Electrochemical Method for Oxygen Determination in Gases 42. G. JACOBSON
J . T . Ryan Memorial Laboratory, Mine Safety Appliances Co., Pittsburgh, Pa. The depolarization by gaseous oxygen of a carbon cathode polarized in a galvanic cell showed promise for the development of a method for the measurement of oxygen concentrations in gas mixtures. A study of this effect was made which resulted in the establishment of the basic theoretical concepts and experimental requirements that are important for the use of such electrodes as measuring elements. A brief outline of these concepts and requirements is given in this paper. On the basis of these results,
a portable and a continuous oxygen indicator were developed. The latest improved version of the continuous oxygen indicator is described in detail as to construction, operation, performance, and maintenance. The instrument is produced in ranges from 0 to 1% to 0 to 25f70 oxygen, is capable of an accuracy of 2Yo of full scale range, and is unaffected by carbon monoxide and up to 24% carbon dioxide. I t is easily operated by unskilled personnel, and requires very little maintenance.
E
VER since the creation by Grove of a galvanic cell using gaseous hydrogen and oxygen for electrodes, there have been numerous attempts to make such electrodes and cells available for the measurement of concentrations of hydrogen, oxygen, chlorine, and other ion-forming molecules in gas mixtures. The hydrogen electrode has been successfully developed for a number of laboratory applications and owing to the fact that it is reproducible nithout too much difficulty, is accepted as a primary standard for electrode potential measurements. A4ttempts to develop an oxygen electrode rn hich could be used in a similar manner Gave so far met only with very limited success, The reason usually given is that the oxygen electrode-even when great care is taken with various conditions and precautions-does not behave in a completely reversible manner. Cnfil the chemical and electrochemical processes taking place at an oxygen electrode are fully elucidated it is unlikely that it will be developed as a primary standard. The work of Berl ( 1 ) at Carnegie Institute of Technology and of Weisz and Jaffe (12)of the Thomas A. Edison Co. has s h o m that “in alkaline electrolytes formation of hydrogen peroxide is a major factor and the exchange of a proton between a water molecule and an oxygen molecule is the probable mechanism.” But it has not been proved that some other process-as, for instance, a direct combination of oxygen atoms or ions with hydrogen ions-is completely ruled out or that it does not take place concurrently. For acid electrolytes, it has not even been shown that the hydrogen peroxide formation is the major factor. I t is the author’s bdief, based on observations of his own and of others, that in addition to the hydrogen peroxide formation, other processes take place, and that in acid electrolytes these processes become significant. In determining oxygen concentrations by means of e.m.f. measurements in a practical instrument, there is yet another fact which makes the use of a primary oxygen electrode more difficult: Oxygen is bivalent and therefore in the well-known eypression
Thus, the change from 1 to 2% oxygen would produce a change of only about 4 mv. in e.m.f., and from air to the danger limit of IS%, the change produced is only about 1.5 mv. Twenty years ago or more, when this method was first considered, the small e.m.f. differentials were a serious shortcoming, but a t the present time %-henthere are available a number of good electronic amplifiers, potentiometer recorders, and other means for relatively easy and accurate measurement of small electric potentials, this obstacle is not too serious. However, there is a more serious shortcoming of the primary oxygen electrode, which makes it impractical for applications outside the laboratory-namely, its slow response-which with the very best design and under very favorable conditions is of the order of 3 minutes and in most cases is considerably longer. Realizing these difficulties, in 1933 Paris (11) proposed a different electrochemical method. Instead of a cell of the Grove type, a cell of the Fery type is used with a zinc anode and carbon cathode around which the gas containing oxygen is passed, and not the e.m.f. but the electric current, a t a substantially constant
@Xfl
for the change in e.m.f. when going from partial pressure p , to fi, n must be equal to 4 (3). From this formula, it follows, that for a tenfold change in oxygen concentration, the e.m.f. changes only by 14.5 mv. When a truly reversible oxygen electrode is realized, the standard potential, with 100% oxygen a t atmospheric pressure and 25”C., is 1.220 volts ( 2 ) :
(Air)
Oxygen, % 20.8 16 2 1
0.2
AMXl
Y l N x y l S (RRISABLT TO CAS.
