483
V O L U M E 27, NO. 4, A P R I L 1 9 5 5 LITERATURE CITED
Berzins, T., and Delahay, P., J . Am. Chem. SOC.,75,4205 (1953). Butler, J. A. V., and ilrmstrong, G., Proc. R o y . SOC.( L o n d o n ) , 139A, 406 (1933).
Butler, J. A. V., and Armstrong, G., T r a n s . Faraday SOC.,30, 1173 (1934).
Cottrell, F. G., 2. physik. Chem., 42, 385 (1902). Delahay, P., J . Am. Chem. SOC.,75, 1430 (1953). Delahay, P., Office of Naval Research, Project NR-051-258, Rept. 14, 1953; Discussions Faraday SOC.,in press. Delahay, P., and Berzins, T., J . Am. Chem. SOC., 75, 2486 (1953). TIME A
Figure 8.
Delahay, P., and Mattax, C. C., Ibid., 76, 874 (1954). Delahay, P., Mattax, C. C., and Berzins, T., O5ce of Kavd Research, Project NR-b51-258, R e p t . 15, 1954; Appendix by G. Mamantov and P. Delahay. Delahay, P.,and Strassner, J. E., J . Am. Chem. Soc., 73, 5219
TIME
B
Graphic determination of transition time
(1951).
other electrochemical methods of analysis and in particular conventional polarography: good precision; no fluctuation in the measured quantity (in contrast with the fluctuations of the diffusion current in polarography); possibility of determining concentrations as low as 10-eM; possibility of using solid or mercury electrodes; possibility of analyzing certain two-component systems without preliminary separation (see above); and utilization of instruments in which the electrolysis can be stopped automatically a t the transition time, as was demonstrated by the work of Sartiaux ( $ 3 ) . Two disadvantages should be mentioned: no steady reading is observed; and consumption of mercury is larger than in polarography. Finally, voltammetry a t constant current is a useful tool in electrochemical kinetics
Evans, M. G., and Hush, X . S., J . chim. phys., 49, C 159 (1952). Gierst, L., and Juliard, A., J . P h y s . C h a . , 57, 701 (1953). Gierst, L., and Juliard, A., Comit6 intern. thermodynam. et cinht. dlectrochim., Compt. rend. 2nd RBunion, M i l a n , 1951, pp. 117, 279.
I
HeyrovskS., J., A n a l . C h i m . Acta, 8 , 283 (1953). Heyrovskg. J., Discussions Faraday SOC.,1, 212 (1947). Karaoglanoff, Z . , 2. Elektrochem., 12, 5 (1906). Kolthoff, I. M., and Lingane, J. J., “Polarography,” 2nd ed., Interscience, New York, 1952. Koutecky, J., Chem. Listy, 47,323 (1953). Lineane. J. J.. I n d . E n a . Chem.. A n a l . Ed.. 15. 588 (1943). Reihy, C. K.,Everett,-G. W., and Johns, R. H., ANAL. &EM.,
ACKNOWLEDGMENT
27,483 (1955). (21) Rius, A., Llopis, J., and Polo, S., A n a l e s f i s . y qulm. ( M a d r i d ) , 45,1029 (1949). (22) Sand, H. J. S., P h i l . M a e . . 1.45 (1901). (23) Sartiaux, J., thesis, Licencib en Sciences, University of Brussels, 1952. (24) Smutek, M., Collection Czechoslm. Chem. Communs., 18, 171 (1953). (25) Stackelberg, M. van, Pilgram, M., and Toome, V., Z. Elektrochem., 57, 342 (1953). (26) Turner, R. C., and Winkler, C . A., J . Electrochem. Soc., 99, 78 (1952). (27) Weber, H. F., W i e d . Ann., 7, 536 (1879).
This investigation was sponsored by the Office of Naval Research. The authors take pleasure in acknowledging their indebtedness to this organization.
RECEIVE forDreview M a y 24, 1954. Accepted August 4, 1954. Presented before the Division of Analytical Chemistry a t the 126th Meeting of the A M E R I C ACHEMICAL N S O C I E T YNew , York, E.Y . Apparatus for application of the method will be made available by Sargent & Co., Chicago, Ill.
(6-8).
Voltammetry at constant current appears to be a promising new analytical tool. I n future work it might be worth while to designate this method by the term “chronopotentiometry,” which is less cumbersome than “voltammetry a t constant current.”
Voltammetry at Constant Current Experimental Evaluation CHARLES
N. REILLEY,
G R O V E R W. EVERETT, and R I C H A R D H. JOHNS
University of North Carolina, Chapel Hill, N . C.
The feasibility of voltammetry at constant current (chronopotentiometry) as an analytical method is elucidated in the cathodic reduction and anodic oxidation of simple ions at platinum and mercury pool electrodes where transition times vary between 4 and 60 seconds. Interpretation of potential-time curves yields successful analytical results for solutions of single and mixed ions in concentrations of 5 X 10 -s to 1 X 10 + M . Theoretical and experimental comparisons to other polarographic methods are discussed. Several supporting electrolytes are examined, and practical apparatus and technique are described.
