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The use of normal pulse polarography in the study of electrode kinetics
Electmchimica Acta.
1966. Vol.Il.
pp.
1525 to 1529. Rrgunon
Ptcsa Ltd. PrInted
fn Notthcm
Ircland
THE USE OF NORMAL PULSE POLAROGRAPHY THE STUDY OF ELECTRODE KINETICS*
IN
J. H. CHRISTIE~,E. P. PARRY and R. A. OSTERYOUNG North American Aviation Science Center, Thousand Oaks, California 91360, U.S.A. Abstract-The equations of Barkerfor normal pulse polarography have been applied to the study of the kinetics of Zn(II) reduction in NaN08. Results in good agreement with literature are obtained. Rhm16-011 applique les equations de Barker pour la polarographie normale a pulsations a la cinetique de la reduction du Zn(II) en solution de NaNO s. Les n%ultatsobtenus sont en bon accord aveo eeux de la litterature. B-Die Rarker’sehenGleichungen ftlr die normale Impulspolarographie wurden bei einer Untersuchung der Kinetik der Zn(II)-Reduktion in NaNOI verwendet. Man erhiilt Ergebnisse, welche sehr gut mit den Literaturdatentibereinstimmen. PULSE polarography
was originally developed as a trace analytical technique,l but Barker et ala have suggested that normal (as opposed to derivative) pulse polarography
should have applications in the study of electrode kinetics. In the normal pulse polarographic method, a series of pulses of successively increasing amplitude are applied to a dropping electrode, one pulse per drop, applied at a tied time in the life of the drop. The drops are detached mechanically to ensure that the area is always the same at the time at which the pulse is applied. The starting potential is well in front of the polarographic wave and no current flows before the pulse is applied. Since the capacitance current decays much more rapidly than the faradaic current, the current measured at a time of 2040 ms after the pulse application is essentially faradaic. An i/E curve is obtained which resembles an ordinary polarogram. The determination of the kinetic parameters of the electrode reaction from such an i/E curve is quite similar to the analysis of irreversible polarographic waves developed by Koutecky. 3 Since the effective time scale is much shorter than in polarography, faster reactions can be studied by normal pulse polarography. In this paper, we discuss the application of normal pulse polarography to the study of the kinetics of Zn(I1) reduction in varying concentrations of NaNO, as supporting electrolyte. Koryta4 has studied this system by “rapid” polarography (mechanical detachment of the drops with a period of 0.55 s) and has found that the rate of the reaction increases as the concentration of the supporting electrolyte is decreased. EXPERIMENTAL
TECHNIQUE
The pulse polarograph employed was constructed in this laboratory. For the purposes of this paper, the essential differences between the instrument employed here and the one described by Barker1 are that the instantaneous current is measured rather than the average current over the last half of the duration of the pulse and that the time at which the current is measured may be varied over the range of 20-40 ms. + Manuscript received 12 November 1965. t Present address: Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California. 1525 9
1526
E. P. PARRYand R. A.
J. H. Cmsm,
OSERYOUN~
Solutions were prepared from stock solutions of reagent grade NaNOs and Zn(NO& The Zn(NOJa solution was standardized by EDTA titration with Erio T indicator. THEORY
The current potential relation for normal pulse polarography is’ j=
nFA*Ck,“D$2 02”
anF(E - E:/J RT
exp (3LBt) erfc (W2),
(1)
where *C is the bulk concentration of depolarizer, k,” the apparent standard heterogeneous rate constant, a the transfer coefficient, A the electrode area (assumed constant during the duration of the pulse), EG, the reversible half-wave potential, t the time after application of the pulse at which the current is measured, and
-
$(E
- Ec2)](1 + exp pRiEG”)).
(2).
For E - E5, Q 0, (1) reduces to the Cottrell equation for a diffusion-limited current, ii ‘=
nFAd(D,,)*C d77t *
(3)
Dividing (1) by (3) gives k [ 1 + exp (g
(E - El,&)]
= dw At112exp (XQ)erfc (~a).
(4)
The value of AN2 corresponding to any value of i/id may then be determined from a plot of dr W2 exp (A2L2t) erfc (W2) 0s Atl /2. From these values of W2, the quantity Kpl2 =
k ‘=t’P
a D=#,t$-“,/2
exp (5)
can be obtained. A plot of log and a value at E = E[,2 of log
K =
log
K us
E should be linear, with slope -(mF/2~303RT)
k,” -;logD,-7
(’ - a) log Do
allowing determination of both k,” and a. RESULTS
AND
DISCUSSION
Figure 1 shows normal pulse polarograms for the reduction of Zn(I1) in two different concentrations of NaNO,, showing that the reduction becomes more irreversible as the concentration of supporting electrolyte is increased. In O-014 F NaNOa, the wave appears to be reversible and gives a plot of log ((id - i)/i) us E with a reciprocal slope of 29 mV. Figure 2 shows plots of log WI2 and log ~tll~ for two different values of the time after pulse application at which the current was measured (sampling time). The
Normal pulse pelarography for study of electrode kinetics
1527
calculation of rate constants from these data yields essentially the same value for k,” for both sampling times.
