Kinetic and equilibrium study on formic acid decomposition in relation to the water-gas-shift reaction

Article abstract of DOI:10.1021/jp0626768

Kinetics and equilibrium are studied on the hydrothermal decarbonylation and decarboxylation of formic acid, the intermediate of the water-gas-shift (WGS) reaction, in hot water at temperatures of 170-330°C, to understand and control the hydrothermal WGS

Full text of DOI:10.1021/jp0626768

11082
J. Phys. Chem. A 2006, 110, 11082-11090
Kinetic and Equilibrium Study on Formic Acid Decomposition in
Relation to the Water-Gas-Shift Reaction
Yoshiro Yasaka, Ken Yoshida, Chihiro Wakai, Nobuyuki Matubayasi, and Masaru Nakahara*
Institute for Chemical Research, Kyoto UniVersity, Uji, Kyoto 611-0011, Japan
ReceiVed: May 2, 2006; In Final Form: July 14, 2006
Kinetics and equilibrium are studied on the hydrothermal decarbonylation and decarboxylation of formic
acid, the intermediate of the water-gas-shift (WGS) reaction, in hot water at temperatures of 170-330 °C, to
understand and control the hydrothermal WGS reaction. 1H and 13C NMR spectroscopy is applied to analyze
as a function of time the quenched reaction mixtures in both the liquid and gas phases. Only the decarbonylation
is catalyzed by HCl, and the reaction is first-order with respect to both [H+] and [HCOOH]. Consequently,
the reaction without HCl is first and a half (1.5) order due to the unsuppressed ionization of formic acid. The
HCl-accelerated decarbonylation path can thus be separated in time from the decarboxylation. The rate and
equilibrium constants for the decarbonylation are determined separately by using the Henry constant (gas
solubility data) for carbon monoxide in hot water. The rate constant for the decarbonylation is 1.5 × 10-5,
2.0 × 10-4, 3.7 × 10-3, and 6.3 × 10-2 mol-1 kg s-1, respectively, at 170, 200, 240, and 280 °C on the liquid
branch of the saturation curve. The Arrhenius plot of the decarbonylation is linear and gives the activation
energy as 146 ( 3 kJ mol-1. The equilibrium constant KCO ) [CO]/[HCOOH] is 0.15, 0.33, 0.80, and 4.2,
respectively, at 170, 200, 240, and 280 °C. The van’t Hoff plot results in the enthalpy change of ∆H ) 58
( 6 kJ mol-1. The decarboxylation rate is also measured at 240-330 °C in both acidic and basic conditions.
The rate is weakly dependent on the solution pH and is of the order of 10-4 mol kg-1 s-1 at 330 °C. Furthermore,
the equilibrium constant KCO2 ) [CO2][H2]/[HCOOH] is estimated to be 1.0 ×102 mol kg-1 at 330 °C.
1. Introduction
∼200 °C); and (iv) it is rather difficult to quantitatively analyze
such main gaseous products as CO, CO2, and H2 in the
heterogeneous system because of their distribution between the
gas and liquid phases. In the present analysis, we decouple the
two decomposition pathways of formic acid in eqs 1 and 2 by
exploiting the catalytic effect of acid on the decarbonylation.
The surface-catalytic effect is avoided by choosing quartz as a
reactor material. HCl is employed for the time-scale separation
of the relevant kinetic paths. All of the gaseous products are
In recent years,1-6 formic acid has been found to decompose
without catalysts in the following ways:
HCOOH a CO + H2O
HCOOH a CO2 + H2
(decarbonylation)
(decarboxylation)
(1)
(2)
The reversibility of the decarbonylation has been evidenced by
the direct conversion of carbon monoxide to formic acid in hot
water7 and furthermore by the stability analysis based on the
free energies for the species (HCOOH, CO, CO2, H2, and H2O)
involved in reactions 1 and 2.8 The reversibility and the coupling
of the reactions given by eqs 1 and 2 clearly indicate that formic
acid exists as an intermediate in the water-gas-shift (WGS)
reaction,9-11 which has long been known to generate hydrogen
from water as a clean fuel.12 Now the WGS reaction is expressed
as
1
quantified in the sealed reactor by H and 13C NMR spectros-
copy, and the carbon mass balance is confirmed.
Formic acid is involved as a key compound not only in the
WGS reaction but also in a number of organic reactions recently
revealed in hot water.14,15 We need to establish the kinetics and
mechanisms of the hydrothermal formation and decomposition
reactions of formic acid, in view of the following three pro-
cesses. (1) Formic acid, as an aldehyde (C1, single-carbon con-
tained), is involved in the noncatalytic cross-disproportionations
of aldehydes; an aldehyde is reduced to the corresponding
alcohol and formic acid oxidized to carbonic acid or carbon
dioxide.14 (2) Formic acid reacts with formaldehyde (C1
aldehyde) in the presence of acid to form a C2 compound,
glycolic acid, through the C-C bond formation as a chemical
evolution process.14 (3) Carbon monoxide, which is in hydro-
thermal equilibrium with formic acid, is released through the
decarbonylation of aldehydes that can be generated by the
heterolytic fragmentation of ethers.15
CO + H2O a HCOOH a CO2 + H2
(3)
and the kinetics and equilibrium of the WGS reaction can be
comprehensively established by examining the rate and equi-
librium constants for the decarbonylation and the decarboxyla-
tion of formic acid. The kinetics and equilibrium study has been
hampered by the following: (i) the reaction order of reaction 1
has not yet been established; (ii) these reactions can be catalyzed
by metals used for reaction cells;4,6,13 (iii) although the non-
catalytic decarbonylation can be dominant in hot water, the
reaction rate is very slow (a time scale of days to weeks below
The decomposition of formic acid has been studied for more
than a decade as previously referred to,7 but its kinetics and
equilibrium have not yet been established. Among the previous
studies Bro¨ll et al. reported the dominance of the decarbonyla-
* Corresponding author. E-mail: nakahara@scl.kyoto-u.ac.jp.