C
LASSICAL polarography has in 20 years attained a position of unique importance in analytical chemistry. While there has been great progress in instrumentation and technique, the method is hampered by two characteristics of the dropping
mercury electrode itself: The charging current of the growing drop is exceedingly large, and the pulsating nature of the meaaured current variable makes its evaluation difficult. These factors constitute a practical limitation to analytical polarography in lower concentration ranges where the diffusion currents encountered are small. Several recent contributions to the polarographic field have been directed toward enhancing the sensitivity of the method by lessening the charging current of the system caused by an increasing electrode surface area. Stationary and moving platinum electrodes are advantageous in this respect, but lack the surface reproducibility and favorable hydrogen overvoltage of mercury. Mercury macroelectrodes have proved advantageous in oscillographic polarography but, because of the short scanning interval involved, the charging current density is relatively great (5). From the analytical standpoint (especially for voltammetry a t constant current, chronopotentiometry, where voltage-scan or transition times are made relatively long for accurate measure-
ANALYTICAL CHEMISTRY
484
ments), the quiet mercury pool electrode would seem ideally suited. Its surface is constant and reproducible, and its hydrogen overvoltage is high. The strictly linear diffusion problem encountered with a pool may be treated more rigorously than that of a growing spherical drop. While the surface area of the electrode has no theoretical influence upon the detectability of the electroactive species, a large pool is practically advantageous in being flatter and more reproducible. The pool used here is slightly less than 2 cm. in diameter, and platinum electrodes used for comparative studies are of similar area. The measurement of transitory phenomena affords a unique analytical advantage: The combined ability to use quiet solutions (because a state of complete rest can be better reproduced than a state rvith a definite stirring action) and electrodes of constant area (to minimize charging current). The transitory methods might be classified along the following pattern: A. Application of potential to electrode-solution interface and measurement of resulting transitory current 1. Potential constant with time 2. Potential varies linearly with time 3. Potential varies sinusoidally aith time 4. Potential varies as square-wave with time 5 . Potential with small superimposed alternating current potential varies linearly with time 6.
...
B. Application of current to electrode-solution interface and measurement of resulting transitory potential 1. Current constant with time (“chronopotentiometry”) 2. Current varies sinusoidally with time 3.
C.
tween their half-wave potentials. Furthermore, in method A 2 as the time required for the total scan should not exceed about 60 seconds, the wider the separation of the half-wave potentials between the first and last waves, the greater will be limitation on the minimum rate of scan that can be tolerated. Thus two species with half-wave potentials very widely separated cannot be determined in as low concentrations as for two species with halfwave potentials closer together. S o consideration of this type is necessary for chronopotentiometry. Streuli and Cooke (6) have used quiet mercury pools in the A 2 technique, and have obtained better sensitivity than that available in conventional dropping mercury electrode polarography; a comparison b e b e e n their results and those obtained by chronopotentiometry is therefore of interest.
Ag/AgCI
.
Indirect application and measurement of current and/or potential 1. Bridge methods 2.
Methods A 2 and B 1 have the advantages of covering a potential spectrum in a single trial and yielding results that may be interpreted in a relatively simple and straightforward manner. I n addition, these two methods have properties which allow the distorting effect of the charging current to be minimized. I n chronopotentiometry, the charging time component varies inversely with the current density, whereas the transition time for the diffusion-controlled electrochemical reaction varies inversely with the square of the current density. Thus halving the current density will double the charging time, but will increase the transition time four-fold. The use of smaller current densities, necessary for very low concentrations, actually produces an enhancement of the response ratio of the system, and yields a great overall sensitivity. The ultimate limitation for increasing the response ratio by decreasing the current density occurs when the transition time becomes greater than approximately 1 minute. After about 1 minute, convection currents begin to contribute and abnormally large and erratic transition times are encountered. Linear voltage-scan polarography, transient method A 2, has a similar advantage. The charging current is proportional to the scanning rate. Hence, for less distortion, lower scanning rates must be used, but this in turn causes the peak-current response t o decrease. This decrease in peak-current response may be compensated t o some extent by using more sensitive current recorders. The real limitation in decreasing the scanning rate is caused whenever the time required to scan the voltage from the foot of the first wave to the peak of the last wave exceeds about 1 minute. If longer times are employed, convection currents will begin to contribute and results will be erratic. Chronopotentiometry has a definite advantage over method A 2 for systems containing more than one reducible species. I n method A 2 the peak current for the second wave depends upon the concentration of the species yielding the first wave, the concentration of the species yielding the second wave, and the difference between the two half-wave potentials. I n chronopotentiometry, the height of the second wave depends upon the concentrations of both species, but is independent of the difference be-
1 1 Figure 1. Chronopotentiometry cell
The present evaluation of chronopotentiometric analysis is based upon constant-current, diffusion-controlled electrolysis in unstirred solutions ( 3 ) . Included are a study of single- and multiple-iron reductions at the mercury pool electrode; an investigation of several background electrolytes; and a comparison of theoretical and practical relationships among current, concentration, and transition time. Use of the platinum electrode is investigated and discussed for the sake of comparison with polarographic techniques. APPARATUS AND MATERIALS
Electrolysis Cell. The cell used for chronopotentiometry is adapted from the design of Streuli and Cooke ( 5 ) , and is illustrated in Figure 1.
