Pressure Stabilization and Solvation Thermodynamics of a Hemiketal Reaction Intermediate

Article abstract of DOI:10.1021/jp0028352

This work reports the first pressure stabilization of a hemiketal intermediate, 2-methoxy-2 propanol, formed in the reaction of acetone and methanol, observed using Raman spectroscopy. Acetone dissolved in methanol is found to undergo a two-step reaction, with the ketal 2,2-dimethoxy-propane as the final product and the hemiketal observed as an intermediate. In a more dilute stoichiometric mixture of acetone and methanol in liquid tetrahydrofuran (THF), quantitative formation of the hemiketal is observed at pressures above 2 GPa. The complete set of reaction thermodynamic functions (ΔH⁰, ΔV⁰, ΔS⁰, ΔG⁰, ΔU⁰, ΔA⁰) is obtained for the hemiketal formation reaction in THF as a function of temperature and pressure and compared with previous measurements of ΔH⁰, ΔS⁰, and ΔG⁰ for acetone dissolved in methanol. Comparisons with quantum calculations for the isolated reactant and product species are used to completely quantitate the effects of solvation on the hemiketal formation reaction.

Full text of DOI:10.1021/jp0028352

© Copyright 2000 by the American Chemical Society
VOLUME 104, NUMBER 49, DECEMBER 14, 2000
LETTERS
Pressure Stabilization and Solvation Thermodynamics of a Hemiketal Reaction
Intermediate
Alan D. Gift and Dor Ben-Amotz*
Department of Chemistry, Purdue UniVersity, West Lafayette, Indiana 47907
ReceiVed: August 4, 2000; In Final Form: October 19, 2000
This work reports the first pressure stabilization of a hemiketal intermediate, 2-methoxy-2 propanol, formed
in the reaction of acetone and methanol, observed using Raman spectroscopy. Acetone dissolved in methanol
is found to undergo a two-step reaction, with the ketal 2,2-dimethoxy-propane as the final product and the
hemiketal observed as an intermediate. In a more dilute stoichiometric mixture of acetone and methanol in
liquid tetrahydrofuran (THF), quantitative formation of the hemiketal is observed at pressures above 2 GPa.
The complete set of reaction thermodynamic functions (∆H°, ∆V°, ∆S°, ∆G°, ∆U°, ∆A°) is obtained for the
hemiketal formation reaction in THF as a function of temperature and pressure and compared with previous
measurements of ∆H°, ∆S°, and ∆G° for acetone dissolved in methanol. Comparisons with quantum
calculations for the isolated reactant and product species are used to completely quantitate the effects of
solvation on the hemiketal formation reaction.
Introduction
Calibrated Raman peak area measurements are used to
determine the pressure and temperature dependence of the
hemiketal formation equilibrium constant. The results are used
to completely characterize the thermodynamics of this reaction
by determining Gibbs free energy (∆G°), enthalpy (∆H°),
entropy (∆S°), partial molar volume (∆V°), internal energy
(∆U°), and helmholtz free energy (∆A°) vs P and T. Comparison
with quantum calculations for the isolated reactant and product
species yields the solvent excess contribution to the reaction
thermodynamics as a function of temperature and pressure. To
the best of our knowledge, this is the first example of such a
complete thermodynamic analysis of the effects of solvation
on any chemical reaction.
The reaction of carbonyl and hydroxyl groups plays a central
role in a wide variety of important organic and biological
processes.1-5 A prime example is the intramolecular hemiacetal
formation responsible for the cyclization of glucose. More
generally, acetals and ketals are formed from the reaction of
aldehydes or ketones, respectively, with alcohols. The hemiacetal
or hemiketal species, which are thought to be intermediates in
these reactions, are typically unstable under ambient conditions
and thus have rarely been studied directly.2 We report the first
quantitative conversion of acetone and methanol to the hemiketal
2-methoxy-2-propanol (MP, eq 1) dissolved in tetrahydrofuran
(THF) under high pressure.
In a neutral solution, the hemiketal formation equilibrium
strongly favors the reactants (1 M solution of acetone in
methanol contains 7.32 mM of MP).2 When this reaction takes
place in the presence of an acid catalyst, along with the removal
of water, the reaction equilibrium is shifted to the formation of
10.1021/jp0028352 CCC: $19.00 © 2000 American Chemical Society
Published on Web 11/14/2000

11460 J. Phys. Chem. A, Vol. 104, No. 49, 2000
Letters
the thermodynamically stable ketal product 2,2-dimethoxy-
propane (DMP, available commercially as a 98% pure liquid,
eq 2).
