Accurate rate constants for decomposition of aqueous nitrous acid

Article abstract of DOI:10.1021/ic202081z

Decomposition of nitrous acid in aqueous solution has been studied by stopped flow spectrophotometry to resolve discrepancies in literature values for the rate constants of the decomposition reactions. Under the conditions employed, the rate-limiting reaction step comprises the hydrolysis of NO ₂. A simplified rate law based on the known elementary reaction mechanism provides an excellent fit to the experimental data. The rate constant, 1.34 × 10^-6 M^-1 s^-1, is thought to be of higher accuracy than those in the literature as it does not depend on the rate of parallel reaction pathways or on the rate of interphase mass transfer of gaseous reaction products. The activation energy for the simplified rate law was established to be 107 kJ mol^-1. Quantum chemistry calculations indicate that the majority of the large activation energy results from the endothermic nature of the equilibrium 2HNO₂? NO + NO ₂ + H₂O. The rate constant for the reaction between nitrate ions and nitrous acid, which inhibits HNO₂ decomposition, was also determined.

Full text of DOI:10.1021/ic202081z

Article
pubs.acs.org/IC
Accurate Rate Constants for Decomposition of Aqueous Nitrous Acid
Mark S. Rayson, John C. Mackie, Eric M. Kennedy, and Bogdan Z. Dlugogorski*
Process Safety and Environment Protection Research Group, School of Engineering, The University of Newcastle, Callaghan,
New South Wales 2308, Australia
*
S Supporting Information
ABSTRACT: Decomposition of nitrous acid in aqueous solution has been
studied by stopped flow spectrophotometry to resolve discrepancies in litera-
ture values for the rate constants of the decomposition reactions. Under the
conditions employed, the rate-limiting reaction step comprises the hydrolysis
of NO . A simplified rate law based on the known elementary reaction
2
mechanism provides an excellent fit to the experimental data. The rate
−6
−1 −1
constant, 1.34 × 10
M s , is thought to be of higher accuracy than those
in the literature as it does not depend on the rate of parallel reaction pathways
or on the rate of interphase mass transfer of gaseous reaction products. The
−1
activation energy for the simplified rate law was established to be 107 kJ mol .
Quantum chemistry calculations indicate that the majority of the large activa-
tion energy results from the endothermic nature of the equilibrium 2HNO ⇆
2
NO + NO + H O. The rate constant for the reaction between nitrate ions and
2
2
nitrous acid, which inhibits HNO decomposition, was also determined.
2
INTRODUCTION
decomposition of nitrous acid is essential to safely implementing
nitrosation reactions
■
Motivation for the study of nitrous acid decomposition is
diverse, with the reactions playing important roles in many
industrial and environmental processes. Industrially, decom-
position of nitrous acid is a significant process occurring in the
HNO + NH → N + 2H O
(1)
2
3
2
2
The reaction kinetics of the decomposition of nitrous acid were
10
first elucidated by Abel and Schmidt, who discovered a rate law
fourth order in nitrous acid concentration and inversely pro-
portional to the square of the NO partial pressure (i.e., NO con-
centration), in a well-mixed gas−liquid reactor. Assuming that
dissolved NO was in equilibrium with the gas phase in accordance
with Henry’s law, the kinetics follow eq 2. The reaction was
demonstrated to have a stoichiometry of three moles of nitrous
acid decomposing to produce two moles of NO and one mole of
nitric acid (reaction 3).
manufacture of nitric acid, wherein a gaseous NO stream is
absorbed in water, and in synthesis reactions involving nitrous
x
1,2
acid (i.e., nitrosation reactions) where the NO side products
x
3,4
pose a toxicity hazard. In atmospheric chemistry, reactions of
nitrous acid and NO have received attention owing to their
x
importance in acid deposition on the earth’s surface and their
5
role in smog formation, while the reactions may be of biological
importance under certain conditions where nitrous acid decom6-
position could contribute to NO production in the body.
Decomposition of nitrous acid can be employed as a source of
[HNO2]4
7
d[HNO2]
= kfwd
NO in the laboratory and has been implicated in the release of
−
8
[NO]2
nitrogen oxides from plants. Because of these considerations,
dt
(2)
(3)
the kinetics of nitrous acid decomposition have received con-
siderable attention in the literature; however, the reported rate
constants exhibit significant disagreement.