It consists principally of a glass cylinder, 2 cm. in diameter, connected through a sintered disk to a silver-silver chloride reference electrode. A stopcock at the bottom of the cell permits easy draining, and an integral glass jacket provides for the circulation of constant-temperature water (25’ f 0.1” C.). The ground-joint top supports a small platinum wire electrode and a bubbling tube terminating in a sintered disk; the fritted glass increases the dispersion of nitrogen used in sweeping, thereby decreasing the time necessary for oxygen removal. A threeway stopcock may be adjusted for the initial sweeping of the solution, or alternatively. for the passage of nitrogen above the solution during electrolysis. The pool electrode consists of about 5 ml. of mercury, to which
V O L U M E 2 7 , NO. 4, A P R I L 1 9 5 5
485
electrical contact is made by a platinum wire fused into the glass; the area of the pool was calculated to be 2.76 cm. A coating of Beckman Desicote on the inner surface of the cell prevents wetting of the glass by mercury or solution, thus maintaining a mercury-solution interface of constant area. An auxiliary cell top supports a platinum foil electrode for use in electrolysis a t the platinum surface. Delahay ( 2 ) developed the cell shown in Figure 2. He and RIamantov used it to obtain the very precise results in the electrolysis of iodate which are presented in Table I. ThelolTer plug is of Lucitc, and the mercury cavity is accurately machined on a lathe. Because Lucite is n e t by neither mercury nor solution, the interface is constant and reproducible. The area of a mercury pool depends upon the potential because the extent of curvature around the edge of the pool depends upon the interfacial tension, which in turn depends upon the potential. The use of large pools minimizes this consideration. The reference electrode is very close to the mercury surface, thus minimizing the effect of ohmic potential differences caused by the electrolyzing current.
ez-T 3
4
;ti
METER
I
RECORDER POTENTIAL INTERVAL
I
Figure 3.
7
~ S T R I P ~ ~ C H A R T
TIMER
1.5 V.
POTENTIOMETER
S. C. E.
e
Current Supply. Electrolysis current is supplied by a bank of five 45-volt dry batteries connected in series and tapped for various potentials as shown in Figure 3. A series of fixed resistances is inserted in the circuit in such a way that, by varying both voltage and resistance, a large variety of constant currents from 10-3 to 10-7 ampere may be obtained. Current values were calibrated, while electrolysis was in progress, by measuring‘ the potential drop across a standard resistance by means of a potentiometer.
E.
Circuit for chronopotentiometry
Series of 45-volt batteries with tans for 90-225 volts
R1. R2. el. ex. e3.
ereg. ei-eg.
Polarizing current circuit Potential indicating circuit
LBrS pH meter, line-operated Model 7664
Figure 2.
Table I.
Chronopotentiometry cell (2)
Precision for Transition Time Determinations with Mercury Pool 7 Dev.,
sec. 58.5 58.4 58.55 57.9 58,5 58.6 58.95 58.6 58.8 58 45 58.5
5%
0 -0.17 -0.08 -1.03 0 0.17 0.77 0.17 0.51 -0.08 0.30
5.5.15 55.9 55.45 54,s 55.1 55.3 55.35 54.9 55.0 55.05 55.2
-0.09 -1.27 0.45
-0.73 -0.18 0.18 0.27 -0.54 -0.36 -0.27 0.43
56.9 57.65 57.5 57.35 57.8 57.5 57.85 57.0 57.5 57.5 57.5
-1.04 0.26 0 -0.26 0.52 0 0.61 -0.87 0 0 0.36
x
10-4~d++. Moles{L. (4, 6) 7, Dev..
see.
%
37.5 37.7 38.9 39.1 38.5 38.3 37.3 39.1 38.0 37.5 38.2
-1.8 -1.3 1.8 2.4 0.78 0.26 -2.4 2.4 -0.52 -1.8 1.55
\_.6y”Supporting electrolyte 0.1M KNOs, I measured at -0.578 volt (S.C.E.). b D a t a supplied b y Delahay a n d M a m a n t o v (9).
Measuring Circuit. The changing potential of the working electrode is followed during electrolysis by a direct-reading millivolt meter of high input resistance. -4 Leeds and Xorthrup Catalog 7664 pH meter serves the purpose, and its output n-as connected t o a potentiometer-type strip-chart recorder. The Brown Electronik recorder with a full-scale scanning speed of 4.5 seconds and a chart speed of 8 inches per minute \vas used. The changing potential may be followed with fair accuracy by watching the millivolt. meter and timing the scanning interval between t n o points by means of a stop watch. Automatic interval timing could be attained by connecting the output of the meter of a trigger relay system, which would start and stop a timer a t predetermined potentials. Chemicals and Solutions. Chemicals used \yere of reagent grade and n-ere analyzed as necessary by conventional procedures. Stock 0.lM solutions Tvere prepared from the nitrates of thallium, copper, cadmium, bismuth, lead, and zinc; solutions of potassium ferrocyanide, ferric chloride, and ferrous chloride were also prepared, and all were diluted volumetrically to the concentrations used in electrolysis. I t was found that water produced by a Barnsted Bantam ion exchange demineralizer contained less electro-reducible contamination than the available distilled water. The standard supporting electrolyte was potassium nitrate in either 0.1 or 0.01M concentration. Hydrochloric, nitric, and sulfuric acids were used where noted, as well as potassium chloride and buffered phosphate (pH 7.2). Commercially obtained mercury was found to contain impurities which caused erratic results. Mercury ?vas redistilled in the laboratory and freed of last traces of oil by allon-ing it to stand for a few hours in a grease-free buret. Nitrogen used for sweeping was of the oxjgen-free Seaford grade (hir Reduction Co.), and was used without further purification. I t was saturated n ith water vapor a t 25” and led to the cell through a system of Tygon tubing. PROCEDURE
The cell is mounted on a special heav3- stone ring stand, springsupported and further cushioned n-ith sponge rubber to minimize vibration. A pump provides circulation of constant-temperature water to the outer jacket of the cell. Five milliliters of mercury are run into the cell to form the pool electrode. Alternatively, the pool is omitted and a platinum foil electrode, supported by an auxiliary cell top, is used. Approximately 20 ml. of solution are added, and the three-way stopcock is adjusted for bubbling of the liquid with nitrogen. After a bubbling period of 10 to 20 minutes, the gas flow is changed for
ANALYTICAL CHEMISTRY
486
sweeping of the upper portion of the cell, and the system is allowed to come to a complete state of rest before electrolysis is begun. A double-pole single-throw switch could serve to start the electrolyzing current and the chart drive of the recorder simultaneously. However, more accurate results are obtained by allowing the chart drive to come up to full speed before the electrolyzing current is turned on. When no electroactive species is present, the cathode potential sweeps rapidly and continuously to the decomposition voltage of hydrogen ion, and the recorded potential-time curve, of the type shown in Figure 5, registers merely the charging of the double layer of the working electrode. If, on the other hand, a n electroactive ion is present in the solution. the Dotential scans raDidlv. as before. to the decomDosition potential ion; then'a potential occurs concentraas'a dEusion layerbfis that established. When a stateholdup of complete tion polarization is attained, the scan continues, but a t a reduced
Pb
0
40-
W
Zn
H -
+
Cd 20-
......
