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is pinned on the capacity of isotopic concentrations of boron measured from the calcareous
tests of foraminifera to reflect the pH of the early oceans. The boric acid of seawater is a
weak acid and boron is found in two different states governed by the reaction:
)
4
H
+
H
3
BO
3
+
H
2
O
⇔
B
(
OH
+
(7.41)
8.75) and the prod-
uct of the equilibrium constant of this reaction by the [H
2
O] molarity of water, which is
very close to 55.6 in all natural waters. The proportion of the two species clearly depends
on the pH of the solution and we can formulate the fraction of boron stored for each of
them, for example
We note the apparent dissociation constant of H
3
BO
3
as
K
B
(p
K
B
=
ϕ
H
3
BO
3
, in the usual way:
H
+
H
+
+
[H
3
BO
3
]
[H
3
BO
3
]
ϕ
H
3
BO
3
=
+
B
)
4
=
(7.42)
(
OH
K
B
Clearly, the sum of
ϕ
B
(
OH
)
4
is unity. Moreover, an isotopic equilibrium
equation between the two boron carrier species can be written:
ϕ
H
3
BO
3
and
11
B
10
B
H
3
BO
3
/
B
(
T
)
11
B
10
B
B(OH)
4
=
α
(7.43)
/
B
(
T
) is the isotopic fractionation coefficient between the two species of boron
present in the solution. The residence time of boron in seawater being several million years,
it can be considered that neither its content nor its overall isotopic composition change
between glacial and interglacial periods, which alternate over a time scale of 100 000 years.
The mass balance condition for the
11
B/
10
B ratio can therefore be written as:
where
α
11
B
10
B
ocean
=
ϕ
H
3
BO
3
11
B
H
3
BO
3
+
ϕ
B
(
OH
)
4
11
B
10
B
(7.44)
10
B
B(OH)
4
Only the charged borate B(OH)
4
seems to be incorporated in the calcite of foraminifera.
The previous two equations can therefore be combined in the form:
11
B
10
B
ocean
11
B
10
B
foram
=
11
B
10
B
/
=
)
+
1
−
ϕ
H
3
BO
3
(7.45)
B
ϕ
H
3
BO
3
α
(
T
B(OH)
4
If we know the
11
B/
10
B ratio of the ocean from measurement of present-day seawater, the
growth temperature of foraminifera (given by oxygen isotopes), and isotopic fractionation
α
B
(
T
) (0.978 at 20
◦
C), we can deduce
ϕ
H
3
BO
3
and therefore, in principle, the pH of the
identified species for which isotopic fractionation of boron occurs reproducibly, which is a
significant limitation for the time being.