10.1021/jp0626768 CCC: $33.50 © 2006 American Chemical Society
Published on Web 09/02/2006

Formic Acid Decomposition
J. Phys. Chem. A, Vol. 110, No. 38, 2006 11083
where the subscript T represents the temperature. Note that the
filling factor FT at a reaction temperature T is larger than that
at room temperature 30 °C, Fr, due to the expansion of water
when Fr > 0.33 (at densities higher than the critical density of
water); compare Figure 1a and Figure 1b. The gaseous reaction
product is in dissolution equilibrium at each temperature (Fig-
ure 1c). The value of FT can be calculated from Fr by using the
tabulated density of water along the saturation curve.16
Each sample was heated for a specified reaction time in a
programmable electric furnace kept at the reaction temperature
(170-330 °C) with an accuracy of 1 °C. At the reaction tem-
perature, the liquid and gas phases coexist and the reaction
proceeds in the liquid phase. After the sample was quenched
Figure 1. Definition of the filling factor of the sample at (a) room
temperature Fr and (b) the reaction temperature FT. The filling factor
at the reaction temperature is larger than that at room temperature due
to the decrease of water density at elevated temperature for Fr > 0.33.
The expansion of the total length L of the quartz reactor is negligible
in view of the thermal expansion coefficient of quartz. (c) Illustration
of the dissolution equilibrium of CO in a sample.
by air, H and H-decoupled 13C NMR spectra were observed
at 30 °C with a NMR spectrometer (JEOL ECA400, magnetic
field strength of 9.4 T). Such gaseous products as CO, CO2,
and H2 coexist in the liquid and gas phases, and the NMR
spectra were measured for each phase by the method described
elsewhere.15 The spectral measurements were carried out as a
function of reaction time to examine the time evolution of the
reactant and products.
1
1
tion path in the decomposition at low temperatures without
kinetic analysis.5 As for the decarboxylation, there are much
more quantitative studies,2-5,13 and the reaction rate has been
obtained mainly under the surface catalytic effect of metals.
Savage and co-workers studied the decomposition of formic acid
2.2. Yield Analysis. The concentration of formic acid
1
[HCOOH] was estimated by the H peak intensity relative to
that of solvent H2O (55.5 M) in the liquid phase. The fraction
of residual formic acid, denoted as xHCOOH, is expressed by
in a flow reactor made of Hastelloy C-276 at 0.02 M (mol dm-3
)
in the temperature range of 320-500 °C and showed that the
main product was CO2.2 Other authors also reported at higher
concentrations (0.13 and 1 M) that the decarboxylation is the
main decomposition path.3,4 McCollom et al. examined the
decarboxylation of formic acid using a gold bag reactor with
and without minerals and clarified that the catalytic effect is
not given by minerals but by the transition metals except for
gold.13 They also observed the formation of formate ion from
CO2 and H2 in basic conditions, which indicates the reversibility
of the decarboxylation. Here we perform the detailed analysis
of the decarbonylation and decarboxylation paths in noncatalytic
quartz tube in a wide range of temperatures, concentrations,
and pH values, with an attempt to establish the kinetics and
equilibrium of the hydrothermal WGS reaction.
The experimental part is described in section 2. In section 3,
results and discussion are given. In section 3.1, the reaction
rate law of the decarbonylation is derived and its rate constant
is determined. The equilibrium constant of the decarbonylation
is determined in section 3.2. In section 3.3, the rate of the
decarbonylation in the absence of strong acid is analyzed and
the acid dissociation constant of formic acid is semiquantitatively
estimated. The decarboxylation kinetics and equilibrium are in
section 3.4. In section 3.5, a scheme to control the WGS reaction
is presented. Conclusions are given in section 4.
[HCOOH]
xHCOOH
)
(5)
[HCOOH]0
where [HCOOH]0 is the initial concentration of formic acid.
To determine the yields of gaseous products, CO, CO2, and H2,
we measured their concentrations in both the liquid and gas
phases. The concentration of CO or CO2 dissolved in water was
evaluated by the liquid-phase 13C spectrum using HCOOH as
the internal reference; [HCOOH] was determined in advance
by the 1H spectrum. For the gas-phase 13C spectrum, HCOOH
in the liquid phase of the same sample was used as the external
reference to quantify the gas-phase concentration of CO or CO2.
Thus the total yield of CO, expressed as xCO, is calculated by
1 - Fr
[CO]liq + [CO]gas
Fr
xCO
)
(6)
[HCOOH]0
Here, [CO]liq and [CO]gas are the concentrations of CO in the
liquid and gas phases, respectively, obtained at 30 °C, and the
subscript r indicates the temperature (30 °C) at which the NMR
analysis is performed. The coefficient (1 - Fr)/Fr (the volume
ratio of the gas to the liquid phase) is the conversion factor for
the gas-phase concentration to that in the liquid phase. The same
procedure was used for CO2. It was found that the carbon mass
balance was maintained during the reaction within 10%. The
source of error is the absence of an internal reference in the
estimate of the gaseous products and the magnetization transfer
from proton to carbon through the C-H bond of formic acid
when the 1H-decoupled 13C spectrum is taken.17 The maintained
mass balance indicates that CO and CO2 do not leak through
the reactor walls. The yield of H2 was estimated by the gas-
2. Experimental Section
2.1. Materials and Apparatus. 13C-enriched formic acid (99
atom % and 95% (w/w) in H2O) and sodium formate (99 atom
%) were obtained from ISOTEC and used as received. Aqueous
solutions of HCl (0.01, 0.02, 0.05, 0.1, and 1.0 M) were obtained
from Nacalai. A reactor was made of a sealed quartz tube of
1.5 mm i.d. and 3.0 mm o.d. and 10-20 cm long. As shown in
Figure 1, the reaction solution was introduced to occupy a
specified portion (controlled with an accuracy of 1%) of the
tube reactor. The volume (length, lTliq) ratio of the liquid phase
to the total (L) is hereafter denoted as the filling factor:
1
phase H spectrum using solvent H2O of the same sample as
the external reference. The concentration of dissolved H2 was
not incorporated into the yield, since it is not measurable by
the interference of the strong solvent peak. This may lead to an
underestimate of the yield by ∼5%. In addition, the smallest
molecule H2 escapes out of the quartz reactor with a time scale
liq
lT
the volume of the liquid phase
the total volume of the reactor
FT )
)
(4)
L

11084 J. Phys. Chem. A, Vol. 110, No. 38, 2006
Yasaka et al.
