Anal. Chem. 1980, 5 2 , 340-344
340
Double Charge Step Chronocoulometry P. H. Daum" and M.
L. McHalsky
Department of Chemistry, Northern Illinois University, DeKalb, Illinois 601 15
A double charge step method for determining the rates of chemical reactions coupled to electrochemical processes is described. The method Involves application of successive charge pulses of opposite sign to an electrode, with subsequent recording of the open circuit potential relaxations. The magnitude of the potential relaxations is converted to charge using charge-potential data for the electrode whlch have been determined coulostatically. The rates of coupled chemical reactions are determined from the ratio of charges consumed In the two steps using the working curves developed for chronocoulometry. Computerized instrumentation for performing the experiment is discussed. Application of the technique to a reversible system and two chemically complicated systems Is demonstrated.
A number of transient electrochemical techniques have been developed to measure the rates of chemical reactions which are coupled to electrochemical processes. Though these methods have been widely employed in the study of reaction mechanisms, all become difficult to apply when the rate of the coupled reaction becomes rapid. Under these conditions, it is necessary both to apply the perturbation and to measure the electrode response very rapidly. Most electrochemical techniques encounter difficulty under these conditions because of the well known effects of electrode capacitance and uncompensated solution resistance. These factors work together and may limit observation of meaningful cell response to times which are too long to provide information about the coupled chemical reaction. In an effort to minimize these limitations and thereby expand the range of reaction rates to which electrochemical methodology can be applied, we have developed a new double-step technique based on coulostatic methodology. The experiment is performed by perturbing the potential of the test electrode from a value where no electrochemical reaction occurs to a potential which corresponds to the diffusion limiting region, by application of a charge pulse. The potential is allowed to decay a t open circuit for a predetermined time, T , whereupon the potential is perturbed to the diffusion limiting region in the reverse direction by application of charge pulse of opposite sign. The potential is again allowed to relax at open circuit until a total time 27 has elapsed. Kinetic information about the electrode reaction is obtained by measuring the ratio of the charge consumed during the reverse relaxation, to that during the forward, Qr/Qf. I t has been shown ( I ) that this ratio is identical with that obtained from the technique of double-potential step chronocoulometry. The charge consumed by the electrochemical process during a coulostatic relaxation can be estimated in several ways. In our original work ( I ) and that of others ( 2 ) ,it was assumed that the electrode capacitance remained constant over the range of potentials encompassed by the relaxations, and that the charge could be satisfactorily estimated from the relationship Q = CAE, where C is the electrode capacitance, and AE is the magnitude of the potential decay which occurs during the relaxation time, T . The ratio Qr/Qf was computed from the ratio 0003-2700/80/0352-0340$01 .OO/O
w
=
2
7
i.e.
This assumes that not only is the capacitance constant during a relaxation, but that it is the same over the potential range encompassed by both forward and reverse relaxations. In any general experimental situation, this assumption is not valid since the capacitance of an electrode usually varies with potential. Under these circumstances, estimating the charge ratio from the potential ratio gives erroneous results. T o make our method applicable under a wide variety of conditions, we have devised a way of determining the charge consumed during a coulostatic relaxation, which is independent of how the capacitance varies with potential. The method involves measuring the charge on the electrode under the experimental conditions of interest as a function of potential. The charge measurement is accomplished by poising the electrode a t an appropriate potential (usually the initial potential which is to be used in the kinetic experiments), and then applying coulostatic pulses of varying sign and magnitude. The change in electrode potential caused by application of the pulse is measured. The charge on the electrode a t the new potential relative to that a t the initial value is equal to the charge content of the coulostatic pulse. By systematic variation of the pulse size, charge-potential data over the entire potential range of interest can be obtained. The charge-potential curves thus generated, can then be used to determine the charge consumed during a coulostatic relaxation. The manner in which this is done can be made clear by reference to Figure 1, which schematically illustrates a double charge step experiment. The charge Qf which is used by the faradaic process in the first relaxation is equal to the difference in charge on the electrode at potentials E, and E,, the potentials a t the beginning and end of the first coulostatic relaxation respectively. Likewise, the charge Qb consumed in the second step is equal to the difference in charge on the electrode at potentials E2 and E2,. Since the charges measured in this fashion are independent of electrode capacitance, the effect of capacitance variation during the relaxation is eliminated from the experiment.
