1082
COMMUNICATIONS TO THE EDITOR
K2+and 02+ions to N205,followed by the fragmentation of the N206molecule adds to the complexity of the system. RENSSELAER POLYTECHNIC INSTITUTE TROY, NEWYORK 12181
G. LIUTI S. DONDES P. HARTECK
RECEIVED DECEMBER 4, 1967
Homogeneous Chemical Kinetics with the Rotating Disk Electrode. The ECE Mechanism -2
Sir: The application of the rotating disk electrode to the study of the ECE electrolysis mechanism
has recently been discussed by Malachesky, Jlarcoux, and Adams.’ They presented this approximation for the limiting current
i,
(3)
the result is
i,
=
I
0
k/o
Figure 1. Plot of napp/nUS. log ( k l w ) . Solid line shows curve calculated from eq 5 ; dashed line shows curve calculated from eq 6. It is assumed that D = cmz/sec and that y = 10-2 cm2/sec.
Malachesky, Marcoux, and Adams used the apparent n value, napp,to correlate their experimental results.
(2)
where C A . is ~ the bulk concentration of A, D is the diffusion coefficient, y is the kinematic viscosity, w is the angular velocity, and IC is the first- or pseudo-firstorder rate constant. Equation 2 was obtained by combining results from hydrodynamic studies2 with an equation arising in the chronoamperometric treatment of the ECE mechanism for a stationary electrode of constant area.3 The latter describes the instantaneous situation at an electrode with constantly changing concentration profiles. When a limiting current is measured with a rotating disk electrode, however, the concentration profiles are at a steady state and the use of chronoamperometric results can provide only an approximation to the truth. An expression, for the ECE mechanism, describing the variation of current with time in a controlled-potential electrolysis using a macroelectrode has been p r e ~ e n t e d . ~ It J may be used to describe the steadystate current at a rotating disk electrode if one sets t = 0 and substitutes the appropriate expression for the diffusion layer thickness 6. Considering, as did JIalachesky, llarcoux, and Adams, that2 6 = 1,62D’/3y’/~ww-’/~
LOG
From eq 2, they obtain
-
= 0.6”FAC~~D~~~y-’/k’’‘[2exp(-00.834 X
y‘”k/D”‘w) ]
-1
O . ~ ~ ~ F A C A ~ D ” / ” ~X - ’ / ~ W - ’ / ~
nanpp =
2 - e~p(-O.834y”~ICIc/D‘/~w)
(5)
Similarly, from eq 4
Values of napp/n for various values of Ic/w were calculated from eq 5 and 6 with typical values for the constants y and D and are plotted in Figure 1. Although both approaches give qualitatively similar results, they exhibit significant quantitative differences. However, as is apparent from their Figure 1, Malachesky, Marcoux, and Adams varied ic/w over only a rather narrow range (approximately 0.02-0.04) in which their equation yields values indistinguishable from those obtained by the present treatment. In brief, this note presents a treatment of the ECE mechanism for the rotating disk electrode similar in some respects to that previously presented,l but not involving a major approximation made there. Acknowledgment. It is a pleasure t o acknowledge the interest and numerous suggestions of Professor Louis Meites. (1) P. A. Malachesky, L. S. Marcoux, and R. N. Adams, J . Phys. Chem., 70, 4068 (1966). (2) V. G. Levich, “Physicochemical Hydrodynamics,” PrenticeHall, Inc., Ihglewood Cliffs, N . J., 1962. (3) G. S. Alberta and I. Shain, Anal. Chem., 35, 1859 (1963). (4) S. Karp and L. Meites, J . Electroanal. Chem., in press. (5) S. Karp, Ph.D. Thesis, Polytechnic Institute of Brooklyn, 1967.
As in eq 2, it is assumed that nl = n2 = n and that the diffusion coefficients of all species are identical. Equation 4 does not involve an approximation comparable t o the one inherent in eq 2. The Journal of Physical Chemistrg
DEPARTMENT O F CHEMISTRY UNIVERSITY LONGISLAND BROOKLYN, NEWYORK 11201 RECEIVED DECEMBER 18, 1967
STEWART KARP