Previous studies of reaction 2 have used NMR spectroscopy2,6
and UV spectroscopy7,8 to obtain the thermodynamics of the
ketal formation reaction. The trace presence of hemiketal due
to reaction 1 has been detected by NMR in an ambient mixture
of acetone and methanol. This was used to determine the
equilibrium constant for the hemiketal formation as a function
of temperature and derive the reaction thermodynamic functions
∆H° ) -14.1 kJ/mol, ∆S° ) -88.6 J/(Kmol), and ∆G° ) 12.3
kJ/mol in this ambient solution.2 In addition, ab initio calcula-
tions by Wiberg et al. predict ∆U°(gas) ) -32.4 kJ/mol in the
vapor phase, which implies ∆H°(gas) ∼ -35 kJ/mol.2 Although
these previous studies are not sufficient to quantify the complete
thermodynamics of the reaction, comparison of the gas and
solution ∆H° values clearly indicates the significant effect of
solvation on this reaction.
Figure 1. Raman spectra of a solution of acetone and methanol
dissolved in tetrahydrofuran reveal reversible spectral changes attributed
to pressure induced hemiketal formation. Spectra were collected over
a series of increasing pressures followed by a pressure decrease (spectra
are shifted vertically for clarity). The C-C stretch of acetone at ∼780
cm-1 shifts to 800 cm-1 with increasing pressure, as the hemiketal C-C
Experimental Section
peak grows in at ∼760 cm-1
.
The present temperature and pressure studies were performed
using Raman spectroscopy to monitor the concentrations of
acetone and the hemiketal. Dispersive micro-Raman measure-
ments were carried out using a He-Ne excitation laser (20 mW,
632.8 nm), as described elsewhere.9 Pressure and temperature
were varied by placing the sample in a diamond anvil cell
(DAC) immersed in a variable temperature oil bath. The solution
pressure was determined using ruby fluorescence,10 and tem-
perature was measured using a thermocouple placed in the oil
bath next to the DAC.
Reagent grade acetone, methanol, THF, and DMP were used
as received from Aldrich. Raman spectra of each of these
compounds, in their pure liquid state, were measured and used
to assist in the assignment of vibrational bands appearing in
the reactive mixture.
results strongly suggest the assignment of the rapidly formed
species to MP and the more slowly formed product to DMP.
Further confirmation of the above assignments was obtained
by pressure cycling a solution of acetone and methanol dissolved
in THF (with mole fractions of about 0.12 for each solute). In
this case, near quantitative conversion of acetone to a product
with a Raman band around 760 cm-1 was achieved at pressures
over 2 GPa, as illustrated by the Raman spectra shown in Figure
1. These spectra were collected sequentially (from bottom to
top) during the pressurization and then depressurization of the
sample. Note that in addition to the appearance and disappear-
ance of peaks, there is an observable pressure shift in the
vibrational frequencies of each species, which is consistent with
the pressure-induced frequency shift of about 7 cm-1/GPa for
the C-C stretch of acetone.11 The recovery of the acetone
spectrum upon depressurization thus supports our assignment
of the high-pressure product is the hemiketal (MP), since the
ketal (DMP) is stable at 1 atm.
Thus, in a solution of acetone and methanol in THF,
quantitative conversion to the hemiketal is observed without
appreciable production of the ketal. Acetone dissolved in
methanol, on the other hand, undergoes sequential formation
of the hemiketal followed by the ketal (undoubtedly driven by
the presence of excess methanol). These results not only
demonstrate the possibility of quantitatively converting acetone
and methanol to an equilibrated hemiketal, but also confirm that
the hemiketal is indeed an intermediate in the reaction pathway
leading to the ketal.
Results and Discussion
Preliminary high-pressure measurements were performed on
a solution of acetone in excess methanol (with a solute mole
fraction of about 0.2). At ambient conditions, the only observ-
able peak in the 725 to 825 cm-1 range was the C-C stretch
of acetone at 788 cm-1. When the pressure was increased, a
new peak was formed rapidly at about 759 cm-1, while the
acetone peak at 788 cm-1 decreased in intensity. The transfor-
mation of the spectrum occurred within a few seconds after the
pressure was increased, and equilibrated in less than one minute.