The present study aims to establish accurate rate constants
for decomposition of nitrous acid to enable kinetic modeling of
−
+
3HNO → 2NO + NO + H + H O
2
3
2
Equation 2 can be rationalized by assuming that an equilibrium
establishes rapidly between nitrous acid, dissolved NO, and NO2
(
reaction 4) and that hydrolysis of NO (reaction 5) comprises
2
NO formation that results as a side reaction during nitrosation
x
the rate-limiting reaction step. Hydrolysis of NO consists of a
2
reactions, in particular, sensitization of emulsion blasting agents
via ammonia nitrosation. Nitrosation of ammonia (reaction 1)
aims to produce small nitrogen bubbles within the explosive
which act as hot spots to propagate the explosion front through
reaction second order in NO concentration, while two moles of
2
nitrous acid are required to produce one mole each of NO and
NO . This yields an overall rate law fourth order in HNO
2
2
2
4
concentration and gives kfwd = 3K k . Combining reactions 4 and
the bulk explosive and result in more reliable and efficient detona-
5
9
5 yields the stoichiometry identified in reaction 3. Derivations are
tion. Formation of NO as a side product of ammonia nitrosa-
x
tion, however, poses a hazard to miners prior to explosive detona-
tion, particularly in confined underground mines. For industrial
applications such as this, accurate knowledge of the kinetics of the
Received: September 23, 2011
Published: February 3, 2012
©
2012 American Chemical Society
2178
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Article
provided in the Supporting Information.
Table 1. Summary of Rate Constants for Nitrous Acid
Decomposition
2
HNO ⇆ NO + NO + H O, k , k
−4
(4)
(5)
2
2
2
4
Park and
Beake and Schwarz and
Ram and
19
17
18
12
−
+
Lee
22 °C)
Moodie
(25 °C)
White
(25 °C)
Stanbury
2
NO + H O → HNO + NO + H , k5
2
2
2
3
(
(25 °C)
1
−1
Reactions 4 and 5 proceed via N O and N O intermediates,
k
4
(M− s )
13.4
15
5.6
10−25
2
3
2
4
k
−4 (M− s )
1
−1
1.60 × 108
9.00 × 107 3.00 × 107 1.75 × 10
8
respectively, which typically exist in equilibrium with NO and
−8
−7
−7
−8
K4
8.38 × 10
8.40 × 107
0
1.67 × 10
1.00 × 108 7.00 × 107 5.00 × 10
0.005
2.8 × 10
1.87 × 10 5.7−14.3 × 10
NO . Reactions 6−9 below describe the commonly accepted
2
11,12
−1 −1
7
k5 (M s )
elementary mechanism
HNO ⇆ N O + H O
(M− s )
2
−1
0.0089
0.0122
0.16−1.0 × 10
k
−
5
2
(6)
(7)
(8)
2
−1 −1
−7
−6
−6
−6
2
2
3
2
K k (M s ) 5.9 × 10
2.4 × 10
4
5
−7
a
(
9.2 × 10 )
N O ⇆ NO + NO
2
a
2
3
Value in parentheses corrected from 22 to 25 °C using the activation
energy calculated in the present work.
2
NO ⇆ N O
2 2 4
17
Lee studied reactions 4 and 5 by employing a chemilumine-
N O + H O ⇆ HNO + NO + H+
−
2
4
2
2
3
(9)
sence NO analyzer to measure the gaseous concentrations of
x
12
NO, NO , and HNO sparged from a solution of nitrous acid.
2 2
Schwartz and White performed a comprehensive review of
experimental studies related to the absorption of NO and NO2
in water. Part of that study reviewed the decomposition of
nitrous acid, which constitutes the reverse process of NOx
dissolution. The review by Schwartz and White recommended a
set of values for the rate and equilibrium constants of 4 and 5
based on a consensus of literature values, taken from studies
employing a variety of methods including gas absorption,
isotope exchange, flash photolysis, pulse radiolysis, and UV−vis
spectrophotometry. The rate constants determined using
different methods vary greatly, resulting in considerable uncer-
tainty in the suggested values for the rate constants. The majority
of studies reviewed were concerned with either reaction 4 or 5
That study assumed that the concentrations of NO and NO2
were in steady state and that the mass transfer characteristics of
NO and NO were the same (and equal to those of CO ). The
2
2
2
rate constant (i.e., K k ) derived from this study is four times
4
5
smaller than the recommended values provided by Schwartz
and White. A small portion of this difference could be
attributed to the slightly lower temperature of the experiments
in that study (22 versus 25 °C).
