Comprehensive study of the hydration and dehydration reactions of carbon dioxide in aqueous solution

Article abstract of DOI:10.1021/jp909019u

The reversible interactions of dissolved CO₂ with H₂O and OH- to form H₂CO₃ and HCO3- in aqueous solution have been investigated using spectrophotometric stopped-flow measurements. The progress of the reactions

Full text of DOI:10.1021/jp909019u

1734
J. Phys. Chem. A 2010, 114, 1734–1740
Comprehensive Study of the Hydration and Dehydration Reactions of Carbon Dioxide in
Aqueous Solution
Xiaoguang Wang,* William Conway, Robert Burns, Nichola McCann, and Marcel Maeder*
Discipline of Chemistry, UniVersity of Newcastle, Callaghan NSW 2308, Australia
ReceiVed: September 18, 2009; ReVised Manuscript ReceiVed: December 3, 2009
-
The reversible interactions of dissolved CO2 with H2O and OH- to form H2CO3 and HCO3 in aqueous
solution have been investigated using spectrophotometric stopped-flow measurements. The progress of the
reactions was monitored via indicators coupled to the pH changes during the reactions. The study, involving
global analysis of the complete data set, spanned the temperature range 6.6-42.8 °C and resulted in the
evaluation of all rate and equilibrium constants as well as activation parameters for the kinetic data and the
reaction enthalpies and entropies for the equilibrium constants.
Introduction
There is little doubt that the dissolution of CO2 in water,
facilitated by the formation of carbonic acid and carbonate
species, is a fundamentally important process for the planet and
associated life.1-4 It is thus not surprising that there is a long
history of research with the goal of quantitatively investigating
all individual reactions relevant to the overall process.5-22 There
are two reversible reactions of CO2(aq) with water and with
hydroxide to form carbonic acid and bicarbonate, eqs 1a and
1b, respectively. In addition there are three protonation equi-
Figure 1. Reaction scheme of CO2(aq) in aqueous solution.
libria, the protonation of carbonate, of bicarbonate, and of
hydroxide ion, eqs 1c-1e.23
a pH-stat,17 manometric measurements,14,18 and stopped-flow
studies.7-9,11,12,14,16 Under some conditions, the reactions are fast,
CO2(aq) + H2O { k } H2CO3
(1a)
(1b)
(1c)
1
and there is no doubt that stopped-flow measurements are the
most suitable for this investigation. Whereas stopped-flow
measurement using conductivity detection is also fast, the signal
is not specific because it is a linear combination of the
contribution of several ions, many of them not taking part in
the reaction.7 A very powerful technique is to couple the
protonation equilibria to an appropriate indicator and observe
the pH changes spectrophotometrically.8,9,11,12,14,16 In most in-
vestigations, solutions have been buffered to facilitate the
analysis of the measurements. However, buffers have been found
to catalyze some of the above reactions, and thus it is undesirable
to add buffer solution in the hydration of CO2(aq).8,18 There is
one exception, where Soli and Byrne12 obtained the two rate
constants by a spectrophotometric stopped-flow technique
without adding any buffer solution. In this case, approximations
were made in the derivation of the rate equations, and no attempt
was made to determine the rate constants for the hydroxide path.
The kinetics of the reversible reaction of CO2(aq) with the
hydroxide ion, eq 1b, has not been well investigated. With an
increase in pH, the hydroxide path gains in importance, and it
predominates above pH 8.5. It is also known that the reaction
of CO2 with hydroxide has a significant biological role in blood
pH regulation and the transportation of CO2 in living systems.3,25,26
k-1
k2
-
CO2(aq) + OH- { } HCO3
k-2
Ka1
2-
-
CO3 + H+ { } HCO3
Ka2
-
HCO3 + H+ { } H2CO3
(1d)
(1e)
OH- + H+ {KW} H2O
The equilibria with only an equilibrium constant are treated as
instantaneous protonation equilibria; those with two rate con-
stants are treated as observable reactions. Figure 1 represents
the complete reaction scheme in aqueous solution but excludes
the mass transfer of gaseous CO2 between the liquid and gas
phases.