TABLE 1: The Rate Constant k+1 and the Equilibrium
Constant KCO for the Decarbonylation, and the Acid
Dissociation Constant Ka of Formic Acid in the Temperature
Range of 170-300 °C on the Liquid Branch of the
Saturation Curve
T/°C
log(k+1/mol-1 kg s-1
)
KCO
pKa
170
185
200
210
220
230
240
250
260
280
300
-4.82
-4.22
-3.71
-3.29
-2.98
-2.75
-2.43
0.15
0.33
0.44
4.2
3.8
3.8
4.0
4.2
4.6
4.6
4.9
5.0
0.80
1.2
-1.91
-1.20
4.2
parameters a and b are the reaction orders with respect to the
proton (HCl) and formic acid, respectively.
First, we determine a by measuring V+1 with various HCl
concentrations at [HCOOH]0 ) 1.0 mol kg-1 and the temper-
ature of 200 °C on the liquid branch of the saturation curve.
The logarithm of the initial reaction rate is plotted against the
logarithm of the HCl concentration in Figure 2a. The plot is
fitted well to a straight line with a slope of 1.1 ( 0.1. Hence,
we can regard the order a as 1. Second, in order to determine
the order b, we have observed V+1 by varying the initial formic
acid concentration at [HCl] ) 0.10 mol kg-1 and the temperature
of 200 °C. The logarithm of the initial reaction rate is plotted
against the logarithm of the formic acid concentration in Fig-
ure 2b. The slope of the linear fitting line is 1.1 ( 0.1. In conse-
quence, the decarbonylation follows the simple second-order
rate law as
Figure 2. (a) The logarithm-logarithm plot of the initial rate V+1 of
the decarbonylation against [HCl] at the formic acid initial concentration
[HCOOH]0 ) 1.0 mol kg-1 and the reaction temperature of 200 °C.
The line is the linear fit of the experimental data, and its slope is 1.1
( 0.1. (b) The logarithm-logarithm plot of the initial rate V+1 of the
decarbonylation against [HCOOH]0 at [HCl] ) 0.10 mol kg-1 and
200 °C. The line is the linear fit of the experimental data, and its slope
is 1.1 ( 0.1.
V+1 ) k+1[H+][HCOOH]
(8)
The rate law thus established has been further confirmed by
studying the decomposition of HCOONa that hydrolyzes to
generate a basic condition. In this case, the amount of CO pro-
duced from HCOONa was below the detection limit.19
We determined the second-order rate constant k+1 in the
temperature range of 170-280 °C on the liquid branch of the
saturation curve. The results are shown in Table 1 and plotted
against the reciprocal temperature in Figure 3. The Arrhenius
plot is linear, and the activation energy for the decarbonylation
is evaluated to be as high as 146 ( 3 kJ mol-1. For the decar-
bonylation mechanism, we may consider the following:
of ∼100 h. Thus the yield of H2 was estimated only in the study
of the decarboxylation at 330 °C, in which the reaction time
scale is ∼10 h.
In the determination of the equilibrium constants of the
decarbonylation and the decarboxylation, the liquid-phase con-
centration (in situ concentration) of each gaseous product at
the reaction temperature is required. The yields previously
obtained can be converted into in situ concentrations by taking
into account the dissolution equilibrium of the gases at the
reaction temperature (the procedure is described in section 3.2).
For this purpose, the liquid-gas distribution constants (Henry
constants) of CO, CO2, and H2 at elevated temperatures were
taken from ref 18.
3. Results and Discussion
3.1. Decarbonylation Kinetics. We can study the rate law
for the decarbonylation by investigating the initial rate in the
presence of HCl. When the HCl concentration is larger than
2.0 × 10-2 mol kg-1, the decarbonylation is more than 50 times
faster than the decarboxylation and can be separately quantified.
When the decarboxylation can be neglected, the initial rate of
formic acid decomposition is given by
d[HCOOH]
) k+1[H+]a[HCOOH]0
0
(7)
b
First, formic acid is protonated on the oxygen atom of the
carbonyl group (the protonation may proceed on the hydroxyl
group); second, it is dehydrated to form the protonated carbon
monoxide; and finally it releases the proton. The first and third
steps are fast, and the second is the rate-determining step.
V+1 ) -
|
dt
Here V+1 is the reaction velocity, k+1 is the rate constant,
[HCOOH]0 is the initial concentration of formic acid, and the

Formic Acid Decomposition
J. Phys. Chem. A, Vol. 110, No. 38, 2006 11085
Figure 3. The Arrhenius plot of the rate constant k+1 of the
decarbonylation. The line is the linear fit of the experimental data. The
slope of the line gives the activation energy of the decarbonyaltion:
Ea ) 146 ( 3 kJ mol-1
.
It is of interest to compare our result with a previous one
performed without water (in neat conditions). The reaction was
studied in the gas phase by Blake et al.,20 and an activation
energy of 119 kJ mol-1 was reported at ∼500 °C. The activation
energy of the hydrothermal reaction is not smaller but larger
than that of the neat gas-phase one. In the hydrothermal condi-
tions, a heterolytic bond-breakage process leading to an ionic
transition state is more probable because the high polarity of
the solvent can stabilize ionic states and the ionic species are
involved in the hydrothermal process as shown by the scheme
in eq 9. In the gas-phase decarbonylation, on the other hand, a
homolytic bond-breakage process and a neutral transition state
are assumed.20 Any difference in the transition state as well as
the extent of stabilization of relevant species by solvation and
protonation can account for the difference in the activation
energy (and free energy) between the liquid- and gas-phase
reactions. It is desirable to perform a quantum-chemical calcu-
lation for the acid-catalyzed decarbonylation to get insight in
the transition-state structure for the hydrothermal reaction.11,21-23
3.2. Decarbonylation Equilibrium. In this section we deter-
mine the equilibrium constant of the decarbonylation of formic
acid in hot water in the temperature range of 170-280 °C. By
adding such a strong acid as HCl, we can separate the time
scale of the decarbonylation from that of the decarboxylation.
As can be seen in Figure 4a and Figure 4b, the decarbonylation
is accelerated by a factor of ∼10 in the presence of HCl at 0.10
mol kg-1. In the absence of HCl, it takes several tens of hours
for the decarbonylation equilibrium to be attained and the
nonnegligible amount of CO2 is produced in competition with
the decarbonylation.
Figure 4. The time evolution of formic acid decomposition (a) with
and (b) without HCl at 250 °C. The initial compositions are (a) 0.16
mol kg-1 for formic acid with HCl at 0.10 mol kg-1 and (b) 1.0 mol
kg-1 for formic acid without HCl. In panel a, the plotted yield of CO
is calculated as 1 - xHCOOH
.
