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Oxygen Monitor SGM7 10 Appendix
HB_SGM7_eng.docx
33
Gas potentiometry using solid electrolyte sensors
Crystals of mixed oxides from ZrO
2
and CaO or Y
2
O
3
have vacancies in the
oxygen ion sublattices. Oxygen ions can migrate across them at high
temperatures. Thus, they are solid electrolytes (i.e. solid ion conductors). At
platinum layers on ceramic bodies of stabilized ZrO
2
(stabilized against
breaking), electrode reactions with the oxygen ion vacancies V
O
are possible:
1/2 O
2
(gas) + 2 e
-
(platinum) + V
O
(solid electrolyte) = O
2-
(solid electrolyte) ,
H
2
O(gas) + 2 e
-
(platinum) + V
O
(solid electrolyte) = O
2-
(solid electrolyte) +
H
2
(gas)
Oxygen atoms separated off molecular oxygen or water vapor take up
electrons on the surface of the platinum and move to oxygen vacancies of
the solid electrolyte where they form oxide ions. This process, however,
quickly comes to a stand-still if the electrode is in an open circuit, and neither
electrons nor oxygen ions can flow. In this state, the output of chemical work
from the particle transfer equals the effort that has to be made in terms of
electric work. An electrochemical equilibrium exists in this case which is a
dynamic equilibrium. The electrode reactions still occur but equally fast in
both directions. The larger the so-called exchange current density, the less
sensitive is the electrode to disturbances.
In electrochemical equilibrium, the platinum has either given off electrons and
is positively charged, or it has taken up electrons and is negatively charged.
The first is to be expected in oxygen, the second in hydrogen.
If two oxygen electrodes are exposed to different oxygen concentrations on
opposite sides of a gastight sintered ZrO
2
solid electrolyte, the electrode
exposed to the higher oxygen concentration will be charged more positively
than the electrode exposed to the lower oxygen concentration in
electrochemical equilibrium. A cell potential can be measured between the
electrodes. The more the oxygen concentrations at the two electrodes differ,
the higher is the cell potential.
In 1889, NERNST was the first to describe the quantitative connection
between the cell potential and the particle concentrations at the electrodes
with the so-called NERNST equation. In electrochemical thermodynamics
this equation can be derived from the chemical potentials (consisting of
energy and entropy components) of the particles participating in the cell
reaction (i.e. sum of the electrode reactions). The chemical potential of the
oxygen is given by
µ (O
2
) = µ (O
2
)
,
+ R ⋅ T ⋅ ln p(O
2
) .
For a solid electrolyte cell with two oxygen electrodes, the cell reaction is
merely the transfer of oxygen from higher to lower partial pressure. The
chemical work in cell reactions is described with the molar free reaction
enthalpy (Gibbs free energy)
∆
R
G, which equals the difference in chemical
potentials :
∆
R
G = µ (O
2
)' - µ (O
2
)" = R ⋅ T ⋅ ln [p(O
2
)'/p(O
2
)"] .
In isothermal cells, the standard potentials µ (O
2
)
,
on both sides are equally
high, and thus drop out. ∆
R
G equals the maximum work that can be won for
an infinitely slow reaction, i.e. at extremely slow current flowing through the
external circuit. It can be calculated using the equilibrium cell voltage U
eq
, the
molar charge F (Faraday’s constant), and the amount of electrons that are
exchanged in the cell reaction (4 electrons in case of O
2
) :
W
electric
= 4 ⋅ F ⋅ U
eq
.