Most published research has concentrated on the water path,
eq 1a. Several techniques or methods have been used to obtain
the two rate constants k1 and k-1, including isotopic exchange,15,24
Interestingly, however, there are no kinetic data available at
7,13,14,17
physiologically significant temperatures for k2 and k-2
.
In this article, the kinetics of the water and hydroxide paths
with CO2(aq) is comprehensively investigated by the stopped-
flow technique in the temperature range from 6.6 to 42.8 °C.
Depending on the pH of the reacting solution, thymol blue or
* Corresponding authors.
10.1021/jp909019u  2010 American Chemical Society
Published on Web 12/29/2009

Hydration and Dehydration Reactions of CO2
J. Phys. Chem. A, Vol. 114, No. 4, 2010 1735
methyl red indicators were used. The four rate constants at the
five different temperatures are derived using global data analysis
software.27,28 Activation energies and enthalpies and entropies
of activation were obtained on the basis of Arrhenius and Eyring
relationships. Van’t Hoff analysis of the temperature dependence
of the equilibrium constants resulted in reaction enthalpies and
entropies.
Advanced data analysis software proved crucial; it allowed
the omission of buffers and inert salts to maintain constant pH
and ionic strength. The changes in these values were incorpo-
rated into the computations required for the data fitting.27-29
systems of differential equations have no explicit solution.
Numerical integration is straightforward; however, as the pH
changes during the reaction, special attention is required, and
standard packages cannot be employed. Consider, as an example,
the differential equation for CO2(aq)
δ[CO2(aq)]
) -k1[CO2][H2O]-k2[CO2][OH-] +
δt
-
k-1[H2CO3] + k-2[HCO3 ] (2)
-
Here the species OH-, H2CO3, and HCO3 undergo equilibria
Experimental Section
instantaneously, and the equilibrium composition needs to be
computed continuously to calculate the derivatives such as in
eq 2.28 The relevant protonation constants are KW, Ka1, and Ka2,
as defined in eqs 1c-1e. In addition, the protonation constant
of the indicator (Kind in eq 3) has to be included.
High purity CO2 gas (BOC), N2 (Core Gas), analytical grade
sodium carbonate (Merck, 99.9%), sodium hydroxide (Merck),
potassium hydrogen phthalate (KHP, Ajax Chemicals), thymol
blue (Sigma-Aldrich, ACS reagent), methyl red (M&B Labora-
tory Chemicals), and hydrochloric acid (Ajax Chemicals) were
used without any further purification. The concentration of
sodium hydroxide stock solution was standardized by KHP,
whereas the concentration of hydrochloric acid stock solution
was determined by the standardized sodium hydroxide. Ultrahigh
purity Milli-Q water was boiled to remove CO2 gas. All samples
were prepared and stored in a nitrogen-purged glovebag.
The kinetics of hydration of CO2 and that of dehydration of
Ind + H+ {KInd} IndH+
(3)
Debye-Hu¨ckel approximations for activity coefficients for all
ionic species have been implemented. The approximations are
based on the expression
-
H2CO3/HCO3 were performed on an Applied Photophysics
DX-17 spectrophotometer equipped with a J&M Tidas MCS
500-3 diode-array detector. All pH changes were observed over
the wavelength range 400-700 nm via coupling to thymol blue
or methyl red indicators. The reactions were studied over the
temperature range of 6.6-42.8 °C. Samples were thermostatted
to within (0.1 °C, and the exact temperature was recorded via
a thermocouple within the stopped-flow apparatus.
2
√
-Azi µ
log γi )
(4)
√
1 + µ
Here γi is the activity coefficient, zi is the charge of the ith ion,
A has a value of 0.242 for aqueous solutions, and µ is the ionic
strength of the solution. Therefore, activities for all species
instead of concentrations are used throughout the computations,
for example, in eq 2 and eqs 1a-1e. For the low concentrations
used in this study, the approximations are reasonably accurate.
Global Analysis. All of the reactions are intimately inter-
twined so that they cannot be investigated or analyzed individu-
ally. Global analysis of series of measurements acquired at one
temperature under different conditions to reveal information
about all aspects of the total reaction mechanism is the most
obvious method for this investigation. We have introduced
global analysis30 and successfully employed this technique in
other investigations.31 In fact, for the present investigation, at
each temperature, a set of five forward reactions, type (a), and
four back reactions, type (b), were analyzed as one unit, resulting
in the fitted rate and equilibrium constants. Because there were
five replications of all measurements at each temperature,
resulting in five sets of fitted parameters, this allowed a proper
statistical analysis of the parameters.