E, mV(sce) FIG. 1. Normal pulse polarograms. [zlM?I)] = @19mF (a) @014F NaNO,; El,, = -0.895 V&e) (b) l-05 F NaNOs; Ells = -0.985 V(sce) Curreut measured 20 ms after pulse applied. In the analysis of the pulse polarograms, it is necessary to know the value of the reversible half-wave potential. This was obtained from ordinary polarograms obtained with drop times of about 6 s. A plot of log ((id- i)/i) us E is almost linear under these conditions for all concentrations of NaNOa. The reversible half-wave potential was taken as the point at which the straight line tangent to the log ((id- i)/i) us E plot at the most anodic potentials intersected the log ((id - i)/i) = 0 axis. This is the procedure used by Koryta4 in his study of Zn(I1) reduction. The values of E& obtained in this way change with the NaNO, concentration because of the different junction potentials between the NaNO, solution and the saturated calomel reference electrode. Table 1 shows the values of the rate constants k,” obtained from the values of Ktli2 at E = El,,. The values of a were all in the range O-25430. The diffusion coefficients used in the calculation of the values of k,” were insnitely dilute values and were D, = DR = 7.2 x 10-g cm 8/s .6 Some small error is introduced by using this value and assuming D,, = DR. Figure 3 shows a plot of the observed rate constants trs the supporting electrolyte concentration. The values obtained are in good agreement with those of Koryta’
J. H. CHIWIIE, E. P. PARRYand R. A. OS~RYOUNG
1528
O.lP
I
-0.96 -0.96
I
I
I
-1.00
-1.06
I
-1.06
-I.
V (see)
E,
FIG. 2. hlla (upper) and ~tl’* o(~~m~ ;)
TABLE
I
-1.04
-1.02
for two different sampling times.
2oms:
1. APPARENT STANDARD RATE CONSTANT FOR Zn(II) REDUCTION FOR VARIOUS CON'IIONSOF NaNOs NaNO, F
k” cm/set Sampling time, 20 ms
0.014 0.105 0.350 0.490 1.05 2.45
>5 -2 6.5 40 3.4 3.1 2.4
x x x x x x x
10-L 10-x 1O-‘L 10-a 10-a 10-a lo-’
Sampling time, 40 ms
4.2 3.2 3.0 2.5
x x x x
lo-’ lo-’ lo-’ lo-’
Normal pulse polarography for study of electrode kinetics
1529
and of Randles and SommertorP (faradaic impedance) which are also shown in the figure. The values of rate constants above 1 x 1W2 cm/s are rather imprecise, since this is very close to the upper limit of applicability of the method. The same is true of the values in the same range obtained by Koryta,4 since his method of analysis involves a comparison of twice the current at the reversible half-wave potential with
A Randles and Somerton
l\
Koryto
l
+ This work
\ \ \
I
‘.
+\
\
‘\ c 5
\
‘\ 10-Z -
\
“. \’
o>
+\-
\ ‘4 +
io-33_ 0. I
p;,
\
. I-
-.
-+
1.0
[NoNO,], F
FIG. 3. Rate constant for Zn@) reduction as a function of NaNOs concentration.
the diffusion current. For k,” = 2 x 10-2 cm/s and t = 0.55 s, these differ by only about O-5%, making his reported determination of the rate constant very imprecise. The upper limit of applicability for the determination of k,,’ of the normal pulse polarographic method is about 2 x 1O-2cm/s for D = lo-5 cm2/s and t = 20 ms. Barker et al2 have cited a value an order of magnitude greater than this, but they seem to have inadvertently used a polarographic rather than a pulse polarographic equation to arrive at this limit. The pulse polarographic procedure appears to compare quite favourably with the “rapid” polarographic approach, and the fact that the time of measurement is at least lO-fold faster than in “rapid” polarography should permit a higher accuracy in the determination af kinetic constants. REFERENCES 1. G. C. BARKERand A. W. GARDNER,A.E.R.E. C/R 2297 (1958). 2. G. C. BARKER,H. W. NURNBWC and J. A. BOLZAN,presented at the 14th Meeting of CITCE., Moscow (1963). 3. J. KOUIECKY,Colln. Czech. them. Commun. 18, 597 (1953). 4. J. KORYTA.Electrochim. Actu 6,67 (1962). 5. R. PARSONS,Hadwok of Eiectrochemical Constants, p. 79. Butterworths, London (1959). 6. J. E. B. RANDLESand K. W. SOMERTON, Trans. Faraday Sot. 48,951 (1952).
