Chemistry Reference
In-Depth Information
excess Gibbs energy of a multisolute and multisolvent mixture in the symmetrical
convention:
X
s
P
j
X
j
G
js
t
js
P
j6¼c
X
j
G
jc;ac
t
jc;ac
P
k6¼c
X
k
G
kc;ac
X
X
X
c
X
a
G
E;
SR
;
sym
n
T
RT
¼
X
a
P
a
0
X
a
0
P
k
X
k
G
ks
þ
s
c
P
j
6¼
a
X
j
G
ja
;
ca
t
ja
;
ca
P
k6¼a
X
k
G
ka;ca
X
X
a
X
c
X
c
P
c
0
X
c
0
þ
;
(99)
a
where subscript
s
refers to a solvent component, and subscripts
c
and
a
refer to
anionic and cationic species, respectively, regardless of their source (either from a
polyion or from an added salt). Subscripts
j
and
k
stand for any of the species in the
mixture and primes are used to distinguish different species of the same type. The
composition of the mixture is described by “modified mole fractions”
X
j
:
X
j
¼
x
j
z
j
;
(100)
where
x
j
is the mole fraction of species
j
and
z
j
is (for a charged species) its
(absolute) charge number, and for any uncharged species
z
i
¼
1
There are two types of interaction parameters that are distinguished by the
number of subscripts:
G
ji
and
t
ji
on one side and
G
ji;ki
and
t
ji;ki
on the other side,
which are expressed using binary parameters
g
ji
for interactions between species
j
and
i
and by binary and ternary nonrandomness parameters
a
ji
and
a
ji;ki
:
G
ji
¼
exp
a
ji
t
ji
(101)
with:
g
ji
g
ii
t
ji
¼
(102)
RT
and:
G
ji;ki
¼
a
ji;ki
t
ji;ki
exp
(103)
with:
g
ji
g
ki
t
ji;ki
¼
:
(104)
RT
Danner et al. used Manning's results for the long-range contribution to the
activity coefficient of the counterions in an aqueous solution of a single polyion:
2
z
p
z
CI
LR
;ð
c
Þ
ln
g
¼
for
lz
p
z
CI
1
(105)
CI
