Geoscience Reference
In-Depth Information
Equilibrium between pure solid and gaseous phases (
Appendix C
)
allows us to write:
ln
P
H
2
O
=
H
RT
+
constant
(10.2)
where
H
is the heat (enthalpy) of the reaction. Other reactions involve other gases, such
as carbon dioxide, but they are treated in the same way.
The behavior of oxygen is particularly important. The redox reaction between two types
of common oxides in igneous and metamorphic rocks:
⇔
+
6Fe
2
O
3
4Fe
3
O
4
O
2
(10.3)
(hematite)
(magnetite)
is equivalent to the sum of the two half-reactions:
2e
−
⇔
2O
−
6Fe
2
O
3
+
4Fe
3
O
4
+
(10.4)
2O
−
⇔
2e
−
O
2
+
(10.5)
This shows that redox reactions are merely a trade in electrons between acceptors (oxidants
such as oxygen) and donors (reducing agents such as Fe
2
+
). There is nothing wrong, for
example, in considering ferrous iron Fe
2
+
as a complex of ferric ion Fe
3
+
with an electron.
As the vast majority of rocks are good electrical insulators, electrons must be conserved
throughout mineralogical reactions and phase changes. Appealing to an externally imposed
oxygen “fugacity” would be misleading: each and every reduction reaction, i.e. any gain
in electrons by one species, must be offset by loss of electrons by another species. No
local surplus or deficit of electrons is permitted and species having more than one state of
oxidation (above all Fe, C, and S) must engage in balanced electron exchanges. As with
water, oxygen pressure can be formulated by the mass action law. For example, for the
relationship between hematite and magnetite, we write the equation:
[Fe
3
O
4
]
4
magnetite
P
O
2
[Fe
2
O
3
]
hematite
=
H
RT
+
ln
constant
(10.6)
in which the square brackets indicate the molar fraction of the species in question in each of
the solid solutions containing hematite and magnetite, and
P
O
2
is oxygen pressure. Rela-
tionships like this can be used either for estimating temperature if the redox state of the
system is known, or vice versa for measuring oxygen pressure if temperature is known.
The fugacity of oxygen in many natural rocks is distributed around the famous QFM
(quartz-fayalite-magnetite) buffer:
3Fe
2
SiO
4
+
O
2
⇔
3SiO
2
+
2Fe
3
O
4
(10.7)
(fayalite)
(quartz)
(magnetite)
This equation does not mean that these minerals are present in the rocks, but that the
electron balance of the actual mineral assemblage is on average close to that of this buffer.