Ram and Stanbury examined reactions of the IrCl62
redox couple in nitrous acid over a variety of nitrous acid,
nitrate, and hydrogen ion concentrations under conditions
where the overall reaction rate was dependent on the rate of
reactions 4 and 5. The results of that study depended on the
values employed for rate constants of parallel reactions
pathways; hence, any errors in the rate constants assumed for
parallel reaction pathways in simulations would result in errors
19
−/3−
(
or their component reactions such as reactions 7 and 8)
occurring in isolation. For example, the value of k comes from
the isotope exchange experiments of Bunton and Stedman and
the diazotization experiments of Hughes and Ridd, while the
6
13
14
in the rate constants for reactions 4 and 5. The resulting values
value of k was recommended based on a consensus of rate
9
−1 −1
of k ranged from 10 to 25 M
s
depending on the
4
constants from studies concerned with the dissolution of gaseous
2
4
experimental conditions, leading to K k values ranging from
5
NO /N O in water and the pulse radiolysis or flash photolysis
2
2
4
−7
−6
18
−1 −1
1
.6 × 10 to 1 × 10
M
s .
of nitrite solutions, for which different estimates of the rate
constants varied over an order of magnitude. Although selec-
tion of the “recommended” values in themselves appears quite
reasonable, it is unclear whether the combination of rate constants
determined by different methods will result in the correct value of
Beake and Moodie studied the decomposition of HNO by
2
UV spectrophotometry at 385 nm in solutions saturated with
atmospheric oxygen. The presence of oxygen results in
oxidation of NO to NO via reaction 10, which influences
2
2
2
the reaction kinetics by reducing the NO concentration, hence
driving reaction 4 to the right.
K k . The quantity K k determined from the individual rate
4
5
4
5
−6
−1 −1
constants of Schwartz and White is 2.4 × 10 M s , which is a
−7
−1 −1
factor of 2.5 larger than the value of 9.4 × 10
M
s
inferred
2
NO + O → 2NO , k
(10)
2
2
10
10
from the data of Abel and Schmidt assuming a Henry’s constant
−3
−1 15
for NO of 1.9 × 10 M atm . Thus, it is unclear which rate
constants should be selected when attempting to accurately model
The approach taken was to assume values of the rate
constants k , k , and k from the literature and to determine
4
5
10
formation of NO and NO from nitrous acid decomposition.
the value of k−4 by solving the set of ordinary differential
equations describing the reaction mechanism and varying k−4 to
provide the best fit to their experimental data. The results
2
Three studies relating to nitrous acid decomposition have
been published since the review of Schwartz and White, the
results of which are summarized in Table 1. There are con-
siderable differences in the reported rate constants; these have a
2
provide a value of K k similar to that of Schwartz and White
4
5
and considerably larger than that of Park and Lee. An important
6
dramatic effect on the predicted rate of NO production.
distinction, as outlined by Butler and Ridd, should be made
x
In addition, hydrolysis of NO has been recently studied with
regarding the rate-limiting reaction step in gas−liquid systems
versus purely liquid-phase experiments. In gas−liquid experi-
ments, rapid removal of reaction products can result in rate-
limiting formation of N O (reaction 6), while in purely
2
7
−1 −1 16
k determined as 4.8 × 10 M s . Figure 1 illustrates the
5
discrepancies in the literature rate constants, wherein
production of NO from decomposition of a 0.01 M nitrous
acid solution has been simulated based on the rate constants of
the studies in Table 1.
2
3
aqueous systems reaction 4 rapidly reaches equilibrium and
dissolution of NO via reaction 5 becomes the rate-limiting
2
18
Discrepancies in the reported results are likely caused by the
differences in the methods deployed to study the reaction and
the assumptions employed when analyzing the data. Park and
step. Thus, while Beake and Moodie claim to be determining
k , the result would actually depend on the initially chosen
−4
values for k and k .
4
5
2
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Figure 1. Formation of nitric oxide predicted using literature rate constants for HNO decomposition.
2
Owing to the discrepancies between reported values for rate
constants for nitrous acid decomposition, it is desirable to study
the reaction kinetics without the complications of (i) mass transfer
between the aqueous and gas phase and (ii) the pre-
sence of parallel reaction pathways that influence the reaction
kinetics. This can be established by monitoring the decom-
position of nitrous acid spectrophotometrically, with precautions
taken to prevent any transfer of gases into or out of the reacting
solution. Such conditions can be readily achieved in a stopped flow
mixing device, wherein two reactant solutions contained in gastight
syringes are mixed together rapidly before flowing to a UV−vis
observation cuvette. Such a study may yield an accurate value for
forming in the solution. Had gas bubbles formed, an increase in
absorbance at 500 nm would be observed due to light scattering. The
1
0 mm path length of the RX-2000 dual path cell was employed for
concentrations of 20 mM and below and the 2 mm length utilized for
higher concentrations. The total concentration of nitrous acid
−
(
[NO ] + [HNO ]) was determined using eq 11, where A is the
2
2
absorbance at a particular wavelength
A
[
HNO ]
= [HNO ]
2 Total,initial
2
Total
A
(11)
initial
Equation 11 is valid provided that the ratio of the nitrous acid to nitrite
ion concentration remains constant. Employing an excess of hydrogen
ions in the experiments ensures that this criteria is met. The reaction
kinetics were analyzed by fitting the data from individual experiments
over the first 1200 s of reaction to the integrated form of eq 2, which is
provided in the Supporting Information. The fitting procedure was
performed by employing the solver function in Microsoft Excel to find
2
the quantity K k suitable for modeling NO formation from
4
5
nitrous acid decomposition during nitrosation reactions.
EXPERIMENTAL SECTION
■
2
Decomposition of nitrous acid was studied at concentrations ranging
from 2.5 to 100 mM using UV−vis stopped flow spectrophotometry.
The setup comprised an Applied Photophysics RX-2000 rapid mixing
accessory coupled to a Varian Cary50 spectrophotometer. The
temperature of the stopped flow cell was regulated via a Varian Cary
peltier thermostatted cell holder, while the drive syringes of the rapid
mixing accessory were surrounded by water connected to a circulating
cooling/heating bath at the desired reaction temperature. Nitrous acid
was generated in situ by reacting a solution of sodium nitrite with a
solution of perchloric acid, with an excess of perchloric acid of at least
the value of K k that produced the minimum error between the
4
5
experimental data and that predicted from the integrated rate equa-
tion. In the case of the experiments involving dissolved oxygen at low
HNO2 concentrations, a system of ordinary differential equations
describing the reaction mechanism was solved in Polymath 5.1 for
2
different values of K k .
4
5
Quantum chemistry calculations were performed with the Gaussian
2
0
03 software package to investigate the thermochemistry of nitrous
2
1
22
acid decomposition. G3B3 and CBS-QB3 methods were employed
for accurate determination of gas-phase reaction free energies, while
enthalpies and free energies of solvation were determined at the
0
.02 M, providing near complete conversion of nitrite ions into nitrous
2
3
24
acid. The precise fraction of nitrite converted to nitrous acid was
determined by examining the absorbance at 371 and 386 nm as
outlined in the Supporting Information.
B3LYP/6-31G(d,p) level with the PCM model (UAHF radii). This
was established by comparing the PCM energies to those cal-
culated for the gas phase with the same method and basis sets. Com-
bination of the calculated solvation free energies with the gas-phase free
energy of reaction by means of the thermochemical cycle depicted in
Figure 2 enabled calculation of the aqueous-phase reaction free energies.
Thermochemical parameters calculated in Gaussian are based on a
standard state pressure of 1 atm, while aqueous free energies of reac-
tion employ the 1 M standard state. Results for reaction free energies
must therefore be corrected for the change in entropy associated with
the transition from a pressure of 1 atm to a concentration of 1 M. This
The ionic strength ranged from 0.08 to 0.2 M, with increasing
concentrations of NaNO necessitating higher HClO concentrations
2
4
−
for complete protonation of NO . Small changes in the ionic strength
2
do not affect the reaction rate because the rate depends only on the
concentration of neutral species, whose activity changes minimally
with increasing ionic strength. Prior to each kinetic experiment, oxygen
was removed from the solutions by sparging them with high-purity
nitrogen for at least 20 min. Degassing for longer time periods
produced identical results. Reaction kinetics were determined based on
the decrease in absorbance at 357.5, 371, and 386 nm. The absorbance
2
5
correction has been discussed by Bryantsev et al. and acts to make
the free energy of each species 7.9 kJ/mol more positive. Thus, there is
no net correction for reactions where there is no change in the number
of moles in a reaction, while reactions exhibiting a greater number of
at 500 nm (where neither NO or HNO absorbs) was monitored in
2
each experiment to confirm that gas bubbles of nitric oxide were not
2
180
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Inorganic Chemistry
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of reaction declines such that the fraction of nitrous acid decom-
posed in the time frame of the experiments becomes quite low,
leading to small changes in absorbance. Thus, we place the highest
confidence in the results obtained for nitrous acid concentrations
of 20 mM or greater. Figure 3 shows kinetic traces for 0.02−0.1 M
HNO including the best fit of eq 2 to the data. Complete
2
experimental results are tabulated in Appendix A.