IIpERKI\BLE TO LIQUID)
~ T A T I C A L L cmam V
Volts 1.210
1.2085 1.195 1.191 I . 181
Figure 1. Schematic Flow and Assembly Diagram of Mines Safety Appliances’ Oxygen Indicator Type C Model 2
586
587
V O L U M E 25, N O . 4, A P R I L 1 9 5 3 external resistance, is measured. I n such a cell, the oxygen acts not directly, but by cutting down the polarizing action of the hydrogen ions. When there is no oxygen present a t the cathode, the electric current quickly drops to near zero; nhen oxygen is present, a relatively steady electric current is reached in a matter of less than 1 minute corresponding to an equilibrium condition in which all the hydrogen ions reaching the cathode and/or all the secondary ions formed by them in unit time are removed by combination Aith oxygen. Since currents of the order of 1 to 2 ma. through several hundred ohms are easily obtained, changes of 20 mv. and more per 1% of oxygen are available in this way. Paris showed that this method can be used successfully for measurement of oxygen concentrations up to 2y0 in all nonacid gases, including hydrogen. His curves show a straight line calibration n i t h one type of his carbon electrodes; this, in the light of our present knowledge, appears rather questionable but, even with a nearly straight line characteristic and a range limited to 0 to 2% oxygen, calibration on two knon n oxygen concentrations was necessary, probably, because of the considerable currents at zero oxygen content in Paris’ cells. The work of Paris was repeated and considerably extended in 1939 by two Russian chemists: Noysseef and Brickman (IO). The results of Paris-except for the sti aight-line calibrationnere confirmed; these authors also found independence of gas flow within wide limits and response times of the order of less than 1 minute under some conditions. They established that the response time decreased A ith the external circuit resistance. They also established the fact that this oxygen cell is responsive t o the partial pressure of oxygen, that is, the same current is obtained from 21yo oxygen a t 0.5 atmosphere pressure, as from 10.5y0 oxygen a t 1 atmosphere pressure. They also found a very considerable temperature coefficient (1.9% of the current for 1’ (3.). They showed that the method can be used for up to Y i % oxygen and that n-ith some types of carbon electlodes, it does not matter )\hethe1 the balance of the mixture contains nitrogen or hydrogen. They did riot introduce any changes in Paris’ electrical circuit (see Figure 3, B). The slightly moistened, powdered ammonium chloride used as an electrolyte by LIoysseef and Brickman is of questionable value because of the nonuniform drying out and caking of this material. Work on this method of oxygen determination a t the authoi’s laboratory was started in 1940 and soon led t o the establishment of the folloaing basic principles (6, 6): 1. The current density a t the carhon cathode is of major iinportance in these depolarization cells; it must be kept high in order to have a t all times a quantity of hydrogen ions large enough to avoid fast and substantial depletion of these ions a t the electrolyte carbon interface even bv the largest number of oxygen molecules reacting with them. ( I t should be remembered that this interface is not only a t the exterior surface of the carbon but also extends for some distance inside the pores.) Othernisc a secondary polarization with a creeping approach to equilibrium and a slow response is obtained. 