The reversible interactions of CO2 with water/OH- to form
H2CO3/HCO3- were investigated by two series of measurements:
(a) for the hydration of carbon dioxide, water saturated with
CO2 (22-64 mM) was mixed with 4.0-36.0 mM Na2CO3 in a
1:1 v/v ratio. The reaction kinetics were monitored by the
absorbance change of thymol blue indicator; (b) for the
dehydration of carbonic acid/bicarbonate, 4.0-36.0 mM Na2CO3
solutions were mixed with 40 mM HCl solutions, again in a
1:1 v/v ratio. The reaction kinetics was monitored by the ab-
sorbance change of methyl red indicator.
All reactions were measured until equilibrium was completely
reached. Each measurement was performed five times, allowing
for standard deviations to be derived for the calculated rate
constants based on experimental statistics rather than error
estimates derived from the fitting procedures.
Data Analysis. Advanced data analysis is a critical element
of this work. Not one of the reactions can be observed and
analyzed individually, because all are intimately coupled, and
the process has to be regarded as a whole. In fact, it is best to
regard each measurement as an ensemble of reactions moving
from the initial conditions to a new equilibrium. Whereas there
are reactions that could theoretically be observed independently,
for example, the reaction of CO2 with water, eq 1a at low pH,
CO2 cannot be introduced into aqueous solution in the time
frame required for the process to be observed directly. In a
similar vein, the reaction of CO2 with OH- at high pH is much
faster than the water path and thus could be observed exclu-
sively, but at high pH, the pH changes are very small and
difficult to observe, notwithstanding the fact that the reaction
can be too fast to observe using stopped-flow technology.
The computation of the concentration profiles of all species
as a function of time is not possible explicitly because the
Parameters. The reaction scheme of Figure 1 encompasses
four rate constants and three equilibrium constants. Kw and Ka1
are not defined by our measurements, and their tempera-
ture-dependent values were taken from the literature.32-34
The protonation constant Ka2 for the bicarbonate is not
well established; however, the equilibrium CO2(aq)
+
H2O {K
\
} HCO3 + H+ is well known, and its equilibrium
3
-
constant is related to K1 and Ka2 as K3 ) K1/Ka2. In the fitting,
we defined Ka2 as a function of known K3 and both k1 and k-1
with Ka2 ) k1/(k-1K3). Furthermore, as a result of microscopic
reversibility, we defined k-2 as a function of known K3 and k2
and Kw, with k-2 ) k2/(KwK3). Therefore, there are three known
,

1736 J. Phys. Chem. A, Vol. 114, No. 4, 2010
Wang et al.
2-
Figure 2. Absorbance change at 600 nm with time in the reaction of 33 mM CO2(aq) with various concentrations of CO3 at 6.6 °C with 0.10
mM thymol blue (left); the absorbance change at 550 nm for the reaction between 20.0 mM HCl and various concentrations of CO32- at 6.6 °C in
the presence of 0.10 mM methyl red (right). Black lines: experimental; red dashed lines: fitted results.
2-
Figure 3. Calculated concentration profiles for the reaction of 33 mM CO2(aq) with 8 mM CO3 at 6.6 °C in the presence of 0.10 mM thymol
blue. The right-hand plot features a logarithmic concentration axis.
and fixed values for Kw, Ka1, and K3; there are three indepen-
dently variable and fitted values for k1, k-1, and k2.
Figure 2 shows the absorbance changes (at 550 nm) observed
in the dehydration of HCO3-/H2CO3 mixtures, which were
generated by the reaction of various concentrations of CO3
2-
We have treated the protonation of carbonate as an instan-
taneous equilibrium rather than a reversible reaction. This is
not completely accurate as the deprotonation reaction occurs
on a time scale similar to our fast measurements. However, the
value for this deprotonation reaction is not known. Furthermore,
numerical experimentation with reasonable rate constants for
this protonation equilibrium had only minor effects on the values
of all other rate and equilibrium constants. We decided to retain
the instantaneous protonation equilibrium for the analysis.
A set of secondary parameters was also required for the
modeling and fitting of the measurements; these included the
concentration of CO2 in water, which was based on saturated
solutions, as well as the protonation constants of those indicators
for which the temperature-dependent values are not published.
As will be discussed later, these parameters are well-defined
and consistent with published values for those available in the
literature.
with HCl.
There are several interesting observations. The absorbance
changes with time for the reaction of 33 mM CO2(aq) with different
concentrations of carbonate feature the surprising observations that
they resemble zeroth-order kinetics and that the reactions appear
to become progressively faster at lower carbonate concentrations.
The explanation lies in the fact that the reaction is followed by pH
change and not any of the actual reactants, and that increasing the
concentration of CO32- results in increased buffer action with
concomitant slower change in the free proton concentration.
The right part in Figure 2 shows the absorbance change at 550
nm with time for the reaction between 20.0 mM HCl and various
concentrations of CO32- at 6.6 °C in the presence of 0.10 mM
methyl red. The apparent autocatalytic behavior is again explained
by the fact that only pH changes are observed directly, rather than
the reactant concentrations.
Figure 3 displays the concentration profiles for the reaction
of 33 mM CO2(aq) with 8.0 mM Na2CO3 at 6.6 °C; it is the
middle trace represented in the left part of Figure 2. To give a
complete picture, the profiles in Figure 3 are also plotted with
a logarithmic concentration scale.
Results
Figure 2 represents a complete data set at 6.6 °C. The left-
hand side of Figure 2 features the absorbance changes (at 600
nm) for reactions of CO2 with CO32-; the right-hand side of

Hydration and Dehydration Reactions of CO2
J. Phys. Chem. A, Vol. 114, No. 4, 2010 1737
TABLE 1: Calculated Rate and Equilibrium Constants in the Hydration of CO2(aq) and Dehydration of Carbonic Acid at
Various Temperatures
T (°C) k1 (M-1 s-1
)
k1* (s-1
)
k-1 (s-1
)
k2 (M-1 s-1
)
k-2 (s-1
)
K1 (M-1
)
K1*
K2 (M-1
)
pKa2
6.6
8(2) × 10-5
4.5(9) × 10-3
15(2) × 10-3
37(2) × 10-3
112(4) × 10-3
236(7) × 10-3
4.2(1)
2.3(1) × 103 1.54(4) × 10-5 1.9(4) × 10-5
1.1(2) × 10-3 15.1(1) × 107 3.54(9)
1.5(3) × 10-3 7.59(1) × 107 3.59(8)
1.5(1) × 10-3 3.02(1) × 107 3.70(3)
1.7(1) × 10-3 1.28(1) × 107 3.52(2)
16.0 2.7(4) × 10-4
25.0 6.6(4) × 10-4
34.0 2.0(1) × 10-3
42.8 4.2(1) × 10-3
10.3(3)
4.2(3) × 103
5.6(3) × 10-5 2.6(4) × 10-5
40(1) × 10-5 2.7(2) × 10-5
24.8(4) 12.1(4) × 103
60(2) 25.0(2) × 103 107(1) × 10-5 3.4(2) × 10-5 1.86(5) × 10-3 2.35(1) × 107 3.58(1)
139(3) 48.8(8) × 103 381(7) × 10-5 3.0(1) × 10-5
TABLE 2: Calculated Activation Parameters and Enthalpies and Entropies of Reaction for the Hydration of CO2(aq) and
Dehydration of Carbonic Acid
Arrhenius
Ea (kJ mol-1
Eyring
∆Sq (J mol-1 K-1
van’t Hoff
∆Hø (kJ mol-1 ∆Sø (J mol-1 K-1
)
)
A
∆Hq (kJ mol-1
)
)
)
k1
81(2)
1.2(8) × 1011
9(2) × 1013
2(1) × 1014
3(3) × 1016
79(2)
-41(6)
14(2)
40(4)
63(7)
10(2)
-55(7)
CO2
98 H2CO3
k-1
71.6(6)
64(1)
69.1(6)
62(1)
H2CO3 8 CO2
k2
CO2 + OH- 98 HCO3
-
-50(1)
-23(5)
k-2
-
HCO3
8 CO2 + OH-
114(2)
112(2)
The rate constants, initial concentrations of CO2, and the log Ka
of the indicators are fitted to the measurement of the hydration of
CO2(aq) and dehydration of carbonic acid by using global data
analysis software. The experimental data are well fitted, as
demonstrated in Figure 2. The four calculated rate constants at
various temperatures (6.6, 16.0, 25.0, 34.0, and 42.8 °C) are listed
in Table 1, indicating, not unexpectedly, that the rates of the reaction
increase with temperature.
