Geoscience Reference
In-Depth Information
In many cases like this, the trace element (Rb, a few tens of ppm) displaces only a tiny
fraction of the major element (K, 10% or more). Molar fractions of potassium may be
considered constant and we can write:
ln
x
mica
Rb
x
feld
Rb
ln
K
(
T
,
P
)
=
(C.32)
where
K
is the partition coefficient of rubidium between mica and feldspar. In practice, it
is equivalent to an equilibrium coefficient of the mass action law, particularly with respect
to the equation controlling its dependence on temperature and pressure.
Finally, let us consider a heterogeneous equilibrium, i.e. which involves solid, liquid,
and gaseous phases at the same time. For example, let us examine the decarbonation of a
siliceous limestone:
CaCO
3
+
SiO
2
⇔
CaSiO
3
+
CO
2
(C.33)
(calcite)
(quartz)
(wollastonite)
to produce wollastonite CaSiO
3
, a silicate similar to pyroxene, and carbon dioxide. The
equality of the chemical potentials can be written:
ln
x
CaSiO
3
P
CO
2
x
CaCO
3
x
SiO
2
=−
G
0
(
T
,
P
)
RT
(C.34)
Assuming the minerals to be relatively pure, the molar fractions, such as
x
CaCO
3
,areall
very close to unity, and we obtain the equation:
ln
P
CO
2
=−
G
0
(
T
,
P
)
RT
(C.35)
We say that the calcite-carbonate-silica assemblage buffers the CO
2
pressure. For con-
be transcribed as:
∂
=−
ln
P
CO
2
∂
H
0
(
T
,
P
)
R
(C.36)
(1
/
T
)
where
H
0
is the latent heat (enthalpy) of reaction of the equilibrium in question. If
the latent heat varies little within the temperature range considered, the equation can be
integrated as:
ln
P
CO
2
=−
H
0
(
T
,
P
)
RT
+
constant
(C.37)
Similar equations can be written for the water vapor pressure (dehydration reactions),
oxygen pressure (oxidation-reduction reactions), and for many other species. Similar
equations are also valid for solubility of a pure solid phase in a solution:
∂
ln
x
i
=−
H
i
(
T
,
P
)
R
(C.38)
∂
(1
/
T
)
where
H
i
(
T
,
P
) is the heat absorbed by dissolution of a mole of component
i
in the
solution (melting-point depression). It should be remembered that the non-ideal character
of mixtures of gases and of solutions has been ignored all along.