2 . The current density a t the cathode can be made high in several ways. I t has been the tendency of workers in this helti ( I , 9 ) to cover the surface of the carbon cathode s i t h various catalysts in order to obtain greatly increased current capacities; but, although the current density with respect to the apparent outside surface is thus increased many times, the true current density with respect to the actual entire active area-including all the contact areas inside the small pores-is in most cases decreased. In addition, a ith these catalysts, especially those containing various metals, the carbon cathodes cease to be pure oxygen electrodes, showing considerable and varying e.m.f. in the absence of oxygen and, moreover, they become very hard to standardize. The increase of current density by increasing the available e.m.f. by means of auxiliary outside power sources, is limited by the undesirability of hydrogen discharge. The decrease of resistance to values very lorn XTith respect to the internal cell resistance, which in turn is limited by geometrical and constructional factors, introduces large and rapid secondary polarization effects. Thus, the only advantageous way to have high current density in an oxygen detection cell-as dis-
tinguished from a dry or wet cell for power supply-is to make the surface area of the cathode as small as manufacturing considerations and the minimum current output needed for the particular measuring system used will permit. 3. The author has established that by making the active cathode area very small (5 to 40 sq. mm.), not only is a very fast response ( 1 to 2 seconds) obtained, but also a straight-line calibration is approached. I n the author’s laboratory it has been found that current density increased approximately in inverse proportion to the square root of the apparent surface area. On the basis of the above principles, a carbon electrode wae developed which consists of a carbon tube, or a carbon rod drilled through all the way along its axis; all its outside surface is covered with insulating varnish, except for one to four small recesses (windows, see Figures 1 and 2). The electric contact between the electrolyte and the carbon cathode is made only on the external surface of these nindows. The gas sample is conducted through the interior bore of the electrode and penetrates by diffusion through a layer of carbon to the interface between the electrolyte and carbon where any oxygen present combines with the hydrogen ions.
OUTLET
1 CATHODE
. x
I SAMPLE INLET Figure 2.
Carbon Electrode
By 1942 a portable oxygen deficiency indicator was developed, using the above features and concepts (6-7). This instrument was satisfactory for use in the laboratory and in those field a p plications where air for recalibration was available at all times, but was only of limited use in mines, submarines, etc., where rapid temperature fluctuations occur and air for recalibration is not available, unless carried along in the form of a compressed air cylinder or the like. I t appeared a t that time that some shortcomings of this method, especially the temperature dependence, could more easily be taken care of in a continuous instrument than in a portable. There n a s a need for a continuous oxygen indicator that would require less maintenance than the old M.S.B. oxygen indicator with the rotating copper oxidation-reduction electrode (4, 14). Therefore, it was decided to develop this method into a continuous oxygen indicator. In 1944 three continuous oxygen indicators using a depolarization type oxygen detector cell were put out for field tests; after running successfully for about a year, they were put through the engineering and production preparation stages and, in 1947, were put on the market. By 1950 a re-engineering of the instrument n-as undertaken. The instrument described below, the Type C Model 2, is the result of this re-engineering. 3lODEL 2 TYPE C OXYGEN INDlCATOR
Figure 1 shows a schematic flow and assembly diagram of this instrument.
588
ANALYTICAL CHEMISTRY
The heart of the indicator, the oxygen detector cell, is shown in thelowerpartofFigure1 andinFigure 2. It ismadeofaLucitecontainer of about 80-cc. capacity with an anode of zinc and a tubular carbon cathode. This carbon cathode has from one to four recesses, called "windows," the number of windows depending on the oxygen range to be covered. The electrical connection to the carbon electrode is made by means of a metal nipple which is tightly pressed onto its lower part, located outside the cell.