When the sample was allowed to sit at high pressure for 1 day,
the peak at 759 cm-1 decreased in intensity and a new peak
formed at 739 cm-1, indicating the slow transformation to a
second product. When the pressure was decreased back to 1
atm, the 759 cm-1 product reverted to acetone (759 cm-1), while
the 739 cm-1 product remained. The Raman spectrum of pure
DMP [Aldrich D13,680-8] has a strong C-C stretching
vibration at 730 cm-1 in the 1 atm liquid state, which
corresponds well with the 739 cm-1 peak after a pressure-
induced frequency shift is taken into consideration.11 Further-
more, quantum calculations using B3LYP/6-31G* theory level
predict strong Raman active C-C stretch vibrations at 786, 757,
and 737 cm-1 for acetone, MP and DMP, respectively. These
To quantitate the reaction thermodynamics of the hemiketal
reaction, further measurements were performed on a similar THF
solution of acetone and methanol at four temperatures and three
pressures. Peak areas were determined for the C-C stretching
bands of acetone and MP in the 725-825 cm-1 region (Figure
1) and for the solvent THF. The acetone and MP peak areas
were divided by the THF peak area to provide an internal
standard. This normalization procedure has the effect of
compensating for changes in laser power, collection efficiency,
and changing sample thickness with increasing pressure. The

Letters
J. Phys. Chem. A, Vol. 104, No. 49, 2000 11461
TABLE 1: Reaction Thermodynamics for the Formation of Hemiketal from Acetone and Methanol
solvent excess
thermodynamic functions
reaction thermodynamics
(at 25 °C and 1 M concentration)
in THF
at 1 atm
in THF
at 2 GPa
in methanol
at 1 atm
gas phase
at 1 M
in THF
at 1 atm
in THF
at 2 GPa
∆G° (kJ/mol)
∆H° (kJ/mol)
∆S° (J/Kmol)
∆V° (cm3/mol)
∆U° (kJ/mol)
∆A° (kJ/mol)
15.1
-12.9
-94
4.0
-25.2
-98
12.3
-14.1
-89
-
13.7b
-34.9b
-163
0
1.4
22.0
69
-9.7
9.7
65
6
19.5
0.1
6.0
6.0
6
-12.9
15.1
-12.9
16.3
-
-32.4d
16.2b
19.5
-1.1
-
a Derived from NMR measurements of Wiberg et al.2 b Values obtained using ∆U°, T∆S°, the ideal gas law (PV ) nRT), and standard
thermodynamic relations.14 c Quantum calculation using CBS-4 extrapolation method (this work). d Quantum calculation by Wiberg et al. using
CBS-4 extrapolation method.2 e Under ideal gas 1M standard state conditions ∆V° ) (∂∆G°/∂P)T ) 0..
resulting normalized acetone peak areas were plotted as a
function of the normalized MP peak areas. The slope and
intercept of the resulting line, along with the known initial
concentration of acetone (in molality units), were used to relate
the measured peak areas to concentrations of acetone of MP at
every experimental temperature and pressure. The methanol
concentration was determined by subtracting the concentration
of MP from the initial concentration of methanol. The resulting
concentrations were converted to molarity units using the
compressibility of THF, as predicted by the van der Waals-
Carnahan-Starling equation of state.12,13 Thus the equilibrium
constant, K ) [MP]/[acetone][methanol], was determined at each
temperature and pressure.
Measurements of K as a function of both temperature and
pressure were used to determine the complete set of thermo-
dynamic functions, ∆H°, ∆G°, ∆S°, ∆V°, ∆U°, ∆A°, at a
standard state concentration of 1 M. In particular, the standard
state Gibbs free energy was related to K using the following
Figure 2. The logarithm of the equilibrium constant is plotted as a
function of pressure (P) and inverse temperature (1/T). The slopes of
expression:9
the best fit lines yield (A) reaction volumes of ∆V)-5.5, -5.3, -6.2,
∆G° ) -RT ln K
(3)
and -5.8 cm3/mole at T ) 373, 348, 323, and 293 respectively, and
(B) reaction enthalpies of ∆H ) -25.2, -27.5, and -30.1 kJ/mol at
P ) 2.0, 2.4, and 2.8 K, respectively.
