Hot Water Induces an Acid-Catalyzed Reaction in Its Undissociated Form

Article abstract of DOI:10.1246/bcsj.77.691

Hot water in its undissociated form has been kinetically proven to induce a chemical reaction that does not undergo under ambient conditions in the absence of a strong acid. The water-induced and acid-catalyzed rate constants were separately determined for the dehydration of 1,4-butanediol by varying the oxonium ion (H⁺) concentration. It was found on the kinetic level over a wide range of temperature from moderate to supercritical that the undissociated form of water promotes the reaction at an effective acid concentration of 10^-4-10^-6 M. A strong density dependence of the reaction rate constant was further observed under supercritical condition, and is related to the anomalous temperature dependence of the rate constant near the critical point.

Full text of DOI:10.1246/bcsj.77.691

Ó 2004 The Chemical Society of Japan
Bull. Chem. Soc. Jpn., 77, 691–697 (2004)
691
Hot Water Induces an Acid-Catalyzed Reaction
in Its Undissociated Form
ꢀ
ꢀ
Yasuharu Nagai, Nobuyuki Matubayasi, and Masaru Nakahara
Institute for Chemical Research, Kyoto University, Uji, Kyoto 611-0011
Received September 29, 2003; E-mail: nagai@nmr.kuicr.kyoto-u.ac.jp
Hot water in its undissociated form has been kinetically proven to induce a chemical reaction that does not undergo
under ambient conditions in the absence of a strong acid. The water-induced and acid-catalyzed rate constants were sep-
þ
arately determined for the dehydration of 1,4-butanediol by varying the oxonium ion (H ) concentration. It was found on
the kinetic level over a wide range of temperature from moderate to supercritical that the undissociated form of water
promotes the reaction at an effective acid concentration of 10 4–10 M. A strong density dependence of the reaction
rate constant was further observed under supercritical condition, and is related to the anomalous temperature dependence
of the rate constant near the critical point.
ꢁ
ꢁ6
Hot water has attracted much attention recently as a novel
solvent for chemical processes of synthetic, environmental, or
geological importance and as an environmentally benign alter-
the forward and backward reactions in Scheme 1 need acid or
In contrast, many ether reactions, includ-
ing Scheme 1, are found to proceed under hydrothermal condi-
metal catalysts.2
2–25
1–20
2–5,7,13,16,18
native to harmful organic solvents.
Unlike ambient water,
tions without adding acids from outside.
Our purpose
water under hydrothermal conditions mixes well with organic
compounds. It also acts as a noncatalytic medium to often in-
duce a chemical reaction that does not proceed without acidic
or basic catalysts on a practically accessible time scale under
ambient conditions. The noncatalytic reactivity in water under
hydrothermal conditions is often presumed to be a catalytic ef-
is to perform detailed kinetic analyses on the model reaction
given by Scheme 1, rather than to add another example of non-
catalytic reaction in hot water.
Our kinetic analysis of Scheme 1 is based on a general ex-
pression for the reaction rate constant of an acid-catalyzed re-
þ
action. When the concentration of the oxonium ion is [H ],
the observed rate constant kobs of an acid-catalyzed reaction
is expressed as
þ
ꢁ
fect of H or OH produced by the autoprotolysis of water. In-
deed, the ion product of water increases with the change of the
þ
thermodynamic state from ambient to hydrothermal, and [H ]
ꢁ
þ
kobs ¼ kwater þ kacid½H ꢂ;
ð1Þ
and [OH ] grow correspondingly by one to two orders of mag-
nitude. On the other hand, the reaction rate constant is gener-
21
where kwater is the first-order rate constant under the hypothet-
þ
þ
ally a strong function of the thermodynamics state, and [H ] or
ꢁ
ical condition that H is absent in the aqueous system, and kacid
þ
[OH ] may not be the sole factor to govern the reaction rate
variation upon temperature elevation. Thus, quantitative kinetic
is the second-order rate constant in the presence of H . A sche-
þ
matic illustration of Eq. 1 near [H ] = 0 is given in Fig. 1. As
illustrated, it should be emphasized that kwater is the limiting in-
þ
ꢁ
measurements are necessary to identify the role of H or OH
in a noncatalytic reaction in hot water. In this paper, we focus
on a model ether reaction under hydrothermal conditions, and
þ
tercept in Eq. 1. Since H is always present due to the autopro-
þ
tolysis of water, [H ] = 0 needs to be hypothetically set to de-
þ
scrutinize the contribution of H in the noncatalytic kinetics.