EXPERIMENTAL Instrumentation. Charge pulses were provided by a Chronetics (Mt. Vernon, N.Y.) PG-32 pulse generator suitably modified to gain access to internal timing pulses. Potential control of the
electrode prior to application of the charge pulses was by a conventional three-electrode potentiostat. A PDP8-L minicomputer (Digital Equipment Corp., Maynard, Mass.) was used to control the experiment, acquire data, and do preliminary computations. Data acquisition by the computer occurred through a fast transient recorder (Biomation 805). Operation of the instrumentation can be understood with reference to the block diagrams Figures 2 and 3 and to the system timing diagram Figure 4. A typical experiment was performed by entering into the computer the initial potential to be applied to the cell along with the data acquisition rate of the transient 0 1980 American
Chemical Society
ANALYTICAL CHEMISTRY, VOL. 52, NO. 2, FEBRUARY 1980 h -
f
Figure 1. Simulated potential time decays for a double ch rge step experiment
recorder. The computer with a command pulse (65541, Figures 2 and 4, then initiates the formation of new mercury drop by activating the drop knocker through FF-1, MS-3, and MS-4. Concurrently FF-1 closes FET-1 and FET-3 and opens FET-2. The action of FET-1 and FET-2 causes the initial potential to be applied to the cell. Closing FET-3 connects the output of >ATA SUSS 6551
voltage follower F, to the input of the sample and hold amplifier, thus providing a reference signal from which the decay is measured. The 6554 command pulse is also used to arm the transient recorder through the RMA input, Figure 3. The computer then enters a 15-8 delay cycle, Figure 4, which allows the Hg drop to become large enough so that change in drop area during the relaxations is minimized. Upon completion of the delay, the computer generates a command 1/0pluse (6551) to trigger the pulse generator. The pdse generator then provides two charge pulses of opposite polarity through two zener diodes to the cell, Figure 2. The zener diodes serve to isolate the cell from the charge injection electronics during the potential relaxations. The duration and separation of the charge pulses are controlled by signals within the pulse generator. Two of these pulses SET-1 and RESET-1 which are used internally to start and stop the first
. PG32
FET-I
1
--+ 5871.2 Rr3SEl1,I I
I
t
I I
DATA
lsu55 6554
6611
BIOMATION Y
FET-3
T
Figure 2. Block diagram of the potential control and charge injection circuitry )ATA
BlOMATlON 805
4uss
6554
-
r\
I RMA
DATA BUSS DIGITAL OUT
J
6551
652 1
6431
SKP-2
3 SKP-3
-SKP-1 CLR
Figure 3. Block diagram for the transient recorder/computer interface
341
342
ANALYTICAL CHEMISTRY, VOL. 52, NO. 2, FEBRUARY 1980 6611 (ON )
6654
U I
DIA POT.SET
r+
I5 SEC
I
I I
I
RMA BlOMATlON DROPKNOCKER
1I fl
d I 1
I I
11
SET I RESET 1
II 'I
PG TRIG ( 6 5 5 1 )
]I I 1
ON CHARGE PULSES
u
I
1;i
II I 1
OFF
1
U
CELL RESPONSE
DATA AQUSlTlON
JII ...... . ..._....... . .....1
DATA TRAWFER CALC. AND OUTPUl
I
I
J
1
Figure 4. System timing diagram
charge pulse are also used externally to time events in the experiment. The SET-1 pulse through the SET input of FF-1 is used to open FET-1 and close FET-2, thus isolating the potentiostat from the cell during the coulostatic experiment. SET-1 is also used to isolate the input of the reference sample and hold amplifier, Figure 2, from the measurement circuit when the potentiostat is disconnected by opening FET-3. The potential stored by the S/H amplifier is used by the instrumentation amplifier (Analog Devices 605) as a reference voltage. The instrumentation amplifier follows and amplifies the potential relaxations obtained from follower F. The output of the instrumentation amplifier is connected to the input of the transient recorder, Figure 3. RESET-1 which terminates the first pulse is used to trigger the transient recorder. At this point, the computer enters a short delay cycle to allow the potential relaxations to occur and data to be logged. When the delay is complete, the computer supplies another command instruction (6552) to initiate another experiment. Meanwhile, data from the transient recorder are displayed on an oscilloscope for evaluation. If the data are to be transferred to the computer, a switch (PBl), Figure 2, is set to start the data transfer and storage procedure. The switch sets the Q output of FF-6 to the 1state. This output state combined with the 6612 computer instruction pulse results in a E - 1pulse to the computer which starts the program used to transfer data from the recorder to the computer. The instruction (6524) sets the OPT input of the recorder to the 0 state causing the recorder to go into the digital output mode. The recorder responds by setting the OFF output to the 1 state, thus signaling the computer with a SKP-2 pulse that it is ready to transfer data. The computer then checks the status of the FLG. If FLG is in the 1 state, a data word is present a t the output of the recorder, and is transferred with a 6431 instruction pulse. The computer's 1/0 pulse (6434) to the WDC input acknowledges this transfer and allows the recorder to transfer the next data word into its output register. The computer again checks the FLG status and the process is repeated until all data are transferred. Not all data taken by the recorder are stored by the computer. The first 50 ws of the potential relaxation following each pulse contains spurious data due to electronic relaxation of the instrumentation amplifier and is rejected. For the data that are stored, the time at which each point was taken is determined by the use of a counter which is incremented by every point transferred to the computer from the transient recorder. The T value
is determined by having the computer compare the difference in magnitude of successive data points with the difference of the two previous points. When a large difference is detected, the point is identified as the start of the second pulse and the time corresponding to the point is recorded as 7. After all data are stored, the computer performs a regression analysis to determine the slopes and initial potentials of the relaxations. Following output of this data on the terminal, the computer cycles back to the beginning of the program and another experiment is started. A copy of the assembler program which operates the experiment is available upon request. Chemicals. All electrolyte salts were reagent grade and used as received. Water was redistilled from alkaline permanganate solution. Titanium solutions were prepared from TiC14. Bromocresol purple was purified once by the carbonate method ( 3 ) . Solutions were deaerated using prepurified nitrogen which had been passed through a vanadous tower. Procedure. All electrochemical experiments were performed at a dropping mercury electrode. Charge potential curves were obtained using the procedure outlined in the introduction. In all cases the solutions were identical to those used in the subsequent kinetic experiments. Blank corrections were made by noting the charge consumed during the relaxations in solutions containing all components except for the electroactive species. These charges were then substracted from those observed during the kinetic experiments. In many cases, the blank corrections were negligible.
RESULTS Simple Systems. To test our methodology under difficult conditions, experiments were done using the Cd(II)/Cdo (Hg) couple in 0.10 M KC1. T h e E,,* of this couple occurs in a region where the capacitance of Hg undergoes a large change with potential (20-40 yF/cm2 over a 0.4-V range). Because of this, the system serves as a n ideal case with which t o demonstrate the effect of capacitance changes during the potential relaxations on estimates of Q b / Q f gotten from 1E,,2,/AEt=r, and to demonstrate that conversion of the potential relaxations to charges with the use of experimentally determined charge potential curves can account for this and give the correct results. A typical charge potential curve for this system is shown in Figure 5. Since the curves were obtained using a n initial
ANALYTICAL CHEMISTRY, VOL. 52, NO. 2, FEBRUARY 1980
343
Table I. PotentialRelaxation Data for the Cd2+/Cd(Hg)' System'
-0.717 -0.725 -0.712 -0.718 -0,520 -0.615
-0.445 -0.445 -0.431 -0.436 -0.255 -0.338
0.248 0.288 0.350 0.426 0.193 0.162
0.180 0.215 0.280 0.356 0.125 0.083
0.250 0.261 0.249 0.248 0.257 0.285
a 0.1 mM Cd(NO,), in 0.1 M KCl electrolyte. Potentials in volts referenced t o -0.525 V vs SCE. 7 = 4.42 ms for all measurements.
