl originally suggested this idea. David N. Bailey contributed several helpful design modifications.
Volume 86
Number 2
February 1989
169
