Chemistry Reference
In-Depth Information
chemical potential
m
, i.e.,
m
ideal
m
excess
z}|{
z}|{
m
¼
m
0
þ
kT lnc
þ
kT ln
g
:
ð
3
Þ
The quantity
m
0
is an uninteresting reference chemical potential and c the
concentration. It is straightforward to calculate
g
in an MC simulation, and we
can also obtain it from the DH approximation,
Z
2
e
2
k
8
pe
0
e
r
ð
1
þ
k
d
hc
Þ
:
kT ln
g
DH
¼
ð
4
Þ
The important quantity in Equation (4) is the inverse screening length
k
, which
is related to the ionic strength:
X
e
2
e
0
e
r
kT
k
2
¼
c
i
z
i
:
ð
5
Þ
i
Figure 2 shows how
g
varies as a function of salt concentration for two different
salts. The accuracy of the simple DH theory is surprisingly good. The main
discrepancy comes from the too approximate treatment of the excluded volume
effect, i.e., the hard-core interaction.
A knowledge of
g
allows us to calculate a number of interesting quantities.
For example, we can calculate the dissolution of carbon dioxide in the ocean.
The high salt content of the oceans increases the solubility of CO
2
, which is
apparent from the equilibrium relations,
K
1
z}|{
g
HCO
3
g
H
þ
g
H
2
CO
3
K
1
¼
C
HCO
3
C
H
þ
C
H
2
CO
3
H
2
CO
3
Ð
HCO
3
þ
H
þ
;
;
ð
6
Þ
K
2
¼
C
CO
2
3
C
H
þ
C
HCO
3
|{z}
K
2
g
CO
2
3
g
H
þ
g
HCO
3
HCO
3
Ð
CO
2
3
þ
H
þ
;
:
ð
7
Þ
Note that the thermodynamic equilibrium constants, K
1
and K
2
, are true
constants, in contrast to the stoichiometric ones, K
1
and K
2
. Table 1 presents
experimental and simulated activity factors for some salts relevant to sea water.
The departure from ideality (
g
¼
1) is non-negligible, and as a consequence the
dissolution of CO
2
in sea water is significantly larger than in fresh water. The
excellent agreement between measured and simulated activity factors in Table 1
gives a strong support for the primitive model.
9.3 A Charged Macromolecule in a Salt Solution
We can use the activity factors in order to study how the binding of a charged
ligand to a charged macromolecule is affected by addition of salt or by changes
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