Determination of Charge Passed Following Application of Potential Step in Study of Electrode Processes SIR: I n a recent coinmunication n e described a new methcd for the determination of adsorbed electroactive species b y measuring the number of coulombs of charge that pass when the potential of an electrode is increased linearly with time ( 5 ) . Experimental results obtained with thit technique have also recently been published (6). The present note is to point out the virtues of a measurement of tht, charge passed following the application of a potential step to the electrode Such a procedure appears to offer advantages in electrochemical kinetic ,studies as well as for the determination 3f any adsorbed electrode reactant. The equation for the current-time behavior following application of a potential step. as derived by Gerischer and Vidstich ( d ) , but following Delahay's ncltation ( I ) , mag be written: i
=
K exp y2e f c y
(1)
where K
=
nFAk,OC,, X
( -r p [ ( l
-
The magnitudes of K and X can be determined from the slope of the plot of Q us. t 1 I 2 and Equations 6 and 7 . Values for the heterogeneous rate constant and transfer coefficient can be calculated from Equations 2 and 4. T h e n the magnitude of the potential step is sufficiently large so that the last term in Equation 4 becomes negligible
x
=
nFCozDoz1~2L4
(8)
and
Q
?
=
zF2nF =lCo,l>,,'
'tl
-
Thus, if the potential steps are large enough, the slopes of the Q us. t1I2 plots will be (6nFC,, Doz1'2)/~1'2. The same value for the slope can also be obtained by integration of the familiar equation for the purely diffusion limited current which results when the concentration of reactant a t the electrode surface is assumed to be zero for times greater than zero ( 2 ):
a)7[F(E- Eo)
+ R D,'
(4)
> 5 , may
(10)
2
IZ,O is the apparent ztandard heterogeneous rate constant in em. per see., t is the time since the potential of the electrode n a. changed from its initial value to E , and the other symbols h a r e their usual cignificanoe. The initial potential is sufficiently tinodic so that no current flon s prior to t t e potential step and only the oxidized form of the reactant is initially present in the solution. Equation 1 may be integrated with respect to time to yield
which, for g
Thus a plot of Q us. tilZ, once y > 5, will be linear and have an intercept, t,' 2, on the t1 axis such that
be simplified to
Yote, however, that Equation 11 predicts that the Q us. P2plot should pasthrough the origin while Equation 9 predicts a positive intercept on the t1 2 axis even when the potential step ip large enough t o produce the slope that results when the rate of the electrode reaction is much faster than the diffusion rates. As the magnitude of the potential step iq made still greater, X increases until the becond term on the right hand side of Equation 9 becomes negligible and the CJ z's. t1 2 plot appears to pass through the origin. It is seen from Equation 4 that X n i!1 have a minimum in the viciiiit! of C ,
[This has been pointed out by Delahay As a result, the extrapolated intercept, t,' 2, on the t l / * axis should start near the origin for potential steps to the foot of the polarographic wave, increase as the potential step magnitude increases, achieve a maximum value, and then decrease and give an apparent zero intercept for sufficiently large potential steps. I n the event that the electroactive species is adsorbed, the Q us. t112 plots should yield positive intercepts on the Q axis for potential steps sufficiently large to make the second term in Equation 9 negligible. Thus, even with an electrochemically irreversible system, it should be possible to detect the presence of adsorption. This is a distinct advantage of the potential step method over the previously described potential sweep method (5, 6). Preliminary experimental work has confirmed the above considerations and a full account will be presented a t a later date. (S).]
LITERATURE CITED
(1) Delahay, P., "Advancrs in Electro-
chemistry and Electrochemical Engineer-
ing," 1-01, I. p. 247, Interscience, Sew Tork. 1961. ( 2 ) Ibid.jp. S i .
(3) Delahay, P.,
"Sew Instrumental Methods in Electrochemistry," p. 51, Interscience, New York, 1954. (1)Gerischer, H., T'ielstich, W., 2.Physik C'heria. 3 , 16 (1955). ( 5 ) Osteryoung, R., Lauer, G., Anson, F. C., .%SAL. CHEM.34, 1833 (1962). ( 6 ) Osteryoung, R., Lauer, G., Anson, F. C., J . Electrochem. SOC. 110, 926 (1963). J. €1. CHRISTIE GEORGE LAKER R. A. OSTERYOVXG Sorth American Aviation Science Center 8437 Fallbrook Ave. Canoga Park, Calif. and
F. C . Axsox
1)ivision of, Chemistrj- and Chemical Ikgineenng
California Institute of Technology Pasadena, Calif. RECEIVED for review July 22, 1963. Accepted August 26, 1963. Contribution S o . 3002 from the Gates and Crellin Laboratories of Chemistry.
VOL. 35, NO. 12, NOVEMBER 1963
a
1979
