Theory of Stationary Electrode Polarography for a Multistep Charge Transfer with Catalytic (Cyclic) Regeneration of the Reactant DANIEL S. POLCYN and IRVING SHAlN Chemistry Department, University o f Wisconsin, Madison, Wis.
b The theory of stationary electrode polarography (chronoamperometry with linear potential scan) has been exterlded to the case of a multistep charge transfer with a catalytic (cyclic) chemical reaction coupled to the first charge transfer. Four fundamentally different cases are possible since the two charge transfers can be reversible or irreversible independently. For each case, the boundary value problem was converted into two integral equations which were solved numerically on a digital computer. Theoretical current potential curves were calculated, and the interaction of the two charge transfers with the chemical step was investigated as a function of the potential separation (AE') between the two charge transfers, the scan rate, and other experimental parameters. To test the theory, the reduction of the Fe(lll) complex with triethanolamine in the presence of hydroxylamine was investigated.
W
a chemical reaction is coupled to a multistep charge transfer, numerous kinetic schemes can result from combinations of the chemical reaction with reversible or irreversible charge transfers (19). Stationary electrode polarography provides a powerful method of investigating the kinetic parameters of such systems. Although several systems involving a single charge transfer have been studied previously (6, 12-24), the only one involving a multistep charge transfer with a coupled chemical reaction was the ECE mechanism (7'). I n this work another esaniple of esperimental importance was investigated: a multistep charge transfer coupled with a catalytic (cyclic) reaction in the solution. This study \vas limited to the case in which a n irreversible catalytic chemical reaction is coupled with the first charge transfer:
376
HEN
ANALYTICAL CHEMISTRY
-1s in the previous study of inultistep charge transfers in stationary electrode polarography ( y ) , the charge trariqfers mny be reverdde or irreversible; both were included here. Qualitatively, the effect of a catalytic chemical reaction coupled to two charge tranders as in Reaction I is to enhance the masimum current for the first charge transfer because of the chemical regeneration of A . However, in the potential region where the second charge transfer becomes iinportant, the catalytic effect disappears because A is reduced directly to C. Thus, for reasonable values of the effective rate constant, the first wave evhibits a plateau typical of a catalytic reaction ( 6 , l Z )followed by a decrease in current in the potential region of the second wave. This general behavior is espected for systems such as the reduction of the Fe(II1) complex with triethanolamine in the presence of "?OH. I n the potential region of the first wave, the product of the reduction is an Fe(I1) complex which reacts with the hydrosylamine to regenerate the Fe(II1) complex. I n the potential region of the second wave, the product is Fe(0) which does not react further, and the catalytic regeneration of the Fe(II1) species ceases.
-111 teims are the same as those defined previously (IO), except Cz, which is the concentration of Substance 2 in solution, and k , which is the formal rate constant for the catalytic chemical reaction. Substance 2 is not electroactive in the potential range of interest, and it is assumed that Cz >> CA, so the chemical reaction can be considered as pseudo first-order with the pseudo first-order rate constant k, = kCz. For reversible chemical reactions, the effect of the back reaction could be included by replacing k by k(1 1/K) where K is the equilibrium constant for the reaction between B and 2, and by adding the appropriate kinetic terms to Equations 1 and 2. T o solve this problem it is necessary to know the nature of the charge transfer and the explicit form of the potential dependence. If quasi-reversible systems are not considered, four sets of conditions are possible depending on the reversibility of the charge transfers. For convenience, these systems are referred to as R-C-R, R-C-I, I-C-R, and I-C-I, where C refers to the catalytic reaction and the charge transfers are in sequence. Using a procedure analogous to t h a t ('7, 9) the described previously boundary value problems were converted to dimensionless integral equations (Table I). Each pair of integral equations was solved numerically to obtain theoretical stationary electrode polarograms. The numerical methods used were similar to those described previously (6, y). Calculations Lvere carried out for various values of k,/a for selected values of potential separation and nl or
+
712.
