Constant Current Conductance ROBERT P. TAYLOR AND N. HOWELL FURMAN Frick Chemical Laboratory, Princeton University, Princeton, N. J . This investigation was undertaken to study the possibility of using direct rather than alternating current for conductance measurements. Theoretical considerations indicated that if a constant direct current were passed across a solution through a pair of platinum primary electrodes, the voltage drop across a pair of tungsten secondary electrodes should be inversely proportional to the conductance of the solution. This conclusion was verified experimentally. The constant current was obtained from a 540-volt battery source in series with a high
D
I R E C T current conductance involves the difficulty of electrode polarization. This difficulty was overcome by Andrew and Martin ( I ) , who measured the conductance of potassium chloride solutions by using calomel electrodes and low current density. hnother method for measuring direct current conductance, introduced by Newbery ( 7 ) , involved impressing a constant direct current voltage across a pair of nonpolarizable primary electrodes and measuring the voltage drop across the two nonpolarizable eecondary electrodes. As the primary electrodes weie not polarized, the current was constant and readily measured. Substitution of values for voltage across the secondary electrodes and for current into Ohm's law yielded the relative resistance of the solution across the secondary electrodes. The proportionality factor or cell constant was either deduced from the geometry of the cell ( 7 ) or determined from the conductance of the cell filled with mercury (3). Investigators ( 4 , 5 , 8 )have obtained direct current conductanre values of various standard solutions which were within 0.03c"c or better of the accepted alternating current values, and consequently in direct current work the cell constant may be conveniently determined by measuring the conductance of a solution whose specific conductance is knov, n from alternating current measurements. Although direct current conductometry gives accurate results, it appears t o have found little application. The neglect of the method seems to be due to the cumbersome experimental requirements. It is necessary to use small current to prevent electrode polarization, and the ZR drop across the secondary electrodes has to be sufficientl\ high for convenient measurement. These two conflicting requirements were met by the use of long, narrow conductance cells. Such cells are not adapted to routine specific conductance measurements and the difficulty of stirring the solution practically precludes employing them in conductometric titrations.
resistance. By plotting reciprocal voltage drop 2's. volume of titrant, the usual conductance curves were obtained. Several different conductometric determinations were carried out. The cell constant was shown to remain constant over a hundredfold conductance range. Since the direct constant current method described uses a pH meter to measure CO,Iductance, the specialized or inconvenient apparatus of alternating current conductometry is avoided. Accuracy and precision compare favorably with usual conductance measurements.
Another difficulty is the necessity of using nonpolarizable electrodes. Investigators have used calomel ( 7 ) , mercurous sulfate ( S ) , quinhydrone (IO),and hydrogen electrodes (8). Iiot only are such electrodes less convenient than the platinum electrodes of alternating current conductometry, but they must he changed to conform to the solution being measured. The direct current conductance cell described below has neither of these disadvantages. APPARATUS
The conductance cell, shown in Figure 1, consists of a 150-ml. beaker with two platinum and tn-o tungsten electrodes. The platinum electrodes are placed close t o the walls of the beaker and the tungsten electrodes are placed close to the platinum. This arrangement permits lowest current for given ZR drop across the tungsten electrodes. The platinum primary electrodes through which constant current passes are made of 0.0126-inch platinum wire, cut flush with the glass. The electrodes are inverted to permit escape of the evolved gas. T o aid further in the escape of the gas bubbles, thc platinum electrodes occasionally were washed 1%-ith a few drops of cleaning solution.
R12
k*-zM'
MAGNET IC STIRRER
p= L pH METER
Figure 2. Direct Current Conductance Circuit Diagram R1. R2. R3. R4. R5.
50,000 ohms 0.1 megohm 1 megohm 5megohms 10 megohms
R6. R7. R8. R9. R10.
18 megohms 80.3 ohms 130.1 ohms 405.9 ohms 1298 ohms
R11. 3961 ohms R12. 6759 ohms R13. 13160 ohms
The secondary electrodes are 0.025-inch tungsten xire, approximately 0.5 inch long. This metal JWLS chosen because it acts as a somewhat nonpolarizable electrode. Brfore the tungsten electrodes were fused into the cell, they were cleaned in molten sodium nitrite. All the electrodes have short copper wire leads. At the platinum electrodes the contacts are soldered; a t the tungsten electrodes mercury contacts are used. The external openings of the electrodes are sealed with wax to prrvent breaking thP platinum wire and t o seal in the mercury. The electrical circuit is shown in Figure 2 .