C
Figure 3. Basic Circuits for Oxggen Indicator Using Electrochemical Polarization
The electroljte, to xhich the trade name of oxylite has been given, is a composite solution with a pH of 3.0. With this electrolyte and with the new electric circuit, it is no longer necessary to scrub out carbon dioxide from the sample gas in concentrations up to 24% by volume. I n order to shorten the stabilization time and increase the accuracy, especially in the 0 to 1% oxygen range, the Oxylite is subjected to a deoxidation procedure, which removes dissolved oxygen down to less than 0.01%. This process is carried out after the Oxylite has been placed in small bottles and just before sealing them. Figure 3 shows the three basic circuits used with this method. Circuit A is a simple series resistance circuit in which the electric current obtained with various oxygen concentrations is measured after adjusting the external resistance to a desired value and then keeping it constant for a series of tests. This is used by the author in many testing procedures. Circuit B is the circuit used by Paris (II), by Moysseef and Brickman (IO), and in the first portable model designed in the author's laboratory. The resistance of the electric meter branch is made large relative to the potentiometer part that is in shunt with the meter and therefore the circuit is substantially a constant external resistance circuit. I t differs from circuit A in that it permits setting of the instrument on air to a reading of 20.8% and use of a scale made up in accordance with an experimentally established curvature. Heretofore, calibration on a t least asecond oxygen concentration was required because the curvature varied between individual electrodes and for the same electrode u ith age. Circuit C is the basic R1.S.A. circuit. An auxiliary cell, mostly a h-0. 2 dry cell, is introduced by a connection somewhat similar to the compensating battery of a potentiometer, the oxygen cell being in the position of the measured e.m.f. The main objects of this arrangement are: (1) to cut the current through the oxygen cell down to not over 100 or 50 pa. while keeping the circuit resistance as low as desired; (2) to obtain fast response and a close approach to a straight-line calibration; ( 3 ) in the first continuous model, this circuit was also used to reduce greatly the slow longterm drift, by opposing a nearlj- equal drift in the dry cell output to the drift in the detector cell; and (4) to allow a wide adjustment of the calibration, without introducing large changes in the total circuit resistance. In the latest circuit (Figure 4), the drift correction function has been transferred t o a different circuit, powered by another dry cell: Briefly, the electrochemical basis for the improvements provided by circuit C are as follows: Kumerous tests have shown that when the oxygen detector cell is inserted in any of the electric circuits of Figure 3, and all electrical circuit elements exterior to the detector cell are kept constant M hile the oxygen concentration, C, is being changed, the total change in electric power, W ,is proportional to the change in concentration. Khen the electric poner in the absence of oxygen is also zero, Tye have (simple as this and the folloaing relationships appear, their theoretical derivation by thermodynamics of irreversible processes ir rather complicated; moreover,
The cell is placed inside the air well of a thermostatically controlled water bath. An electric heater operates from 24 volts alternating current and a Fenwal thermostat is used to control the temperature within =t1% and a t a point a few degrees higher than the highest ambient temperature likely to occur. Sample flow does not influence the indication as long as it is more than 20 cc. per minute and as long as it does not become high enough to change materially the temperature or pressure at the carbon electrode. Flows up to 2 liters per minute through the electrode are oermissible and nressures un to 6 inches of watkr. To keep thebressure cdnstant, an automatic check valve and an automatic pressure regulator on the sampling line are employed. I n order to decrease the time for bringing the sample to the instrument, large flows of 10 liters per minute or more are employed, of which the major part is by-passed back to the source or out to the atmosphere. After passing the electrode, the sample goes throughan electric flon-indicatorwith a full-scale deflection of 150 cc. per minute. From there it passes through a bubbler filled with a longlasting silicone liquid. Besides indicating the presence or absence of sample flow, this bubbler serves to prevent oxygen from entering the cell from the exhaust by diffusion or by gusts of wind. The electrical flow indicator, even though the detector is not flow-sensitive, is useful for the sake of economy in the bottled zeroing and calibration gases, scrubbing materials, etc. The windows of the M.S.A. carbon electrodes are machined to exact tolerances which a good Figure 4. machine shop can maintain without difficulty.