I "C-EPI-
A-
::ol+.s
.i
-:'.525
r'5
ICE)
Flgure 5. Differential charge of a Hg electrode in 0.1 M KCI. (-) Values
Table 11. Charge' Relaxation Data for the Cd2+/Cd(Hg)' System
calculated from the data of Grahame. ( 0 )Experimental values
lQalQcl 0.302 0.200 0.168 0.111 0.559 0.201 0.140 0.575 0.306 0.200 0.301 0.195 0.253 0.194 0.557 0.299 0.197 0.233 0.174 0.578 0.225 0.132 0.122 0.066 0.602 0.262 0.162 0.096 0.032 0.640 a Obtained from data of Table I. All charges in WC (absolute values) referenced to -0.525 V vs. SCE.
electrode changes linearly with potential, i.e. if Q = CV. It ~ is obvious from Figure 5 that this ~ is not the case in the potential range of our experiments, and deviation from the 0.5858 value is expected. Table I1 lists the charge data obtained by transforming the corresponding potential data of Table I to charge with the data contained in Figure 5. The charge ratios were calculated from Q,/Q, = (Q2 - Q z r ) / ( Q 1 - 8,). The average charge ratio using this method was 0.585 f 0.032 at the 95% confidence level. This value is identical to the theoretical value of 0.586 within experimental error and is a definite improvement over the value of 0.258 estimated from the potential relaxation ratio. Charge ratios for these data were also calculated from the data of Grahame and a value of 0.586 f 0.032 a t the 95% confidence was obtained. This is excellent agreement with both theory and with our experimental results, demonstrating the validity of our approach. Chemically Complicated Systems. The ability of our method to obtain quantitative kinetic information about the rates of coupled homogeneous reactions was tested by application to two systems. The f i t was the reduction of Ti(IV) in the presence of hydroxylamine. The mechanism of this reaction has been shown to be of the catalytic type; Ti(1V) is reversibly reduced to Ti(II1) which is then oxidized by the hydroxylamine to regenerate Ti(1V). The catalytic rate constant for the reaction has been measured by several authors using a variety of electrochemical techniques (5-11). A summary of these results is listed in Table 111. In most cases, the studies were made with hydroxylamine in excess, thus making the rate pseudo-first-order. There is some scatter in the rate constants reported by various authors, especially those using the chronopotentiometric techniques. In addition, several authors have measured the temperature dependency of the rate constant and determined the activation energy. A rather large difference in the reported values exists which is somewhat surprising since it appears that similar
9, -
QTb
92 -
Q2rb
potential of -0.525 V vs. SCE, both the charge and potential are referenced to their respective values at this potential. For comparative purposes, charge values for Hg in 0.1 M KCl relative to that at -0.525 V vs. SCE were computed from the data of Grahame ( 4 ) and are also plotted. Since the area of our working electrode was not determined, Grahame's data were multiplied by an area which gave the best fit of his data to ours. (The area was 0.0222 cm2, which is not unreasonable for a DME.) Although they are not identical, the pattern of the potential dependency of the curves is essentially the same; shifting either by 10 mV will superimpose the two. These results suggest that our technique is an appropriate way of obtaining charge potential information from which potentials in the coulostatic decay can be converted to charge. Estimates of the anodic to cathodic charge ratios for the reduction and subsequent re-oxidation of cadmium were obtained using both the ratio AEt=2r/AEt=,, and by converting the potential relaxation data to charge using the data in Figure 5. The potential relaxation data are listed in Table I1 along with the corresponding values of AEt=,,/AEt=,, which were computed from the ratio (E2,- &)/(El - ET),El, E,, E,, and Ezl are as defined in Figure 1. It is evident from the data in column 5 that estimates of the charge ratio obtained in this fashion are grossly different from the 0.5858 value predicted by theory. Reference to Figure 5 reveals why. Correct answers using this method will be obtained only if the charge on the