Figure 1. Conductance Cell
1931
1932
ANALYTICAL CHEMISTRY
Constant current is obtained by passing 540 volts through high variable resistors R2, R3, and R4. Where the solution resistance is large, either R5 or R6 can be thrown into the circuit. The voltage supply consists of twelve 45-volt radio B batteries in series. R1 is placed in the circuit both as a safety precaution and to prevent accidentally overloading the other resistances in the circuit. R7 through R13 are precision resistors which were calibrated after installation to 0.1% on a Wheatstone bridge. The current is measured by throwing one of these standard resistances into series and measuring the voltage drop across it. Of course, the current cannot be measured with the apparatus shown when R5 or R6 is in the circuit. If the apparatus is not to be used for specific conductance measurements, it is not necessary to know the current, and the precision resistors may be omitted from the circuit. This would mean that instead of connecting the leads of the pH meter to the double-pole, double-throw switch, 52, they may be connected directly across the secondary electrodes. The voltage drop across the secondary electrodes and across the precision resistors is measured with a Leeds & Sorthrup pH meter by throwing switch 5 2 into the required position. A magnetic stirrer was used, the stirrer itself being made from a piece of iron nail fused into a glass tube about 10 mm. long. Two pieces of asbestos board were placed between the magnetic stirrer and the conductance cell to prevent the motor from heating the solution. When several titrations were performed in succession, the asbestos boards Tere changed.
Unknown and titrant are made up using solvent a t room temperature, but except for the use of asbestos squares under the conductance cell, there is no other temperature control during the titration. EXPERIMENTAL
The following direct current conductance titrations were carried out: hydrochloric acid with sodium hydroxide, hydrochloric acid and acetic acid with sodium hydroxide, silver nitrate with sodium chloride, and perchloric acid with aniline in glacial acetic acid. Stock solutions of unknown and titrant were determined relative to each other by some nonconductometric procedure. These standard stock solutions were then diluted if necessary to give solutions of the normality desired for the conductometric titrations. The conductometric titrations of hydrochloric acid with sodium hydroxide, hydrochloric acid and acetic acid with sodium hydroxide, and silver nitrate with sodium chloride have been explained by Britton ( 2 )and are not elaborated on here. The stock solutions of 0.2 N hydrochloric acid and 0.2 N acetic acid were standardized potentiometrically against 0.2 A- sodium hydroxide. The 0.2 N silver nitrate stock solution was standardized against dried sodium chloride using Mohr's method.
PROCEDURE
The sample to be titrated was placed in the conductance cell and diluted to 100 ml. The solution was stirred a t a moderate constant rate during the titration, the stirrer being left on as a matter of convenience when a conductance reading was made. With the leads connected as shown in Figure 2 the p H meter was connected through switch 82, across the secondary electrodes. The pH meter was usually set on the 700-mv. scale, as this setting requires only half as much current as the 1400-mv. scale for given I R reading. To compensate for any polarization across the tungsten electrodes, the meter was zeroed with the zero switch up. Stvitch 81 was then closed and R2, R3, and R4, which may be thought of as a coarse, medium, and fine control, were adjusted to give a suitable I R reading.
For best accuracy the upper part of the millivolt scale should be used, as in that region a given change in conductance will result in the largest scale deflection. However, if the initial scale reading is set too high, there is the danger of having the I R drop a t the end point off the millivolt scale. The voltage may be brought back on the scale by switching the p H meter to the 1400-mv. scale, but the change from one scale to the other is likely to introduce inaccuracies and this procedure is not recommended. The correct setting for the initial I R drop may be estimated from a consideration of the type of conductance curve expected. For a titration in which the conductance remains approximately constant up to the end point, as in the titration of silver ion with chloride, the initial I R reading is set a t approximately 600 mv., so that the ZR drop after the end point occurs a t the upper end of the scale. If the conductance rises throughout the titration, the initial voltage drop is set a t 700 mv. For the titration of a strong acid with a strong base the initial I R drop is adjusted to about 250 mv. For other titrations in which the conductance decreases before the end point, a somewhat higher setting is used. After the current has once been adjusted to give the required I R drop across the secondary electrodes, the variable resistances are left unchanged throughout the titration. The first I R reading is not recorded. The constant current is turned off for a minute and then turned on for a second I R reading, which is recorded, The titration is then performed in the usual manner by adding 1- or 2-ml. increments from a 10-ml. microburet. Each increment is stirred for about a minute. The pH meter is rezeroed if necessary, the constant current turned on, the I R drop read, and the current turned off. The constant current is left on as little as possible, both to save the batteries and to prevent battery polarization which would cause variation in the current. An average conductance reading requires about 5 seconds and an average titration about 15 minutes. The reciprocals of the I R readings are obtained from a table and these values are corrected for volume and plotted against volume to give the usual conductance curves.
