Chemistry Reference
In-Depth Information
can be considered in this connection. The expanded virial form of Eq. (2-72) for
this property is
Δ
P
1
5
μ
1
2
P
G
1
1
M
1
V
1
c
2
Cc
2
1
?
RT
52
Bc
2
1
(3-31)
P
is difficult because of
the small
mag
nitude of the effect. (At 10 g/liter concentration in benzene, a poly-
mer with
M
n
equal
Δ
(Recall
Eqs. 3-16 and 3-26
.) Direct measurement of
to 20,000 produces a vapor pressure lowering of about
10
2
3
mm Hg at room temperature. The limits of accuracy of pressure mea-
surements are about half this value.) It is more accurate and convenient to convert
this vapor pressure difference into a temperature difference. This is accomplished
in the method called
vapor phase osmometry
. The procedure is also known as
vapor pressure osmometry or more accurately as thermoelectric differential vapor
pressure lowering.
In the vapor phase osmometer, two matched thermistors are located in a
thermostatted chamber which is saturated with solvent vapor. A drop of solvent is
placed on one thermistor and a drop of polymer solution of equal size on the
other thermistor. The solution has a lower vapor pressure at the test temperature
(
Eq. 3-20
), and so the solvent condenses on the solution thermistor until the latent
heat of vaporization released by this process raises the temperature of the solution
sufficiently to compensate for the lower solvent activity. At equilibrium, the sol-
vent has the same vapor pressure on the two temperature sensors but is at differ-
ent temperatures.
Ideally the vapor pressure difference
2
3
Δ
P
in
Eq. (3-31)
corresponds to a tem-
perature difference
Δ
T
, which can be deduced from the Clausius
Clapeyron
equation
ΔT 5ΔPRT
2
=ΔH
v
P
1
(3-32)
H
v
is the latent heat of vaporization of the solvent at temperature
T
. With
the previous equation
Δ
where
RT
2
Δ
Δ
T
c
2
5
1
M
1
H
v
V
1
Cc
2
1
?
Bc
2
1
(3-33)
Thus, the molecular weight of the solute can be determined in theory by mea-
suring
T
is small in prac-
tice,
T
may be taken without serious error as the average temperature of the two
thermistors or as the temperature of the vapor in the apparatus.)
In fact, thermal equilibrium is not attained in the vapor phase osmometer, and
the foregoing equations do not apply as written since they are predicated on
the existence of thermodynamic equilibrium. Perturbations are experienced from
heat conduction from the drops to the vapor and along the electrical connections.
Diffusion controlled processes may also occur within the drops, and the magnitude
Δ
T/c
2
and extrapolating this ratio to zero
c
2
. (Since
Δ