The reaction between CO2 and water is a second-order reaction
with water as one reactant. It is common to define this reaction as
a pseudo-first-order reaction, assuming the water concentration to
be constant at 55.6 M. We have adopted both notations in Table
1, where the constants of k1 and K1 are based on the second-order
reaction. (See Figure 1.) k1* and K1* are the corresponding pseudo-
first-order reactions.
the activation enthalpy, Sq is the activation entropy, Hø is the
enthalpy, and Sø is the entropy of the reaction.
The Eyring analysis for the rate constants is represented
graphically in Figure 4; the analogous Arrhenius plots can be
found in the Supporting Information (Figure 1). Both represen-
tations display excellent linear relationships with well-defined
slopes and thus activation energy, Ea, and activation enthalpy,
∆Hq. Intercepts are less well-defined, resulting in larger error
estimates for both A and ∆Sq.
The equilibrium constants, K1, for the formation of carbonic
acid from CO2 and water, and, K2, for the formation of
bicarbonate from CO2 and OH-, eqs 1a-1e, at the five different
temperatures are also listed in Table 1. A graphical representa-
tion is given in Figure 5. Figure 2 of the Supporting Information
displays our results in the context of published values for the
There is a competition between the reactions of CO2 with H2O
and with OH- to form carbonic acid or bicarbonate. The second-
order rate constant of the reaction of CO2 with OH- (k2 ) 12.1(4)
× 103 M-1 s-1 at 25 °C) is ∼107 times faster than that with H2O
(k1 ) 6.6(4) × 10-4 M-1 s-1 at 25 °C). As a result, at high pH,
the hydroxide path is faster, whereas at low pH, the water path is
faster, with the crossover pH of ∼8.5.
Table 2 lists the results of the analyses of the temperature
dependence of the rate constants in terms of the Arrhenius and
Eyring relationships as well as the analysis of the equilibrium
constants based on the van’t Hoff relationship, eq 5
-Ea
RT
Arrhenius:
Eyring:
k(T) ) A exp
k′T
(
)
∆Hq - T∆Sq
(5)
k(T) )
exp
(
)
h
RT
∆Hø
RT
∆Sø
R
van’t Hoff:
K(T) ) exp -
+
(
)
Figure 4. Eyring plot of ln(k/T) versus 1/T for the hydration of CO2(aq)
and dehydration of carbonic acid in the temperature range of 6.6 to
42.8 °C. Tilted squares represent the reaction with H2O, squares
represent the reaction with OH-, full markers represent the forward
reactions, and empty markers represent the back reactions.
In the above equations, A is a pre-exponential factor, R is the molar
gas constant, k′ is the Boltzmann constant, h is Planck’s constant,
T is the absolute temperature, Ea is the activation energy, ∆Hq is

1738 J. Phys. Chem. A, Vol. 114, No. 4, 2010
Wang et al.
Figure 5. Van’t Hoff plots for the equilibrium constants K1 and K2 (eqs 1a and 1b).
same equilibrium constants. The equilibrium constant K1
decreases marginally over the temperature range, whereas the
equilibrium constant K2 decreases significantly with temperature.
A van’t Hoff analysis of the data results in reaction entropies
and enthalpies, listed in Table 2.
The protonation constants (Ka2) of bicarbonate in the tem-
perature range from 6.6 to 42.8 °C were derived from data
fitting. The slope of log Ka2 versus 1/T is (80 ( 280), which
within the error limits, is zero. (See Figure 3 of the Supporting
Information for a graphical representation.) The protonation
constant is essentially constant in the above temperature range.
The second protonation constant, log Ka2, is not well-defined,
resulting in substantial scatter in Figure 3 of the Supporting
Information and also in the graphs for K1 (Figures 2 and 5 of
the Supporting Information), which are derived from published
values for K3 and log Ka2.