THEORETICAL CORRELATIONS
I n the integral equations in Table I, the rate constant alxays appears as the ratio k,/a, and the effect of the chemical reaction on the theoretical stationary electrode polarogram is directly dependent on this kinetic parameter. TO make the theoretical correlations, k,/a
Table
I. Integral Equations for Multistep Charge Transfers for TWO Electroactive Species with a Coupled Catalytic Chemical Reaction
R-C-R:
R-C-I:
I-C-R:
I-GI:
nas varied over a wide range, and simultaneously the effect of changing LE", n2/n1,and the reversibility of the chaige tranbfers was determined. Only cases R-C-R and R-C-I were elaniined in detail, and in both, the catalytic part of the cheinical ieaction is coupled with a reversible charge transfer. Reversible Charge Transfers (R-C-R). T h e kinetic effects can most conveniently be discussed by comparing t h e behavior with t h e stationary electrode polarogram which were described previously (IO) for uncomplicated two-step chaige tiansfer processes. For those caseb in which the waves are well separated, the first wave has all the characteristics of a simple catalytic reaction without the second charge tranbfer (22). For this iaolated first wave catalytic reaction, if k,/a is small (-0.001), the chemical reaction has no effect on the charge transfer and a reversible stationary electrode polarogram is obtained. ;is the value of the kinetic parameter is increased, the effect of the chemical reaction becomes more important and the current is enhanced through the chemical regeneration of the reactant (Figure 1). At large values of & / a no peak is observed; the stationary electrode polarogram shows a broad plateau and the current is proportional to independent of the scan rate. Simultaneously, the peak potential (or half-wave potential when no peak is
dg
observed) shifts cathodically about 60/n mv. for a 10-fold increase in k J a . For Wave 11, a distinct wave is observed for values of k,/a u p to about 1.0, but for larger values of k,/a, the composite polarogram shows only Wave I, with a broad plateau which falls off sharply at potentials where the re-
duction of B to C proceeds faster than the chemical regeneration of A . rlt potential separations less than about 180 mv., and for small values of the kinetic parameter, the individual waves merge and become distorted, as in Case R-R (IO). For larger values of k c l a ,the merged waves shorn the current plateau due to the catalytic reaction, but the plateau is naiiower and the drop in current near E2" tends to give the wave a broad peak. This phenomenon is also observed for very large values of k c l a , even when AE" is as much as 180 niv., a separation normally sufficient to prevent interaction between the two waves. This is caused by the cathodic potential shift of the catalytic wave with increasing values of the kinetic parameter, and the aqsociated decrease in the effective potential separation of the charge transfers. Typical polarograms calculated for a value of AEo in which this overlap occurs are shonn in Figure 2. When AE" is zero, or is positive, the catalytic effect is no longer observed as B is reduced at the electrode before it can undergo chemical ieaction. Vnder these circumstances, the stationary electrode polarograms are the same as for Case R-R (IO). The effect of the number of electrons is similar to Case R-R, in that both the shape and position of the wave change with nl and n2. For cases of interest other than nl = n2, additional calculations can be carried out.
(E - E:)n, mv.
Figure 1. Stationary electrode polarograms for Case R-C-R A€' = - 500 mv., n2/n1 = 1 .O
VOL. 38, NO. 3, MARCH 1966
377
3.0
2.5
e z
2.0 I
( E - E;)n, mv. Figure 2. Stationary electrode polarograrns for Case R-C-R A€' =
- 1 8 0 mv., n2/n1
= 1 .O
I n contrast to Case R-R, where, for suitable values of AEO, the two waves could be considered as isolated individual waves, the interaction between the catalytic wave and the second charge transfer prevents separate investigation of the second wave, even for small values of the kinetic parameter. On the other hand, if the waves are well separated, Wave I is esactly the same as for similar values of k,/a in the absence of the second charge transfer. Under these circumstances, theoretical stationary electrode polarograms for the first wave can be constructed from the data presented previously (6). CYCLIC TRIAXGCL.4R W.4VE VOLTAMMETRY. For cyclic triangular wave experiments, when the waves are well separated, the potential scan can be reversed after the first wave or after the second wave. I n the former case, provided the switching potential is a t least 35/72 mv. cathodic of the peak potential of Wave I, the stationary electrode polarogram has all the characteristics described previously (6) for the case vvhere a catalytic reaction is coupled with a single reversible charge transfer. On the other hand, if the switching potential is selected after Wave 11, the anodic wave furnishes distinct qualitative information about the kinetic process. Provided a switching potential is selected a t least 65/n mv. past the formal reduction potential of the second charge transfer, the anodic curve shows an anodic peak characteristic of the second charge transfer, and the height of this peak decreases with increasing values of k,/a. At more anodic potentials (near E l 0 ) ,the reverse scan approaches 378
ANALYTICAL CHEMISTRY
