Solutions to exercises
267
This chain thus constitutes a SO 3(g) sensor. It operates as a second species
sensor because it requires Ag 2 SO 4 . The presence of two membranes allows
us to eliminate the oxygen partial pressure.
2. Numerical evaluation
a. Value of the potential for P
b ar
10
SO
Mes
7
3
=
−
at 500 °C
E
2 96 480
286 330 (64.8 773) 336 800 (279 773)
2 96 480
8.14 773
ln 10
7
Δ =
−
+
+
−
+
−
#
#
#
#
#
E
1.133 V
Δ = −
b. Change in potential when P SO
Mes
3
reaches 2 # 10
−6
bar at 500 °C
( E)
2F
RT
ln P
P
Mes 1
Mes 2
SO
SO
3
3
δ Δ =
^
^
h
h
( E)
2 96 480
8.14 773
ln 10
2 10
7
6
δ Δ =
−
−
#
#
#
( E) 0.099 V
δ Δ =
3. The resistance R of the device is equal to the sum of the resistances R o of
the oxide ion conducting electrolyte, denoted o, and R Ag of the silver-ion
conducting electrolyte, denoted Ag,
R = R o + R Ag
R
1 S
1 S
o
o
Ag
Ag
,
,
σ
σ
=
+
`
`
j
j
Because the pellets have the same geometric factor
k
S
S
o
A g
,
,
=
=
`
`
j
j
we have
R k
1
1
o
A g
σ
σ
=
+
c
m
Determination of the conductivities of both electrolytes
2 Oxide ion conducting electrolyte
σ o = σ O 2− + σ e
100 e
10 P e
o
6 O
kT
0.8 eV
2
kT
3.5 eV
1 4
σ =
+
−
−
−