Chemistry Reference
In-Depth Information
The right-hand side is solved in two steps. In the first step, the integration is
carried out starting from pure water to a polyelectrolyte-free but salt-containing
solution:
Dm
w;
1
2
RTM
w
¼
I
m;
MX
1
:
5
m
MX
m
o
þ
p
A
'
1
þ
1
:
2
I
m;MX
2
h
i
p
m
MX
m
o
a
ð
0
Þ
a
ð
1
Þ
MX
þ
MX
exp
2
I
m;MX
;
(176)
where
a
ð
0
Þ
MX
and
a
ð
1
Þ
MX
are binary interaction parameters between ions
M
and
X
and
I
m;MX
is the ionic strength (on molality scale) of the polyelectrolyte-free aqueous
solution of
MX
.
In the second step, the molality of the salt is fixed at
m
MX
and the molality of the
polyelectrolyte increases from zero to
m
p
:
"
#
M
w
ð
m
p
m
p
¼
0
m
o
m
p
@m
p
@
m
p
d
m
p
Dm
W;
2
¼
(177)
m
MX
m
MX
m
o
M
w
m
MX
ð
m
MX
;
m
p
Þm
MX
ð
m
MX
;
m
p
¼
0
Þ
;
where
2
3
"
#
m
MX
¼
!
ð
m
p
ð
m
p
m
o
m
o
ln
g
ðmÞ
m
p
@m
p
@
m
p
d
m
p
m
p
m
o
þ
m
p
@
d
m
p
p
4
5
:
RT
(178)
@
m
p
m
p
¼
0
m
p
¼
0
m
MX
The integral is solved numerically using (
158
) for the activity coefficient of the
polyelectrolyte.
The final equation for the activity of water in an aqueous solution of a strong
electrolyte
MX
and a polyelectrolyte
P
(where both
MX
and the repeating unit of the
polyion are 1:1 electrolytes) is:
I
m;
MX
1
:
5
1
M
W
2
m
MX
m
p
m
o
þ
ln
a
w
¼
m
o
2
A
'
p
1
þ
1
:
2
I
m;MX
2
h
i
p
2
m
MX
m
o
a
ð
0
Þ
a
ð
1
Þ
MX
þ
MX
exp
2
I
m;MX
m
MX
m
o
RT
m
MX
ð
m
MX
;
m
p
Þm
MX
ð
m
MX
;
m
p
¼
0
Þ
2
3
!
ð
m
p
m
o
ln
g
ðmÞ
m
p
@
d
m
p
p
4
5
:
ð
179
Þ
@
m
p
m
p
¼
0
m
MX
