Physical Chemistry Third Edition

602 13 Chemical Reaction Mechanisms II: Catalysis and Miscellaneous Topics

EXAMPLE13.9

Evaluate the concentration overpotential at a cadmium amalgam electrode, the diffusion flux

of Cd^2 +ions, and the current per square centimeter for 298.15 K. Assume thatd 200 μm,

that the concentration at the electrode is 0.0100 mol L−^1 , and that the concentration in the

bulk is 0.0200 mol L−^1. The diffusion coefficient for Cd^2 +ions at this temperature equals

8. 7 × 10 −^10 m^2 s−^1 .a

Solution

|ηconc|

(8.31435 J K−^1 mol−^1 )(298.15 K)

2(96485 C mol−^1 )

ln

(

0 .0200 mol L−^1

0 .0100 mol L−^1

)

 0 .00890 V

J(Cd^2 +)D(Cd^2 +)

∂c(Cd^2 +)

∂x

≈(8. 7 × 10 −^10 m^2 s−^1 )

0 .0100 mol m−^3

200 × 10 −^6 m

 4. 35 × 10 −^8 mol m−^2 s−^1

j(Cd^2 +) 2 FJ(Cd^2 +)2(96485 C mol−^1 )(4. 35 × 10 −^8 mol m−^2 s−^1 )

 8. 4 × 10 −^3 Am−^2  8. 4 × 10 −^7 Acm−^2

aA. J. Bard and L. R. Faulkner,op. cit., p. 154.

Equation (13.5-8) gives the concentration overpotential for one electrode. The con-

centration overpotential of the Daniell cell contains also a contribution from the other

electrode, from which newly formed copper ions diffuse into the bulk of the solution.

It is sometimes possible to study the behavior of a single electrode by the use of a

reference electrodeand a third electrode, called acounter electrode. A common choice

for a reference electrode is a silver/silver chloride electrode in a saturated potassium

chloride solution. The counter electrode is placed in a container with a porous plug,

which forms a liquid junction. The liquid junction potential is presumably fairly small

and nearly constant if the KCl solution is much more concentrated than the cell solu-

tion. The liquid junction is placed close to the surface of the electrode to be studied (the

working electrode), as in Figure 13.17. The potential difference between the reference

electrode and the working electrode is measured without allowing a current to pass

between the reference electrode and the working electrode, but allowing a controlled

current to pass between the working electrode and the counter electrode.

Reference
electrode Working
electrode

Counter

electrode

Porousplug

Figure 13.17 An Electrochemical
Cell with aThird Electrode.

The Activation Overpotential This part of the overpotential is due to chemical pro-

cesses at the electrode. For example, consider a cation that can be further oxidized by

losingnelectrons at an inert electrode such as a platinum electrode. An example of

such a half-reaction is

Fe^2 +
Fe^3 ++e− (13.5-9)

wheren1 in this example. We assume that the progress of the oxidation half-reaction

can be represented by a potential energy depending on the distance traveled by an ion

toward the electrode as shown in Figure 13.18a. This distance represents a type of

reaction coordinate. Increase in the value of the reaction coordinate (from left to right in

the diagram) represents a complicated process: the ion moves toward the electrode, the

electrons detach from the ion, and the electrons move into the electrode. The region near

an electrode surface can be a region of very high electric fields. A potential difference

of 1 V across an interface region with a thickness of 10 nm corresponds to a field of

1 × 108 Vm−^1.