the level of the cathodic curve and has the shape of an uncomplicated catalytic anodic curve. This behavior is shown in Figures 1 and 2, particularly for those curves corresponding to large values of k,/a. At AEO = 0, or for positive AE", where only one cathodic wave is observed, the anodic behavior is the same as for Case R-R (IO). Second Charge Transfer Irreversible (R-C-I). Since the catalytic chemical reaction is still coupled t o a reversible charge transfer for this case, the major differences from Case R-C-R will appear in the potential region of the second charge transfer. When the waves are well separated, the second wave is lower and more drawn out on the potential asis. Peaks are observed for values of k,/a up to about 0.1, but for larger values of the kinetic parameter, Wave I1 is very small. Similarly, for k,/a = 1.0, Wave I has a broad plateau as in Case R-C-R, but it does not fall off as rapidly in the potential region of Wave I1 as in the previous case (Figure 3). At potential separations less than 180 mv., and for small values of the kinetic parameter, the waves merge and become distorted as for Case R-I (IO). For larger values of k c l a , the merged waves show the current plateau, but the irreversible charge transfer has less effect on lowering the current a t potentials in the region of Wave I1 than a reversible charge transfer. The effect is further complicated because in addition to the shift in potential of the catalytic wave, the irreversible nave shifts 3O/an, niv. cathodic for a 10-fold change in scan rate. Hence the effective poten-
3.0
2.5
5
2.0
F
0
z 3 LL
1.5
w
1.c
+z a: (r
3
0.5
0.c I
I
0
-300
I
-600
(E - Eqln, mv. Figure 3. Stationary electrode polarograms for Case R-C-/ A€' = - 5 0 0 mv.,
n2 = nl, a = 0.5
25-
z
6z
k
E
2015-
10-
(L
0500-
90
0
-90
-180 -270
(E - EqIn, mv. Figure 4. Stationary electrode polaro g r a m for Case R-C-/ A€' =
- 1 8 0 mv., n2 = n l , a
= 0.5
tial separation varies with k,/a. Typical stationary electrode polarograms for a case in which the waves merge for large values of k,/a are shown in Figure 4. For cases in which the effective wave separation is zero, or positive, the stationary electrode polarograms are the same as for Case R-I. CYCLICTRIAXGCLAR WAVEVOLTAMLIETRY. When the waves are well separated, the scan may be reversed after the first or the second wave. Reversing the scan after the first wave, the stationary electrode polarograms are identical to those described for Case R-C-R. Reversing the scan after the second wave, no anodic wave is observed, as espected for irreversible charge transfers (Figures 3 and 4). At potentials near E l o ,the reverse scan returns to the level of the cathodic wave, similar to the simple catalytic cyclic behavior. When the effective wave separation is zero, where only one cathodic wave is observed, the anodic behavior is the same as for Case R-I. Diagnostic Criteria. As in previous work on the theory of stationary electrode polarography (6, 7 ) ,the variation of the peak current as a function of scan rate provides the most useful characterization of the kinetic system, and offers the simplest way of summarizing the correlations discussed in the preceding section. Classification according to the reversibility or irreversibility of the charge transfers is provided by the form of the anodic waves as the scan rate is varied. These trends are summarized in Figures 5 and 6. For the cathodic waves, the current functions were determined by measur-
0
1
01 01
1.0
IO VOLTS
100
Figure 5. Diagnostic criteria showing the variation in peak current function with changes in scan rate for Case R-C-R AE' = -500 mv., n?/nl = 1.0
ing to the zero current axis for the first charge transfer and to the extension of the first wave for the second charge transfer. For the anodic waves, the currcnt functions were measured to the extension of the second wave. 1 1 though the data can he used quantitatively if additional parameters are knoivii (electrode area, diffusion coefficient etc.), the main application is qualitative. Thus, experimental data can 1)e plotted as i,,/4 us. to define the trends satisfactorily. The data in Figures 5 and 6 n-ere based on a value of AI?' of -500 mv. For smaller values of wave separationj the wave forms arc comples and estensive calculations are required. The d a t a include the condition that n l = n2 = 1.0 and an. = 0.5. For other values of these parameters, the peaks woul(1 have to be normalized, but the geilel.31 trends indicated would still be valid. These diagnostic criteria, when coiisidcred n i t h those presented previously (6, 7 ) % extend the applicability of stationary electrode polarography. Thus, the method is probably one of the most versatile for qualitatively investigating electrode mechanisms; and with computing facilities available, the method can readily be used for kinetic iiiea>urements of complex mechanisms. zt
EXPERIMENTAL VERIFICATION
X a n y systems such as Reaction I have been reported in the polarographic literature, and it had been assumed that selection of a demonstration system would be relatively straightforward. However, in every case the kinetic system was considerably more complicated than the theoretical model. Furthermore, no system was found in which the actual mechanism is known with certainty. However, after esploratory experiments on several systems, the reduction of Fe(II1) complexed with triethanolamine in alkaline solution, in the presence of hydroxylamine,
1.0
I
IO VOLTS
I
100
Figure 6. Diagnostic criteria showing the variation in peak current function with changes in scan rate for Case R-C-I Wave 111 is absent.
