Chemistry Reference
In-Depth Information
As the Gibbs energy is the sum of contributions from all components,
G
id
:
mix
:
and
G
E
are also sums of contributions by all components:
X
G
id
:
mix
:
¼
id
:
mix
:
i
n
i
m
;
(13)
i
X
G
E
E
i
¼
n
i
m
(14)
i
or
X
ref
i
G
¼
n
i
ðm
þ
RT
ln
a
i
Þ:
(15)
i
Therefore, the following relation holds:
id
:
mix
:
i
E
ref
i
m
i
¼ m
þ m
i
¼ m
þ
RT
ln
a
i
:
(16)
By definition, component
i
experiences in an ideal mixture the same inter-
molecular forces as in the reference state and therefore all differences between
m
id
:
mix
:
i
ref
i
and
m
are caused by differences in the concentration (i.e., dilution) only:
id
:
mix
:
i
ref
i
RT
ln
a
id
:
mix
:
i
m
¼ m
þ
:
(17)
Consequently, the activity of component
i
in an ideal mixture,
a
id
:
mix
i
, is known
from the composition of the real solution. However, the actual expression for
a
id
:
mix
:
i
depends on the choice of reference states and the concentration scale applied. The
reference state for the solvent (in this case water) is usually the pure liquid at the
temperature and pressure of the mixture:
ref
s
m
¼ m
s
;
pure liquid
ð
T
;
p
Þ:
(18)
However, various reference states are used for a dissolved component. One
common reference state is a hypothetical solution of that component in water at a
concentration of 1 mol/kg water (i.e., a one molal 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 molality
m
i
and activity coefficient
g
ðmÞ
:
i
a
ðmÞ
i
m
i
g
ðmÞ
¼
;
(19)
i
where superscript (
m
) indicates both the reference state and the concentration scale.
The activity coefficient of a solute species
i
becomes unity in an ideal solution and,
