Solutions to exercises
131
4. a. In the linear range established in question 1, the relation σ e = f (P O 2 ) can
be written in the form
P
e
O
1/n
2
σ
α
=
−
where α is a constant and n ≈ 3.5.
b. To interpret this relation theoretically, we must express
2 the reaction for doping CeO 2 with CaO
CaO $ Ca ′′ Ce + O
#
O + V
••
O
2 the equilibrium with the gaseous phase
O
#
O m 2
1
O 2 + V
••
O + 2e ′
K g = [V
••
O ] n
2
P
½
O 2
from which we deduce
n = K
½
g # [V
••
O ]
−½ # P
−¼
O 2
Assuming that the oxygen vacancies of extrinsic origin dominate
([V
••
O ] = [Ca ′′ Ce ]), we arrive at
n = kP
−¼
O 2
where k is a constant. We find that the equation giving the variation in
electronic conductivity with P O 2 deduced from this model is close to that
established experimentally [see 4(a)].
Solution 3.4 – Electronic transport number in a glass
1. The following electrode reactions occur at
2 the cathode
Ag
+ + e $ Ag
2 the anode
Ag $ Ag
+ + e
Considering the activity of Ag
+
ions to be constant in the electrolyte, the
emf ∆E at the cell terminals at equilibrium (i = 0) is expressed as
E (1 t ) F
RT
ln a
a
e
Ag
(1)
Ag
(2)
Δ = − r
where t e
r is the average electronic transport number.
2. a. The phenomenon responsible for this variation is the electronic conduction
in the electrolyte. Any difference in the silver chemical potential between
electrodes (1) and (2) will lead to a transfer of silver between the two compartments. This phenomenon is called electrochemical semipermeability.