Geoscience Reference
In-Depth Information
2. Aragonite is a denser polymorph of calcite CaCO
3
and is therefore more stable at
high pressure than calcite. Using the following values
H
0
= +1132 J mol
−
1
,
S
0
=
0.146 J mol
−
1
K
−
1
, and
2.78 10
−
6
m
3
for the calcite
−
V
0
=−
⇔
aragonite reaction,
calculate the pressure of the transition at 500
◦
C.
3. Show that the constant in
(10.2)
is equal to
R
, the entropy of the reaction
in standard conditions (hint: refer to
Appendix C
and use the definition of the free
enthalpy to show that
S
0
(
T
,
P
) /
G
0
(
T
,
P
)
=
H
0
(
T
,
P
)
−
T
S
0
(
T
,
P
)
). When the solids
1 bar, in particular when solid and gaseous phases are
identical, a small correction for mineral expansivity is necessary but is usually very
small.
4. The reaction described by Eq. 10.1 has a
are maintained at a pressure
>
of 111,090 J mol
−
1
H
0
(
298.1
)
and a
of 188.9 J mol
−
1
K
−
1
. Assume that these two values remain constant,
use the result of the previous exercise, and calculate
P
H
2
O
for temperature range of
450-650
◦
C.
5. The reaction described by
(10.7)
has a
S
0
(
298.1
)
of 528,600 J mol
−
1
H
0
(
298.1
)
and a
of 235.8 J mol
−
1
K
−
1
. Assume that these two values remain constant
and calculate
P
O
2
for range temperature of 800-1200
◦
C.
6. Magnesite (MgCO
3
) reacts with quartz to produce forsterite according to the reaction:
S
0
(
298.1
)
2MgCO
3
+
SiO
2
⇔
Mg
2
SiO
4
+
2CO
2
(magnesite)
(quartz)
(forsterite)
of this reaction is 173,000 J mol
−
1
350.2 J
mol
−
1
K
−
1
. Assume that these two values remain constant and calculate
P
CO
2
for
temperature range of 350-550
◦
C.
7. Calculate the
P
CO
2
as in the previous exercise for a carbonate with equal molar
proportions of calcite (CaCO
3
) and magnesite (MgCO
3
).
8. Use
(10.13)
to retrieve the
The
H
0
(
298.1
)
and the
S
0
(
298.1
)
S
0
values for quartz dissolution in water at
atmospheric pressure. From thermodynamic data tables, we find that
H
0
and
V
0
between the
10
−
6
m
3
. Calculate the solubil-
ity of silica at 300
◦
C at the surface and 0.1 GPa. Discuss the potential implications for
the interpretation of the chemistry of hydrothermal solutions.
9. Olivine is a solid solution of forsterite (Mg
2
SiO
4
) and fayalite (Fe
2
SiO
4
). Write the
simultaneous equations of weathering by pure water (hydrolysis) reactions of fayalite
to magnetite (Fe
3
O
4
) and of forsterite to serpentine Mg
3
Si
2
O
5
(OH)
4
and explain why
low-temperature alteration of peridotites is a source of hydrogen. How many moles
of mantle olivine fo
90
(with 90 mole percent forsterite and 10 percent fayalite) does
it take to produce one mole of H
2
? Assuming that a mass equivalent to 10 percent
(
molar volume of dissolved silica and quartz is
−
9.1
×
2km
3
y
−
1
) of the annual production of oceanic crust is serpentinized, what is the
annual flux of hydrogen from the mid-ocean ridges to the ocean and the atmosphere?
What do you think its fate is?
10. Fresh mid-ocean ridge basalts (MORB) contain about 10 wt% FeO. Upon reaction
with sulfate from seawater infiltrated into the young oceanic crust, some of the Fe
2
+
is oxidized to Fe
3
+
. How many grams of seawater with a concentration [SO
2
4
≈
] = 28.9