As the reaction takes place in the subcritical water along the
saturation curve, not all of the CO produced by the decarbonyl-
ation remains in the liquid phase, but a considerable amount of
CO is accommodated in the gas phase of the sample. Hence
QCO is larger than KCO. To determine KCO we need to calculate
the fraction, â, of CO distributed in the liquid phase.
moles of CO in the liquid phase
â )
(12)
(13)
total moles of CO
Then the relation of QCO and KCO is written as
âxCO
KCO
)
) âQCO
xHCOOH
where formic acid is considered to be present only in the liquid
phase.
The equilibrium constant of the decarbonylation in hot water
is defined as
The value of â is dependent on the solubility (Henry constant)
of CO at the reaction temperature and the filling factor defined
by eq 4. To evaluate the value of â, we assume the following:
(1) The dissolution of the gases is sufficiently faster than the
decarbonylation and the decarboxylation. (2) The Henry law
holds for the dissolution of CO into hot water. (3) The equation
of state for the ideal gas holds for CO in the gas phase. The
Henry constant kH is the mole ratio of liquid H2O to CO
dissolved in hot water which is in dissolution equilibrium with
hypothetical ideal gas of CO at 1 MPa.
[CO]liq
[HCOOH]liq
KCO
)
(10)
|
eq
where the symbol |eq represents the value evaluated at equilib-
rium, and water as a reactant species is not contained since it is
present in excess as a solvent. What is directly obtainable from
the yield analysis (see eqs 5 and 6) is not KCO but a quantity
denoted as the decarbonylation quotient QCO
:
When the partial pressure of CO is given by pCO/MPa, we
have the molar (volume) concentration of dissolved CO as
xCO
QCO
)
(11)
|
xHCOOH eq
p
COdT
kH
[CO]liq
)
(14)
where xHCOOH and xCO are provided by eqs 5 and 6, respectively.

11086 J. Phys. Chem. A, Vol. 110, No. 38, 2006
Yasaka et al.
where dT is the molar concentration of liquid water at the
reaction temperature T on the saturation curve. The gas-phase
molar concentration of CO is expressed by
pCO
[CO]gas
)
(15)
RT
according to the ideal gas law; R is the gas constant. Using eqs
10-15, we can evaluate the value of â as
[CO]liqFT
[CO]liqFT + [CO]gas(1 - FT)
â )
)
FT
KD(CO)(1 - FT) + FT
(eq)
(16)
Figure 5. The observed equilibrium yield xHCOOH of formic acid
against the filling factors FT at 240 °C. Open circles correspond to the
initial composition of 0.043 mol kg-1 for formic acid with HCl at 0.040
mol kg-1, open squares to 0.16 mol kg-1 for formic acid with HCl at
0.10 mol kg-1, and filled circles to 1.0 mol kg-1 for formic acid with
HCl at 0.10 mol kg-1. The equilibrium yield of formic acid calculated
by eq 19 with KCO ) 0.8 is shown by the solid line.
where the liquid-gas distribution constant is introduced by
[CO]gas
[CO]liq
kH
KD(CO) )
)
(17)
RTdT
different initial concentrations of formic acid, 0.040, 0.16, and
1.0 mol kg-1, and for each concentration the monotonic increase
of xHCOOH with FT is evident. For the initial concentrations
and FT is the filling factor at the reaction temperature. The Henry
constant kH taken from ref 18 and the molar concentration dT
of pure water tabulated in ref 16 are used to evaluate KD(CO).
As the temperature increases along the saturation curve, liquid
water is expanded and CO becomes more soluble in water in
the temperature range studied here; KD(CO) ) 29.6, 13.8, and
8.4 at 170, 240, and 280 °C, respectively. The value of ln KD-
(CO) and its temperature dependence are in good agreement
with those in a previous computational study.8 Now the
equilibrium constant KCO is explicitly written in terms of the
directly measurable quantities QCO and FT as
(eq)
of 0.040 and 0.16 mol kg-1, the results are fitted well to eq 19
using the value of KCO in Table 1. The good fit indicates that
eq 19 represents well how the phase distribution of CO affects
the decarbonylation equilibrium. When the initial concentration
is increased to such a high value as 1.0 mol kg-1, the equilibrium
concentration of formic acid is considerably lower than that
expected with KCO ) 0.8 at a high filling factor FT > 0.8; see
Figure 5. One may consider the high pressure of CO gas as
one of the reasons for the low xHCOOH(eq). The CO pressure is
estimated as 20, 10, and 3 MPa, however, for FT ) 0.95, 0.80,
and 0.50. According to the Redlich-Kwong equation of state,24
the corresponding fugacity coefficient is not far from 1. Thus
the deviation from the ideal-gas approximation does not account
for the small xHCOOH(eq). Another reason can be considered as
described below. It has been often observed that formic acid
decomposes beyond the equilibrium limit (chemical-potential
crossover) and then very slowly recovers through the backward
reaction involving the liquid-gas distribution of CO; thus the
formic acid concentration oscillates. The oscillation is more
likely to occur when the initial concentration of formic acid is
as high as 1.0 mol kg-1 and at the same time HCl accelerates
the decarbonylation. Probably the oscillation is caused from the
delay of the dissolution of CO against the decarbonylation (the
assumption of the fast equilibrium of the dissolution is not valid).
When the oscillation takes place, a longer time is required for
the system to attain the true equilibrium state, making an accu-
FT
KCO
)
QCO
(18)
KD(CO)(1 - FT) + FT
On the basis of this equation, we can determine KCO by
(eq)
measuring the equilibrium mole fraction xHCOOH of formic
acid under a given filling factor FT. We can evaluate QCO in
(eq)
eq 18 from eq 11; xCO
) 1 - xHCOOH(eq). Values of the
equilibrium constant KCO as the average of two measurements
(13 measurements for 240 °C) of different filling factors are
listed in Table 1 at 170-280 °C.
Equation 18 is also viewed as an expression for the variation
(eq)
of xHCOOH with the filling factor FT. Solving eqs 11 and 18
with respect to xHCOOH(eq), we obtain
1
(eq)
xHCOOH
)
(19)
K
COKD(CO)
(eq)
KCO + 1 - KCOKD(CO) +
rate determination of xHCOOH almost impossible. The equi-
FT
librium constant KCO was successfully determined at such dilute
formic acid concentrations as 0.04 and 0.16 mol kg-1
.
