Geoscience Reference
In-Depth Information
We will note
R
and
W
the mass of rock and water, respectively, reacting with each other,
and neglect the fact that water and rock contain slightly different oxygen concentrations.
We can write the isotopic mass balance during the reaction as
18
O
FR
+
18
O
MW
=
18
O
HR
+
18
O
HW
R
δ
W
δ
R
δ
W
δ
(10.17)
where HW refers to the hydrothermal solution, which, unfortunately, can no longer be
sampled and analyzed. Rearranging, we get the water/rock (
W
/
R
) ratio as:
18
O
FR
−
δ
18
O
HR
W
R
=
δ
(10.18)
18
O
HW
−
δ
18
O
MW
δ
18
O value of igneous whole-
rocks is similar to that of their feldspar. This property allows us to estimate the
It is often observed that, for mass balance reasons, the
δ
18
Oof
δ
18
O of the altered rock and the fractionation factor of
18
O/
16
O between feldspar and water at 350
◦
C, i.e:
the hydrothermal water from the
δ
18
O
feldspar
=
δ
18
O
HW
+
δ
4
(10.19)
Rearranging, we get the water/rock (
W
/
R
) ratio as:
W
R
=
5.5
−
(
−
2)
10)
=
1.875
(10.20)
(
−
2)
−
4
−
(
−
Water/rock ratios in the range 1-5 are very common. These values are in general mini-
mum values and much higher values (up to several hundred) are not exceptional, especially
during diagenesis. Examples based on Sr isotopes may be constructed in a similar way.
Exercises
1. Show that if the changes of enthalpy
H
(
T
,
P
)
, entropy
S
(
T
,
P
)
, and volume
of a reaction are approximately constant,
(C.11)
in
Appendix C
can be
integrated into
V
(
T
,
P
)
G
(
T
,
P
)
≈
H
0
−
T
S
0
+
V
0
(
P
−
1
)
(10.21)
where
is the free enthalpy of the reaction at
T
and
P
and the subscript
0 denotes a reference state (usually 298 K and 1 bar). Show that at equilibrium, this
relation provides an equation for the reaction curve. Use the previous result to draw
the reaction curve defining the onset of the eclogite facies:
G
(
T
,
P
)
NaAlSi
3
O
8
⇔
NaAl
2
SiO
6
+
SiO
2
(albite)
(jadeite)
(quartz)
in which the sodic plagioclase breaks down into a sodic pyroxene, which dissolves into
ambient clinopyroxene and quartz. Use the following values:
2115 J mol
−
1
,
H
0
=−
32.25 J mol
−
1
K
−
1
, and
17.0 10
−
6
m
3
.
S
0
=−
V
0
=−