.. .. 0
,
-0.3
Figure 4.
-0.7
.05
-09
-1.1
Potential-time curve for lead, cadmium, and zinc ions
.
Merciirv KXOa .~ -~". no01 urine - . .0.1M ~~ ~ Lead ion 1 X 10-3 M , 1.8 X 1 0 - 4 ampere Cadmium ion 6.90 X 10-4 M , 1.8 X 10-4 ampere Zinc ions 1.15 X 10-3 M ,2.73 X 10-4 ampere ~
~
~
~~
o
02
-02
-04
-06
-0.8
POTENTIAL (vs.S.C.E.,
-io
-12
-14
-16
volts )
as the working electrode, solutions of 0.1 or 0.01.44 potassium nitrate are found to be the most useful. The generation of hydrogen does not begin until well beyond 1.0 volt (os. S.C.E.) for currents of 3.5 X 10-6 ampere or larger, and hence would cause no interference in the reduction of many ions. The method of plotting is taken to resemble purposefully that of polarographic convention, in which cathodic currents are represented by a positive current scale and anodic currents by a negative one. As time is the measured variable in chronopotentiometry, cathodic transition times are plotted above the zero axis while anodic transition times are measured below it. One effect must be realized which may be ascribed to the adsorption of oxygen or a thin layer of mercuric oxide on the mercury surface, since it persists despite prolonged sweeping of the solution with nitrogen. It was often noticed that an
-
60-
-$
I
I
~
The coupling circuit between the pH meter and recorder is so arranged that the full strip-chart width corresponds to a scan of 1 volt. A variable auxiliary 1.5-volt source, placed in series with the input to the meter, provides a bucking potential which allows any 1-volt scan within the range of -2.5 to +2.5 volts to be recorded. Two runs per solution may be made with reproducible results.
If more trials are attempted, the transition times decrease, owing
layer, showed practically complete elimination of this wave. Also the transition times of ions reduced a t more negative potentials than this anomalous wave were practically the same for the two trials. Had this anomalous wave been caused by an impurity in the solution, the height of the subsequent waves would have been enhanced, following the general theory of consecutive reductions discussed later. Bowden and Rideal ( 1 ) in their
Table 11. Chronopotentiometric Analysis of Potassium Ferrocyanide Solution by Anodic Oxidation with Platinum Electrode I ~ I I ~ C Z I! I+!=, 4
6
8
10
RESULTS
Background Electrolytes. Potential-time curves resulting from the electrolysis a t several current densities of two supporting electrolytes are shown in Figure 5. With the mercury pool
Amp. 104 2.93 4.40 5.87 7.47 4.40 5.87 7.47 8.90 11.9 5.87 7.47 8.90 11.9 15.0 7.47 8.90 11.9 15.0
x
to reduction of the bulk concentration in solution. The deviation becomes more pronounced for smaller currents and larger pools. The requirement of frequent changes of a relatively large quantity of mercury constitutes one of the most serious disadvantages of the method. Transition times may be arbitrarily varied over wide limits by appropriate selection of electrolyzing currents. In practice, scans of less than 4 seconds are likely to be distorted by the lag in response of the recorder, while scans appreciably longer than 1 minute are more subject to the effects of convection in the solution ( 4 ) . The diffusion layer extends further into solution with longer times and hence is more susceptible to distortion by vibration.
35.8 15.4 8.4 5,3 35.8 19.5 12.2 8.4 4.5 37.9 23.6 16.1 8.8 5.6 35.5 24.9 13.5 8.4
Amp. Sec.l/' x 108 1.75 1.73 1.70 1.72 2.64 2.59 2.61 2.58 2.52 3.60 3.60 3.57 8.54 3.56 4.44 4.44 4.37 4.35
Average Average deviation % ' average deviation a
C in moles/ml.
