Chemistry Reference
In-Depth Information
quadrupole moment and found that the solubility was significantly lower
for CO
2
and slightly lower for N
2
when compared to the results with a quad-
rupole moment. Finally, the authors computed the solubility of water in the
ionic liquid. Because water is a liquid under the conditions they studied, a ther-
modynamic integration process was used. They determined that the infinite
dilution activity coefficient of water in [C
4
mim][PF
6
]is4
:
7
3
:
6, which
agrees well with the experimental value of 5.36.
76
Shah and Maginn
77
carried out a Monte Carlo study of CO
2
solubility in
[C
4
mim][PF
6
] to compute the Henry's law constant of CO
2
using the test
particle insertion free energy perturbation method. The Henry's law constant
for solute 2 dissolved in solvent 1,
H
2;1
, is defined as
f
2
x
2
H
2;1
¼
lim
x
2
!
½
8
0
where
f
2
is the fugacity of the solute in the gas phase, and
x
2
is the mole frac-
tion of the solute in the liquid phase. The fugacity is related to the excess che-
mical potential according to the following expression:
e
2
k
B
T
m
H
2;1
¼
k
B
T
r
1
exp
½
9
where
k
B
is the Boltzmann constant and
r
1
is the liquid-phase density. The
excess chemical potential is obtained from the test particle insertion method
by inserting many noninteracting CO
2
molecules into the liquid over the
course of a constant temperature and pressure simulation and computing
the ratio
k
B
T
ln
h
V
exp
ð
U
test
=
k
B
T
Þi
ex
2
m
¼
½
10
h
V
i
where
U
test
is the energy of the test molecule inserted into the system and the
angled brackets signify ensemble averages. Their simulations predicted that
CO
2
solubility in this ionic liquid is 2-3 times higher than what is observed
experimentally; the computed partial molar enthalpy of absorption is about
7 kJ/mol more negative than experiment as well.
Part of the inaccuracy of these results can be attributed to the force field
used, which included a united-atom model for the cation and an explicit-atom
model for the anion. This model,
77
unlike Shah and Maginn's previous united-
atom model,
39
underestimated the pure liquid density by about 5%, which
should lead to higher gas solubilities on the basis of free volume arguments.
The other source of error rests with the simulation method itself. Kofke and
Cummings
78
have shown that single-stage free energy perturbation methods