2
The value of K k presently deduced amounts to approxi-
4
5
12
mately one-half that recommended by Schwartz and White
and determined by Beake and Moodie. It exceeds the largest
value of Ram and Stanbury by 30% and surpasses the value of
Park and Lee by a similar margin, after correcting that result
from 22 to 25 °C. The difference between the present result
and that derived from the values recommended by Schwartz
and White most likely stems from the uncertainty in the
individual constants k , k , and k of that study, in particular
18
19
17
Figure 2. Thermochemical cycle for determining aqueous free energy
change of reaction for reaction A → B + C. The value 24.46 reflects
the ratio of the molar volume of a gas at 1 atm to that at 1 M.
12
moles of products than reactants become less favorable in the 1 M
standard state and vice versa.
4
−4
5
k−4, for which the upper and lower estimates span an order of
magnitude. The study of Beake and Moodie employed a similar
method to the present study (UV spectroscopy, but with stoppered
cells rather than stopped flow) and recorded a significantly larger
rate constant. That study concentrated on relatively low HNO2
concentrations (2−8 mM) and very long reaction times (>3 h),
which could have allowed the measurements to be influenced by a
slow rate of oxygen diffusion past the cell stopper. In contrast to
the measurements of Beake and Moodie, the present result
RESULTS AND DISCUSSION
■1
. Kinetics at 25 °C in Anaerobic Solution. Over the
concentration range of interest, reaction 4 is sufficiently rapid
to be at equilibrium and the rate of nitrous acid decomposition
is therefore dependent on the rate of hydrolysis of NO , leading
to the simplified rate law given in eq 2. Equation 2 provided an
2
2
4
excellent fit to the data, with the value of K k remaining con-
5
2
−
6
−1 −1
coincides relatively closely with the values of K k deduced from
stant at 1.34 (±0.06) × 10
M
s
for nitrous acid concen-
4
5
the measurements of Park and Lee and Ram and Stanbury,
supporting the present determination.
trations ranging from 0.02 to 0.1 M nitrous acid, demonstrating
the validity of this rate law under the present experimental con-
ditions. The kinetics show an initial period of rapid decom-
position, after which accumulation of nitric oxide in solution
causes a continued decline in the reaction rate. The importance
of completely removing oxygen from the reaction medium
cannot be stressed enough, particularly at low nitrous acid con-
centrations where small amounts of oxygen have a significant
impact on the reaction kinetics and cause a deviation from the
simplified rate equation. As expected from eq 2, the rate of
decomposition increases significantly with increasing nitrous
acid concentration. At low concentrations of nitrous acid, the rate
2
. Kinetics at 25 °C in the Presence of Oxygen. To
extend our measurements to lower concentrations of nitrous acid
2.5 mM), experiments were performed with solutions initially
(
saturated with atmospheric oxygen. This had the advantages of
both increasing the change in absorbance and removing the error
associated with the presence of a small amount of residual oxygen
in the degassed solutions, which can have a significant effect on the
kinetics at low concentrations of nitrous acid. It does, however,
introduce some uncertainty owing to the fact that oxidation of NO
by O could become at least partially rate limiting, and hence, the
2
2
Figure 3. Experimental and simulated nitrous acid decomposition results for 20−100 mM NaNO . For simulations, K k remains constant at 1.34 ×
2
4
5
−
6
−1 −1
1
0 M s .
2
181
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Inorganic Chemistry
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Figure 4. Comparison of experimental result and simulations for decomposition of 2.5 mM HNO in air-saturated solutions.
2
values determined would depend on the rate constant assumed for
that reaction. Oxidation of NO to NO by O is a third-order
comparison of a kinetic trace for 0.1 M NO − to an equivalent
3
experiment with no added nitrate. The constant k−5 was
evaluated by performing a series of experiments with different
hydrogen and nitrate ion concentrations and ascertained to be
2
2
26
reaction, second order in NO and first order in O2 (reaction 10).
Rate constants for that reaction have been determined in a6
number of studies with estimates ranging from 1.6 to 2.9 × 10
−3
−2 −1
5.9 (±0.6) × 10 M s at an ionic strength of 0.18 M. This result
−
2
−1 27
6
−2 −1
M
s . A value of k =2.1 × 10 M s , consistent with the
10
26
2
is 20−40% smaller compared to previous values reported in the
12
results of Lewis and Dean, provides an identical value of K k to
literature at zero ionic strength. This discrepancy arises as a result
4
5
that in the anaerobic experiments. Figure 4 compares the results
of nonunity activity coefficients of nitrate and hydrogen ions at
0.18 M ionic strength, which reduce the observed rate of the reverse
reaction. Our result lies in close agreement with the prior deter-
for decomposition of 2.5 mM HNO in air-saturated solutions to
2
2
4
simulations for different values of K k .