was selected for comparison with theory. The complicating factors (primarily, a succeeding chemical reaction coupled with the first charge transfer and considerable confusion as to the actual mechanism) appeared to lie less formidable than with other Without hydroxylamine present, the polarographic behavior of iron in alkaline triethanolamine solutions has been studied by several xvorkers ( 4 , 1 7 , I S , e l ) . I n general, the fiwt charge transfer appears reverqible and the second charge transfer is irreversible. The second wave is very close to the solvent decomposition potential aiid depends on both the triethanolamine arid base concentrations. One Fe(II1) apparently is complexed with one triethanolamine and with wrying numbers of OH-, depending on the p H (11). ALfter the reduction of the Fe(II1) complex, a dissociation reaction involving the ferrous triethanolamine complex appears to take place (16-18). I n the presence of hydroxylamine, the polarographic reduction of the Fe(II1) complex of triethanolamine exhibits a catalytic chemical reaction, first studied by Iioryta ( 5 ) . Data rvere consistent with an overall reaction in which two ferrous ions are consumed for every molecule of hydroxylamine. Rate constants were reported ranging from 198 (All/'l)-l see.-' in 0.131 triethanolamine and 1.031 sodium hydroxide, to 595 ( - l I ~ ' l ) - ~see.-' in 0.131 sodium hydroxide. .\ dip in the catalytic limiting current, observed at potentials near the final current rise, was ascribed to a masiinum of the second kind. Furlani and Xorpurgo (3) studied the same system using current reversal chronopotentiometry, and reported a rate constant' of 50 ( M / l ) - I see. -1 in 3-11potassium hydroxide, which is consistent with Iioryta's results. However, the rate constant varied nonlinearly with hydroxylamine concentration and the reaction ratio of Fe(II)/ X H 2 0 H was less than two, which indicated that the system was more complicated than the theoretical model proposed. Fischer, Dracka, and Fischerova ( 2 ) also investigated this system using chronopotentiometry, reported a rate constant slightly lower than t'hat
A€' = -500 mv., ni/nl = 1.0,
LY =
0.5
obtained by Koryta, and indicated a reaction ratio Fe(II)/NHYOH of 1.7. Other studies were carried out by Smith (16) using a.c. polarography. I3ecause of the added csperimental complications present in the Fe(lI1)triethariolaiiiine-hyclroxylaininesyst,em, exact experimental correlation with the theory was not possible. Nevertheles?, the kinetic aspects of the electrode reaction could be studied u3ing stationary electrode polarography. Vithout hytlrosylamine ])resent, the Fe(1II)-triethanolamine . studied over a wide range to characterize the chciiiical reaction following the charge transfer. Then, with hydroxylamine pre;ent, the catalytic reaction was invedigated, using the experimental data in several ways to calculate the rat'e constant,. From , it waq shown that for this tern, the succeeding cheinis reversible, aiid in addition, the general shape of the catalytic wave was characterized. Experimental. -111 experiments were carried out n-ith a three-electrode controlled potential circuit. The circuit configuration, signal generators, detectors, and cell5 Tvere similar to those described previously (1, 8.9). Triethanolamine (Matheson, Coleman, and Bell, comiiiercial grade) was redistilled at, 10 niin., and the fraction boiling a t 185-7" C. was collected. The concentration wai determined by p H titration. 1 1 1 other chemicals were reagent grade, and were used without further purification. The hydroxylamine hydrochloride solutions were standardized by titration with potassium bromate (20). Noncatalytic System (Hydroxylamine Absent). The reduction of the Fe(II1)-triethanolamine complex at, a stationary electrode shows two xaves, with characteristics which can be correlated with the results obtained a t the dropping mercury electrode (Figure 7). The first lvave at -1.06 volts us. S.C.E. corresponds to a reversible charge transfer with E , Epj2 = 55 mv., compared with t'he theoretical value of 56.5 mv. The second wave, which corresponds to the reduction of the Fe(I1) complex, apVOL. 38, NO. 3, MARCH 1966