The remaining thermodynamic functions were derived from the
corresponding standard identities.9,14
gas-phase results from our solution measurements in THF,
extrapolated to 1 atm.
∂ ln K
∂(1/T)
∂ ln K
∂P
∆H° ) -R
∆V° ) -RT
(4)
(
)
(
)
P
T
Some care must be exercised in interpreting the results in
Table 1, in view of potential uncertainty in the experimental
and/or theoretical values. The accuracies of the experimental
values are believed to be about (2 kJ/mol, whereas those of
the theoretical gas-phase results are more difficult to estimate.
In particular, although the CBS-4 extrapolation method used
by Wiberg2 et al. is considered to yield reliable energies, we
have found that much smaller negative (or even positive) gas
phase ∆U° predictions may be obtained when using different
ab initio algorithms and basis sets (the largest value we found
was ∆U° ) +13.8 kJ/mol, obtained using a B3LYP/6-311G**
energy calculation at the B3LYP/6-31G* optimized geometry).
The calculated entropy factors, T∆S°, in the gas phase are found
to be less sensitive to the calculation level and did not vary by
more than about (2.0 kJ/mol (the reported value is that obtained
using the same CBS-4 extrapolation method used by Wiberg2
et al. to obtain the gas phase ∆U° given in Table 1).
The similarity of the thermodynamic parameters measured
in the two solvents at 1 atm (THF and methanol) is noteworthy,
as these are far more similar to each other than they are to the
corresponding gas phase or high-pressure values. Notice that
the solution results are obtained by very different experimental
techniques (NMR and Raman), and the THF solution values
are derived from an extrapolation of our high-pressure results
T∆S° ) ∆H° - ∆G°
∆U° ) ∆H° - P∆V°
∆A° ) ∆U° - T∆S°
(5)
In practice, the natural logarithm of the equilibrium constant at
four temperatures (20, 50, 75, 100 °C) was first plotted as a
function of pressure. Data points were interpolated to three fixed
pressures (2.0, 2.4, and 2.8 GPa) and then graphed as a function
of temperature. Figure 2 shows plots of these interpolated data
points both as a function of pressure and inverse temperature.
The slopes of these best fit lines shown in Figure 2 were used
to experimentally determine ∆H° at each pressure and ∆V° at
each temperature. The results reveal that ∆G° increases linearly
with temperature and decreases linearly with pressure. The
enthalpy, ∆H°, decreases with pressure but is independent of
temperature, while ∆U°, ∆S°, and ∆V° are all constant within
experimental error over the entire experimental temperature and
pressure range.
Table 1 contains our experimental results extrapolated to 1
atm and 2 GPa, along with other experimental and theoretical
values,2 all pertaining to the hemiketal reaction at 25 °C (eq 1).
The excess solvation thermodynamic parameters in the last
column of Table 1 are obtained by subtracting the theoretical

11462 J. Phys. Chem. A, Vol. 104, No. 49, 2000
Letters
to 1 atm, whereas the equilibrium constant is far too small to
allow direct Raman measurements of the hemiketal concentra-
tion.
namic results which we have presented, serve as an experimental
bench-mark against which to test both fundamental solvation
theories and semiempirical solvation modeling strategies.9,22-24
A further important feature of the results is the similarity of
the 1 atm ∆H° and ∆U° values, which also requires that ∆G°
and ∆A° must be the nearly equal.14 However, when the pressure
is increased to 2 GPa, the values of ∆H° and ∆U° (or ∆G° and
∆A°) diverge as a result of the increasing magnitude of P∆V°.
This behavior beautifully illustrates the importance of ∆V° in
dictating the pressure dependence of reaction thermodynamic
values. Although ∆V° typically plays a negligible role for reac-
tions carried out under ambient conditions, it may become a
dominant contribution to some high-pressure industrial pro-
cesses, or even for exotic biological processes occurring in deep
ocean hydrothermal vents or extraterrestrial environments.15,16
The difference between the liquid and gas-phase reaction
thermodynamic functions represents the solvent contribution to
the chemical equilibrium (see the last few columns of Table
1). The excess potential energy of reaction, ∆Ux, indicates that
the solvation energy of the reactants (acetone + methanol) and
product (hemiketal) differ by about 20 kJ/mol in THF at both
1 atm. and 2 GPa. The large excess entropy of reaction, ∆Sx,
implies that solvent structural rearrangement plays a significant
role in solvation thermodynamics (an effect which is difficult
to reproduce using dielectric continuum solvation models).17,18
Like ∆Ux and ∆Sx, the excess reaction volume, ∆Vx, is also
approximately pressure independent. The constancy of these
functions implies that there is little change in solvent structure
with pressure. On the other hand, because our experiments span
more than a 10 000-fold increase in pressure, the associated
change in P∆Vx produces dramatic changes in ∆Hx and ∆Gx.