The equilibrium fraction xHCOOH(eq) is a monotonically increasing
function of FT. When the filling factor is small (a small fraction
of the reactor volume is occupied by the reaction solution), the
equilibrium apparently favors the CO side of eq 11. This is
because the CO produced by the decarbonylation escapes into
the gas phase and induces further decomposition of formic acid.
When FT approaches the maximum value of 1 (fully filled), the
equilibrium fraction steeply rises to the limiting value of 1/(KCO
+ 1), resulting in QCO ) KCO. Note that eq 19 holds only when
the reaction solution is so dilute that the assumptions for the
formulation of eqs 14 and 15 are valid.
The equilibrium constants KCO at 170-280 °C are listed in
Table 1, and the van’t Hoff plot of the decarbonylation is shown
in Figure 6. The enthalpy change of the decarbonylation ∆HCO
may be defined along the saturation curve as
∆HCO
)
∂ ln(KCO[H2O])
∂ ln KCO ∂ ln [H2O]
-R
) -R
+
(20)
(
)
∂(1/T)
∂(1/T)
∂(1/T)
Here, the partial differentiation is done along the saturation curve
instead of constant pressure. According to the van’t Hoff plot
and the equation of state for water, ∆HCO is obtained as 58
The equilibrium fraction xHCOOH(eq) of formic acid is plotted
against FT at 240 °C in Figure 5. There are included results for

Formic Acid Decomposition
J. Phys. Chem. A, Vol. 110, No. 38, 2006 11087
The difference between KCO and QCO is also striking in their
temperature dependence. As the temperature dependence of KCO
is expressed by the enthalpy change ∆HCO, we define the
corresponding quantity for QCO as
∂ ln(QCO[H2O])
∆H′CO ) -R
(21)
∂(1/T)
where again the partial differentiation is along the saturation
curve. By virtue of eqs 18 and 20, it follows that
∂ ln KD(CO)
∂(1/T)
1
∆H′CO ) ∆HCO - R
1 +
)
FT
Figure 6. The van’t Hoff plots of the equilibrium constants KCO and
KD(CO). The filled circles indicate KCO, and they are fitted to the solid
line. The slop of the solid line gives the enthalpy change of the
decarbonylation ∆H ) 58 ( 6 kJ mol-1. The dashed line represents
KD(CO) taken from ref 15.
KD(CO)(1 - FT)
1
∆HCO
+
∆HD (22)
FT
1 +
KD(CO)(1 - FT)
where the value of FT is fixed and ∆HD is the dissolution
enthalpy of CO. KD(CO) ) 8.4 at 280 °C and is larger at lower
temperatures. In this case, the coefficient of ∆HD in eq 22 is
approximately unity except for a very high filling factor, thus
we have ∆H′CO ) ∆HCO + ∆HD and ∆HD ) -24 kJ mol-1
.
Therefore, the apparent enthalpy change of the decarbonylation
is ∼40% smaller in magnitude than the thermodynamic one due
to the coupling of the dissolution equilibrium heat of CO. It
should be noted that the product yields of such a reaction in
subcritical water are modified by the liquid-gas distribution
of gases.
3.3. Decarbonylation Kinetics without HCl. In the absence
of strong acid, the decarbonylation is considered to be driven
by the proton dissociated from formic acid.23 The acid dissocia-
tion constant of formic acid, Ka, leads to the expression for the
proton concentration in formic acid solution as
Figure 7. The temperature dependence of QCO. Each of the contours
corresponds to a fixed filling factor FT indicated in the figure. The
dashed line corresponds to the filling factor of 1 (totally filled), where
QCO ) KCO
.
( 6 kJ/mol. Using the heat of formation and the heat capacity
of gaseous CO, CO2, and H2O,25,26 the enthalpy change for the
gas-phase reaction is 28 kJ mol-1 at 250 °C. This means that
the enthalpy difference between the initial (HCOOH) and the
final (CO + H2O) states is increased by ∼30 kJ mol-1 due to
the solvation of each species and the condensation of water.
The dissolution heat of gaseous formic acid is expected to be
considerably larger than the condensation heat of water (45 kJ
mol-1 at 30 °C). Matubayasi et al. calculated the free energies
of the formic acid and carbon monoxide in hot water and derived
the equilibrium constant of the decarbonylation at 25-400 °C.8
The enthalpy change obtained by the temperature differentiation
of the equilibrium constant is somewhat smaller (∆HCO ) 23
kJ mol-1) than the experimental one. This magnitude of dis-
crepancy is reasonable as the calculated values of the standard
[H+] ) [HCOOH]K
(23)
x
a
Here we have neglected the activity coefficients for the ions.
Combining eqs 8 and 23, we have the decarbonylation rate in
the absence of strong acid as follows:
d[HCOOH]
-
) k+1 K [HCOOH]1.5
(24)
x
a
dt
It is important to confirm the reaction order 1.5 that comes from
the second-order rate expression given by eq 8. The formic acid
concentration was varied over a wide range of 0.44-2.9 mol
kg-1 at 240 °C. The filling factor Fr was sufficiently small (0.50)
so that the backward reaction may be neglected. We have plotted
the logarithm of the initial rate of the decrease of formic acid
against the logarithm of the initial concentration of formic acid
(Figure 8). The experimental results are fitted to a straight line,
and its slope gives the rate order with respect to formic acid as
1.6 ( 0.1. This is consistent with the expression of eq 24,
supporting the validity of eq 8. The dependence of the reaction
rate on the concentration of formic acid is larger in the absence
of HCl than that in the presence.
free energy of reaction differ by ∼2 kcal mol-1
.
We have determined KCO and discussed the thermodynamic
property of the decarbonylation. On the other hand, the
decarbonylation quotient QCO is more useful for practical use,
since it is directly related to the product yield as eq 11. Now
we can demonstrate how the decarbonylation quotient QCO is
controlled by the temperature and the filling factor by using
KCO obtained above from eq 18. The result is plotted against
the temperature in Figure 7 for FT ) 0.30, 0.50, 0.80, 0.90, and
1. When the filling factor is lowered, the equilibrium shifts to
the CO side; a large portion of the CO produced by the
decarbonylation is accommodated not in the liquid phase but
in the gas phase.