379
i
I
maximum possible variation is only about 10% for a change in the kinetic m from zero t o inparameter K finity. However, the anodic portion of the cyclic stationary electrode polarogram is very sensitive to the kinetic parameter, and the ratio of the anodic peak current to the cathodic peak current decreases markedly with increasing scan rate. This ratio also is a function of the switching potential, Ex, and t o make quantitative correlations between experiment and theory, it was necessary to calculate theoretical anodic values of at) for the esperimental switching potential. For these experiments the switching potential parameter, defined as -40
2 1
I
.8 -1.0
I
I
I
-1.2
-1.4
-1.6
VOLTS vs. Figure 7. Reduction ethanolamine complex
S.C.E. of
Fe(ll1)-tri-
5.32 X 1 O-4M Fe(lllJ; 0.02M triethanolamine; 1 .OM sodium hydroxide Curve A: dropping mercury electrode polarogram Curve 6: stationary electrode polarogram. Scon rote: 102 mv./second
pears only as a shoulder on the electrolyte decomposition wave and cannot be studied. Cyclic stationary electrode polarograms, scanning either the potential range of the first charge transfer or the potential range of both charge transfers, show only a single anodic wave for the oxidation of the Fe(I1) complex to the Fe(II1) complex. No anodic wave is observed near the potentials of the second cathodic wave. To study the chemical reaction which follows the first charge transfer, data were obtained over the potential region of the first wave for correlation with the theory of stationary electrode polarography presented previously as Case Ti in Reference (6). For this mechanism, the ratio i,v% does not vary markedly with scan rate, and the
Table 11.
Cyclic Stationary Electrode Polarographic Data for 5.32 Fe(lll), 0.02M Triethanolamine, and 1 ,OM Sodium Hydroxide
Scan rate, volts/second 121 52 20.9 10.1 5.0 1.99 1.01 0.52 0.203 0.104 0.050
380 *
was equal to -232 mv. From these calculations, a working curve was constructed of the ratio i,(anodic)/ i,(cathodic) as a function of the kinetic parameter K G in a manner similar to Figure 10 in Reference (6). The experimental results are summarized in Table I1 along with the values of the kinetic parameter K l / a / l determined from the working curve. For this range of values for Kl/aX the cathodic peak current function should not vary more than about 4%, (from 0.446 to 0.465). Using a value of 7.0 X cm.*,’second for the diffusion coefficient of the Fe(II1)triethanolamine comple.:, as determined from potentiostatic current time curves ( I @ , t h e peak current function i,/ n F A 4 D a Ca* was found to be essentially constant, with an average value equal to 0.45. The values of K l / a / l from Table-I1 were plotted as a function of l/a, and from the slope of the straight line which was obtained, a value of 0.028 second-1’2 was calculated for K / d C I n the theoretical treatment of this case, the rate constants, k f and kb, and the equilibrium constant, K, do not occur independently. Hence, some other experimental method would be needed to obtain either the equilibrium constant or one of the rate constants so that the other parameters could be obtained from the stationary electrode polarographic treatment. However,
E, (cathodic), volts us. S.C.E.
-1.09
i, (cathodic), Pa. 250 157 94 65 46
-1.09 -1.09 -1.09 -1.09 -1.09
22 16 9.5 6.8 4.9
-1.11
-1.10 -1.09
-1.08 -1.11
ANALYTICAL CHEMISTRY
30
Peak current ratio, io/&
0.74 0.73 0.77
0.83 0.87
0.90 0.94 0.96 0.97 0.98 0.99
X 10-4M
Kinetic parameter, w a l l 0.94 0.99 0.80
0.53
0.38 0.26
0.17 0.11
0.08
0.04
0.03
I
I
I
I
I
-1.0
-1.2
-14
-1.6
-1.8
VOLTS vs. S.CE.
