Solutions to exercises
261
We have
n
M
m
M
V
ρ
=
=
where ρ, M, and V are respectively the density, molar mass, and volume of
the reference electrode. The lifetime is given by
t
I
n F
I M
V F
ρ
=
=
#
#
#
#
Numerical evaluation gives
t
2.92 10
23
0.97 0.4 10
96 480
7
4
=
−
−
#
#
#
#
#
t = 5.57 # 10
5
s
t
h
155
=
4. Figure 107 shows, for three temperatures, the change in the theoretical emf
of the sensor as a function of the logarithm of the CO 2 partial pressure. The
lines intersect at the isoelectric point P i , where the emf is independent of
temperature.
A linear regression allows us to determine the theoretical equation governing
the change in the emf as a function of CO 2 partial pressure
2 at 298 K
ΔE = 2.95 # 10
−2
log P CO 2 + 3.40
2 at 353 K
ΔE = 3.49 # 10
−2
log P CO 2 + 3.32
We deduce the CO 2 partial pressure at the isoelectric point of the sensor
(3.49 − 2.95) # 10
−2
log P CO 2 = 3.40 − 3.32
( .
. )
.
.
log P
3 49 2 95 10
3 40 3 32
CO
2
2
=
−
−
−
#
log P CO 2 = 14.81
and
.
P
b ar
6 45 10
CO
14
2
=
#
This result is far from the pressure of CO 2 in the ambient air.