In the absence of HCl, the apparent rate constant k+1(Ka)1/2
of eq 24 allows us to approximately evaluate the pKa of formic
acid by the reaction-rate measurement; note that the value of
k+1 is already determined in section 3.1. The values of pKa are
listed in Table 1 in the temperature range of 200-300 °C along
the liquid branch of the saturation curve. The pKa value at

11088 J. Phys. Chem. A, Vol. 110, No. 38, 2006
Yasaka et al.
Figure 8. The logarithm-logarithm plot of the initial rate V+1 of the
decarbonylation at 240 °C against the initial formic acid concentration
[HCOOH]0. The solid line is the linear fit of the experimental data,
and its slope is 1.6 ( 0.1.
200 °C (4.2) is similar to that at 30 °C (pKa ) 3.75).27 As the
temperature rises to 300 °C, the acidity of formic acid decreases
by a factor of 10. The decrease of the acidity between 200 and
300 °C is qualitatively in agreement with the behavior of the
dielectric constant ꢀr; ꢀr ) 35 and 20 at 200 and 300 °C, respec-
tively. Between room temperature and 200 °C, pKa seems to
change weakly with temperature. This indicates the compensa-
tion of the decrease in solvation energy and the increase in the
entropy term with increasing temperature from 30 to 200 °C. It
is known that the dissociation of formic acid is weakly depend-
ent on the temperatures in ambient conditions. According to
the precise electrochemical measurements, pKa varies only by
0.06 pKa unit in the temperature range of 0-60 °C with a
shallow minimum at around 25 °C.27
3.4. Decarboxylation Kinetics and Equilibrium. Now we
proceed to the kinetic study of the decarboxylation. In the de-
composition of sodium formate in hot water, the decarboxylation
is the dominant pathway as shown in Figure 9a. This indicates
that the ionic species HCOO- is involved in the decarboxyla-
tion,28 and the following simple rate law is expected:
Figure 9. The time evolution of the reactant and product yields for
the decomposition at 240 °C and FT ) 0.95 of (a) HCOONa at 1.0 mol
kg-1 and (b) HCOOH at 1.0 mol kg-1 with HCl at 0.10 mol kg-1
.
where Ka is the acid dissociation constant of formic acid, cT )
[HCOOH] + [HCOO-], the stoichiometric concentration of
formic acid, and R ) [HCOO-]/cT, the degree of dissociation
of formic acid. The first term is important in strongly acidic
conditions where the acid dissociation of formic acid is
suppressed; V+2 f kacidKacT as R f 0. The second term, in turn,
is important for the reaction of sodium formate where R ≈ 1.The
rate law (eq 27) predicts that the decarboxylation rate is
independent of the concentration of HCl added to formic acid;
formic acid is a weak acid and its dissociation is negligible in
the presence of HCl. This is indeed what is observed experi-
mentally; the decarboxylation rate of formic acid at 1.0 mol
kg-1 with HCl at 0.080 mol kg-1 was equal (within the
experimental error) to that of formic acid at 1.0 mol kg-1 with
d[CO2]
) V+2 ) k[HCOO-]
(25)
dt
However, eq 25 is found to contradict the decarboxylation rate
of formic acid in the presence of HCl. In such acidic conditions,
where a small fraction of formic acid dissociates to HCOO-,
the decarboxylation rate is observed to be still of the same order
of magnitude with that of sodium formate in aqueous solution;
compare Figure 9a and Figure 9b. The weak pH dependence of
the decarboxylation rate can be explained in the following way.
We assume that the decarboxylation through HCOO- is induced
by both the acid and the neutral water molecule. Thus the rate
law is written as
HCl at 0.020 mol kg-1
.
Maiella et al.4 performed kinetic analysis of the decarboxyla-
tion based on a different reaction mechanism. They assumed
that the species HCOOH and HCOO- simultaneously decar-
boxylate with respective rate constants, and the total decarbox-
ylation rate is given by the sum. McCollom et al. also adopted
this assumption.13 The rate law derived is coincident in form to
eq 27 despite the difference in the reaction mechanism. It is
therefore of interest to do a computational study on the transition
state for distinguishing the reaction mechanism.28
V+2 ) kacid[H+][HCOO-] + kwater[HCOO-]
(26)
The rate constants kacidKa and kwater are determined, respec-
tively, by measuring the decarboxylation rate in strongly acidic
and basic conditions, according to eq 27. The results obtained
are summarized in Table 2. The precision of the rate constant
is relatively low (∼10%) because the 13C NMR measurement
lacks an internal reference. In addition, the surface of the quartz
tube is corroded in basic conditions and the reaction analysis
can be carried out only at an early stage. Two rate constants
where kacid and kwater are, respectively, the rate constants for
the acid-induced and water-induced decarboxylation. The
reactivity of the neutral water molecule is revealed by kinetic
studies on recently found hydrothermal reactions.14 In order to
clarify the pH dependence of the decarboxylation rate given by
eq 26, it is useful to rewrite eq 26 as
k
acidKa and kwater are of the same order. This indicates that the
V+2 ) kacidKa[HCOOH] + kwater[HCOO-] )
decarboxylation rate changes only weakly with pH in contrast
to the decarbonylation. The magnitude relation between kacidKa
k
acidKacT(1 - R) + kwatercTR (27)

Formic Acid Decomposition
J. Phys. Chem. A, Vol. 110, No. 38, 2006 11089
calculations by McCollom et al.13 and statistical-mechanical
calculations.8
3.5. Control of Water-Gas-Shift Reaction. In the previous
sections, we have established the kinetics and equilibrium of
the decarbonylation and the decarboxylation of formic acid
which constitute the hydrothermal water-gas-shift (WGS) reac-
tion. Based on the above analysis, here we propose a scheme
for controlling the WGS reaction for hydrogen storage in the
form of formic acid.
