260
5 – Applications
E
2F
1
2 Na
CO
2
1 O
N a CO
2
2
2
3
μ
μ
μ
μ
Δ =
+
+
−
^
h
The term in parentheses is the opposite of the change Δ r G T in the free
enthalpy of the following reaction:
2Na + CO 2 + 2
1
O 2 m Na 2 CO 3
which gives
E
2F
G
r T
Δ
Δ
= −
E
2F
1
G
RT ln P
2
RT
ln P
r T
CO
O
2
2
Δ
Δ
=
−
+
+
°
`
j
where Δ r G T ° is the change in the standard free enthalpy of reaction (1)
and P CO 2 and P O 2 are the partial pressures of CO 2 and O 2 , respectively,
expressed in bars.
2. Numerical evaluation gives
E 2 96 480
1
742 370 276 473
8.314 473 ln10
2
8.314 473
ln0.21
3
#
#
#
#
#
#
Δ =
−
+
+ `
^
^
h
j
h
6
B
E 3.014 V
=
3. The potential difference between the sensor terminals for P CO 2 = 10
−5
bar is
E 2 96 480
1
742 370 276 473
8.314 473 ln10
2
8.314 473
ln0.21
5
#
#
#
#
#
#
Δ =
−
+
+
−
`
^
^
h
j
h
6
B
ΔE = 2.92 V
The small input impedance R of the voltmeter used in the measurement
causes a current I that ceases when all the sodium of the reference electrode
is consumed.
The current I is given by
I
R
E
Δ
=
.
.
I
A
10
2 92
2 92 10
7
7
=
=
−
#
The lifetime t of the sensor is given by the charge Q that passes through the
circuit,
Q = I # t = n # F
where n is the number of moles of sodium contained in the reference electrode.