Handbook of Solvents - George Wypych - ChemTech - Ventech!

174 Christian Wohlfarth
where:
ΔT
ebull
2
RT
=−
Δ H
vap
0
1
ln a
[4.4.30]
1
T measuring temperature (= boiling point temperature of the pure solvent)
ΔT ebull
temperature difference of boiling point elevation
0
H molar enthalpy of vaporization of the pure solvent 1 at temperature T.
Δ vap 1
The ratio M1RT 2 0
/Δvap H1 is called the ebulliometric constant. For the determination of
solvent activities from ebulliometric data, tabulated ebulliometric constants should not be
used, however. On the other side, it is sometimes recommended to use reference solutes to
establish an experimental relationship for the equipment in use, i.e., unprecise data for the
enthalpy of vaporization or perhaps some non-equilibrium effects cancel out of the calculation.
Enthalpies of vaporization are provided by several data collections, e.g., by Majer and
Svoboda, 129 or through the DIPPR database. 130
The data reduction of vapor-pressure osmometry (VPO) follows to some extent the
same relations as outlined above. However, from its basic principles, it is not an equilibrium
method, since one measures the (very) small difference between the boiling point temperatures
of the pure solvent drop and the polymer solution drop in a dynamic regime. This temperature
difference is the starting point for determining solvent activities. There is an
analogy to the boiling point elevation in thermodynamic equilibrium. Therefore, in the
steady state period of the experiment, the following relation can be applied if one assumes
that the steady state is sufficiently near the vapor-liquid equilibrium and linear non-equilibrium
thermodynamics is valid:
st
ΔT
=−k
VPO
2
RT
Δ H
vap
0
1
ln a
[4.4.31]
1
where:
T measuring temperature (= temperature of the pure solvent drop)
ΔT st
temperature difference between solution and solvent drops in the steady state
kVPO VPO-specific constant
0
Δ vapH1 molar enthalpy of vaporization of the pure solvent 1 at temperature T .
Recent examples of solvent activity measurements by VPO in aqueous solutions of
poly(ethylene glycol) by Eliassi et al. 128 and of poly(ethylene glycol) or dextran by Gaube et
al. 126,127 demonstrate the obtainable high quality if precise experiments were made.
The so-called VPO-specific constant contains all deviations from equilibrium state
and it is to be determined experimentally. It depends on certain technical details from the
equipment used and also on the temperature and solvent applied. It is assumed not to depend
on the special solute under investigation and can therefore be obtained by calibration. Equation
[4.4.31] can also be used if not the steady state, but the temperature difference extrapolated
to a measuring time of zero is determined by the experimentator. However, the values
of kVPO are different for both methods. A more detailed discussion about calibration problems
can be found in the papers of Bersted, 131,132 or Figini. 133-135
Usually, VPO-data are reduced to virial coefficients and not to solvent activities.
Power series expansion of Equation [4.4.31] leads to the following relations: