Handbook of Solvents - George Wypych - ChemTech - Ventech!

748 Roland Schmid
Packing density η
minimum maximum
≈ 0 0.4 - 0.6 0.74
perfect gas liquids cubic close packed
These considerations ultimately
offer the basis of a genuinely
molecular theory of solvent effects,
as compared to a mean-field theory.
Thus, packing and repacking effects
accompanying chemical reactions
have to be taken into account for any
realistic view of the solvent’s role
played in chemical reactions to be attained.
The well-known cavity formation
energy is the work done
against intermolecular repulsions.
At present, this energy is calculated
for spherical cavities by the Boublik-Mansoori-Carnahan-Starling-Leland (BMCSL) mixed
HS equation of state 45,46
Table 13.1.2. Packing densities in some liquids
Liquid η free volume, %
H2O n-C6 0.41
0.50
59
50
Benzene 0.51 49
MeOH 0.41 59
Et2O 0.47 53
n-C16 0.62 38
( )
3
2
2
ΔGrep
ηd
ηd
ηd
− d + d + 1
3 2
= 2 + 3 + 3
+ ( − 2d + 3d − 1)
ln( 1− η ) [13.1.10]
3
2
RT ( 1−η)
( 1−η)
( 1−
η)
where d = σ σ
0 / is the relative solute size (σ 0 is the solute HS diameter, and σ is the solvent
diameter). Quite recently, a modification of this equation has been suggested for high liquid
densities and large solute sizes. 47 Notice that under isochoric conditions the free energy of
cavity formation is a totally entropic quantity. Ravi et al 48 have carried out an analysis of a
model dissociation reaction (Br 2 → 2Br) dissolved in a Lennard-Jones solvent (Ne, Ar, and
Xe). That and the previous work 49 demonstrated that solvent structure contributes significantly
to both chemical reaction volumes (which are defined as the pressure derivatives of
reaction free energies) and free energies, even in systems containing no electrostatic or dispersion
long-ranged solvent-solute interactions.
Let us now turn to the more difficult case of intermolecular attractive forces. These
may be subdivided into:
Long-ranged or unspecific
• dispersion
• induction
• dipole-dipole
• higher multipole
Short-ranged or specific
• electron overlap (charge transfer)
• H-bonding
For the first three ones (dispersion, induction, dipole-dipole forces) adequate calculations
are just around the corner. Let us give some definitions.