Circuit Diagram for Ox)-gen Indicator
589
experimental curves agree with those derived from formula 2 xithin better than 2% for I and better than 501, for E , except for oxygen concentration below 2%) m-here the experimental errors are higher. The curves of Figure 5 show that when Y = 0.9, a close approach to a straight-line relationship for the electric current produced by oxygen from 20.8% domn to very low oxygen concentrations is obtained, and that the e.m.f. for the same oxygen concentrations changed according to the formula mith the exponent Z = 0.1: Khen the current change mas expressed by curve Y = 0.7, the e.m.f. followed curve Z = 0.3. In other R o d s , the more rapid the change in the electric current, the less rapid the change in the e.m.f. Inspection of circuit C (Figure 3) shows that, although the electric currents (going through the oxygen detector cell) derived from the cell itself and from the dry cell, respectively, are opposed to each other, and the net electric current is the difference between the two, the e.m.f.’s from the oxygen cell and the outside source are in the same direction and add up to a higher concen. - net e m f . With varying- oxygen trations, only the e.m.f. and current of the oxygen cell change, while the e.m.f. derived from the outside cell having sufficiently high resistance in series with it, remains substantially constant. Hence, this arrangement provides a slon-er change in the e.m.f. and a faster change in the electric current corresponding to a higher Y and a lower Z in Formulas 2 and thus a closer approach to a straight line calibration than would have been possible with circuits 3 A or 3 B. Expression 3 above suggested that if the oxygen measurement is conducted in such a way as not to keep I?,,,. constant but t o change ReIt. for every new oxygen concentration, in order t o bring I back to a constant value lo,then for two oxygen concentrations C, and CI,
it involves several assumptions as to the electrochemical processes a t the electrode and their thermal characteristics, which are still highly controversial, and therefore the writer prefers a t this time to present these formulas simply as an expression of experimental results):
W
=
K,C
(1)
Both the electric current, I , and the e.m.f., E, as a function of the oxygen concentration, C, can be expressed by formulas of the type : I = kCu and E = k2C8 (2) Electric pon er W being equal to 1 X E,
IE
klk2Cuiz
K,C
(3)
Hmce, l / + z = l
(4)
The correctness of this conclusion is evidenced by the curves, Figure 5, which were obtained by direct measurements of the electric currents obtained for varying oxygen concentrations and by calculating the corresponding e.m.f. from the Ohm’s laly relationship E -I X (R,,, +RInt ) after having measured the internal resistances for each point by the method of Mance (8). All
Figure 7 .
Calibration Curve
For very high external resistances, Rint. can be neglected and then 5 is replaced by: IT* =
R,r?
T’I
next 1
=
‘21
(6)
where V is the terminal voltage which can be measured directly. Inasmuch as the electric current is the major determining factor of
590
ANALYTICAL CHEMISTRY
the internal resistance, the latter, when I is kept constant, is subject only to very mmll changes and, therefore, as was confirmed by numerous experiments, a straight line relationship was obtained between oxygen concentration C and V or Re,$. for very wide ranges of oxygen variations, even with moderate external resistances, and thus without having to use very small currents. This gives a method whereby, with any pure carbon electrode having a good zero,only a single test on a known oxygen concentration is necessary to determine any number of known oxygen concentrations.
bigure 9. Oxygen Indicator
meter scales and special recorder charts made, SO that no earrections are necessary. Thus, there is no loss in &ccur&cyhut a considerable gain in ease and quickness of operation. Figures 8, 9, and 10 show photographs of the latest model. Figure 8 shows the outside view with the case entirely closed. Figure 9 shows a view of the panel, after the outside door is opened. This panel has three oontrol knobs and one switch. Figure 10 shows the inside of the instrument case after swinging out the hinged panel. PERFORMANCE
Figure 8. Continuous Oxygen Indicator
It is, obviously, possible instead of returning t o a constant current I, t o return t o a constant e.m.f., E; but inasmuch as E in denolariaation cells is extremelv difficult to measure directlv with
..
