Chemistry Reference
In-Depth Information
Other colligative properties can similarly be shown to be related to the left-
hand side of
Eq. (3-10)
. Vapor pressure lowering is related, for example, through
Raoult's law and
Eq. (3-2)
. Reference should be made to standard introductory
physical chemistry textbooks.
The difference
V
1
in
the osmotic pressure experiment. Other colligative properties are similarly mea-
sured in terms of the difference between a property of the pure solvent and that of
the solvent in solution, at a particular concentration and common temperature.
Specifically, boiling point elevation (ebulliometry) measurements result in
G
1
2μ
1
Þ
ð
is measured by the difference
½ð
P
1
1πÞ 2
P
1
=
RT
b
V
1
=Δ
c
2
-
0
ðΔ
lim
T
b
=
c
2
Þ 5
H
v
M
(3-18)
where
ΔT
b
is the difference in temperatures between the boiling point of a solu-
tion with concentration
c
2
and that of the pure solvent
T
b
, at the same pressure,
and
ΔH
v
is the latent heat of vaporization of the solvent. Freezing point depres-
sion (cryoscopy) measurements yield
RT
f
V
1
=Δ
c
2
-
0
ðΔ
lim
T
f
=
c
2
Þ 5
H
f
M
(3-19)
where the symbols parallel those that apply in ebulliometry and vapor pressure
lowering experiments ideally result in
P
1
V
1
=
c
2
-
0
ðΔ
lim
P
=
c
2
Þ52
M
(3-20)
where
P
is the difference between the vapor pressure of the solvent above the
solution and
P
0
, which is the vapor pressure of pure solvent at
Δ
the same
temperature.
3.1.3
Osmotic Pressure Measures, M
n
Equation (3-16)
shows that
is related to the molecular weight of the solute. If
the latter is polydisperse in molecular weight, then an average value should be
inserted into this equation in place of the symbol
M
.
For a mixture of monodisperse macromolecular species, each with concentra-
tion
c
i
and molecular weight
M
i
,
π
RT
X
c
i
M
i
RT
c
2
π5
M
5
(3-21)
from
Eq. (3-17)
. Since
c
i
5
n
i
M
i
,
c
2
5
RT
X
n
i
X
n
i
M
i
5
RT
M
n
(3-22)
Thus, the reduced osmotic pressure (
π/c
) measures
M
n
.