The model chemical reaction treated in the present work is
the conversion between 1,4-butanediol and tetrahydrofuran
fine kwater. In the following, kwater and kacid are called the water-
induced and acid-catalyzed rate constants, respectively.26 In a
typical acid-catalyzed reaction at room temperature, kwater is
too small to be detected on the practical time scale of seconds
to days. In this case, kobs is dominated by the second term of Eq.
(THF), expressed as Scheme 1. The forward reaction is dehy-
dration and the backward one hydrolysis. This reaction is a sim-
plest reaction involving ether bonding. The ether bonding is a
building component of coal and cellulose, and its reaction un-
der hydrothermal conditions is important from energy and food
concerns. Furthermore, the dehydration process in Scheme 1 is
of synthetic utility for preparing an industrially important sol-
vent, THF. Under ambient conditions, it is well known that both
þ
1 and appears to be proportional to [H ]. In contrast, when the
undissociated form of water becomes kinetically manifest on a
practically accessible time scale, the water-induced term kwater
will be appreciably different from zero. A nonzero intercept is
to be revealed, as illustrated in Fig. 1, in the plot of kobs against
þ
[H ]. On the basis of this idea, we determine both kwater and
kacid for the model reaction as functions of temperature by vary-
þ
ing [H ] in the low-concentration range. The role of water as a
solvent can then be clarified by decomposing kobs into the kwater
and kacid terms at neutral (nonacidic) conditions, where no acid
is added from outside and only the oxonium ion by the autopro-
tolysis of water is present. The determination of both kwater and
Scheme 1. Reaction of interest.
Published on the web April 2, 2004; DOI 10.1246/bcsj.77.691

6
92 Bull. Chem. Soc. Jpn., 77, No. 4 (2004)
Water-Induced Reaction at Hydrothermal State
ꢃ
where the temperature was 400 C and the water density was 0.4
3
g/cm . The concentration of HCl added was on the order of
0
ꢁ
5
þ
1
M. In this case, HCl is only weakly dissociated and [H ]
was estimated according to the dissociation constant of HCl.21
The kinetic measurements at the neutral condition were further
ꢃ
performed at subcritical states of 310, 330, 350, and 365 C on
ꢃ
the saturation curve and supercritical states of 385 and 400 C with
3
the water density ranging between 0.1 and 0.6 g/cm . A sealed
tube of quartz was used as a vessel for the reaction. The sample set-
up and the sample state along the temperature elevation are de-
scribed in our previous papers.30,31
The solution of 1,4-butanediol in heavy water (D2O) was sealed
in a quartz tube with 1.5 mm i.d. at 1.0 M. 1,4-Butanediol, HCl, and
HNO3 were purchased from Nacalai, and D2O (more than 99.9%
purity) was from CEA, France. They were used without further pu-
rification. D2O was employed as the solvent so that the identifica-
tion of the reactant and product is convenient by the proton NMR
þ
measurement. We actually write the oxonium ion as H , rather
Fig. 1. Schematic illustration of the dependence of the ob-
served rate constant kobs on the oxonium ion concentration
þ
32
than D , in the following unless any confusion will arise. It
should be noted that the ion product of D2O is smaller than that
of H2O typically by an order of magnitude.21 1,4-Butanediol was
chosen as the starting material, rather than THF, in the present
study since THF is more abundant at equilibrium. The filling fac-
tor, which is defined as the ratio of the solution volume to the ves-
sel volume at room temperature, was set to 50% for the samples
þ
[
tercept under the hypothetical condition that H is not
H ] for an acid-catalyzed reaction. kwater is the limiting in-
þ
þ
present in the system. The acid-catalyzed part kacid[H ]
þ
is proportional to [H ].
kacid is possible under hydrothermal conditions since the water-
induced path is thermally accelerated to a practically accessible
rate.
ꢃ
reacted at temperatures of 350 C or lower, and it was 40% for
ꢃ
the samples reacted at 365 C. The filling factor also determines
the (water) density under the supercritical conditions,30,31 and
was set for the samples reacted at the supercritical temperatures ac-
cording to the desired density. The length of the solution portion in
each quartz tube was 4 cm for a quick, high-resolution NMR
measurement. The total length of the quartz tube was then deter-
mined by the filling factor, and the reactor volume amounted to
The determination of the rate constant of a chemical reaction
in hot water is often based upon a multistep kinetic scheme to fit
the observed reaction profile. On the other hand, our model re-
action given by Scheme 1 is suitable to single out the kinetic
þ
effect of H . It is found to involve no side reaction even when
an acid is added from outside, and a simple kinetic analysis is
possible with minimal reference to the detailed mechanism. In
this paper, we present a kinetic analysis of the model reaction
based on Eq. 1. An analysis based on Eq. 1 was also performed
by Narayan and Antal for the dehydration of 1-propanol and by
Taylor et al. for the hydrolysis of tert-butyl methyl ether.3
They determined the dependence of the rate constant on the
0
.12–0.71 mL, depending on the filling factor.