..
straight line is obtained. (One possible reason for this, in addition t o neglect of power loss inside the cell and, probably, low current density, is the distinctive feature of these electrodesthe incorporation of five or more various metals in the carbon, which makes them not pure oxygen electrodes but produces a potential which is an agglomeration of oxygen potential and several metal and metal oxide potentials,) Very wide variations in curvature for different individual electrodes of the same material and construotion are obtained necessitating standardization tests on at least two known oxygen concentrations before determinations of unknown concentrations can be made. Thus, no advantage is gained over the methods of former workers in this field (6, 10, 1 1 ) . The procedure is also considerably complicated by the additional potential measurements required in every test, especially if carried out, as suggested by the authors, by means of a potentiometer (9). Even thoueh returnine the electric current to a constitnt value is much simpler than returning the e.m.f. or even the terminal voltage, the simple deflection method is used in the latest continuous M.S.A. instrument. The external resistance R is kept substantially constant. Owing to the circuit arrangement and close standardieationofeleetrodes,theinstrumenthasconstantcalifar oxygen ranges and all electrodes. This bration ~~
~
Operations Required. To operate this instrument, a source of a gas mixture with a known oxygen concentration is necessary for all ranges, except the one from 0 to 25%, which uses air for standardization. Also, a source of zeroing gas is needed. Calibration on known oxygen is required once every 24 hours. Zero check and adjustment every 24 hoursfor the first Zdaytys, after that once a week, except with the 0 t o 1%range in cases when the sample normally contains less than 0.2% oxygen, are necessary. Accuracy for several hours after recalibration is 8 s close as the chemical analysis of the known cylinder can be made. Usually this is better than 2% of the full-scale range, except for coneentrations below 0.5% oxygen.
Figure 10. Oxrgen Indieator
~
calibration curve shown in Figure 7 is somewhat farther away from a straieht line than in thehasic circuit. C. hecauseoftheintroduction of the improved drift circuit. However, there are special
The drift in indicators with automatic recorders can n o n easily he adjusted t o he less than 5% of the full-scale range in 24 hours. Sensitivity is 1/100 a i the full-scale range. ~h~ start of operations from standstill takes 0.5 hour until spot tests can be made and about 1.5 hours until recording for a t least an 8-hour unattended period can be made, Electrolyte is checked usually once a week; if low, electrolyte is added, &hout removing or disconnecting the cell; operation is interrupted for 15 to 20 minutes. M:hen the sample is not exceptionally drv. sddition of electrolvte is not needed oftener than once in 2 or 3 ceeks.
591
V O L U M E 25, NO. 4, A P R I L 1 9 5 3 The electrodes last on an average for 6 weeks with a minimum of 3 weeks. The drift circuit dry cell lasts a minimum of 1 week, and an average of 3 weeks; the other 2 dry cells usually last for the entire life of the electrode. Exchange interruption lasts about 15 minutes. ACKNOWLEDGMENT
In the later phases of this development work, the author was ably and devotedly assisted by Frank J. DeLuca of the Mines Safety rlppliance Research Laboratory and in the re-engineering by A. C. McInnes of the Engineering Department, to both of whom a feeling of deep gratitude is herewith expressed. LITERATURE CITED
(1) Berl, W. G., Trans. Electrochem. Soc., 83,253 (1943). (2) Glasstone, S., “Electrochemistry of Solutions,” 2nd ed., p. 335, Kew York, D. Van Nostrand Co., 1937. (3) Glasstone, S , “Textbook of Physical Chemistry,” p. 928, New Tork, D. Van Sostrand Co., 1940.
Jacobson, 11.G. (to Mine Safety Appliances Co.), U. 5. Patent 2,156,093 (.May 2, 1939). Ibid., 2,464 087 (March 8, 1949). Ibid., 2,540,674 (Feb. 6, 1952). Ibid., application pending. Kohlrausch, F., “Pratische Physik,” 17th ed., p. 569, Sew York, Rosenberg, 1944. Kordesch, K., and hfarco, -i., Nikrochemie ver. Microchim. Acta, 36, 420 (1950). Moysseef. A. S., and Brickman. N. M..APPZ. .. Chem. (U.S.S.R.). 12, 620 (1939). Paris, 9.,Chimie & industrie,31, 253 (1933). Weisa, R. S I and daffe, S. S., Trans. Electrochem Soc., 93, 128 (1948) Wiener Isolierrohr, Batterie &- hletallwarenfabrik, Austrian Patent 167,840 (March 10, 1951). Yant, W. P., Jacobson, M. G., and Strange, J. P. (to Mine Safety dppliances Co.), U. S. Patent 2,401,287 (May 28, 1946). RECEIVED for reiiew J u l y 28, 1953. Accepted January 12, 1953. Presented before the Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy, March 1952.
