Chemistry Reference
In-Depth Information
consequently (as follows from the Gibbs-Duhem equation), the activity of the
solvent (represented by subscript
s
) in an ideal mixture is:
X
1000
M
s
ln
a
ðmÞ
s
:
¼
m
i
;
(20)
;
id
:
mix
i6¼s
where
i
represents any (but only) solute species.
Another common reference state for a solute is a hypothetical solution of one
mole of that solute in one liter of water (i.e., a one molar solution) where the solute
experiences interactions only with water, i.e., as if infinitely diluted in water. With
that reference state, it is also common practice to replace the activity of a solute
species
i
by the product of molarity
c
i
and activity coefficient
g
ðcÞ
:
i
a
ðcÞ
i
c
i
g
ðcÞ
i
¼
;
(21)
where superscript (
c
) indicates both the reference state and the concentration scale.
The activity coefficient of a solute species
i
becomes unity in an ideal solution
and, consequently (following again from the Gibbs-Duhem equation), the activity
of the solvent
s
is:
X
1
r
s
ln
a
ðcÞ
s;
id
:
mix
:
¼
c
i
;
(22)
i6¼s
where
r
s
is the molar density of water (in moles per liter).
As usual, the following relations also hold for the excess part of the chemical
potential of a solute
i
and a solvent
s
:
a
i
a
i;
id
:
mix
:
i
m
¼
RT
ln
i
;
(23)
a
s
a
s;
id
:
mix
:
E
m
s
¼
RT
ln
:
(24)
One has to keep in mind that the excess parts of the chemical potentials depend
on the selection of the reference state for a solute component, as both the activity of
a solute component and the activity of the solvent in an ideal mixture depend on
the reference states of the solutes. The activity coefficients of a solute on molality
scale,
g
ðmÞ
i
, and on molarity scale,
g
ðcÞ
i
, are related by:
m
i
g
ðcÞ
i
¼ g
ðmÞ
i
c
i
r
s
;
(25)
where
r
s
is the specific density of the pure solvent in kg/dm
3
.