The high-temperature reaction was performed in an electric fur-
nace. The sample was put into a furnace heated in advance at each
reaction temperature. The temperature in the furnace was homoge-
ꢃ
3
6
neous within ꢄ1 C. The reaction time was in the range of 10 –10
,4
s. After the reaction time, the sample was removed from the fur-
nace quickly and quenched in a cold-water bath. It took less than
þ
H concentration and argued that the reaction is acid-catalyzed.
6
0 s for the sample to heat up and cool down. Actually, the time
We reveal, by using Eq. 1, that the reaction of interest is mainly
water-induced. When the effect of an acid catalyst is to be ex-
amined, it is desirable to fix the thermodynamic state. Since the
chemical reaction rate constants are generally strong functions
of the temperature and pressure of the system, it is misleading
to change the thermodynamic state in a discussion of the effect
scales for the sample heating and cooling were much shorter than
those for the reactions at the thermodynamic states of interest. The
sample was subjected to a proton NMR measurement (JEOL
EX270 and ECA400), and the product and residual reactant were
quantified; a solution of 1,3,5-trioxane in D2O was sealed in a ca-
pillary and used as an external reference. The effects of the reactant
concentration and the container surface on the rate constants were
negligible within our experimental precision. This was confirmed
by varying the reactant concentration and the quartz vessel diam-
eter.33,34
þ
of the [H ] variation.
Experimental
The forward and backward reactions of Scheme 1 were studied
kinetically under neutral and acidic conditions at temperatures of
ꢃ
Results and Discussion
1
tion curve of water. In the kinetic measurements under acidic con-
50, 200, 240, 270, and 290 C on the liquid branch of the satura-
þ
In Fig. 2, the proton spectrum is shown as a function of time
ꢃ
ditions, [H ] was controlled by adding HCl. The concentration of
HCl was on the order of 10 4–10 M (M = mol dm ), and HCl is
ꢁ
ꢁ3
ꢁ3
for the sample reacted at 350 C. It is seen that the reaction in
Scheme 1 was found to proceed reversibly without any added
catalysts under hydrothermal conditions. Furthermore, no by-
products were detected within our NMR precision and the mass
balance was maintained throughout the reaction. This is a con-
venient property as a model reaction. At the supercritical tem-
fully dissociated in the temperature and concentration range of in-
ꢃ
21,27
þ
terest.
ꢁ
Nitric acid was also used to provide H at 270 C and
4
1
0
M; HNO3 is considered to be fully dissociated in the exper-
imental range.28,29 It was then seen that the change in the anion
did not cause any observable effect on the kinetics. The effect of
acid on the kinetics was further studied at a supercritical state
ꢃ
perature 400 C, the pyrolytic reactions other than the dehydra-

Y. Nagai et al.
Bull. Chem. Soc. Jpn., 77, No. 4 (2004)
693
Fig. 4. The equilibrium constant Keq of the reaction ex-
pressed as Scheme 1 as a function of the temperature T
along the liquid branch of the saturation curve of water.
The line is the linear fit of ln Keq against 1=T. The reaction
is apparently endothermic.
Fig. 2. The time evolution of the proton spectrum of the
ꢃ
sample reacted at 350 C without acids added from outside.
Keq ¼ ½THFꢂ=½1,4-butanediolꢂ;
ð2Þ
is given in Fig. 4 as a function of the temperature along the liq-
uid branch of the water saturation curve. According to Fig. 4,
THF becomes more favourable than 1,4-butanediol when the
temperature is elevated. This behaviour is related to the hydro-
gen bonding ability of water with THF and 1,4-butanediol. Un-
der ambient conditions, 1,4-butanediol is strongly hydrated at
the two OH groups. The temperature elevation (and density re-
duction) then leads to the loss of the hydrogen bonding and
lessens the relative stability of 1,4-butanediol. At the supercrit-
ical states, the equilibrium is too one-sided to determine the
equilibrium constant Keq. No 1,4-butanediol was found at equi-
librium in our experimental precision.