x
C lo+'
0.438 0.433 0.425 0.430 0.440 0.432 0.435 0.430 0.420 0.450 0.450 0,446 0.442 0.445 0.444 0.444 0.437 0.435 0.438 0.0068 1.55
487
V O L U M E 27, NO. 4, A P R I L 1 9 5 5
that cleaning decreased the hydrogen overvoltage of the electrode but did not alter its effective area. With the platinized platinum electrode, the curves were neither as reproducible nor as well defined. The evolution of hydrogen from the hydronium ion as well as from water began a t more positive potentials, as would be expected Platinizing an electrode will increase its projected area only slightly, but its microscopic u $ 10area will be increased manyfold. At low current densities, the diffusion layer will extend W 0.5 M H C I well beyond the surface roughness and the transition time will therefore depend more upon the projected area than upon the microscopic area. IO Thus the height of the hydrogen wave is in1.0 0.8 0.6 0.4 a2 o -02 -04 -as -0.8 -1.0 creased relatively little by platinization. The steep slope of the curve in the region just beyond P O T E N T I A L ( v s . A g CI reference ) the transition period is attributed to the greatly Figure 6. Effect of supporting electrolytes using platinum electrode increased microscopic area with its large doublelayer capacitance and its increased ability to elec1. 1.50 X 10-8 ampere 2. 3.00 X 10-6 ampere trolyze the water. 3. 6.12 X 10-8 ampere 4. 2.25 X 10-6 amuere Single-Ion Reductions. Delahay and Maman5. 4.50 X 10-6 ampere tov ( 3 ) have presented equations describing var6. 1.35 X 10-4 ampere A . Wave due t o adsorbed oxygen (1.35 X 10-4 ampere) ious chronopotentiometric processes. The key B . Wa7.e due t o adsorbed hydrogen (1.35 X 10-4 ampere) relationships for interpretation of potential-time curves from single-ion reactions are as follows: (symbols are those of Delahay and hlamantov; I is current 6ot and A is electrode area)
I
-
Y
~~~~
-
I
PLATINIZED
PLATINUM
40.
0
0 u )
W
z t
20-
I -02
-04
POTENTIAL
Figure 7.
PLATINUM
BRIGHT
-06
OF
"4
-0 8
i o
PLATINUM ( v s AgCl )
Potential-time curves for hydrogen evolution 0.001M HC1 in 0.1M KCI
study of the electrolytic behavior of thin films observed the same phenomenon. Other supporting electrolytes examined with the mercury pool were potassium chloride, sodium acetate, and hydrochloric, nitric, and sulfuric acids. The working range of acid solutions is limited, of course, by the evolution of hydrogen. Potassium chloride and buffered phosphate solutions offer a wide potential range for oxidation or reduction reactions a t the platinum electrode with currents of 2 X 10-6 ampere per square centimeter or larger. Again, the effects of adsorbed films are evident a t low currents; the dotted curves of Figure 6 show the effect of perhaps A , oxygen, and B, hydrogen films. Figure 7 illustrates the potential-time curves for hydrogen evolution from a solution of 0.001M hydrochloric acid in O.1M potassium chloride a t bright and platinized platinum electrodes of almost the same projected geometrical area. Well-defined curves are obtained for the bright electrode; the quarter-wave potentials for the electrode varied considerably with its "cleanliness," a freshly-cleaned electrode evolving hydrogen a t more positive potentials. An interesting result is that the same transition time was obtained for the various stages of cleanliness. This implies
P 0 T E N T IA L ( v s, S.C.E.)
Figure 8. Effect of electrolyzing currents on potential-time curves Mercury pool Cadmium nitrate (5 X lOPM in 0.1M K S O I ) 1. 6.00 X 10-6 ampere 2. 7.50 X 10-5 ampere 3. 9.00 X 10-5 ampere 8 . 1.35 X 10-4 ampere
For a particular ion and a constant electrode area it may be seen from Equation 2 that:
'$
= a constant
(3)
If chronopotentiometry is to be of value as an analytical method, experimental data should be consistent with theoretical conclusions. Equation 1 was verified in this laboratory by preparing from a
A N A L Y T I C A L CHEMISTRY
4aa
- t”2
T1/2
wave a plot of log 7 versus the voltage, E. The results (3) showed the relation to be linear, and the slope yielded n-values within 1% of theory. The evaluation of the theoretical relationship of current, time, and concentration (Equation 2 ) is presented by Figures 8, 9, and 10, and by the data of Table 111. Before the initial phase of the work and without the authors’ knowledge, data for the proof of Equation 2 had been taken with fairly short transition times (1 to 10-3 second) using oscillographic techniques. Because longer transition times could be more accurately and easily measured, the authors’ data were taken to shoi7 the validity of Equation 2 for transition times between 4 and 60 seconds Figure 8 illustrates the effect of current upon the potential-time curves obtained in the ion-amalgam reduction of a given concentration of cadmium ion. Figures 9 and 10 illustrate the linearity between ~ 1 ’ 2and concentration; according to the equation, such a plot should be a straight line with slope dependent upon electrolyzing current. This is seen t o be the case, both in the ion-amalgam reduction of cadmium (Figure 9 ) and in the reversible oxidation of potassium ferrocyanide a t the platinum electrode (Figure 10).
IO-
A
8
6
: 1.0 X
c
10
5.0
X
= 2.3 x I
o -
charging current component. Empirical calibration curves must then be constructed from data on standard solutions. The precision obtained in graphical transition time determinations for mercury pool reductions is shown in Table I. The iodate data, contributed by Delahay and Mamantov (S), show precision superior to those obtained in this laboratory for cadmium ion. This would be anticipated from the increased dilution in the case of cadmium, and from the possibility of distortion due to the amalgamation of cadmium a t the mercury surface. It is also probable that the cell design employed by Delahay and Mamantov gives a more constant mercury surface area. Examination of Equation 1 reveals that when the scanning time, t, is equal to one fourth the total transition time, T , the potential of the electrode becomes E, 4 , the “quarter-wave”
AMP. AMP. AMP. ~
CONCENTRATION
OF
K,Fe(CN),
-
M x IO3
Figure 10. Relationship of concentration cs. various current values
/ C O N C E N TI RI dAsTMI O N
1. 2. 3. 4.