There are several auxiliary parameters that were fitted to the
measurements. They include the saturation concentration of CO2
at the five different temperatures and the temperature-dependent
protonation constants for the indicators thymol blue and methyl
red (eq 3). The calculated concentrations of CO2(aq) are in
excellent agreement with previous reports; for a graphical
representation, see Figure 4 of the Supporting Information.35,36
The protonation constants of thymol blue and methyl red were
obtained from the fitting of the kinetic data. They decrease with
the increase in temperature, with plots of log Ka versus 1/T
(Figure 5 of the Supporting Information) linear for both
indicators, and a van’t Hoff analysis results in ∆Hø ) 36(3)
and 20(1) kJ mol-1, and ∆Sø ) 19(10) and -108(4) J mol-1
K-1 for methyl red and thymol blue, respectively. These results
are consistent with published values,37,38 but no attempt was
made to review the complete literature on the temperature
dependence of these indicator protonation constants.
We start the discussion with the rate constants k1 and k-1 for
the water path. Figure 6 of the Supporting Information reveals
that there is no significant deviation between our values and
the collection of published rate constants; this is true for the
individual rate constants at the different temperatures, and as a
consequence, the activation parameters as well.
Visual inspection of Figure 6 of the Supporting Information
reveals a slight discrepancy for k2, the reaction between CO2
and OH-. In this case, the collection of published values seems
to be marginally lower by a factor of about two. No attempt
was made to quantify the relationship; however, considering
the difficulties in the determination of this fast rate constant
and the lack of available instrumentation some 50 years ago
when most of the values were published, the analysis presented
here is more likely the most reliable. Note, however, that the
activation parameters are not very affected. The situation for
k-2 is different insofar as there are very few published values
and, in particular, there is no published study of the temperature
dependence of this rate constant. Therefore, the activation
parameters for the reversible reaction of carbon dioxide with
hydroxide are novel. Visual inspection of Figure 6 of the
Supporting Information reveals no statistically significant dis-
crepancies between the few published values and our value.
Figure 6 shows a graphical representation of the reaction
energies and activation parameters for the water path and the
hydroxide path at 25 °C. For the water path (left), the
equilibrium is on the side of CO2 and water, with ∼0.1% of
dissolved CO2 existing as carbonic acid. For the hydroxide path
(right), the equilibrium is strongly on the bicarbonate side, with
essentially no free CO2 at high pH.
Activation entropies are relatively small for the water path
as only neutral molecules are involved. Therefore, upon
formation of the transition state from the starting materials, there
is a moderately small reduction of the entropy (-41 J mol-1
K-1), consistent with the reduction of the number of independent
molecules. This also suggests that CO2 is not highly hydrated.
Indeed theoretical studies (ab initio molecular dynamics, AIMD,
see also below) have shown that CO2 only coordinates weakly
to water O and H atoms through its C and O atoms, respectively,
and is effectively hydrophobic.23 The formation of carbonic acid
from the transition state occurs with an additional reduction of
entropy, which is explained by the creation of stronger hydrogen
bridging, as expected for carbonic acid.
In passing, it is noted that the excellent linear behavior of
the protonation constants of the indicators and the correct values
for CO2 solubility at the different temperatures are a strong
indication of the inherent robustness and thus correctness of
the global data analysis.
Discussion
The reversible hydration of CO2 in aqueous solution is a very
important and thus very well investigated reaction. Not surpris-
ingly, there is a considerable number of published values for
some of the rate constants, whereas for others, there are only a
few published values.
Entropy changes are much more pronounced for the hydrox-
ide path because ionic species are involved with strong
concomitant hydration effects. The complexity of the hydration

Hydration and Dehydration Reactions of CO2
J. Phys. Chem. A, Vol. 114, No. 4, 2010 1739
are expected to be small for the interaction of CO2 with H2O to
form carbonic acid because there are no ions involved (Figure 7
of the Supporting Information). Forward and back reactions for
the hydroxide path involve anions and thus ionic strength effects
are expected. Unfortunately, there are insufficient values for
similar plots for the other rate constants.