Suppose in Eq. 1 that kwater is negligible compared to
þ
þ
þ
kacid[H ] in the experimental range of [H ]. Note that [H ]
is not zero even at the neutral condition, where no acid is added
þ
from outside and only H produced by the spontaneous disso-
ciation of the water molecule is present in the system. Under the
Fig. 3. The time evolution of the concentrations of 1,4-buta-
ꢃ
nediol and THF at a temperature of 270 C and an acid con-
proportionality supposition of the observed rate constant kobs to
ꢁ
4
centration of 0:9 ꢆ 10 M. The acid added from outside is
HCl for the open symbols, and is HNO3 for the filled sym-
bols. The solid and dashed lines stand for the fits to the re-
versible first-order rate law.
þ
[
H ], since the ionization of the water molecule (D2O) gives
ꢁ
6
þ
ꢃ
rise to 10 M of oxonium ion (D ) at 270 C in the neutral
condition,21 for example, the addition of 10 M HCl is to in-
crease kobs by two orders of magnitude. Figure 5(a) then illus-
trates the experimentally determined dependence of kobs on
ꢁ4
tion were actually observed. The overall pyrolytic rate constant
5
is then ꢅ10ꢁ
s
ꢁ1
, and its weight against the dehydration in-
creases with the density reduction. The pyrolysis and dehydra-
[H ] for the dehydration of 1,4-butanediol to THF at tempera-
ꢃ
þ
tures of 150 and 270 C on the water saturation curve. Evident-
þ
3
ꢁ4
tion was found to be comparable in rate at ꢅ0:2 g/cm .
ly, kobs in the [H ] range of ꢅ10 M is only 2 or 3 times as
Figure 3 illustrates the time dependence of the concentra-
ꢃ
large as kobs at the neutral condition. In other words, the inter-
þ
þ
tions of 1,4-butanediol and THF at 270 C and [H ] = 0:9 ꢆ
cept in the [H ] dependence of kobs is evidently nonzero under
ꢁ4
1
0
M. It is evident that both the first-order rate constants
our experimental conditions. According to the values of kwater
þ
for the dehydration and hydrolysis can be determined accurate-
ly from the time evolution of the proton spectrum. In addition,
the equilibrium constant Keq expressed as35
and kacid determined from Eq. 1, kacid[H ] contributes by less
than ꢅ5% to kobs at the neutral condition when the temperature
ꢃ
is lower than 290 C on the saturation curve. Furthermore, Fig.

6
94 Bull. Chem. Soc. Jpn., 77, No. 4 (2004)
Water-Induced Reaction at Hydrothermal State
hydrate only by heat. The presence of the aqueous medium is
necessary for dehydration. Water is thus revealed, at the level
of kinetics, to promote the reaction in its undissociated form.
The transition state of the dehydration reaction along the wa-
ter-induced path has been proposed by Takahashi through
quantum-chemical calculations and found to be stabilized
through strong coupling with the water molecule.36 Actually,
Takahashi showed that a water-wired form also appears in
the ethanol oxidation in supercritical water and greatly reduces
the electronic energy of the transition state.37 It has been found
that the hydration induces a large dipole moment for
Takahashi’s structure and leads to the further stabilization. In
a subsequent paper, a full account of the quantum-chemical cal-
culation of the transition state will be described and the effect of
hydration is treated with the QM/MM (quantum mechanical-
molecular mechanics) simulations and free energy calcula-
tions.36 In this connection, it is also of theoretical interest to
note under supercritical conditions that water controls the reac-
3
38
tion pathway even at a density lower than 0.1 g/cm .
In Fig. 6, we show kwater, kacid, and kobs at the neutral condi-
tion as functions of the temperature T along the liquid branch of
the water saturation curve. As expected, kobs increases with the
ꢃ
temperature in the range of 150 to 330 C. The further elevation
ꢃ
of the temperature above 330 C, however, causes an apparent
reduction in the rate constant. The apparent inversion of the
temperature dependence of kobs at the neutral condition is con-
sistent with the density dependence of the rate constants in su-
percritical water. The relationship for the rate constant between
the strength of the density dependence and the apparent anom-
aly near the critical point is described parametrically in the Ap-
pendix.
