Physical Chemistry Third Edition

354 8 The Thermodynamics of Electrochemical Systems

PROBLEMS

Section 8.1: The Chemical Potential and the Electric
Potential

8.1Assume that the electric field in a region near a phase

boundary in an electrochemical cell is equal to

1. 0 × 107 Vm−^1. Find the magnitude of the concentration

gradient (derivative of the concentration with respect to

position) of a univalent ion that is necessary to make the

total chemical potential uniform if the concentration of the

ion is 0.100 mol L−^1 and the temperature is 298.15 K.

8.2Assume that the concentration of Cd^2 +ions varies from a

value of 0.0100 mol L−^1 near a cadmium electrode to a

value of 0.100 mol L−^1 at a distance of 8.0 nm from the

first position. Find the electric potential difference between

these two positions.

8.3Assume that the equilibrium concentration of Ag+ions

near an electrode varies from a value of 0.0010 mol L−^1 at

the electrode to a value of 0.100 mol L−^1 at a distance of

5.0 nm from the electrode.

a.Find the difference in electric potential between a

location at the electrode and at a distance of 5.0 nm

from the electrode.

b.Find the electric field in this region.

8.2 Electrochemical Cells

Anelectric currentis the passage of charged particles. A current in a metal is the passage

of electrons, and a current in an electrolyte solution is the passage of ions. An electro-

chemical cell is a device in which the passage of an electric current is accompanied

by the progress of an oxidation-reduction reaction in the cell. In anelectrolytic cella

current is passed through the cell by an external voltage, causing an otherwise nonspon-

taneous chemical reaction to proceed. In agalvanic cellthe progress of a spontaneous

chemical reaction causes an electric current to flow.

Galvanic cells are named for Luigi
Galvani, 1737–1798, an Italian
anatomist who showed that electricity
caused frog muscles to contract and
that dissimilar metals in contact with the
muscle tissue could produce an electric
current. They are also called voltaic
cells after Alessandro Volta.

Anequilibrium electrochemical cellis at the state between an electrolytic cell and

a galvanic cell. The tendency of a spontaneous reaction to push a current through

the eternal circuit is exactly balanced by an external voltage that is called acounter

electromotive forceorcounter e.m.f.so that no current flows. If this counter voltage is

increased the cell becomes an electrolytic cell and if it is decreased the cell becomes a

galvanic cell.

Electrochemical cells always contain several phases. There are two or moreelec-

trodesmade of materials that conduct electrons (usually metals or graphite). These

electrodes can be connected to an external circuit atterminals. There must be at least

one electrolyte solution in contact with each electrode. Under certain conditions sol-

vated electrons can occur at low concentrations in solutions,^1 but we will consider

uncombined electrons to be insoluble in electrolyte solutions and to occur only in

the electrodes. The materials of the electrodes are insoluble in the solutions, and the

components of the solutions are insoluble in the electrodes.

Figure 8.2 schematically depicts a particular electrochemical cell. A figure such as

this is called acell diagram. This cell belongs to a class calledcells without liquid

junction, which means that both electrodes are in contact with the same solution. If a

cell contains two different solutions in contact with each other the interface between

the solutions is called aliquid junction. The electrode at the left in Figure 8.2 is a

hydrogen electrode. It has a platinum surface that has been “platinized” (plated with

(^1) L. Kevan and B. Webster, eds.,Electron-Solvent and Anion-Solvent Interactions, Elsevier, New York,
1976.