(IIercury electrode. Metal Ion
171’2
Z W
Pbti
C“ and 7 2 ~ 0 from ~
the experimental ion-amalgam reductions of lead, cadmium, and zinc, are summarized in Table 111. From a quantitative standpoint, reproducibility in these values determines the applicability The average value of
for all ions studied nm2 171’2
C,
Moles/L. x 104 10.0 10.0 10.0 LOO 5.00 5.00 1.24 1.24 1.24
Effect of current-density and concentration)
I,
Amp,3 x io 0.273 0.366 0.180 0.183 0.136 0,0898 0.0328 0.0258 0.0263
Cd . +
had an average deviation of 4.3’3,. Considering the range of concentrations and currents employed, this deviation is not excessive and confirms the usefulness of Equation 2. 4 s a further check of the validity of Equation 2, the value of the area of the mercury surface was computed using this equation and the experimental average of
on platinum 5. 5.87 X 10-4 ampere 6. 4.40 X 10-4 ampere 7. 2.93 X 10-4 ampere
Table 111. Chronopotentiometry of Lead, Cadmium, and Zinc Ions
Mercury pool
of the method.
Anodic waves ampere ampere ampere ampere
X 10-3 X 10-3 X 10-4 X 10-4
at
OF C d ”
Figure 9. Relationship of concentra% various current values tion us. ~ ‘ 1at
Calculated values for the constants
1.50 1.19 8.90 7.47
r1/2
z 4 2 COD'/^. The computed result
was 2.72 sq. em. as compared with 2.76 sq. em. calculated on the basis of the geometry of the pool. In practice, the effective area of the working electrode should be determined by running a chronopotentiogram on a standard solution and using Equation 2. Lead ions give well defined waves with platinum and mercury electrodes and stable lead solutions are easily prepared. At the lower concentrations, graphical measurement of transition times is complicated by the greater slope in the upper regions of the curves, resulting from the increased relative value of the
Znti
11.5 11.5 11.5 5.75 5.75 5.75 1.15 1.15 1.15
0.462 0.366 0.273 0.136 0.183 0.0898 0.0263 0.0410 0.0565
Ir1/2, Amp. Sec.112 x 104
ITllla
13.9 13.6 14.1 6.86 7.02 6.97 1.89 1.81 1.82
10-3 1.39 1.36 1.41 1.37 1.40 1.39 1.53 1 46 1.47
nC D1/1
8.82 8.64 8.38 8.40 4.13 4.37 4.05 4.48 1.37 1.35 1.36
1 28 1.25 1.22 1.22 1.20 1.27 1.17 1.30 1.37 1.35 1.36
2 38 2.33 2.28 2 28 2 24 2 36 2.18 2.42 2.56 2.52 2.54
13.3 13.7 13.7 7.00 6.95 7.08 1.56 1.53 1.46
1.16 1.19 1.19 1.22 1.21 1.23 1 35 1.33 1.26
2.17 2 22 2 22 2 28 2 26 2 30 2 52 2 48 2 35
x
Average Average deviation 47c average deviation 5
C in moles/rnl.
Ir’J2a
C
x
10-5 2.22 2.18 2.25 2.19 2.24 2.22 2.44 2.34 2.35
2.32 0.10 4.3%
V O L U M E 2 7 , NO. 4, A P R I L 1 9 5 5
489
potential. Quarter-nave potentials are characteristics of the ion itself, independent of its concentration, and are comparable to polarographic half-wave potentials. I n the case of mixtures, the scanning time corresponding to the polarographic half-wave potential varies b e h e e n ' / a r (in the case of no preceding waves)
I
0 -01
-0 3
-0
POTENTIAL
Figure 11.
5
-0 9
-0 7
Ag CI )
(vs
Potential-time curves for various metallic ions
Platinum electrode Supporting electrolyte 0.1.21 KC1 Current 2.70 X 10-4 ampere Copper, lead, and cadmium ions each 1 X 10-3 M .
Table IV.
and 1/27. (in the case of larger preceding waves). The reproducibility of quarter-wave potentials was examined in replicate runs on lead-cadmium mixtures. The data in Table V (columns 8 and 9 ) show average deviations of 1 and 2 mv. for cadmium and lead, respectively. For the purpose of qualitative identification of ions in mixtures by chronopotentiometric means, this precision seems encouraging. Platinum Electrode. While the cathodic working range of platinum is limited by the smaller hydrogen overvoltage, the electrode is advantageous in the respect that plated metals may be anodically stripped back into solution, and the solution reused for a subsequent run. Potential-time curves for the deposition of metal ions on platinum are illustrated in Figure 11. The curve for lead is as well defined and as reproducible as with the mercury electrode, but there has been a negative shift in the quarter-wave potential of about 0.15 volt. This shift is noted for all metal ion reductions, and is expected, as amalgam formation a t the mercury electrode decreases the activity of the deposited metal, The upper portion of the curve for the cadmium ion is distorted by the simultaneous reduction of hydrogen ion. The case of the cupric ion (chloride media) is of particular interest; the curve shows three distinct potential holdups. The hydrogen ion reduction potential is altered by the presence of plated copper a t the electrode.