The most important feature of the hydrothermal WGS reaction
is the existence of the intermediate, formic acid. When the time
scales of the decarbonylation and the decarboxylation are
separated, the WGS reaction can be regarded as a stepwise
reaction and it is possible to isolate the intermediate (formic
acid) from the reaction mixture before the second slow step
initiates. In the presence of HCl, the decarbonylation has a much
shorter time scale than does the decarboxylation. In this case,
the process for hydrogen production from carbon monoxide can
be divided into two parts: the production of formic acid which
can be used as a compact and handy hydrogen source, and the
hydrogen supply from formic acid when hydrogen energy is
needed. The first part is the reverse decarbonylation, and the
second is the decarboxylation. The conversion ratio of the former
process (formic acid production) is governed by the quotient
Figure 10. The time evolution of the reactant and product yields for
the decomposition of 1.0 mol kg-1 formic acid at 330 °C and FT ≈
0.99 (the volume of the gas phase is negligible). The temperature is
too high to follow the decarbonylation kinetics. Note that the graduation
of the ordinate is changed at 0.13.
TABLE 2: The Rate Constants kacidKa and kwater in the
Temperature Range of 200-330 °C on the Liquid Branch of
the Saturation Curve
T/°C
log(kacidKa/s-1
)
log(kwater/s-1
)
200
230
240
260
280
300
330
-6.6
-5.7
-6.1
-5.9
-5.4
-4.6
-4.1
QCO mentioned in section 3.3, and more formic acid is yielded
-6.4
-5.5
-4.9
-4.3
-3.4
(small QCO) at a lower temperature and/or a higher filling factor,
as seen from Figure 7. For the latter process (the decarboxylation
of formic acid), the equilibrium constant KCO2 is relatively large
(∼100 at 330 °C) and formic acid can be converted into CO2
+ H2 almost completely. The hydrogen-generating process
should be carried out in weakly acidic conditions so that the
decarboxylation may be the main decomposition path of formic
acid. Basic conditions are, however, not appropriate, because
basic conditions will stabilize the reactant (formic acid) in the
form of the formate anion; formic acid is by far a stronger acid
than CO2. In addition, to run the reaction sufficiently fast for
practical use, a catalyst such as a common stainless steal
SUS316 can be introduced.
and kwater changes at ∼280 °C, and at the higher temperature of
∼330 °C, kwater overwhelms kacidKa. The smaller temperature
dependence of kacidKa than that of kwater can result from the
decrease of Ka with temperature (Table 1). Taking advantage
of the different pH dependence of the decarbonylation and decar-
boxylation rates, the path control of the hydrothermal decom-
position of formic acid can be realized. The decarbonylation is
the major path in acidic conditions due to the catalytic effect
of the proton, while the decarboxylation becomes dominant
when pH > 4.
4. Conclusions
Here we mention the decarboxylation equilibrium. We have
followed the decarboxylation for a sufficiently long time and
showed the time evolution of products at 330 °C as in Fig-
ure 10. As can be seen, the fast decarbonylation attains the
equilibrium within an hour, and this preequilibrium is maintained
(xCO/xHCOOH ∼ 5) during the course of the slow decarboxylation.
The parallel decrease of formic acid and carbon monoxide
almost stops at ∼20 h, and this indicates that the decarboxylation
equilibrium is attained. The equilibrium yield of each component
is 0.96, 0.78, 0.04, and 0.007 for CO2, H2, CO, and HCOOH,
respectively. The yield of hydrogen is too small compared with
that of CO2, and it is due to the leakage of hydrogen through
the reactor walls (the time scale of the leakage is estimated to
be ∼100 h from long-time experiments). The equilibrium
constant of the decarboxylation is defined by
We have succeeded in establishing the kinetics and the
equilibrium of the decomposition of formic acid, the WGS
reaction intermediate, on the basis of the NMR spectroscopic
analysis of the reactant and products. First the catalytic effect
of acid on the decarbonylation is quantitatively analyzed, and
it is found that the decarbonylation rate is first-order with respect
to the concentration of formic acid and the proton, respectively.
The equilibrium of the decarbonylation has been investigated
under strongly acidic conditions where the competitive decar-
boxylation is negligibly slow. In determining the equilibrium
constant of the decarbonylation, we have formulated the effect
of the filling factor (the ratio of the liquid-phase volume to the
total reactor volume) on the product yield. The equilibrium
constant of the decarbonylation varies from 0.15 to 4.2 as the
temperature rises from 170 to 280 °C on the liquid branch of
the saturation curve, and this indicates that the decarbonylation
can be controlled either to the formic acid side or to the CO
side depending on the temperature and the filling factor. The
low temperature and the high filling factor shift the equilibrium
to the formic acid side. As for the decarboxylation path, the
pH dependence of the reaction rate suggests that the decar-
boxylation consists of acid-induced and water-induced pathways,
where the former is dominant in acidic conditions and the latter
in basic conditions. The difference in the pH dependence
[CO2]liq[H2]liq
KCO2
)
(28)
|
[HCOOH]liq
eq
By taking account of the liquid-gas distribution of H2 and CO2
in the same way as that described in section 3.2, the value of
K
CO2 at 330 °C is estimated to be 1 × 102 mol kg-1. Our result
shows that the decarboxylation equilibrium strongly favors the
CO2 side, and this is consistent with the thermodynamic

11090 J. Phys. Chem. A, Vol. 110, No. 38, 2006
Yasaka et al.
(18) Ferna´ndez-Prini, R.; Alvarez, J. L.; Harvey, A. H. J. Phys. Chem.
Ref. Data 2003, 32, 903.
between the decarbonylation and the decarboxylation makes it
possible to kinetically control the decomposition product of
formic acid by the pH of the solution; the decarbonylation is
dominant in acidic conditions, while the decarboxylation is dom-
inant in basic conditions.
The detailed knowledge of the decarbonylation and the
decarboxylation has provided a scheme for controlling the water-
gas-shift reaction. We have proposed two examples of applica-
tion taking advantage of the existence of the reaction interme-
diate in the form of formic acid. One is the storage of hydrogen
energy as formic acid. The reaction conditions ideal for the
conversion of CO into formic acid are (i) a relatively low
temperature of ∼200 °C, (ii) addition of such a strong acid as
HCl, and (iii) a high filling factor. The other possible application
is the fixation of CO2 as formic acid through the reverse
decarboxylation in basic conditions.
(19) The amount of CO produced by the decomposition of HCOONa
at 1 mol kg-1 and 240 °C for 300 h was below the detection limit of 0.01
mol kg-1. This means that the decarbonylation rate of HCOONa is not larger
than 10-8 mol kg-1 s-1, which is 104 times as small as that of HCOOH
with 0.10 mol kg-1 HCl. The concentrations of the proton and the neutral
formic acid HCOOH in eq 8 can be estimated from the dissociation constant
of formic acid presented in section 3.3; [H+] ) ∼10-8 mol kg-1and
[HCOOH] ) 10-5 mol kg-1. Thus eq 8 is consistent with the slow
decarbonylation rate observed for HCOONa.