A further interesting feature of the excess thermodynamic results
is the very small, and nearly pressure independent, value of the
excess Helmholtz free energy, ∆Ax. This implies a nearly perfect
cancellation of the large ∆Ux and T∆Sx, reminiscent of the well-
known enthalpy-entropy compensation phenomena.19-21 Our
results suggest that although both ∆Hx - T∆Sx and ∆Ux -
T∆Sx are nearly zero at 1 atm, only the latter cancellation
continues into the high-pressure regime, which may warrant a
theoretical reexamination of such compensation phenomena.
More generally, the sort of global excess reaction thermody-
Acknowledgment. This work was supported by the National
Science Foundation (CHE-9530595).
References and Notes
(1) March, J. AdVanced Organic Chemistry; Wiley: New York, 1992;
889-890.
(2) Wiberg, K. B.; Morgan, K. M.; Maltz, H. J. Am. Chem. Soc. 1994,
116, 11067-11077.
(3) Carey, F. A.; Sunberg, R. J. AdVanced Organic Chemistry Part A:
Structure and Mechanisms, 3rd ed.; Plenum Press: New York, 1990; p
439-444.
(4) Guthrie, J. P. Can. J. Chem. 1975, 53, 898-906.
(5) Streitwieser, A, Jr.; Heathcock, C. H. Introduction to Organic
Chemistry; Macmillan Publishing Co. Inc.: New York, 1976; p 368-378.
(6) Hine, J.; Redding, R. W. J. Org. Chem. 1970, 35, 2769-2772.
(7) Garrett, R.; Kubler, D. G. J. Org. Chem. 1966, 31, 2665-2667.
(8) Bell, J. M.; Kubler, Sartwell, P.; Zepp, R. G. J. Org. Chem. 1965,
30, 4284-4292.
(9) Hu, M.-H. A.; de Souza, L. E. S.; Lee, M.-R.; Ben-Amotz, D. J.
Chem. Phys. 1999, 110, 2498-2507.
(10) Piermarini, G. J.; Block, S.; Barnett, J. D. J. Appl. Phys. 1975, 46,
2774-2779.
(11) Hutchinson, E. J.; Ben-Amotz, D. J. Phys. Chem. B. 1998, 102,
3354-3362.
(12) Ben-Amotz, D.; Herschbach, D. R. J. Phys. Chem. 1990, 94, 1038-
1047.
(13) Ben-Amotz, D.; Willis, K. W. J. Phys. Chem. 1993, 97, 7736-
7742.
(14) Atkins, P. W. Physical Chemistry, 6th ed.; Oxford University
Press: New York, 1998.
(15) Jannasch, H. W.; Mottl, M. J. Science 1985, 229, 717-725.
(16) Chyba, C. F. Nature 2000, 403, 381-382.
(17) Florian, J.; Warshel, A. J. Phys. Chem. B 1999, 103, 10282-10288.
(18) Rashin, A. A.; Bukatin, M. A.; Biophys. Chem. 1994, 51, 167-
192.
(19) Ben-Naim, A. Biopolymers 1975, 14, 1337. Ben-Naim, A. J. Phys.
Chem. 1978, 82, 874-885.
(20) Grunwald, E.; Steel, C. J. Am. Chem. Soc. 1995, 117, 5687-
5692.
(21) Lee, B. Biophys. Chem. 1994, 51, 271-278.
(22) Tapia, O.; Bertran, J. SolVent Effects and Chemical ReactiVity;
Kluwer Academic Publishers: Boston, 1996.
(23) Hanson, J. P.; McDonald, I. R. Theory of Simple Liquids; Academic
Press: New York, 1986.
(24) Chandler, D. Introduction to Modern Statistical Thermodynamics;
Oxford University Press: New York, 1987; 209-213.