Chronopotentiometric Analysis of Anodic and Cathodic Waves
(Comparison of methods for obtaining transition times. Platinum electrode. Anodic oxidation of 10-2.11 ferrous ion) Transition Times b y Potential-Interval Transition Times b y Recorder Method El/ 4 I, IT'f2, I, IT"%, interval, volt, 7, amp. a m p sec.l/l volt 7, amp amp. sec.L/2 u s . AgCl/Ag sec. X 10' X los (us. Ag/$gCl) sec. X 10' x 108
-Potential-
+O. 440
2.78
14.5
2.42
4.39 7.67 10.5 17.5
9%
11.5 8.65 7.15 5,78 Av. average deviation
2.41 2.40 2.31 2.42 2.39 1.3
3.0
14.5
2.51
4.7 8.2 11.6 18.6
11.5 8.65 7.15 5.78
2.49 2.48 2.43 2.49 2.48 0.8
+0.37to $0.60
Cathodic Reduction of Ferric Ion 10-2M +0.420
2.24
14.5
2.18
3.76 7.02 10.3 16.2
11.5 8.65 7.15 5.78 Av. 'X average deviation
Table T'.
2.23 2.29 2.28 2.33 2.26 2.0
+0.37 to +0.60
2.6
14.5
2.34
4.1 7.40 10.7 16.7
11.5 8.65 7.15 5.78
2.38 2.35 2.33 2.36 2.35 0.6
Consecutive Reduction of Two &letalIons
(Rlixtures of lead a n d cadmium ions subjected t o various polarizing currents. 1
2
3
4
5
x Pb++ 0.0450 (10-4) 0.0410 + C d 7 + 0.0565
Mercury pool)
6
7
C2 10-3
n2CzDz1/2
_Q_
x
10-5
8
9
Ei. volt
E2 , volt
(s.c.E.) (s.c.E.)
1.44 1.48 1.53
1.44 1.48 1.53
2.31 2.36 2.44
1.18 1.24 1.14
1.18 1.24 1.14
2.20 2.31 2.12
0,369 0.388 0.366
0.559 0.557 0,560
0.0328
1.39
1.39
2.22
0,570
1.14
2.13
0.371
0.558
0.0362 10-4)
1.36
1.36
2.18
0,560
1.12
2.09
0.374
0.559
Pb++ 0.0410 (lO--P\+ 0.0565 +Cd 0.0450 (2 X 10-4)0.0730
1.40 1.33 1.47 1.50
1.40 1 33 1.47 1.50
2.24 2.13 2.35 1.39
2.54 2.49 2.44 2.46
1.27 1.24 1.22 1.23
2.38 2.32 2.28 2.30
0.366 0.366 0.368 0.366
0.558 0.558 0.558 0.562
1.43 0.06 4.2
2.29 0.10 4.2
1.20 0.05 4.2
2.24 0.10 4.2
0.368 0.002
0,559 0.001
(10-4)
Pb+? 9:-4)
Cd
(5 x
Average Average deviation 70 average deviation
P
= I r i l / 2 a m p . sec.112 Q = I[(rl ~ ) " 2 - r 1 1 / 2 1 a m u . sec.1/2 Ci and Cz expressed a s moles/nil.
+
490
ANALYTICAL CHEMISTRY Table VI.
Consecutive Reduction of Three Metal Ions
(Various mixtures of lead, cadmium, and zinc ions subjected t o various polarizing currents
10
12
11
P b + + (10-4) 0.0565
13
14
15
16
17
Mercury pool.)
18 19 R R C' naCsDs1/2 x io-' x 10-5
1.44
1.44
2.30
1.27
1.27
2.36
1.26
1.26
2.34
0.0450
1.49
1.49
2.38
1.24
1.24
2.31
1.19
1.19
2.23
P b + + (10-4) 0.0565 Cd++ (5 x 10-9
1.50
1.50
2.40
0.616
1.23
2.30
0.645
1.29
2.40
Cd
(10- 4 )
+ +
Zn++ (10-4)
Zn++
0.0410
1.49
1.49
2.38
0.619
1.24
2.31
0.627
1.25
2.34
Pb++ (5 x 10-5)
0.0565
0.819
1.64"
2.62"
1.27
1.27
2.36
0.615
1.23
2.30
0.0410 0.850
1.70a
2.72a
1.27
1.27
2.36
0.615
1.23
2.30
1.48 0.02 1.4
2.36 0.04 1.7
1.25 0.02 1.6
2.34 0.03 1.3
1.24 0.02 1.6
2.32 0.03 1.3
(5 x 10-5)
C _d-+ +
(10-4)
Zn++ (5
x
10-4)
Average Average deviation o/o average deviation a
Not included in average (see text).
Consecutive Reductions. The final problem in this study was t o investigate the qualitative and quantitative analysis of mixtures of cations by means of the chronopotentiometric method. When two or more ions are present in solution which are reduced a t different potentials, the concentration of the ion first reduced may be calculated from its transition time by means of Equation 2. This is not true of subsequently reduced ions, as the total electrolysis current now divides between the diffusion currents of the first and second ions. The state of concentration polarization with respect to the second ion is reached less rapidly, and the transition time is correspondingly enhanced. Potential-time curves for the reduction of three-component mixtures of lead, cadmium, and zinc are illustrated in Figure 13. The solution is 1 X with respect to each of its com-
401
I
' /
40-
1
' 8
10
08
06
04
02
0
-02
-Q4
POTENTIAL ( v s . Ag C I )
Figure 12. Potential-time curves for ferricferrous ions Platinum electrode Supporting electrolyte 0.5M HC1 Current 7.50 X 10-4 ampere 0.005M FeClr A . 0.005M FeClz B . 0.01M FeCln C. 0.01M FeCls
+
I-
./-3
The ferrous-ferric system is of interest because of its commercial importance and because it forms a convenient reversible redox system. Experiments were conducted on the anodic oxidation and cathodic reduction of these ions. Figure 12 shows the results of oxidizing a solution of ferrous ion, C, of reducing a solution of ferric ion, B, and of oxidizing and reducing an equal mixture of the two, A . Theoretical equations for the potential-time curves of this redox pair, A , show that the anodic-cathodic curve should cross the zero-time axis with finite slope and a t the reversible potential of the electrode. Experiments show that this is not quite the case for the slope, and that a measurable degree of irreversibility is present. The degree of irreversibility was found t o decrease with smaller current densities. This effect was shown t o be independent of any ZR drop in the solution or leads.