PERCHLORIC ACID WITH ANILINE
The 0.1 N perchloric acid was made by diluting 0.8 ml. of 70% perchloric acid to 100 ml. with glacial acetic acid, and a 0.1 N aniline solution n-as made by diluting 0.9 ml. of aniline to 100 ml. with glacial acetic acid. The relative standardization of these two solutions n-as obtained by titrating 8 ml. of the aniline solution with perchloric acid. Glacial acetic acid (75 ml.) w a ~ used as the supporting medium and 2 drops of a saturated chlorobenzene solution of methyl violet (6) was used as the indicator.
0
2
Figure 3.
4 6 ml. O F R E A G E N T
8
10
Typical Conductance Curves
1. 0.2668 mmole. AgNOa titrated with 0.04 N NaCl 2. 0.6461 mmole. HCl and 0.7402 mmole. HOAc with 0.2 N NaOH 3. 1.283 mmole. HCI with 0.2 N NaOH 4. 0.6547 mmole. HClOd with 0.1 N aniline i n glacial HAC
Preliminary conductometric titrations of aniline with perchloric acid gave curves from which it appeared that the conductance change was caused largely by the water in the perchloric acid solution and no break was observed. This difficulty wa8 overcome by reversing the procedure and titrating perchloric acid with aniline. In order to exclude moisture partially the conductance cell was stoppered with a large cork through which a hole was bored for the microburet. After the stopper and buret had been put in place, the solution was stirred for several minutes before titrating to allow it to come to equilibrium with the atmosphere in the cell. The conductometric titration was then carried out in the usual manner. Because of the low conductance of glacial acetic acid solutions, an 18-megohm resistor, R6, was introduced into the constant current circuit.
V O L U M E 2 4 , NO. 12, D E C E M B E R 1 9 5 2
1933
Results of various titrations are given in Table I. Except for the silver nitrate solution, only the relative normalities of the stock solutions were known. For purposes of calculation therefore the 0.2 N sodium hydroxide solution was assigned a normality of 0.2000 and the 0.1 N aniline solution was assigned a normality of 0.1Ooo. Typical conductance curves obtained in this investigation are shown in Figure 3. The curves are the type that would be obtained in alternating current conductance titrations. SPECIFIC CONDUCTANCE
As the conductance cell used does not have a defined volume, the cell constant may be expected to vary with volume of solution used. This effect was investigated by adding 0.02 A: sodium chloride solutions from a buret into the conductance cell, and measuring the relative conductance as a function of total volume. The values obtained are plotted in Figure 4. The slope of the graph a t a particular volume gives the accuracy with which the volume of solution must be known for a given accuracy in specific conductance. For example, a t 100 ml., an inaccuracy of 0.5 ml. will cause a 1 part per 1000 inaccuracy in the measured conductance. This conductance change does not affect conductometric titrations, since over the range 100 to 110 nil., the change in conductance with change in volume is practically linear.
Table I. Sample
Table 11. NaCl Molarity 0.1
0.05 0.01
0.0@5 0.001 0.0003
Mmoles Taken 4.275 1.283
Average RImoles No. of Found Detns. 4.274 * 0,001 2 3 1.285 * 0.002 3 0.1282 * 0.0002 3 0.6468 * 0.0030 0 . 7 3 8 0 * 0.0066 1.442 1 . 4 4 4 *tn - . on2 0.2668 0.2664 * 0.0002 0 . 0 5 3 5 2 0.05347 * 0 , 0 0 0 0 4 0.6547 0 . 6 5 2 9 * 0.0015
{xi;
+
IR (Soln.)
I R (Std.)