5
3
0
28
3. Kinetics of the Reverse Reaction. Under the conditions
mination by Abel and Schmidt and Jordan and Bonner.
2
of the present study with relatively low nitrite and acid concen-
trations, nitrate ions are produced at sufficiently low concen-
This provides further support for the value of K k (1.34 ×
0 M s ) determined in the present study as employing this
4
5
−6
−1 −1
1
trations that hydrolysis of NO (reaction 5) can be assumed to be
2
constant in eq 12 results in the same value of k−5 determined in-
2
4
irreversible. In the presence of added nitrate or very high acid
concentrations the reverse of reaction 5 results in formation of
dependently in the literature. Had the value of K k been in error, it
5
would not have been possible to reproduce the correct value of k .
−5
NO , reducing the net rate of nitrous acid decomposition. This
2
4. Temperature Dependence and Thermochemical
Analysis of the Elementary Reaction Mechanism. The
temperature dependence of both the forward and the reverse
reactions was examined between 20 and 55 °C. The rate of
nitrous acid decomposition increased markedly with increasing
reaction exhibits first-order dependencies on nitrous acid,
28,29
hydrogen ion, and nitrate ion concentrations.
Analogous
rate laws are observed for the nitrosation of a range of species by
4
nitrous acid, suggesting that a similar mechanism operates for
the reaction of nitrous acid and nitrate. The rate law for nitrous
acid decomposition can be modified to incorporate the effect of
this reaction by assuming that the rate of decomposition depends
2
temperature, a plot of ln(K k ) yielding an apparent activation
4
5
−1
energy of 106.6 ± 3 kJ mol . The uncertainty represents the
2
standard error obtained from a plot of ln(K k ) versus 1/T,
4
5
on the net rate of NO hydrolysis, i.e., the net rate of reaction 5a.
2
which was determined using the linest function in Microsoft
Excel. This large activation energy may have contributed to the
considerable scatter in the literature data, with a tempera-
2
NO + H O ⇆ HNO
2
2
2
2
4
ture increase of just 1 °C resulting in an increase in K k of
5
−
+
approximately 20% at 25 °C. This underscores the importance
of accurately maintaining a constant temperature when studying
this reaction. The activation energy of the reverse reaction was
+
NO3 + H , k , k
(5a)
5
−5
2
4
d[HNO2]
dt
3K k [HNO ]
4 5 2
=
−
+
−1
[NO]2
determined to be 76 ± 4 kJ mol , in close agreement with the
prior determination of 74 kJ mol− by Akhtar et al.
1
29
+
−
3k [HNO ][H ][NO ]
(12)
A quantum chemistry study was undertaken to determine the
−
5
2
3
2
4
origin of the high activation energy associated with K k . The
5
Experiments with added nitrate ions showed a similar initial
rate of decomposition but did not proceed to as great an extent
as the accumulation of NO eventually makes the two terms of
eq 12 equal, that is, the presence of nitrate causes the reac-
tions to reach an equilibrium position. Figure 5 provides a
gas-phase free energies and enthalpies of reactions 6−9 were
established using the average results of the CBS-QB3 and G3B3
methods. The gas-phase free energy of the proton, −26.3 kJ/mol,
31
was taken from the literature. Nitrous acid exists in both the cis
and the trans conformations, with the energy of the cis isomer
2
182
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Figure 5. Experiment and model for decomposition of 0.02 M HNO in 0.1 M HClO and 0.1 M HNO .
2
4
3
Table 2. Calculated Aqueous Enthalpies and Free Energies of Reactions 6−9 and Comparison of Calculated and Experimental
Equilibrium Constants (all energies are in kJ)
a
reaction
ΔH298G3B3
ΔH298CBS-QB3
ΔG298G3B3
ΔG298CBS-QB3
Kcalcd
Kexpt
unit
M−1
ref
2.65 × 10−
4.30 × 10−
1.39 × 103
1.04 × 10
1.14 × 10−
5
3 × 10
−3
37
12
12
12
12
6
−4.0
50.7
−2.4
46.9
25.2
15.4
27.0
11.6
3
−5
7
8
9
4
3.3 × 10
7 × 10
1.25 × 105
M
4
−1
−69.3
−18.5
46.7
−66.6
−26.9
44.5
−19.4
−24.3
40.7
−16.5
−32.9
38.6
M
5
M
7
−7
(6 + 7)
1.87 × 10
a
Calculated equilibrium constants are based on the average of G3B3 and CBS-QB3 results.