þ
When [H ] is varied at constant temperature and pressure,
Eq. 1 shows that
þ
½
H ꢂ ¼ kwater=kacid
ð3Þ
c
þ
is the crossover concentration [H ]c for the relative importance
of the water-induced and acid-catalyzed paths; the water-in-
Fig. 5. The observed rate constant kobs for the dehydration
of 1,4-butanediol as a function of the oxonium ion concen-
tration [H ] (a) at temperatures of 150 and 270 C on the
liquid branch of the water saturation curve and (b) at a su-
þ
þ
duced path is more important when [H ] < [H ]c and the
þ
ꢃ
þ
þ
acid-catalyzed path is when [H ] > [H ]c. From Figs. 5 and
6, it is seen over the entire temperature range, including a mod-
ꢃ
3
percritical state of 400 C and 0.4 g/cm . The data at near-
þ
ꢃ
þ
ꢁ4
erate temperature of 150 C, that [H ]c is on the order of 10 –
ꢁ
ly zero [H ] correspond to the neutral (nonacidic) condi-
þ
6
10 M. In the thermodynamic range of Figs. 5 and 6, on the
þ
tion and [H ] is not exactly zero due to the autoprotolysis
of water. The linear fits are shown by the lines. In (b), the fit
ꢁ8
ꢁ6
other hand, H is present on the order of 10 –10 M by
the autoprotolysis of water when no acid is added from outside.
ꢁ
5
ꢁ1
to Eq. 1 gives kwater ¼ ð5:1 ꢄ 0:3Þ ꢆ 10
s
and kacid ¼
þ
1
ꢁ1 ꢁ1
s .
Thus, when H is present only due to the autoprotolysis of wa-
ð6:6 ꢄ 1:4Þ ꢆ 10 M
þ
þ
ter, [H ]c ꢇ [H ] holds and the water-induced path dominates
over the acid-catalyzed. Actually, the strength of water to pro-
mote the reaction in its undissociated form can be parameter-
þ
5
of 400 C and 0.4 g/cm . In this case, HCl is only weakly dis-
(b) shows the [H ] dependence of kobs at a supercritical state
ꢃ
3
þ
þ
sociated and [H ] was evaluated from the ionization constant
of HCl listed in Ref. 21. The situation is similar to that observed
for Fig. 5(a). The presence of a nonzero intercept is evident in
ized by an effective acid concentration expressed as [H ]c.
Figs. 5 and 6 show that the role of undissociated water to induce
the reaction as an effective acid is not restricted to the high-
temperature regime. The issue is only the time scale when
the practical time scale of 10 –10 s (hours to days) is con-
cerned. At low temperatures, kwater is practically too small
þ
þ
the [H ] dependence of kobs, and kwater ꢇ kacid[H ] holds at the
32
4
6
neutral condition. Within the fitting procedure of Fig. 5(b),
þ
kacid[H ] contributes by ꢅ5% to kobs at the neutral condition.
þ
Therefore, Fig. 5 demonstrates that hot water accelerates the re-
þ
and a large amount of H needs to be added to detect the reac-
tion. In this case, the practical time scale of experiment requires
action even without the presence of H . Moreover, we con-
firmed that the dehydration does not proceed appreciably in
the dilute gas condition even at high experimental temperatures
þ
þ
a certain value of [H ] that is much larger than [H ]c, and the
þ
observed rate constant kobs appears to be proportional to [H ].
ꢃ
of 350 and 400 C. This shows that 1,4-butanediol does not de-
When the temperature is elevated, kwater increases to a practical-

Y. Nagai et al.
Bull. Chem. Soc. Jpn., 77, No. 4 (2004)
695
the thermodynamic condition is varied over a wide range, how-
ever, the acid-catalyzed rate constant kacid itself in Eq. 1
changes drastically. Therefore, it may be quantitatively insuffi-
cient simply to compare the temperature and density depend-
ence of the observed rate constant kobs at the neutral condition
þ
39,40
þ
only to that of [H ].
reaction, it is desirable to fix the temperature and density and
To elucidate the effect of H on the
þ
to examine the rate of the dehydration against [H ] according
to Eq. 1, as done in the present work.