Dual Intermediates in Coulometric Titrations Equilibria in Copper( +Bromide
Solutions
PAUL S. FARRINGTON: DALE J. MEIER, AND ERNEST 13. SWIFT California Institute of Technology, Pasadena, Calif. The work has a twofold purpose: to demonstrate the feasibility and usefulness of alternately electrolytically generating oxidants and reductants during the course of coulometric titrations, and to show the application of amperometric measurements made with polarized platinum electrodes to the determination of equilibrium constants. Experiments have shown that having a solution of cupric copper and bromide, one can electrolytically generate a known excess of bromine and then quantitatively reduce this by electrolytically generated cuprous copper, or similarly produce an excess of cuprous copper and reduce i t by bromine. Amperometric measurements can be used to determine very small concentrations of bromine and of cuprous copper. The results demonstrate the possibility of making coulometric back-titrations where an excess of reagent is required because of the slowness of the main titration reaction. A value has been obtained for the formal potential of the half-cell reaction CuBr-- = C u + + 2Bre-.
+
+
A
Ti AMPEROMETRIC method, similar in principle to the
dead-stop method of Foulk and Bawden ( 5 ) ,but modified to make use of the measurement of the current flow between two similar platinum electrodes with impressed potential differences ranging from 50 to 300 mv., has been employed for determining the end point of secondary coulometric titrations involving the electrolytic generation of bromine (10, 12), iodine (11). chlorine (S), and cuprous copper (9). Experience has shown that in many cases this method has certain advantages as compared with conventional end-point procedures. Thus, constant readings are attained more rapidly than is the case with potentiometric procedures, and titrations can be made more rapidly. The latter advantage is emphasized by the linear relation between current and concentration of titrant, since the titration can be made rapidly, the equivalence point overrun, and the excess of titrant accurately 1
Present address, University of California, Loa Angeles, Calif.
determined. rllthough concentrations of the above titrants of the order of 1 0 - 7 formal are readily determined, only limited use has been made of this fact for either analytical or physicochemical studies. In addition, the method is unusual in that continuous measurements of concentrations of the above magnitude can be made over extended periods by means of an ordinary microammeter and, although a significant current is continuously passed through the solution during such periods, the composition of the solution remains unchanged because the same half-cell reaction is proceeding in opposite directions a t the two electrodes. The above considerations have seemed to justify amperometric studies of those half-cell reactions of probable value for either analytical or physicochemical measurements. The results of such a study, made with solutions containing both cupric copper and bromide ion are presented below. Bromide solutions have been used for the electrolytic generation of bromine as an oxidant for secondary coulometric titrations, and solutions containing cupric copper have been similarly used for the generation of cuprous copper as a reductant. I n certain titrations with bromine, such as the determination of bromine numbers, it is necessary to add an excess of bromine, to wait for completion of the titration reaction, and then to back-titrate the excess bromine. Since it seemed that this might be done coulometrically in solutions containing both copper( 11)and bromide, a study was undertaken to investigate the indicator currents resulting from alternate anodic and cathodic generation in solutions containing these substances as dual intermediates. In the course of this study it was observed that the indicator current never decreased t o zero but always had an appreciable minimum value. If it is assumed that this minimum indicator current is caused by the cuprous copper and bromine produced by the reaction, 2Cu++
+ 7Br-
= 2CuBrz-
+ Br3-
it is possible to derive a relationship between the minimum indicator current and the equilibrium constant for the above reaction. I n this derivation both anode and cathode reactions are considered. Kolthoff and Lingane ( 6 ) have made similar calcula-