0,275
1.432 1.426 0.632 0.489 1.120 0.625
0,528
0.673 1.028 1.127 1.218
Cell R (Std.) Constant 80.3 80.3 130.1 130.1 1298 1298
0.1645 0.1650 0.1642 0.1650
0.1615 0.1575
The cell constant was measured with standard sodium chloride solutions over the range 0.1 to 0.0005 N . One-hundred-ml. samples of the sodium chloride solutions were brought to 25.0’ C. in a constant temperature bath. The cell was rinsed with a sodium chloride solution of the molarity being measured and the 100-ml. sample transferred t o the conductance cell. The I R drop across the secondary electrodes was measured within 8 seconds to minimize changes in temperature and the I R drop across a standard resistance was also determined. The cell constant was calculated from the formula
K -
I
I
75
k ( I R ) soh. ( R )std. ( I R ) std.
where k is the specific alternating current conductance a t 25’ C. obtained by Shedlovsky (9). The results are shown in Table 11. Essentially the cell constant is unchanged over the concentration range 0.1 to 0.005 M sodium chloride. ELECTROLYSIS
The inaccuracy introduced by electrolysis was investigated. Acid solutions will introduce the greatest error, because they have a high equivalent conductance and therefore require a large current for a given ZR drop. With a 0.1 N hydrochloric acid solution the current amounts to 12 ma. for an I R drop of 0.5 volt.
100
ml. .O2M NaCl
I
I
125
150
Volume of 0.02 M Sodium Chloride Solution
Figure 4.
us. Conductance in Arbitrary Units
___
Effect of Concentration on Cell Constant Specific Conductance
DISCUSSION
The direct current conductance method has certain advantages over the usual alternating current procedure. A p H meter is used to measure the resistance and the method would be useful when the specialized equipment required for alternating current conductometry is not available. The resistance measurements are made more conveniently, because the p H meter is a direct reading instrument. The electrolysis caused by the direct current has been shown to cause a negligible error.
Analytical Results
Titrant 0 . 2 N KaOH 0 2 N XaOH 0 . 0 2 A’ SaOH 0 . 2 NNaOH 0 . 2 N NaCl 0 , 0 4 iV NaCl 0 , 0 0 8 N KaC1 0 . 1 N aniline
1 . 0 6 7 5 10-2 5.555 10-2 1 . 1 8 5 z 10-3 6.032 lb-4 1 . 2 3 7 f 10-4 6 . 2 2 5 i 10-5
This current corresponds to the electrolysis of 1part per 1000in 1.4 minutes. Since during an average titration the current is on less than a minute, negligible decomposition of the solution occurs.
The cell described has the disadvantage of not being useful over the entire conductance range. At the upper limit are those solutions whose conductance corresponds to a 0.5 N sodium chloride solution. At this concentration the volume of gas evolved is sufficient to form a gas bubble a t the primary electrodes, which results in fluctuating current. The upper limit may be extended by use of a low I R drop across the secondary electrodes, but this procedure would cause a decrease in accuracy. The limitation given above is not serious, as solutions titrated or measured conductometrically usually lie within the range over which the method is useful. ACKNOWLEDGMENT
The work presented in this paper originated in a study of physical methods for following the course of extractions by observations on aqueous phases that were in contact with immiscible solvent phases. The work was supported by Contract AT(30-1)937 Scope I of the U. S.Atomic Energy Commission to Princeton University. LITERATURE CITED
(1) Andrews, L. V., and Martin, Pi. E., J . Am. Chem. Soc., 6 0 , 8 7 1 (1938).
Britton,’ H. T. S., “Conductometric Analysis,’’ New York, D. Van Nostrand Co., 1934. (3) Eastman, E. D., J . Am. Chem. Soc., 42, 1648 (1920). (4) Gordon, A. R.. et al.. J. Chem. Phus.. 11, 18 (1943): . ,. 13.
(2)
~
(5) (6) (7)
(8) (9)
(IO)
470, 473 (1945); 16, 336 (1948); 19, 752 (1951). Gunning, H. E., and Gordon, A. R., Ibid, 10, 126 (1942). Keen, R. T., and Fritz, J. S., ANAL.CHEM.,24, 564 (1952). Newbery, E., J . C h a . Soc., 113, 701 (1918). Palmer, R. F., and Scott, A. B., J . Am. Chem. Soc., 7 2 , 4 8 2 (1950). Shedlovsky, T. 8., Brown, A. S., and MacInnes, D. A., Trans. Electrochem. Soc., 66, 165 (1934). Siemens and Halske, A.-G., French Patent 819,625 (Oot. 22, 1937).
RECEIVED for review June 10,1952.
Accepted September 11, 1952.