Hot water in noncatalytic conditions is also found to promote
a chemical reaction, such as Cannizzaro-type disproportiona-
tion, that proceeds under ambient conditions in the presence
of a base.1
0,11,13,15,19,20
In particular, Adschiri et al. revealed,
by examining the hydrolysis rate of a nitrile as a function of
ꢁ
pH, that H2O, rather than OH , is the predominant nucleophile
under hydrothermal conditions. The effective base concentra-
tion [OH ]c of the undissociated form of water can also be de-
fined by an equation similar to Eq. 3. We see according to Ad-
10
ꢁ
ꢁ
ꢁ5
schiri et al.’s results that [OH ]c is on the order of 10 M. Ac-
tually, it is known that H2O is a weak Lewis base and serves as
a nucleophile even under ambient conditions.2
4,25
On the other
hand, several acid-catalyzed reactions are found to proceed un-
der hydrothermal conditions without any acid cata-
In this work, we based our analyses on a
lysts.2
–9,13,14,16,18
well-defined kinetic expression given by Eq. 1, and revealed
quantitatively the role of the undissociated form of water as
þ
an effective acid by controlling the H concentration.
This work is supported by the Grant-in-Aid for Scientific Re-
search (Nos. 10304047, 13440179, 13640509, and 15205004)
from the Japan Society for the Promotion of Science, by the
Grant-in-Aid for Scientific Research on Priority Areas
(No. 15076205) and the Grant-in-Aid for Creative Scientific
Research (No. 13NP0201) from the Ministry of Education,
Culture, Sports, Science and Technology, and by the CREST
(Core Research for Evolutional Science and Technology) of
Japan Science and Technology Corporation (JST). We are also
grateful to Professor H. Takahashi of Osaka University for
insightful discussions.
Fig. 6. (a) The water-induced rate constant kwater and the
acid-catalyzed rate constant kacid and (b) the observed rate
constant kobs at the neutral condition for the dehydration of
1,4-butanediol as functions of temperature along the liquid
branch of the saturation curve. The lines are drawn just for
the eye guide. kacid obtained in the present work is extrapo-
lated through an Arrhenius plot to the previous value at 100
Appendix
ꢃ
C.22 It should be noted that the system is on the saturation
In Fig. 6, the observed rate constant kobs at the neutral condition
exhibits an inversion in the temperature dependence along the liq-
uid branch of the saturation curve. In this Appendix, we show
through a parameterization of the density and temperature depend-
ence of kobs that the inversion is related to the density reduction of
water upon elevation of the temperature. It should be noted that the
arguments in this Appendix refer only to the density and tempera-
ture dependence of the observed rate constant and are not affected
by the molecular mechanism of the reaction. In Fig. 7, we show
kobs at the neutral condition as a function of the (water) density
curve and that the temperature variation accompanies the
changes in both the density and the pressure. Along this
temperature variation, the apparent activation energies
for kwater and kacid are 29 and 25 kcal/mol, respectively.
ly accessible value and the water-induced path becomes mani-
4
6
þ
fest on the time scale of 10 –10 s. In other words, [H ] result-
ing from the autoprotolysis of water is comparable to or smaller
þ
than [H ]c, and the intercept is evident in the plot of kobs against
þ
[
H ] in the practical time scale.
In recent papers, Richter and Vogel investigated the dehy-
ꢃ
at fixed supercritical temperatures of 385 and 400 C. The kinetic
data shown in Fig. 7 can be parameterized by
dration of 1,4-butanediol to THF in an Inconel 625 vessel as
a function of temperature at constant pressure, and found that
the reaction rate constant involves a maximum around the crit-
ꢀ
ꢁ
ꢀ
E
m
kobs ¼ ꢀ exp ꢁ
;
ð4Þ
RT
13,16
ical temperature.
They then adopted the conventional acid-
where ꢀ is the water density, R is the gas constant, T is the temper-
ature, and ꢁE is the apparent activation energy. In this equation,
although we introduced a power m and an activation energy ꢁE,
we do not assume that m water molecules are involved in the reac-
catalyzed mechanism of the dehydration (neglect of the first
term in Eq. 1) and related their finding to the temperature de-
þ
pendence of [H ] due to the autoprotolysis of water. When

6
96 Bull. Chem. Soc. Jpn., 77, No. 4 (2004)
Water-Induced Reaction at Hydrothermal State
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Fig. 7. The observed rate constant kobs for the dehydration
of 1,4-butanediol at supercritical temperatures of 385 and
9
K. Chandler, F. Deng, A. K. Dillow, C. L. Liotta, and C. A.
Eckert, Ind. Eng. Chem. Res., 36, 5175 (1997).
10 C. L. Harrell, M. T. Klein, and T. Adschiri, Adv. Environ.
Res., 1, 373 (1997).
11 Y. Tsujino, C. Wakai, N. Matubayasi, and M. Nakahara,
Chem. Lett., 1999, 287.
