Geology Reference
In-Depth Information
that take place in it, it is the number of
moles
of each
major solute present that matters, rather than the
weight. Dividing the concentration
C
of each com-
pound in the solution (expressed in g dm
−3
) by its
rela-
tive molecular mass
M
r
gives the
molarity
,
c
:
therefore 1 mole of Mg
2
SiO
4
will weigh 140.71 g. The
RMM of fayalite is (2 × 55.85) + 28.09 + (4 × 16.00) = 203.79.
Thus 100 g of the olivine will contain:
(a) 65.0 g of Mg
2
SiO
4
= 65.0/140.71 = 0.4619 moles
Mg
2
SiO
4
;
(b) 35.0 g of Fe
2
SiO
4
= 35.0/203.79 = 0.1717 moles Fe
2
SiO
4
.
r
moldm
3
−
cCM
=
/
(4.1)
Aqueous geochemists measure solute concentrations
using a slightly different quantity called the
molality
,
m
. The molality
m
i
of species
i
in an aqueous solution is
the number of moles of
i per kilogram of water
(solvent,
not solution). There are sound practical and thermody-
namic reasons, however, for expressing molality in a
dimensionless
form (one in which the units of meas-
urement cancel out). For this purpose we use the
activ-
ity
a
i
, which for
dilute solutions
is numerically equal
to the molality:
The mole fraction of Mg
2
SiO
4
in this olivine is
therefore:
molesofMgSiO
totalmoles
0 4619
0 4619 0 1717
.
X
Mg SO
=
2
4
=
=
0 729
. 0
.
+
.
24
(4.3a)
Likewise the mole fraction of Fe
2
SiO
4
in the olivine is:
molesofFeSiO
totalmoles
0 1717
0 4619 0 1717
.
X
Fe SiO
=
2
4
=
=
027
.10
.
+
.
2
4
o
amm
i
= /
(4.2)
(4.3b)
where
m
o
represents what is called the standard molal-
ity, equal to 1 mol kg
−1
. This artifice removes the neces-
sity of associating units with complex formulae like
Equation 4.11.
In this case, checking whether the mole fractions add
up to 1.0000 is a useful way to confirm that no arith-
metical error has been made. Note that a mole fraction
is a
dimensionless number
.
Solids
Gases
In geology, one often deals with heterogeneous reac-
tions between aqueous solutions and solid or gaseous
phases. The concentration of a component in a solid
phase can be expressed in a variety of ways, such as
the mass percentage of each element, or the mass per-
centage of the oxide of each element (Box 8.4). When
considering equilibrium between solids and solutions,
however, we want to express solid compositions in
molar
terms, of which
mole fraction
(
X
) is the most
commonly used form.
Consider a sample of olivine that has been found
to contain 65.0% by mass of Mg
2
SiO
4
(the forsterite
end-member) and 35.0% of Fe
2
SiO
4
(the fayalite end-
member). To calculate the mole fractions of these com-
ponents (assuming no other components are present),
one must first establish their relative molecular masses
M
r
from the following
relative atomic masses
:
A gas is a high-
entropy
state of matter that expands to
fill the volume available (Box 1.3). The concentrations
of individual gaseous species in a gas mixture can be
expressed in three alternative ways:
•
mole fraction
X
i
, expressed either as a fraction of
1.0000 as above for solids, or in molar
ppm
(moles of
component
i
per 10
6
moles of gas mixture);
• volume per cent (Figure 9.3) or parts per million by
volume (ppmv = number of m
3
of pure gas
i
present
in 10
6
m
3
of the gas mixture);
• the
partial pressure
p
i
of component
i
present in the
gas mixture (in Pa - see Appendix D).
These three measures are related through the
Ideal
Gas Law
:
Mg
=
24 31
.
Si
28 09
.
Fe
==
55 85
.
O
16 00
.
=
PV nRT
=
(4.3c)
The relative molecular mass (RMM) of forsterite is
therefore
where
P
is the pressure exerted by the gas mixture on
the walls of its container,
V
is the volume of the
(2 × 24.31) + 28.09 + (4 × 16.00) = 140.71,
and
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