3
5,36
located 2.2 and 2.5 kJ higher than trans for CBS-QB3 and G3B3,
respectively. Owing to the small difference in the calculated
energy of HONO isomers, we use the average energy when
determining all thermodynamic quantities, as previously
ones.
Table 2 presents the calculated aqueous enthalpies
and free energies of reaction for reactions 6−9, including the
calculated equilibrium constants which are compared to
experimental results. Note that the free energies include a
32
25
reported. The first reaction results in formation of dinitrogen
correction for a change in standard state from 1 atm to 1 M
trioxide and involves the combination of two nitrous acid
and that the calculated equilibrium constants are derived based
on the average of G3B3 and CBS-QB3 free energies of reaction.
Table 2 shows that the predicted equilibrium constants for
reactions 6 and 7 deviate from the experimental values by 2
molecules with simultaneous elimination of H O (reaction 6).
2
The transition states (TS) for the gas-phase reaction have
3
3,34
previously been identified,
and because this reaction has been
9
demonstrated to be at equilibrium, we did not investigate the TS
further. N O undergoes homolytic fission producing NO and
orders of magnitude, equivalent to a 12 kJ error in ΔG . The
r
predicted equilibrium constant for reaction 8 is almost 2 orders
of magnitude smaller than the experimental value. The higher
error of the aqueous reaction free energies relative to the gas-
phase results arises due to inaccuracies in the prediction of solva-
tion free energies, which are typically in the order of 4 kJ/mol for
2
3
NO , followed by combination of two NO molecules forming
2
2
N O . The final reaction involves hydrolysis of N O , forming
2
4
2
4
nitrous acid, nitrate, and hydrogen ions. The calculated gas-phase
enthalpies and free energies of reaction are in good agreement
35
38
with experimental values, with mean absolute errors in the gas-
neutral species. With regard to reactions 7 and 8, the
phase ΔH and ΔG of 1.9 kJ and 3.0 kJ/mol respectively,
present method predicts that formation of the compound
oxides N O and N O (from the simple oxides NO and NO ) is
r
r
for reactions 6−8. There was however a significant difference of
2
3
2
4
2
14 kJ/mol between the experimental results for reaction 9 and
considerably less favorable than predicted from experiments.
Considering that the calculated gas-phase energies are in good
agreement with experimental results, it appears that the PCM
model underestimates the solvation free energies of N O and
those calculated with the CBS-QB3 method, inclusion of which
increases the average error in ΔH to 3.5 kJ/mol.
r
The aqueous-phase enthalpies and free energies of reaction
were determined by combining the solvation enthalpies and
free energies determined with the PCM solvent model to the
accurate gas-phase results in accordance with the thermochem-
ical cycle depicted in Figure 2. In the case of water and the
hydrogen cation, the experimental enthalpies and free energies
of vaporization were applied, as opposed to the calculated
2
4
N O relative to the simple oxides NO and NO . Despite the errors
2
3
2
associated with K and K , combining reactions 6 and 7 into the
6
7
overall reaction 4 provides close agreement between the calculated
and the experimental equilibrium constants. The results for reaction
9 with CBS-QB3 and G3B3 differ by 8.6 kJ/mol; however, the
average is fortuitously in excellent agreement with experiments.
2
183
dx.doi.org/10.1021/ic202081z | Inorg. Chem. 2012, 51, 2178−2185

Inorganic Chemistry
Article
The calculated enthalpy of reaction 4 can be employed to
determine the contribution of this reaction to the activation
Table A2. Temperature Dependence of Nitrous Acid
Decomposition
2
energy of K k by means of eq 13. Provided that the enthalpy
4
5
2
NaNO2
(M)
HClO4
(M)
NaClO4
(M)
K k
4 5
−1 −1
of reaction is independent of temperature, a plot of ln(K)
versus the reciprocal of temperature is linear with a slope equal
to the negative of the enthalpy of reaction. Combining the
expression for the equilibrium constant with the Arrhenius
expression for the temperature dependence of reaction 5 yields
experiment
T (K)
(M s )
−
6
7
7
6
5
7
1
1
1
1
1
1
1
1
2
3
4
5
6
7
8
9
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.1
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.08
0.04
308.15
293.15
293.15
303.55
313.35
287.75
288.15
308.15
288.15
5.77 × 10
6.82 × 10
6.82 × 10
3.44 × 10
1.16 × 10
2.73 × 10
4.22 × 10
6.51 × 10
−
−
−
5
yields eq 13, as shown in the Supporting Information. Thus,
−
the apparent activation energy, determined from of a plot of
ln(K k ) versus 1/T, is equal to twice the enthalpy of reaction
−
2
4
5
−7
4
summed with the activation energy of reaction 5.
