264
5 – Applications
2 At the reference electrode (1), we can write
6
2
1
2
RT
ln P°
P
2
2
TiO
O
O
Na
NASICON
e
RE
Na Ti O
2
2
2
2 6 13
μ
μ
μ
μ
μ
+
+
+
+
=
+
°
°
°
u
u
2 and at the measurement electrode (2), we can write
RT ln P°
P
2
1
2
RT
ln P°
P
2
2
CO
CO
O
O
Na
NASICON
e
ME
Na CO
2
2
2
2
2
3
μ
μ
μ
μ
μ
+
+
+
+
+
=
+
°
°
°
u
u
where P° is the standard pressure. By developing the chemical potential of electrons, we obtain
6
2
1
2
RT
ln P°
P
2
2
2F
TiO
O
O
Na
NASICON
e
RE
RE
Na Ti O
2
2
2
2 6 13
μ
μ
μ
μ
ϕ
μ
+
+
+
+
−
=
+
°
°
°
u
and
RT ln P°
P
2
1
2
RT ln P°
P
2
2
2F
CO
CO
O
O
Na
NASICON
e
ME
ME
Na CO
2
2
2
2
2
3
μ
μ
μ
μ
μ
+
+
+
+
+
−
=
ϕ
+
°
°
°
u
Finally, we deduce the emf ΔE T
E
2F
1
6
2F
RT
ln P°
P
T
M E
RE
Na Ti O
C O
T iO
Na CO
CO
2 6 13
2
2
2
3
2
ϕ
ϕ
μ
μ
μ
μ
Δ
=
−
=
+
−
−
+
°
°
°
°
`
j
b. The expression
6
Na Ti O
C O
T iO
Na CO
2 6 13
2
2
2
3
μ
μ
μ
μ
+
−
−
°
°
°
°
`
j is the opposite
of the change in the standard free enthalpy of the operating reaction
G
6
r T
Na Ti O
C O
T iO
Na CO
2 6 13
2
2
2
3
μ
μ
μ
μ
Δ
−
=
+
−
−
°
°
°
°
°
By using
E
2F
G
T
r T
Δ
Δ
= −
°
°
we obtain
E
E
2F
RT
ln P°
P
T
T
CO 2
Δ
Δ
=
+
°
4. a. Expression for E
f(T)
T
Δ
=
°
Given that
G
72 939 149.2 T [J mol ]
r T
1
Δ
= −
+
−
°
we write
E
2F
G
T
r T
Δ
Δ
= −
°
°
E
2 96 480
72 939 149, 2 T
T
Δ
= −
+
#
°