Figure 8. Cyclic stationary electrode polarograms of the catalytic reduction of the Fe(ll1)-triethanolamine complex in the presence of hydroxylamine 5.32 X
10-4M Fe(lll1; 0.02M triethanolamine; 1.OM sodium hydroxide; and 0.06M hydroxylamine. A, scan rate = 10 volts/ second; 6 , scan rate = 0.1 volt/recond
since the kinetic effect is not pronounced except a t high scan rates, the Fe(I1)-triethanolamine complex first produced by the electrode reaction probably is not the predominant form in the solution. Catalytic System (Hydroxylamine Present). Although t h e chemical reaction following the first charge transfer and the poorly defined second wave prevent complete correlation betneen experiment and the theory for a multistep catalytic system, t h e relative rates of the two chemical reactions are such that it is possible to study the catalytic reaction over the potential range of the first wave without significant interference from the dissociation of the Fe(I1) complex. I n effect, therefore, the quantitative part of this study used the theory for single step catalytic reactions presented previously (6, 12), and the correlations were similar to the recent work of Saveant and Vianello (14) who investigated several other chemical systems. Typical S-shaped polarograms were obtained a t slow scan rates indicating kinetic control, while a t high scan rates peak-shaped polarograms were obtained indicating diffusion control. Vsing scan rates where the catalytic effects are obtained, a dip was observed in the plateau of the S-shaped wave a t potentials corresponding to the reduction of Fe(I1) (Figure 8). The presence of this dip a t a stationary electrode supports Vlcek’s proposal (29) that maxima and streaming effects are not responsible for the dip, but that the dip is a manifestation of Nechanism I. The effect of the catalytic mechanism on the peak current function for the first wave is shown in Figure 9. A n each case, the function i P / n F A 1 / D a CA* is high at slow scan rates, and decreases with in-
I
I
I
0.1
I
I.o
I
IO VOLTS
I
I
100
Figure 9. Variation of i , / n F A / d z Cf with the rate of voltage scan Hydroxylamine concentration: D, 0.1 30M
creasing scan rate. K i t h scan rates above about 10 volt lytic step has very little effect on the overall electrode reaction. Rate Constant Comparison of in.to
Measurement :
i,!. One of the
important ways of determining the rate constant involves comparison of t h e catalytic currents with the diffusion controlled currents which would have been obtained if the catalytic reaction had not been present. Values of i,,can be obtained from esperiments in which the catalytic reagent' is omitted, or froin esperiments in which very rapid scans are used so the catalytic effects are minimized. If the latter method of obtaining i,{ is used, in. and i,?are measured a t different scan rates, and the data must be normalized by the relation ?.A/&
=
A, 0; B , 0.060M; C, 0 . 0 9 8 M ;
Tables I and XI1 in Reference (6). This prorided values of k,/a which were plotted as a function of l/o. Straight lines were obtained whose slopes were k , / ( n F / R T ) , and the resulting values of k , and k are summarized in Table 111. Rate
Constant
Measurements :
Slow Scan Rates. A second method of obtaining kinetic d a t a on a catalytic reaction using stationary electrode polarography involves restricting the measurements to values of k , a such t h a t a current voltage curve is obtained Ivith a flat limiting current region. For a reversible charge transfer, a closed form solution describing the entire wave has been presented previouqly ( 6 ):
-1.0
-1.2
-1.4
-1.6
VOLTS vs. S.C.E Figure 10. Stationary electrode pol a r o g r a m for the catalytic reduction of Fe(ll1)-triethanolamine complex with hydroxylamine line, theory; points, experimental, Scan rate = 0.051 volt/recond; k e / a = 1 1 . 1 ; hydroxylamine concentration = 0 . 0 9 8 M