The temperature-dependent study and calculation of activation
parameters for the forward and reverse reaction between carbon
dioxide and water, and the forward and reverse reaction between
carbon dioxide and hydroxide enables the calculation of rate
constants at any temperature within the range 6.6-42.8 °C. The
excellent linear behavior of the Arrhenius and Eyring plots
would allow (with associated error) rate constants to be
calculated outside of this range, assuming that the behavior of
rate constants remains linear with temperature change.
Conclusions
Figure 6. Graphical representation of the reaction energies at 25 °C.
The left-hand side represents the water path, and the right-hand side
represents the hydroxide path at pH 14. Units are kJ mol-1 for ∆Gø
and ∆Hq and J mol-1 K-1 for ∆Sq.
Many important aspects of the reactions of dissolved CO2 in
aqueous solution at different pH values were well investigated,
and reliable rate and equilibrium constants are published; several
other aspects are not well known or not known at all. This is
the first comprehensive study of all of these linked reactions,
their temperature dependence, and thus their activation param-
eters. The stopped-flow methodology based on observation of
pH changes made observable via color changes of indicators is
significantly simpler than most published procedures and,
additionally, they are more direct than say conductivity, isotopic
exchange, or manometric measurements. Where available, our
results agree very well with published values, and this includes
secondary parameters such as the solubility of CO2 and
protonation constants of the indicators at the investigated
temperatures. The correct analysis of these secondary parameters
is a valuable confirmation of the entire procedure including the
data analysis. The novel set of values for the hydroxide path is
a valuable addition to the knowledge base of this important
group of reactions.
interactions renders the interpretation of entropy changes more
difficult. The most dramatic entropy change occurs for the
formation of the bicarbonate ion from the transition state,
indicating a strong increase in the hydration and hydrogen
bonding with the formation of the bicarbonate. Again, theoretical
calculations (AIMD) indicate that HCO3- is strongly hydrated,
with an average of 6.9 water molecules per anion.23 The increase
in entropy on the formation of the transition state from the
staring materials, CO2 and OH-, is explained by the release of
solvent molecules by the strongly hydrated hydroxide ion.
The validity of our activation parameters is supported by
several theoretical studies.23,39,40 Peng and Merz used molecular
dynamics free energy perturbation (MD-FEP) in an aqueous
environment to simulate the kinetics of the reaction of CO2(aq)
with hydroxide, k2, which gave a free energy barrier of 80.3 kJ
mol-1 at 25 °C.40 The CO2 · · ·OH- geometry and charge
distribution were obtained from large basis set ab initio gas-
phase calculations. More recently, Leung et al. computed the
aqueous-phase free energy difference of the reaction after
correcting ab initio molecular dynamics (AIMD) energies with
second-order Moller-Plesset perturbation theory (MP2) and
Acknowledgment. Financial support by a CSIRO Flagship
grant is acknowledged, as is a University of Newcastle RIB
grant, which allowed the purchase of the J&M Tidas MCS 500-3
diode-array detector.
Supporting Information Available: Experimental details
and several additional graphs. This material is available free of
charge via the Internet at http://pubs.acs.org.
found a standard state free energy barrier of 40.6 kJ mol-1 23
.
Therefore, our value of 50(1) kJ mol-1 at 25 °C is perfectly in
the range of the calculated results. Moreover, both theoretical
studies predict that solvation effects contribute to the high
activation energy. Solvation effects conform to our high value
of the entropy of activation as well. Our results also indicate
that the equilibrium constant of K1 depends slightly on tem-
perature, with a standard enthalpy of 10(2) kJ mol-1, which is
close to the ab initio SCF computations (3 kJ mol-1) of Jo¨nsson
et al.39
The protonation constants (Ka) of thymol blue and methyl
red were also obtained from our global kinetic data fitting. Both
decrease with the increase in temperature. The slopes of log
Ka2 versus 1/T gave the enthalpies with values of 36(3) kJ mol-1
for methyl red and 20(1) kJ mol-1 for thymol blue. It is known
that the pKa of the carboxyl group of several amino acids is
nearly independent of temperature, whereas the pKa of the amino
group decreases substantially with increasing temperature.41
The hydration reaction of CO2 (k1) has been investigated at
a range of ionic strengths, ranging from very small to 1.70 M
NaCl, the latter relevant for seawater. According to the
Debye-Hu¨ckel approximations, the effects of the ionic strength
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