196
4 – Electrode reactions
4F
RT
ln 1 I
I
c
c
η =
−
,
c
m
reduces to
4F
RT I
I
c
c
η = −
,
#
under the conditions I % I ℓc . This allows us to deduce the polarization
resistance
R
dI
d
4F
RT I
1
c
c
c
η
=
= −
,
η
#
R
4F I
RT
c
c
=
,
η
I
4FR
RT
c
c
=
,
η
Numerical evaluation gives
.
.
.
I
A
4 96 480 0 565
8 314 913
0 0348
c =
=
,
#
#
#
.
I
m A
34 8
c =
,
4. We can verify that, under these conditions, |I | < | I ℓc | or 7 mA < 34.8 mA.
If we exceed this limit, another reduction reaction is triggered. It may correspond to the reduction of the electrolyte with an increase in the electronic
conductivity and the progressive blackening of the stabilized zirconia.
5. a. Referring to figure 72, we can write
log R η = − α log P O 2
log P
log R
O 2
α
Δ
Δ
= −
η
6 0.74
3.8 0
0.72
α = −
−
=
which gives
R
R P O
0.72
2
=
η
η
°
where R° η is a constant.
Taking into account the relation obtained in question 3, we can write
I
I P
.
c
c O
0 72
2
=
,
,
−
°
where I c
, ° is a constant.
This relation is valid for P O 2 < 7.4 # 10
−3
bar.