1966. Vol.Il.
pp.
1525 to 1529. Rrgunon
Ptcsa Ltd. PrInted
fn Notthcm
Ircland
THE USE OF NORMAL PULSE POLAROGRAPHY THE STUDY OF ELECTRODE KINETICS*
IN
J. H. CHRISTIE~,E. P. PARRY and R. A. OSTERYOUNG North American Aviation Science Center, Thousand Oaks, California 91360, U.S.A. Abstract-The equations of Barkerfor normal pulse polarography have been applied to the study of the kinetics of Zn(II) reduction in NaN08. Results in good agreement with literature are obtained. Rhm16-011 applique les equations de Barker pour la polarographie normale a pulsations a la cinetique de la reduction du Zn(II) en solution de NaNO s. Les n%ultatsobtenus sont en bon accord aveo eeux de la litterature. B-Die Rarker’sehenGleichungen ftlr die normale Impulspolarographie wurden bei einer Untersuchung der Kinetik der Zn(II)-Reduktion in NaNOI verwendet. Man erhiilt Ergebnisse, welche sehr gut mit den Literaturdatentibereinstimmen. PULSE polarography
was originally developed as a trace analytical technique,l but Barker et ala have suggested that normal (as opposed to derivative) pulse polarography
should have applications in the study of electrode kinetics. In the normal pulse polarographic method, a series of pulses of successively increasing amplitude are applied to a dropping electrode, one pulse per drop, applied at a tied time in the life of the drop. The drops are detached mechanically to ensure that the area is always the same at the time at which the pulse is applied. The starting potential is well in front of the polarographic wave and no current flows before the pulse is applied. Since the capacitance current decays much more rapidly than the faradaic current, the current measured at a time of 2040 ms after the pulse application is essentially faradaic. An i/E curve is obtained which resembles an ordinary polarogram. The determination of the kinetic parameters of the electrode reaction from such an i/E curve is quite similar to the analysis of irreversible polarographic waves developed by Koutecky. 3 Since the effective time scale is much shorter than in polarography, faster reactions can be studied by normal pulse polarography. In this paper, we discuss the application of normal pulse polarography to the study of the kinetics of Zn(I1) reduction in varying concentrations of NaNO, as supporting electrolyte. Koryta4 has studied this system by “rapid” polarography (mechanical detachment of the drops with a period of 0.55 s) and has found that the rate of the reaction increases as the concentration of the supporting electrolyte is decreased. EXPERIMENTAL
TECHNIQUE
The pulse polarograph employed was constructed in this laboratory. For the purposes of this paper, the essential differences between the instrument employed here and the one described by Barker1 are that the instantaneous current is measured rather than the average current over the last half of the duration of the pulse and that the time at which the current is measured may be varied over the range of 20-40 ms. + Manuscript received 12 November 1965. t Present address: Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California. 1525 9
1526
E. P. PARRYand R. A.
J. H. Cmsm,
OSERYOUN~
Solutions were prepared from stock solutions of reagent grade NaNOs and Zn(NO& The Zn(NOJa solution was standardized by EDTA titration with Erio T indicator. THEORY
The current potential relation for normal pulse polarography is’ j=
nFA*Ck,“D$2 02”
anF(E - E:/J RT
exp (3LBt) erfc (W2),
(1)
where *C is the bulk concentration of depolarizer, k,” the apparent standard heterogeneous rate constant, a the transfer coefficient, A the electrode area (assumed constant during the duration of the pulse), EG, the reversible half-wave potential, t the time after application of the pulse at which the current is measured, and
-
$(E
- Ec2)](1 + exp pRiEG”)).
(2).
For E - E5, Q 0, (1) reduces to the Cottrell equation for a diffusion-limited current, ii ‘=
nFAd(D,,)*C d77t *
(3)
Dividing (1) by (3) gives k [ 1 + exp (g
(E - El,&)]
= dw At112exp (XQ)erfc (~a).
(4)
The value of AN2 corresponding to any value of i/id may then be determined from a plot of dr W2 exp (A2L2t) erfc (W2) 0s Atl /2. From these values of W2, the quantity Kpl2 =
k ‘=t’P
a D=#,t$-“,/2
exp (5)
can be obtained. A plot of log and a value at E = E[,2 of log
K =
log
K us
E should be linear, with slope -(mF/2~303RT)
k,” -;logD,-7
(’ - a) log Do
allowing determination of both k,” and a. RESULTS
AND
DISCUSSION
Figure 1 shows normal pulse polarograms for the reduction of Zn(I1) in two different concentrations of NaNO,, showing that the reduction becomes more irreversible as the concentration of supporting electrolyte is increased. In O-014 F NaNOa, the wave appears to be reversible and gives a plot of log ((id - i)/i) us E with a reciprocal slope of 29 mV. Figure 2 shows plots of log WI2 and log ~tll~ for two different values of the time after pulse application at which the current was measured (sampling time). The
Normal pulse pelarography for study of electrode kinetics
1527
calculation of rate constants from these data yields essentially the same value for k,” for both sampling times.
