Geoscience Reference
In-Depth Information
of using this hypothetical standard state, the activity coefficients of ions often are
normalized by introducing the ''asymmetrical activity coefficient,'' c
i
defined as
c
i
¼
c
i
;
ð
2
:
11
Þ
c
i
where c
i
?
is the activity coefficient of species i at infinite dilution. If the chemical
potential of species i is expressed in terms of c
i
, we obtain the expression
l
i
¼ l
i
þ
RT ln
ð
x
i
c
i
c
i
Þ
¼l
i
þ
RT ln c
i
þ
RT ln
ð
x
i
c
i
Þ
¼ l
i
þ
RT ln
ð
x
i
c
i
Þ:
ð
2
:
12
Þ
The standard state chemical potential, l
i
¼ l
i
þ
RT 1n c
i
, has the advantage
that it can be measured experimentally.
In the molality concentration scale, the molality m
i
of solute i is the amount of
solute i per kg of solvent. If the solvent is water (subscript w), the following
relation between mole fraction and molality of solute i can be derived:
n
i
n
w
M
w
m
i
¼
)
n
i
¼ m
i
n
w
M
w
ð
2
:
13
Þ
n
i
ions
n
i
þ
n
w
m
i
n
w
M
w
ions
n
i
þ
n
w
x
i
¼
¼
¼ m
i
M
w
x
w
ð
2
:
14
Þ
where n is the number of moles and M
w
is the molecular mass of water (kg/mol).
Using this relation, the chemical potential of ion i can be expressed as a function of
the molality and the molal activity coefficient c
i
:
l
i
¼ l
i
þ
RT ln m
i
M
w
x
w
c
i
c
i
¼ l
i
þ
RT ln m
w
m
0
c
i
þ
RT ln
m
i
m
0
c
i
x
w
m
i
¼ l
i
þ
RT ln
m
0
c
i
ð
2
:
15
Þ
where the term m
0
= 1 mol/kg has been included to make the expression
dimensionless. The standard state chemical potential is l
i
¼ l
i
þ
RT 1n M
w
m
0
c
i
when the molality concentration scale is used. The molal activity coefficient is
related to the asymmetrical mole fraction activity coefficient by c
i
¼ c
i
x
w
, where
x
w
is the mole fraction of water.
2.1.4 Kinetic Considerations and Reaction Rate Laws
Thermodynamic considerations provide a basic approach for predicting what may
or may not happen in a given system. On a practical level, large and growing
numbers of chemical species are contained in thermodynamic databases. Given the
