Chemistry Reference
In-Depth Information
5.2.4 Contribution from Coions
When a neutral salt
S
is dissolved in the aqueous polyelectrolyte solution there is
also a contribution to the Gibbs energy of the aqueous solution by the other ions,
here called coions. When
n
COI
is the stoichiometric coefficient of that coion in
S
,
following the same ideas as explained before for the free counterions, that contri-
bution is:
ref
G
freeCOI
¼
n
freeCOI
m
freeCOI
þ D
G
freeCOI
;
(81)
where:
n
COI
c
s
g
ðcÞ
COI
D
G
freeCOI
=ð
RT
Þ¼n
COI
n
s
ln
:
(82)
The activity coefficient
g
ðcÞ
COI
of the coions (on molarity scale) is treated in the
same way as the activity coefficient
g
ðcÞ
CI
of the counterions (i.e., it is either set to
unity or expressed through the Debye H¨ckel expression).
5.2.5 Contribution from Water
The final contribution to the Gibbs energy results from the presence of water
(subscript
w
):
ref
w
G
w
¼
n
w
m
þ
n
w
RT
ln
a
w
:
(83)
F
ðc
p
on the
The activity of water is approximated by using the osmotic coefficient
molarity scale:
ln
a
w
ln
a
ðcÞ
w;
id
:
mix
:
ln
a
w
F
ðcÞ
p
¼
¼
c
COI
Þ=r
w
:
(84)
ð
c
CI
þ
where
r
w
is the molar density of water in the aqueous solution in moles per liter:
z
p
z
CI
ln
a
w
¼F
ðcÞ
ð
n
CI
þ n
COI
Þ
n
s
þ
ð
z
CI
y
z
Þnn
p
:
1
(85)
p
F
ðcÞ
p
is again either set to unity (that is the common
approach) or taken from the Debye-H¨ckel theory for an aqueous solution contain-
ing
n
s
moles of salt S and
n
ðpÞ
The osmotic coefficient
freeCI
moles of counterions dissociated from the
polyelectrolyte.