ꢃ
400 C against the density of water. The dashed and solid
lines stand for the linear fits of ln kobs against the water den-
ꢃ
sity at 385 and 400 C, respectively.
1
1
2
3
P. E. Savage, Chem. Rev., 99, 603 (1999).
D. Br o¨ ll, C. Kaul, A. Kr a¨ mer, P. Krammer, T. Richter, M.
tion. Eq. 4 is simply a fitting function. When Eq. 4 is transferred to
the subcritical region, the temperature dependence along the satu-
ration curve of water is given by
Jung, H. Vogel, and P. Zehner, Angew. Chem., 38, 2998 (1999).
Y. Ikushima, K. Hatakeda, O. Sato, T. Yokoyama, and M.
Arai, J. Am. Chem. Soc., 122, 1908 (2000).
Y. Ikushima, K. Hatakeda, O. Sato, T. Yokoyama, and M.
Arai, Angew. Chem., 40, 210 (2001).
T. Richter and H. Vogel, Chem. Eng. Technol., 24, 340
(2001).
1
4
ꢀ
ꢁ
@
ln kobs
m
¼ T
@ ln ꢀ ꢀE
@ ln T mRT
1
5
þ
:
ð5Þ
@T
1
6
The inversion of the temperature dependence of kobs is observed at
the T value where the right-hand side of Eq. 5 vanishes. Since
17 T. Sato, G. Sekiguchi, T. Adschiri, and K. Arai, Chem.
Commun., 2001, 1566.
@
ln ꢀ=@T is negative along the liquid branch of the saturation curve
and ꢁE is positive, the inversion temperature is lower when m is
larger. Actually, given that @ ln ꢀ=@T diverges at the critical point,
the inversion temperature is always present when ꢁE and m are
positive. In our case, Fig. 7 provides m ¼ ꢅ4 and ꢁE < ꢅ170
kJ/mol. The inversion temperature is then inferred from Eq. 5 to
18 J. D. Taylor, J. I. Steinfeld, and J. W. Tester, Ind. Eng.
Chem. Res., 40, 67 (2001).
19 H. Oka, S. Yamago, J. Yoshida, and O. Kajimoto, Angew.
Chem., 41, 623 (2002).
20 Y. Nagai, C. Wakai, N. Matubayasi, and M. Nakahara,
Chem. Lett., 32, 310 (2003).
ꢃ
be lower than 360 C, which is in agreement with the one observed
in Fig. 6. According to the discussion in this Appendix, the increase
of kobs with the density as parameterized by Eq. 4 leads, in general,
to an inversion of the temperature dependence on the saturation
curve. The inversion is simply related to the divergent nature of
21 K. S. Pitzer, ‘‘Activity Coefficients in Electrolyte Solu-
tions,’’ 2nd ed, CRC Press, Inc., Boca Raton (1991).
22 B. G. Hudson and R. Barker, J. Org. Chem., 32, 3650
(1967).
@
ln ꢀ=@T toward the critical point. In this sense, the phenomeno-
23 G. Tagliavini, D. Marton, and D. Furlani, Tetrahedron, 45,
1187 (1989).
24 R. P. Bell, ‘‘The Proton in Chemistry,’’ 2nd ed, Cornell
University Press, Ithaca (1973).
25 J. March, ‘‘Advanced Organic Chemistry,’’ 4th ed, John
Wiley & Sons, Inc., New York (1992).
logical inversion of the temperature dependence of the reaction
rate constant does not mean an ‘‘anomalous’’ feature of a reaction
near the critical point, but reflects the general feature near the crit-
ical point that the density varies strongly with the temperature
along the saturation curve.
The dielectric constant " and the ion product of water (pKw) are
increasing functions of the density of water in the supercritical con-
dition. The near-critical inversion of their temperature dependence
along the saturation curve is then derived from an argument similar
to the one given above. Thus, a correlation of the rate constant to "
and/or pKw can be seen, especially when the near-critical inversion
is emphasized. The presence of correlation does not necessarily
26 We avoid such a phrase as ‘‘water-catalyzed’’ to express the
term kwater. The phrase ‘‘water-catalyzed’’ sounds appealing and in-
deed captures the aspect that water promotes the reaction. Howev-
er, the equilibrium constant of the reaction varies with the density
of water and a more modest expression as ‘‘water-induced’’ is ap-
propriate in the present context.
27 K. P. Johnston and J. B. Chlistunoff, J. Supercrit. Fluids,
12, 155 (1998).