−
6
7
−
(
2ΔH(4) + EA(5)
)
ΔS(4)
R
20
0.04
2.35 × 10
2
ln(K k ) = −
+ 2
+ ln(A)
4
5
(13)
RT
Table A3. Rate Constants for Reverse Reaction at 298 K
Reaction 4 is considerably endothermic, with gas-phase
enthalpies of reaction of 34.4 and 37.7 kJ at the G3B3 and
CBS-QB3 levels, respectively. The effect of solvation serves to
make the reaction more endothermic, leading to an average value
of 45 kJ for the aqueous enthalpy of reaction 4. Thus, this reaction
+
NO3− (M)
(M−2 s−1)
experiment
H (M)
NaNO (M)
k
−5
2
−3
2
2
2
2
1
2
3
4
0.05
0.05
0.1
0.05
0.05
0.05
0.05
0.15
0.15
0.1
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
6.48 × 10
−3
6.69 × 10
−3
6.23 × 10
contributes approximately 90 kJ to the apparent activation energy
−3
0.1
5.13 × 10
2
4
of K k due to the second-order dependence on K . It can
−3
5
4
25
0.1
5.33 × 10
therefore be concluded that reaction 5 has a small activation
energy on the order of 17 kJ. Although the solvation energies
−3
2
2
6
7
0.1
5.87 × 10
−3
0.1
5.28 × 10
introduce some uncertainty in the value of ΔH , the contribution
−3
(
4)
28
0.1
0.1
5.83 × 10
2
4
of K to the apparent activation energy is clearly much higher
than the contribution of k . The close agreement between the
experimental and the calculated free energies for reaction 4 gives
us confidence in the calculated enthalpy of reaction.
5
Table A4. Temperature Dependence of Reverse Reaction
+
−
Determined in 0.02 M NaNO , 0.1 M H , and 0.1 M NO
2
3
experiment
T (K)
k
−5
(M− s )
2 −1
CONCLUSION
■
−2
2
3
3
3
3
3
9
0
1
2
3
4
308
308
318
318
328
328
1.44 × 10
Decomposition of nitrous acid including the reverse reaction
between nitrous acid and nitrate ions has been studied by
stopped flow spectrophotometry to resolve discrepancies in
literature values of the rate constants. The value determined
−2
1.18 × 10
−2
3.91 × 10
−2
4.59 × 10
−2
9.45 × 10
2
−6
−1 −1
(
K k = 1.34 ± (0.06) × 10
M
s ) is of higher accuracy
−1
4
5
1.06 × 10
than those previously reported in the literature as it does not
depend on the rate of parallel reaction pathways or on the rate
of interphase mass transfer of gaseous reaction products. The
ASSOCIATED CONTENT
Supporting Information
■
2
4
S
*
activation energy associated with K k is 107 kJ, the majority of
5
Derivation of selected equations, calculated geometries,
frequencies, moments of inertia, enthalpies, free energies,
solvation free energies, and solvation enthalpies. This material
is available free of charge via the Internet at http://pubs.acs.org.
this being attributable to the endothermic nature of the reaction
2
HONO ⇆ NO + NO + H O.
2 2
APPENDIX A: EXPERIMENTAL DATA FOR NITROUS
ACID DECOMPOSITION
■
AUTHOR INFORMATION
■
Corresponding Author
Table A1. Rate Constants at 298 K for HNO2
Decomposition
*Phone: +61 2 4985-4433. Fax: +61 2 4921-6893. E-mail:
Bogdan.Dlugogorski@newcastle.edu.au.
2
NaNO2
(M)
HClO4
(M)
NaClO4
(M)
K k
4 5
−1 −1
experiment
T (K)
(M s )
ACKNOWLEDGMENTS
■
1.39 × 10−
1.37 × 10−
1.33 × 10−
1.35 × 10−
1.33 × 10
1.29 × 10−
6
6
6
6
6
6
6
6
6
6
6
1
2
3
4
5
6
7
8
9
0.02
0.02
0.02
0.02
0.05
0.05
0.05
0.05
0.1
0.04
0.1
0.04
0.08
0.08
0.08
0.05
0.05
0.05
0.05
0.05
0.05
0.05
298.15
298.15
298.15
298.15
298.15
298.15
298.15
298.15
298.15
298.15
298.15
Financial support from Dyno Nobel Asia Pacific Pty. Ltd. and
the Australian Research Council is gratefully acknowledged.
0.1
0.1
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−
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0.1
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