Page 359 - Physical chemistry understanding our chemical world

326 ELECTROCHEMISTRY

Inserting values into Equation (7.41):
The value of RT/F is
0.0257 V at 298 K. 0.001
E = 0.799 V + 0.0257 V ln
+
Ag ,Ag
1
Note how, as a conse-
quence of the laws of so
arithmetic, we multiply E Ag ,Ag = 0.799 V + (0.0257 V ×−6.91)
+
the RT/F term with the
logarithm term before
adding the value of and E = 0.799 V − 0.178 V
+
E O . Ag ,Ag
O,R
E Ag ,Ag = 0.621 V
+
Note how the difference SAQ 7.16 Awireof purecopperisimmersed into asolu-
between E and E O is tion of copper nitrate. If E O = 0.34 V and E =
Cu 2+ ,Cu Cu 2+ ,Cu
normally quite small.
0.24 V, what is the concentration of Cu 2+ ? Assume that
a 2+ is the same as [Cu 2+ ].
(Cu )
The Nernst equation cannot adequately describe the relationship between an elec-
trode potential E O,R and the concentration c of the redox couple it represents, unless
we substitute for the activity, saying from Equation (7.28), a = c × γ ± .
The form of Equation (7.41) will remind us of the equation of a straight line, so a
plot of E O,R as the observed variable (as ‘y’), against ln(a (O) ÷ a (R) ) (as ‘x’) should
be linear with a gradient of RT ÷ nF and with E O as the intercept on the y-axis.
O,R
Worked Example 7.18 Determine a value for the standard electrode potential E O
+
Ag ,Ag
with the data below. Assume that γ ± = 1 throughout.

[AgNO ]/mol dm −3 0.001 0.002 0.005 0.01 0.02 0.05 0.1
3
E Ag ,Ag /V 0.563 0.640 0.664 0.682 0.699 0.723 0.741
+
Figure 7.11 shows a Nernst graph drawn with the data in the table. The intercept of the
graph is clearly 0.8 V.

Why does E AgCl,Ag change after immersing an SSCE in a
solution of salt?
Further calculations with the Nernst equation

Take a rod of silver, and immerse it in a solution of potassium
Care: In some books,
SSCE is taken to mean chloride. A thin layer of silver chloride forms on its surface when
a sodium chloride the rod is made positive, generating a redox couple of AgCl|Ag.
saturated calomel elec- We have made a silver–silver chloride electrode (SSCE).
trode. Now take this electrode together with a second redox couple (i.e.
half-cell) of constant composition, and dip them together in a series