28 J. B. Chlistunoff, K. J. Ziegler, L. Lasdon, and K. P.
Johnston, J. Phys. Chem. A, 103, 1678 (1999).
29 W. L. Marshall and R. Slusher, J. Inorg. Nucl. Chem., 37,
mean, however, the presence of causality. To examine the role of
þ
H
on the rate constant, in particular, a systematic investigation
þ
is needed for the [H ] dependence of the rate constant, as done
in the present work.

Y. Nagai et al.
Bull. Chem. Soc. Jpn., 77, No. 4 (2004)
697
2
165 (1975).
N. Matubayasi, C. Wakai, and M. Nakahara, Phys. Rev.
Lett., 78, 2573 (1997); Phys. Rev. Lett., 78, 4309 (1997).
N. Matubayasi, C. Wakai, and M. Nakahara, J. Chem.
Phys., 107, 9133 (1997).
Since the ion product is different between H2O and D2O, it
definition of the equilibrium constant Keq. This is because water
is present in excess in the system and its concentration is essential-
ly unchanged through the reaction. Keq is thus dimensionless. Sim-
ilarly, the hydrolysis reaction is first-order in the sense that the con-
centration of solvent water is considered unchanged during the re-
action.
3
0
3
1
3
2
is possible that the ionization constant of DCl is different from that
of HCl. In the present work, we assume that DCl is fully dissociat-
ed under the condition that HCl is fully dissociated. At the super-
critical condition, HCl and DCl are not fully dissociated in our con-
centration range and the abscissa of Fig. 5(b) needs to be treated
with care. We used the ionization constant of HCl and the ionic
36 H. Takahashi et al. in preparation. Of course, the number of
water molecules involved in the transition state is not necessarily
equal to the reaction order against the water density. The reaction
rate is affected by the hydration of the reactant and transition state
due to the surrounding water molecules.
37 H. Takahashi, S. Hisaoka, and T. Nitta, Chem. Phys. Lett.,
363, 80 (2002).
þ
product of H2O to identify [H ] in Fig. 5(b) since the values for
the deuterated compounds were not available. This identification
leads to an underestimate of kacid since a deuterated acid typically
involves a smaller ionization constant than the protonic counter-
part. The kwater value is not affected in Fig. 5(b), however, when
the change of the ionization constant upon deuteration is the com-
mon to water and hydrogen chloride. If kwater value is not affected
38 R. E. Westacott, K. P. Johnston, and P. J. Rossky, J. Phys.
Chem. B, 105, 6611 (2001).
39 In this connection, it is of interest to note the following.
3
When the density is varied from 0.1 to 0.6 g/cm at a fixed super-
ꢃ
þ
critical temperature of 400 C, [H ] from the autoprotolysis of wa-
ter increases by six orders of magnitude. The observed rate con-
stant kobs of the dehydration is shown in Fig. 7, on the other hand,
to grow only by three orders of magnitude. Thus, if the reaction is
acid-catalyzed and kwater is negligible in Eq. 1, then kacid needs to
reduce by three orders of magnitude upon the density variation.
40 We do not attempt to write the water-induced term kwater in
the form of kwater = k[H2O], where k is a second-order rate con-
stant. This is because the water molecule contributes to kwater not
only as a reactant but also through solvation. Indeed, Fig. 7 shows
that kwater is nonlinear with respect to [H2O], when kwater is consid-
ered dominant in the observed rate constant kobs. In this case, the k
derived from the form of kwater = k[H2O] is dependent on [H2O]
and does not lead to a clearer representation of the water density
dependence.
þ
by deuteration, the value of kacid[H ] at the neutral condition is not,
either, of course. Thus, it is considered that the relationship kwater
þ
ꢇ kacid[H ] at the neutral condition is valid even when D2O is em-
ployed as the solvent.
3
dissolved quartz is at most 10 in mole fraction in the present ex-
3
As described in Ref. 34, the saturated concentration of the
ꢁ
4
perimental conditions. The dissolved quartz is usually present in
þ
the hydrated form H2SiO3 and produces H by ionization. It can
be shown by virtue of the extrapolation of the data listed in
þ
Ref. 21, however, that [H ] from the dissolved quartz is smaller
þ
by orders of magnitude than [H ] from the autoprotolysis of water.
3
1994).
4
C. E. Manning, Geochim. Cosmochim. Acta, 58, 4831
(
3
5
In Eq. 2, the water concentration was not included in the