tr iethanolamine-hydroxylamine system. The characteristic flat limiting current region is shown in Figure 10, and the correlation between experiment and theory (calculated from Equation 18) is excellent. Kinetic measurements also can be made directly from the limiting current using Equation 19. Since k , = k C z , the current should be proportional to and a plot of the limiting current as a function of d C ? s h o u l d be linear, This with a dope proportional to method of treating the data provided a value of the rate constant k equal to 217 (X/Z)-' second-'. The values of the rate constant, IC, obtained by the various methods of treating the experimental data are reasonably consistent, and agree with the polarographic data of Koryta ( 5 ) . The values obtained measuring id in
dc,
(ik/&)/(?;dj;dt7) (17)
where ti,!' is the rate of potential scan at, which id' is measured. This approach imposes certain requirements on the esperimental procedure., since t o observe diffusion controlled currents, k,/a must not be greater t'han about 0.001. The concentrat'ion of the osidizer can be made m a l l so that the product k C z will be small, but CZ still must' be kept sufficiently large, so that' the ratio of hydroxylamine to Fe(II1) is a t least 100. Under these circumstances, to observe diffusion control, a scan rate of about 100 volts/ second is required. -it these scan rates, the instrumentation used here was near the limit of its rebponse capabilities, but useful data still could be obtained if suitable charging current corrections were made. L-Fing the alternate method of obtaining i d , stationary electrode polarograms were obtained without hydrosylamine present. Then aliquots of hydroq-lamine were added to the solution, and the current is was measured. For both methods of measuring i d , values of i, were obtained for five scan rates ranging from 50 mv./second to 1.02 volts/second. Values of i k / 2 d which were obtained were used with a working curve similar to Figure 14 in Reference ( 6 ) , and calculated from
-0.8
At very cathodic potentials! Equation 18 reduces to a form previously presented by Saveant and Vianello (16) :
Experimental stationary electrode polarograms were obtained a t 50 mv./ second under conditions where Equations 18 and 19 hold for the Fe(II1)Table 111.
dK
Kinetic Data for Reduction of Fe(lll)-Triethanolamine Presence of Hydroxylamine
Complex in
Fe(III), 5.32 X 10-451; Triethanolamine, 0.02.V; Sodium Hydroxide, 1.0M Concn. XH20H Scan rate, volts/second 0.0JI 0.06051 0.098.11 0.130M Peak ctirren t, i, (Ma.) 102 238 238 235 235 1.02 22.8 30.9 37.4 43.8 0.53 16.4 29.4 36.6 43.5 0.20 9.47 28.6 36.4 42.0 0.10 6.69 27.7 35.5 41.8 0.05 4.85 27.9 35.6 41.6 10.8 18.4 25.2 k, (5I/l)-' second-' 181 188 193 13.4 22.1 30.8 k, (.V/l)-I second-' 224 226 237 I i d measured in presence of hydroxylamine I1 i d measured in absence of hydroxylamine
VOL. 38, NO. 3, MARCH 1 9 6 6
381
the presence of hydroxylamine at high scan rates are lom-er, probably because of the uncertainty in correcting for charging current and also from using measurements obtained a t the limiting capabilities of the instrument. Measurement of the reaction ratio between Fe(I1) and hydrosglamine is not poscible, since the stoichiometric coefficient is included in the definition of the pseudo first-order late constant. LITERATURE CITED
(1) Alberts, G. S., Shain, I., ASIL. CHEM.35, 1859 (1963). (2) Fischer, O., Drarka, O., Fischerova, E., Collection Czech. Chem. Cornmuns. 2 6 , 130.5 (1961). (3) Fiirlani, C., lIorpiirgo, G., J . Electroanal. Chem. 1, 351 (19.59/60).
(4) Jessop, G., iyature 158,59(1946). (5) Koryta, J., Collectzon Czech. Chem. Communs. 19, 666 (1954). (6) Kicholson, R. S., Shain, I., A s ~ L . CIIEM.36, 706 (1964). (7) Nicholson, R. S.,Shain, I., Ibzd., 37, 178 (1965). ( 8 ) Ibzd., p. 190. (9) Polcvn, D. S., Ph.D. thesii, University of Wisconsin, lladison, WE.,
(15) Shain, I., Polcyn, D. P., J . Phys. Chem. 65, 1649 (1‘361). (16) Smith, 1). E., .%S.\L. CHEM. 35,
G10 (1!)63). (17) Piibr:ihnianya, R . P., i n “Advances i n Polarography,’’ I. F. Loiigniiiir, ed., 1-01. 11, p. 674, Pergnnion Pres., Sew Tork, 1 9 G O . (18) Siibrahnianya, R . S., Proc. Indian
19G
(16jPolcyn, D. S., Shain, I., r l s . 1 ~ .