2 0-
&I
.04
-0 6
-08
-I 0
-12
P O T E N T I A L ( vs. S.C.E.)
Figure 13. Chronopotentiometric curves for mixtures of lead, cadmium, and zinc ions 'in 0.1M potassium nitrate
V O L U M E 27, NO. 4, A P R I L 1 9 5 5
491
ponents. The effect of enhancement is clearly seen in creasing height of successive breaks in each trace. A equation found applicable to all diffusion-controlled potentiometric systems studied may be used to find the tration of each ion in a mixture:
the ingeneral chronoconcen-
When applied to a two-component mixture, this general equation reduces to Equation 7 of Delahay and Mamantov (3). With proper substitution, it also reduces to Equation 2 or 8 of the same authors. For the analysis of the three-component mixture under consideration here, Equation 4 may be written:
tion of a quantity of lead ion to the solution. This is illustrated in a slightly different manner by Figure 15. If it is assumed, for example, that a given concentration of cadmium ion alone yields a transition time of unity, as portions of the enchancing lead ion are added, the transition time for the added ion will increase as the square of its concentration in solution, shown by A in Figure 15. The enhancing effect upon the transition time of the cadmium ion initially present is shown by B . I t may be shown from Equation 4 that the enhancement of the transition time is directly proportional to the concentration of the added ion. For the general case, the enhancement varies directly as the square root of the sum of all preceeding transition times. .in upper useful limit of the procedure is reached when the concentration of the added ion is tn-o to four times that of the ion initially present.
The graphical transition times from the reduction of various mixtures of lead, cadmium, and zinc were used to calculate the data of Tables V and VI, by means of Equation 5. Reference to columns 4 and 7 (Table V) and 13,16, and 19 (Table VI) indicates fair agreement in values for the fixed concentration of one component, under conditions of varying the concentration of the other components of a mixture. Only one set of values in Table VIshows appreciable errors: The discrepancy in the last two values of the column 13 which is to be expected in view of the small magnitude of the transition times encountered. CONCENTRATION OF
ADDED I O N
Figure 15. Enhancement of transition time of one ion by addition of more easily reduced ion A. B.
01 -.2
I
-.3
EMF
I
- .4
I
-.5 vs. Ag-AgCI
I
-.6
-
I
L
.7
-.8
Figure 14. Potential-time curve for consecutive reductions of two ions at extreme dilution Mercury pool
For analytical purposes, best results are obtained in mixture analysis by using smaller currents for the analysis of the more easily reduced species, so that longer transition times can be obtained and measured. Inspection of Equation 4 shows that the analysis of a given wave does not require a knowledge of the concentrations or kinds of each species reduced a t earlier potentials, but rather the experimental value of the square root of the total time elapsed between the initiation of electrolysis and the commencement of the wave in question. Figure 14 shows the degree of separation of two ions in an extremely dilute mixture. The waves are fairly well defined and transition times can be easily measured. A consequence of the enhancement principle is the possibility of increasing the “detectability” of one ion by the addition of another which is more easily reduced. For instance, the response due to a cadmium concentration, too small to produce an accurately measurable wave, may be increased by the deliberate addi-
Transition time of added ion Transition time of original ion
Potential-Interval Timing. In the absence of a recorder, it is possible to obtain satisfactory transition time measurements by timing the interval between two predetermined potentials, as observed on a pH meter. The recorder and interval-timing methods are compared in Table IV for the oxidation of ferrous ion and for the reduction of ferric ion a t the platinum electrode. The precision of 1r1/2values obtained by potential-interval timing actually exceeds that of the graphical method, but observed timee are invariably somewhat longer. It is projected that an electronic relay be designed which would start and stop a timer a t the two predetermined potentials, thereby making the intervaltiming method automatic. ACKNOWLEDGMENT
The authors gratefully acknowledge the aid of the Research Corp. for support of this project. LITERATURE CITED
(1) Bowden, E. P., and Rideal, E. K., Proc. Roy. SOC.(London),A 120, 59 (1928). (2) Delahay, P.. Discussions Faraday Soc., 17,205 (1954). (3) Delahay, P., and Mamantov, G., ANAL.CHEM.,27, 478 (1955). (4) Laitinen, H. A., and Kolthoff, I. M., J . Am. Chem. Soc., 61, 3344 (1939). (5) Streuli, C. A., and Cooke, W. D., ANAL.CHEM.,25, 1691 (1953). RECEIVED for review M a y 24. 1954. Accepted J a n u a r y 31, 1955. Pre sented before t h e Division of Analytical Chemistry a t the 126th Meeting of t h e AMERICAN CHEMICAL SOCIETY. New York, N. Y., 1954.