(20) Blake, P. G.; Hinshelwood, C. Proc. R. Soc. London, Ser. A 1960,
255, 444.
(21) Takahashi, H.; Hisaoka, S.; Nitta, T. Chem. Phys. Lett. 2002, 363,
80.
(22) Hori, T.; Takahashi, H.; Nitta, T. J. Comput. Chem. 2003, 24 (2,
Jan 30), 209-221.
(23) In hydrothermal conditions, the undissociated form of the water
molecule often plays an active role in determining the reaction pathway.
Indeed, it was demonstrated experimentally that the reaction proceeds
without acid or base in a practical time scale for ether and C1 chemical
reaction.14,15 Correspondingly, several theoretical works investigated the
role of the undissociated form of water in sub- and supercritical water
reactions, and proposed concerted mechanisms which are not catalyzed by
acid or base.9-11,21 In the present work, however, the reaction pathway does
not correspond to the one suggested by Yagasaki et al.11 As shown in the
text, the reaction rate is proportional to the [H+] present in the system. The
reaction pathway corresponding to the neutral, concerted transition state
was not observed within our experimental time scale. The reaction solution
(1 mol/kg HCOOH) is quite acidic (pH ) 2-3) even in the absence of
HCl, and the acid-induced path still overwhelms the neutral concerted path.
This has been strongly supported by the observed rate order of 1.5 for the
decarbonylation in the absence of HCl as shown in section 3.3. If the reaction
is carried out in higher pH conditions and/or at higher temperatures where
the acid dissociation is suppressed, then the neutral reaction path can be
possible. It has not yet been theoretically done to compare the reaction
mechanisms involving the formate ion and the proton.
Acknowledgment. This work is supported by a Grant-in-
Aid for Scientific Research (Nos. 15205004 and 18350004) from
Japan Society for the Promotion of Science, by a Grant-in-Aid
for Scientific Research on Priority Areas (No. 15076205) and
a Grant-in-Aid for Creative Scientific Research (No. 13NP0201)
from the Ministry of Education, Culture, Sports, Science, and
Technology, and by ENEOS Hydrogen Trust Fund.
References and Notes
(1) Tsujino, Y.; Wakai, C.; Matubayasi, N.; Nakahara, M. High-
Pressure Sci. Technol. 1999, 9, 66.
(2) Yu, J.; Savage, P. E. Ind. Eng. Chem. Res. 1998, 37, 2.
(3) Bjerre, A. B.; Sorensen, E. Ind. Eng. Chem. Res. 1992, 31, 1574.
(4) Maiella, P. G.; Brill, T. B. J. Phys. Chem. A 1998, 102, 5886.
(5) Bro¨ll, D.; Kaul, C.; Kra¨mer, A.; Richter, T.; Jung, M.; Vogel, H.;
Zehner, P. Angew. Chem., Int Ed. 1999, 38, 2998-3014.
(6) Wakai, C.; Yoshida, K.; Tsujino, Y.; Matubayasi, N.; Nakahara,
M. Chem. Lett. 2004, 33, 572.
(7) Yoshida, K.; Wakai, C.; Matubayasi, N.; Nakahara, M. J. Phys.
Chem. A 2004, 108, 7479.
(8) Matubayasi, N.; Nakahara, M. J. Chem. Phys. 2005, 122, 074509.
(9) Melius, C. F.; Beergan, N. E.; Shepherd, J. E. Symp. (Int.) Combust./
Combust. Inst., 23rd 1990, 217-223.
(10) Akiya, N.; Savage, P. E. AIChE J. 1998, 44, 405-415.
(11) Yagasaki, T.; Saito, S.; Ohmine, I. J. Chem. Phys. 2003, 118, 2446.
(12) Kroschwitz, J. I. Encyclopedia of Chemical Technology, 4th ed.;
Wiley: New York, 1991.
(13) McCollom, T. M.; Seewald, J. S. Geochim. Cosmochim. Acta 2003,
67, 3625.
(14) Morooka, S.; Wakai, C.; Matubayasi, N.; Nakahara, M. J. Phys.
Chem. A 2005, 109, 6610.
(15) Nagai, Y.; Morooka, S.; Matubayasi, N.; Nakahara, M. J. Phys.
Chem. A 2004, 108, 11635.
(24) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The properties of gases
and liquids, 4th ed.; McGraw-Hill: New York, 1987.
(25) Wagman, D. D.; et al. J. Phys. Chem. Ref. Data 1982, 2, Suppl. 2.
(26) Gurvich, L. V.; Veyts, I. V.; Alcock, C. B. Thermodynamic
Properties of IndiVidual Substances Fourth Ed. Volume 1, O, H (D, T), F,
Cl, Br, I, He, Ne, Ar, Kr, Xe, Rn, S, N, P and Their Compounds;
Hemisphere: Bristol, PA, 1989.
(27) Harned, H. S.; Owen, B. B. The Physical Chemistry of Electrolyte
Solutions; Reinhold Publishing Corporation: New York, 1958.
(28) For the decarboxylation mechanism, the neutral, concerted pathway
was suggested and theoretically studied by Yagasaki et al.11 Based on this
reaction mechanism, the rate law for the decarboxylation is modified from
eq 26 to V+2 ) k′[HCOOH] + k′′[HCOOH][OH-], where k′ and k′′ are rate
constants for the water-catalyzed and base-catalyzed paths, respectively.
This rate law can be shown to be coincident with eq 26 by using the acid
dissociation constant as follows: V+2 ) k′Ka-1[HCOO-][H+] + k′′Ka-1Kw-
[HCOO-], where Kw is the self-dissociation constant of water. This means
that it is impossible to distinguish the reaction mechanisms experimentally.
Theoretical studies including water and neutral formic acid have been carried
out by Yagasaki et al.,11 and now additional studies including ionic species
(H+, HCOO-, and OH-) are required.
(16) Release on the IAPWS Formulation 1995 for the Thermodynamic
Properties of Ordinary Water Subtances for General and Scientific Use.
(17) If the decoupling is not performed, the 13C peak corresponding to
H13COOH has a line shape far from Lorentzian and is not suitable for
quantitative analysis.