Table 111. Summary of the Catalytic Rate Constants Obtained by Various Authors for the Titanium-Hydroxylamine System reference Blazek and Koryta ( 5 ) Delahay et al. ( 6 ) Herman and Bard ( 7 ) Fischer et al. (8) Saveant and Vianello ( 9 ) Christie and Lauer (10 ) Lingane and Christie (11 ) present work
technique polarography chronopotentiometry cyclic chronopotentiometry chronopotentiometry potential sweep chronoamperometry reverse current
h,,, K M - '
42.1k 1.5 30 ( 24)a 3 2a 45.9 i 0.4 42.0 t 1.7
E,, kcal/mol
7.9
35 ( 32)a
chronopotentiometry
double-potential step chronocoulometry
Value calculated by Lingane and Christie ( 1 1) for 298 K.
4 3 . 4 t 1.1
17.2 r 1.1
41.6
15.4 t 0.6
t
1.1
344
ANALYTICAL CHEMISTRY, VOL. 52, NO. 2, FEBRUARY 1980
Table IV. Rate Constants for Disproportionation of Bromocresol Purple Radical at 25 "C A. 0.1 M citrate buffer (pH 4.7) 25% methanol-water
concn, BCP, mM
T , ms
0.0725 0.141 0.141 0.274 0.454
7.51 4.1 1 4.41 0.780 0.439
h, x
5.08 4.95 5.02 5.55 3.38
B. 0.1 M phosphate (pH 7.0) and 1.0 M KCI in H,O concn BCP, mM
r , ms
7.25 x 10-5 1.41 x 10-4 1.41 x
2.20 3.03
2.64
h, x lo-' M-1 s - l
21.1 19.7 15.9
conditions were used in the various studies. Initial experiments were done in the absence of hydroxylamine to determine whether the chemically uncomplicated system gave correct results for the anodic-to-cathodic charge ratio. The experiments were done using solutions containing 0.1 mM Ti(IV), and 0.19 M oxalic acid. Gelatin was added t o a level of 0.006% to prevent complications arising from adsorption. The methodology used to determine the charge ratios was similar to that used for the cadmium study. Charge potential curves relative to a potential of 4 . 2 0 V vs. SCE were obtained. As before, the initial and final potential of each coulostatic decay were converted to charge using these curves and the anodic-to-cathodic charge ratio was computed. A blank correction was applied by subtracting the corresponding charges measured with a blank solution containing all chemicals except the titanium. The average charge ratio observed a t three different T values (2.61, 4.42, and 9.50 ms) was 0.584 f 0.008 a t the 95% confidence level, which is in excellent agreement with theory. After it was determined that the chemically simple titanium couple gave the correct results for the charge ratio, the catalytic agent hydroxylamine was added to introduce the chemical complication. The solutions were identical to the above except for the addition of 1.465 M hydroxylamine. Charge ratios were determined and the value of k,TC obtained by use of a working curve generated in this laboratory. A typical experiment done at 24.6 "C using a T of 21.1 ms yielded a Q,/Q, = 0.275 f 0.016 (95% confidence level) from which a catalytic rate constant of 39.1 M-'s-l was calculated. T o further demonstrate the ability of our method to measure a wide range of reaction rates, the reduction of the sulfonephthalein indicator, bromocresol purple, was studied. T h e reduction mechanism of this indicator was originally proposed as being a disproportionation mechanism by Senne and Marple (12). This mechanism was later confirmed by Kudirka and Nicholson (13) in a more general study which included the evaluation of the second-order rate constants for nine similar indicators. The kinetics of BCP radical disproportionation were studied using two different sets of solution conditions. One set was essentially the same as used by Kudirka and Nicholson and contained 0.1 M citrate buffered a t a pH of 4.7 in a 25% methanol-water mixture. The other was an aqueous solution containing 1.0 M KC1 electrolyte buffered to a p H of 7.0 with 0.1 M phosphate. Both solutions contained 0.02% gelatin. The experimental procedure used to determine the rate constant was essentially the same as that described previously,
