Physical Chemistry Third Edition

356 8 The Thermodynamics of Electrochemical Systems

Since the electrons are produced at the left electrode and consumed at the right

electrode, we have labeled the electrons with (L) and (R). We can rewrite the cell

reaction equation using only electrons and uncharged substances:

H 2 (g)+2AgCl(s)+ 2 e−(R)−→2HCl+2Ag(s)+ 2 e−(L) (8.2-4)

There are several conventions that have been adopted to make the description of elec-

trochemical cells systematic. One convention is: The left electrode in a cell diagram

is assigned to be the anode and the right electrode is assigned to be the cathode.The

choice that we make for the right and left electrodes thus dictates the direction in which

we write our cell reaction equation. Our example reaction turns out to be spontaneous

in the direction it was written, but it can happen that the spontaneous direction of the

reaction is opposite to the way we write it. In the English language one way to remem-

ber which half-reaction goes with which side of the cell is to note that “reduction” and

“right” both begin with the letter “r.”

Acell symbolcommunicates the same information as a cell diagram. In this symbol

the phases of the cell are listed, beginning with the terminal of the left electrode and

proceeding through the cell to the terminal of the right electrode. The symbol for each

phase is separated from the next by a vertical line. The cell symbol for our present

cell is

Pt(s)|H 2 (g)|HCl(aq)|AgCl(s)|Ag(s)|Pt(s)

The platinum terminals are sometimes omitted from cell symbols. The pressure of a

gas and the molality, concentration, or activity of a solute can be included in the cell

symbol. If the molality of the HCl is 0.500 mol kg−^1 and the pressure of the hydrogen

gas is 0.990 atm the cell symbol is:

Pt(s)|H 2 (g,0.990 atm)|HCl(aq,0.500 mol kg−^1 )|AgCl(s)|Ag(s)|Pt(s)

A similar specification of composition can be used for an electrode that is a solid

solution or an amalgam (solution in mercury).

We first leave our galvanic cell on “open circuit” (with the two terminals not con-

nected to any circuit) and allow the cell to stabilize at constant temperature and pressure.

The electric potential will have different values at the two terminals. One way to mea-

sure the electric potential difference between two terminals without changing their

state is to connect them to apotentiometer, which applies an adjustable counter e.m.f.

to oppose the electric potential difference of the cell. This counter voltage is adjusted

until it is just sufficient to stop the flow of electrons in the external circuit, as indicated

by a galvanometer. The cell and the potentiometer are now at equilibrium and the state

of the cell is the same as though the cell were on open circuit. The counter voltage

can be read from the potentiometer and is equal in magnitude to the potential differ-

ence between the electrodes. The value of this potential difference is called the cell’s

reversible potential differenceor itsreversible voltage. To an excellent approximation

the cell reaction is now thermodynamically reversible. If the counter voltage is made

slightly smaller than its equilibrium value, the cell functions as a galvanic cell and a

current flows while the reaction proceeds in the spontaneous direction. If the counter

voltage is made slightly larger, the cell becomes an electrolytic cell and the current

flows in the opposite direction.

Our system at equilibrium at constantT andPcorresponds to a minimum in

the Gibbs energy of the system. If an infinitesimal amount of reactiondξoccurs at

equilibrium we can write