E, mV(sce) FIG. 1. Normal pulse polarograms. [zlM?I)] = @19mF (a) @014F NaNO,; El,, = -0.895 V&e) (b) l-05 F NaNOs; Ells = -0.985 V(sce) Curreut measured 20 ms after pulse applied. In the analysis of the pulse polarograms, it is necessary to know the value of the reversible half-wave potential. This was obtained from ordinary polarograms obtained with drop times of about 6 s. A plot of log ((id- i)/i) us E is almost linear under these conditions for all concentrations of NaNOa. The reversible half-wave potential was taken as the point at which the straight line tangent to the log ((id- i)/i) us E plot at the most anodic potentials intersected the log ((id - i)/i) = 0 axis. This is the procedure used by Koryta4 in his study of Zn(I1) reduction. The values of E& obtained in this way change with the NaNO, concentration because of the different junction potentials between the NaNO, solution and the saturated calomel reference electrode. Table 1 shows the values of the rate constants k,” obtained from the values of Ktli2 at E = El,,. The values of a were all in the range O-25430. The diffusion coefficients used in the calculation of the values of k,” were insnitely dilute values and were D, = DR = 7.2 x 10-g cm 8/s .6 Some small error is introduced by using this value and assuming D,, = DR. Figure 3 shows a plot of the observed rate constants trs the supporting electrolyte concentration. The values obtained are in good agreement with those of Koryta’
J. H. CHIWIIE, E. P. PARRYand R. A. OS~RYOUNG
1528
O.lP
I
-0.96 -0.96
I
I
I
-1.00
-1.06
I
-1.06
-I.
V (see)
E,
FIG. 2. hlla (upper) and ~tl’* o(~~m~ ;)
TABLE
I
-1.04
-1.02
for two different sampling times.
2oms:
1. APPARENT STANDARD RATE CONSTANT FOR Zn(II) REDUCTION FOR VARIOUS CON'IIONSOF NaNOs NaNO, F
k” cm/set Sampling time, 20 ms
0.014 0.105 0.350 0.490 1.05 2.45
>5 -2 6.5 40 3.4 3.1 2.4
x x x x x x x
10-L 10-x 1O-‘L 10-a 10-a 10-a lo-’
Sampling time, 40 ms
4.2 3.2 3.0 2.5
x x x x
lo-’ lo-’ lo-’ lo-’
Normal pulse polarography for study of electrode kinetics
1529
and of Randles and SommertorP (faradaic impedance) which are also shown in the figure. The values of rate constants above 1 x 1W2 cm/s are rather imprecise, since this is very close to the upper limit of applicability of the method. The same is true of the values in the same range obtained by Koryta,4 since his method of analysis involves a comparison of twice the current at the reversible half-wave potential with
A Randles and Somerton
l\
Koryto
l
+ This work
\ \ \
I
‘.
+\
\
‘\ c 5
\
‘\ 10-Z -
\
“. \’
o>
+\-
\ ‘4 +
io-33_ 0. I
p;,
\
. I-
-.
-+
1.0
[NoNO,], F
FIG. 3. Rate constant for Zn@) reduction as a function of NaNOs concentration.
the diffusion current. For k,” = 2 x 10-2 cm/s and t = 0.55 s, these differ by only about O-5%, making his reported determination of the rate constant very imprecise. The upper limit of applicability for the determination of k,,’ of the normal pulse polarographic method is about 2 x 1O-2cm/s for D = lo-5 cm2/s and t = 20 ms. Barker et al2 have cited a value an order of magnitude greater than this, but they seem to have inadvertently used a polarographic rather than a pulse polarographic equation to arrive at this limit. The pulse polarographic procedure appears to compare quite favourably with the “rapid” polarographic approach, and the fact that the time of measurement is at least lO-fold faster than in “rapid” polarography should permit a higher accuracy in the determination af kinetic constants. REFERENCES 1. G. C. BARKERand A. W. GARDNER,A.E.R.E. C/R 2297 (1958). 2. G. C. BARKER,H. W. NURNBWC and J. A. BOLZAN,presented at the 14th Meeting of CITCE., Moscow (1963). 3. J. KOUIECKY,Colln. Czech. them. Commun. 18, 597 (1953). 4. J. KORYTA.Electrochim. Actu 6,67 (1962). 5. R. PARSONS,Hadwok of Eiectrochemical Constants, p. 79. Butterworths, London (1959). 6. J. E. B. RANDLESand K. W. SOMERTON, Trans. Faraday Sot. 48,951 (1952).