Solutions to exercises
257
2 Compartment (1) 2
1
Cl 2(g) + e Me m Cl
−
SE
with
2
1 Cl
(1)
e
Me1
Cl
SE1
2
μ
μ
μ
+
=
−
u
u
Cl
−
is the majority carrier in the solid electrolyte
Cl
SE1
Cl
SE2
μ
μ
=
−
−
u
u
2 Compartment (2) 2
1
Cl 2(g) + e Me m Cl
−
SE
with
2
1 Cl
(2)
e
Me2
Cl
SE2
2
μ
μ
μ
+
=
−
u
u
Combining the three preceding equations gives
2
1 Cl
(1)
e
Me1
2
1
Cl
(2)
e
Me2
2
2
μ
μ
μ
μ
+
=
+
u
u
2
RT
ln P
F
2
RT
ln P
F
2
1 Cl
Cl
(1)
e
Me1
(1)
2
1 Cl
Cl
(2)
e
Me2
(2)
2
2
2
2
μ
μ
ϕ
μ
μ
ϕ
+
+
−
=
+
+
−
°
°
F
2
RT
ln P
P
(1)
(2)
Cl
(2)
Cl
(1)
2
2
ϕ
ϕ
−
=
^
h
By using ΔE = φ
(1) − φ
(2)
, we arrive at
E
2F
RT
ln P
P
Cl
(2)
Cl
(1)
2
2
Δ =
This is the expression for the emf as a function of chlorine partial pressures.
3. a. The electrochemical chain to consider in this case is
Ag-AgCl / SrCl 2 -KCl / Ag,Cl 2
We present the various equilibria in the chain
AgCl (s) + e Ag m Ag (s) + Cl
−
SE
with
AgCl
e
Ag1
Ag
Cl
SE1
μ
μ
μ
μ
+
=
+
−
u
u
Cl
−
being the majority carrier in the solid electrolyte, we have
Cl
SE1
Cl
SE2
μ
μ
=
−
−
u
u
(1) and (2) denote the internal and external faces of the electrolyte.
2
1
Cl 2(g) + e Ag m Cl
−
SE,2
with
2
1 Cl
e
Ag2
Cl
SE2
2
μ
μ
μ
+
=
−
u
u
Combining these reactions gives
AgCl
e
Ag1
2
1 Cl
e
Ag2
Ag
2
μ
μ
μ
μ
μ
+
=
+
+
u
u