Geoscience Reference
In-Depth Information
where g and s indicate whether the compounds are in a gaseous or solid state. As there are
more unknowns than equations, the necessary number of mass action law equations must
be completed. We can write gaseous equilibria of the type:
2H
2
(g)
+
O
2
(g)
⇔
2H
2
O (g)
(12.5)
and relate partial gas pressures by means of the mass action law:
P
H
2
O
P
H
2
P
O
2
=
K
(
T
,
P
)
(12.6)
where
K
(
T
,
P
) is a known function of temperature and pressure. The condensation of
planetary material produces different solid phases, which makes equilibrium calculations
a tedious task. Let us write, for example, that magnesian olivine (forsterite Mg
2
SiO
4
)
appears by condensation of Mg vapor, SiO, and water:
2H
2
(g)
+
O
2
(g)
⇔
2H
2
O(g)
(12.7)
2Mg(g)
+
SiO(g)
+
3H
2
O(g)
⇔
Mg
2
SiO
4
(s)
+
3H
2
(g)
(12.8)
By considering that olivine is nearly pure forsterite, the mass action law can be written:
P
H
2
P
Mg
P
SiO
P
H
2
O
=
K
(
T
,
P
)
(12.9)
where
K
(
T
,
P
) is the constant characteristic of this equilibrium. As most matter is initially
formed from hydrogen it can be assumed that the partial hydrogen pressure
P
H
2
is equal
to total pressure
P
tot
and that, applying Dalton's law, the pressure of each gaseous com-
ponent is proportional to its molar proportion in the gas. Starting with a composition of
solar gas, rather cumbersome calculations can resolve this complex system of equations
with decreasing temperatures. The condensation sequence can be predicted from the most
refractory minerals (such as melilite and perovskite of refractory inclusions of the famous
Allende meteorite) through the common mantle minerals (olivine, pyroxene), the iron in
the core, to the hydrated minerals (serpentine), and even water (
Fig. 12.8
). The mineralogy
of each planet can be predicted fairly satisfactorily from its position in the proto-solar
nebula and therefore from its temperature.
When the temperature of the solar nebula decreases, elements condense in groups: the
refractory siderophile and lithophile elements (e.g., Ti, Si, Ca, Al, Mg, Fe from 1800 to
1300 K) come first, then the alkali elements (Na, K, Rb) and the group of high-temperature
chalcophile elements (Zn, Cu, Ga from 1200 to 900 K), followed by the group of low-
temperature chalcophile elements (Pb, Tl, Hg from 800 to 500 K), and finally by the volatile
atmophile elements (N, H, C, rare gases below 300 K). How effectively volatile elements
are incorporated varies from planet to planet and depends on the distance from the Sun,
which determines the accretion temperature, and also on the early history of each planet,
in particular the massive impacts between planetesimals. If we compare a volatile lithophile
element such as potassium with a very refractory lithophile element such as uranium it can
be seen that the K/U ratio, whose primordial value of 60 000 is given by carbonaceous
