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HALF-CELLS AND THE NERNST EQUATION 325

with the magnitude of E O indicating the oxidizing power: E O =+0.34 V, but
2+
Cu ,Cu
a powerful oxidizing agent such as bromine has a value of E O − =+1.09 V.
Br 2 ,Br
In summary, sodium reacts with water and copper does not in consequence of their
relative electrode potentials.

Why does a torch battery eventually ‘go flat’?

The Nernst equation

A new torch battery has a voltage of about 1.5 V, but the emf decreases with usage
until it becomes too small to operate the torch for which we bought it. We say the
battery has ‘gone flat’, and throw it away.
We need to realize from Faraday’s laws that chemicals within a battery are con-
sumed every time the torch is switched on, and others are generated, causing the
composition within the torch to change with use. Specifically, we alter the relative
amounts of oxidized and reduced forms within each half-cell, causing the electrode
potential to change.
The relationship between composition and electrode potential is
given by the Nernst equation Though it is relatively
easy to formulate rela-
RT a (O) tions like the Nernst
E O,R = E O + ln (7.41)
O,R equation here for a
nF a (R)
cell, Equation (7.41)
properly relates to a
O
where E is the standard electrode potential determined at s.t.p.
O,R half-cell.
and is a constant, E O,R is the electrode potential determined at non
s.t.p. conditions. R, T, n and F have their usual definitions.
The bracket on the right of Equation (7.41) describes the relative activities of
oxidized and reduced forms of the redox couple within a half-cell. The battery goes
flat because the ratio a (O) /a (R) alters with battery usage, so the value of E O,R changes
until the emf is too low for the battery to be useful.

Worked Example 7.17 A silver electrode is immersed into a dilute solution of silver
−3
nitrate, [AgNO ] = 10 −3 mol . What is the electrode potential E Ag ,Ag at 298 K? Take
+
3
E O = 0.799 V.
+
Ag ,Ag
The Nernst equation, Equation (7.41), for the silver couple is

RT a (Ag )
+
O
E Ag ,Ag = E Ag ,Ag + F ln a (Ag) We use the approxima-
+
+
tion ‘concentration
= activity’ because the
For simplicity, we assume that the concentration and activity of solution is very dilute.
+ = 10 . We also assume that the
silver nitrate are the same, i.e. a (Ag ) −3
silver is pure, so its activity is unity.