Solutions to exercises
259
where Δ f H ° AgCl (s) and Δ f S ° AgCl (s) are respectively the change in the standard enthalpy and in the standard entropy of formation of AgCl (s) . This
relationship indicates that the emf is a linear function of temperature
under these measurement conditions, which we verify in figure 106.
c. The change in the free enthalpy of formation of AgCl is given by
Δ f G ° AgCl (s) = − ΔE # F
Numerical evaluation at 350 °C gives
ΔE = − 0.6 # 623 + 1 331
Δ E = 957.2 mV
from which
G
957.2 10
96 480
f 623 K,AgCl
3
(s)
Δ
=−
−
#
#
°
G
92.4 kJ mol
f 623 K,AgCl
–1
(s)
Δ
=−
°
Solution 5.7 – CO 2 sensor (a)
1. a. The electrochemical chain is
Au1,Na / SE / Na 2 CO 3 (O 2(g) ,CO 2(g) ),Au2
α β γ
b. Analytic expression of the emf at the sensor terminals
We consider the following equilibria:
2 at interface α
2e Au1 m 2e Na
2
2
e
Au1
e
Na
μ
μ
=
u
u
2
2F
2
2F
e
Au1
Aul
e
Na
Na
μ
ϕ
μ
ϕ
−
=
−
2 at interface β
2Na m 2Na
+ + 2e
2
2
2
2F
Na
Na
Na
SE
e
Na
Na
μ
μ
μ
ϕ
=
+
−
+
u
2 at interface γ
2Na
+
SE m 2Na
+
Na 2 CO 3
2
2
2
Na
SE
Na
Na CO
Na
2
3
μ
μ
μ
=
=
+
+
+
u
u
u
and 2Na
+ + CO 2 + 2
1
O 2 + 2e m Na 2 CO 3
2
2
2F
Na CO
Na
CO
2
1 O
e
Au2
Au2
2
3
2
2
μ
μ
μ
μ
μ
ϕ
=
+
+
+
−
+
u
Combining the preceding relationships allows us to express the emf ΔE:
ΔE = φ Au2 − φ Au1