CHEM.38, 370 (1966). (11) Iiiha, J.. Z. Phiisik. Chem. (Sonderheft), p. 152, J~ily,’1938. (12) Saveant, J. AI., S-ianello, E., in
“Advances in Polarography,” I. S. Longmuir, ed., Vol. I, p. 367, Pergamon Press, Sew York, 1960. (13) Saveant. J. 11..Tianello., E.., Electrochim. -4ccta’8, 905’(1963). (14) Saveant, J. JI., Vianello, E., Ibid., 10, 905 (1965). ’
1963.
, ‘,Qiiantitative In-
’ 3rd ed., p. 391, John (21) 1Volf>on, H., .Yalure 153,375 (1044). RECEIVED for review Sovember 10, 1965, Accepted January 10, 196G. \\-ark supported in part by funds from the U. s. Atomic Energy Comniis>ioii Contract S O .AT( 11-1)-1083.
Continuous Ohmic Polarization Compensator for a Voltammetric Apparatus Utilizing Operational Am pIifiers DIRK POULI, JAMES R. HUFF,’ and JAMES C. PEARSON* Research Division, Allis-Chalmers Manufacfuring Co ., Milwaukee 7 , Wis.
A voltammetric device has been developed to compensate continuously for the ohmic voltage between reference and working electrodes in an electrochemical cell. Compensation is achieved by inserting an “effective” resistance in series with the cell. The value of this effective resistance i s determined by the iR drop as measured between reference and working electrodes when a square wave current pulse is applied across the cell. The voltage developed across this resistance is sensed by a feedback circuit. As a result of the ohmic voltage compensation, the potential difference between reference and working electrodes equals the input voltage. The same technique may b e used in galvanostatic studies to measure the iR free potential of the working electrode. In this manner, the accuracy of galvanostatic potential measurements may be enhanced when the ohmic voltage is appreciable.
S
applications of operational amplifiers in electrochemical equipmcnt have been reviewed by Schwarz niid Shain ( 7 ) . Further special adaptations of these electronic components were considered in a sympo,’qium on (1). The operational amplifiers problems associated with appropriate earthing points and compensation for EVERAL
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voltage drops across measuring resistors are fully discussed in the articles cited above. One of the major difficulties in electrochemical experimentation is the precise measurement of the potential of the working electrode with respect to a reference electrode. When a continuous current flow betlveen working and counter electrodes, the measured potential of the former always includes an ohmic component. Similarly, when a voltage is applied to the working electrode by means of a potentiostat, the electrochemical potential of this electrode with respect to a reference electrode differs from the imposed voltage by an iR term. The ohmic voltage referred to is due to the fact that the completed circuit for measuring the potential partially coincides with the current path from the xorking to the counter electrode. I n subsequent discussions, “the iR and/or ohmic voltage” refers to this ohmic voltage between reference and working electrodes. A Luggin capillary often has been used to decrease the ohmic voltage to a small value. It is, hoivever, not possible to eliminate the iR term completely in this manner. I n addition, the geometry of the cell precludes the use of the Luggin capillary in some systems. Even when a Luggin capillary can be incorporated, the ohmic voltage may be
appreciable a t current densities of the order of 100 ma. per sq. cin. (based on geometric area) or if the electrolyte concentration is low. For esample, Bockris (2) has calculated the iR drop to be in excess of 1 volt under the following conditions : electrolyte concentration of 10-2 gram ion per liter, a distance of 1 mm. between the tip of the Luggin capillary and the working electrode, and a current’ density of 10 ma. per sq. cm. Correction after measurements have been made is possible only if a steadystate current-voltage characteristic is required. I n voltammetry with a linearly varying potential (LT’P) signal, the current-voltage characteristic often exhibits maxima and minima-Le., the potential is a multivalued function of the current. Many examples of this type of curve are to be found in the literature-e.g., see (8). Correction for the ohmic voltage afterwards is impossible without accurate knowledge of the true current-potential curve. The electrochemical determined parameterse g . , the Tafel slope-may thus be considerably in error. I n addition, small current, maxima or inflections may be lost completely or in part whenever the ohmic voltage is appreciable. 1 Present address, Research Laboratories, Globe-Union, Inc., Milwaukee, \Vis. * Present address, LECO Laboratory Equipment Corp., St. Joseph, llich.