and included a blank correction. A summary of the results for the two different solutions is given in Table IV. The average value of k 2 for BCP in the 25% methanol-water solution a t pH 4.8 was determined to be 4.8 x lo6 M-' d. This value is somewhat larger than the literature value of 1.2 X lo6 obtained by Kudirka and Nicholson in a similar solution using cyclic voltammetry. I t is not known why the discrepancy between the results exists; however, the variation is reasonable considering that different techniques were used and that the literature value was determined a t the limits of the cyclic voltammetric technique. A value of 1.6 X lo7 M-' s-l was obtained for the rate constant in an aqueous solution buffered a t p H 7 with phosphate. No equivalent rate constant for comparison exists in the literature. However, a comparison was made by Kudirka and Nicholson for phenol red in both aqueous and 25% MeOH-H20solutions and they showed that the rate constant was higher in the aqueous solution (3.4 vs. 1.65 X lo2). That trend seems to be affirmed by the present results.
DISCUSSI ON From a review of the experimental results which have been presented, it is evident that the methodology which has been developed can be used to determine the rates of electrochemically coupled homogeneous reactions. For the method to give correct results, it has been demonstrated that it is necessary to measure the differential charge on the electrode as a function of potential, and thereby relate the magnitude of the potential decay which occurs during the relaxation to the charge consumed by the reaction. It has conversely been shown that simple measurement of the magnitude of the AE which occurs during the relaxation cannot be reliably used as an estimate of the charge consumed by the reaction, because the capacitance of an electrode is generally not independent of the potential. This method has rather limited applications, due to the complex nature of the experiments necessary to obtain the required information. Two separate experiments are necessary, one to obtain the charge potential information and the other to obtain relaxation data from which the kinetic information is extracted. These experiments are tedious and involve recording and manipulating large quantities of data. Despite these limitations, the method appears useful in situations where the rate of the coupled reaction is very fast, or in situations where it is desirable to study the reaction under conditions which other methods cannot tolerate. Organic solvents of low dielectric constant where solution resistances are high often lead to the latter situation.
LITERATURE CITED Daum, P. H. Anal. Chem. 1973, 4 5 , 2276-78. Mizota. H; Aoyagui, S. J . Electroanal. Chem. 1978, 87, 165-72. Orndorff, W. R.; Sherwood, F. W. J . Am. Chem. SOC. 1923, 4 5 , 486-500. Grahame, D. C. J . Am. Chem. Soc. 1949, 71,2975-78. Biazek, A,; Koryta. J. Collect. Czech. Chem. Commun. 1953, 18, 326-36. Dehahay, P.; Mattax, C. C.; Berzins. T. J . Am. Chem. SOC.1959, 76, 53 19-24. Herman, H. 9.; Bard, A. J. Anal. Chem. 1964, 36, 510-14. Fischer, 0.; Bracka, 0.; Fischerova, E. Collect. Czech. Chem. Commun. 1961, 26, 1505-19. Saveant, J. M.; Vianello. E. Electrochim. Acta 1965, IO, 905-20. Christie, J. H.; Lauer, G. Anal. Chem. 1984, 36, 2037-38. Lingane, P. J.; Christie, J. H. J . Electroanal. Chem. 1967, 73, 227-35. Senne, J. K; Marple, L. W. Anal. Chem. 1970, 4 2 . 1147-50. Kudirka, P. J.; Nicholson, R. S. Anal. Chem. 1972, 4 4 , 1786-94.
RECEIVED for review June 11, 1979. Accepted November 19, 1979.
