Global thermodynamic atmospheric modeling: Search for new heterogeneous reactions

Article abstract of DOI:10.1021/jp971250d

This article demonstrates quantitatively how far reactions are from chemical equilibrium over the full space of a two-dimensional atmospheric model. This method could be used with data where an instrument-equipped aircraft measures numerous species simultaneously. An atmospheric reaction is displaced from equilibrium by solar radiation and relocation of species by atmospheric motions. One purpose of this study is to seek additional stratospheric or tropospheric gas-phase chemical reactions that might undergo heterogeneous catalysis. Hypothetical cases can be rapidly screened in terms of their thermodynamic potential to react under measured or modeled atmospheric conditions of temperature and local species concentrations. If a reaction is interesting, is slow in the gas phase, and has a high thermodynamic tendency to react, it is a good candidate for a laboratory study to seek a heterogeneous catalyst. If the reaction is thermodynamically unfavorable, there is no catalyst that can cause the reaction to occur. If a reaction is thermodynamically favored to occur but also endothermic, it will tend to be slow at stratospheric temperatures. We find, as expected, that four heterogeneous reactions important in causing the Antarctic ozone hole have high thermodynamic tendencies to occur under atmospheric conditions, but one of these is only weakly thermodynamically allowed in some regions of the atmosphere. The reaction of SO₂ and HNO₃ to form HONO has a high thermodynamic potential to occur, is a well-known laboratory reaction at ice temperature, and may occur in nitric acid-rich sulfate aerosols. Throughout the troposphere and stratosphere, we find that formaldehyde has an extremely high thermodynamic potential to reduce nitric acid. Formaldehyde is known to stick to and remain in sulfuric acid solution, where it adds water to form H₂C(OH)₂. Near room-temperature H₂C(OH)₂ reacts with nitric acid in a two-step mechanism to form two molecules of HONO, but the rate of this process under conditions of stratospheric sulfuric acid aerosols is unknown.

Full text of DOI:10.1021/jp971250d

7350
J. Phys. Chem. A 1997, 101, 7350-7358
Global Thermodynamic Atmospheric Modeling: Search for New Heterogeneous Reactions
D. Howard Fairbrother, Daniel J. D. Sullivan,† and Harold S. Johnston*
Department of Chemistry, UniVersity of California, and Lawrence Berkeley National Laboratory,
UniVersity of California, Berkeley, California 94720
ReceiVed: April 10, 1997; In Final Form: July 8, 1997X
This article demonstrates quantitatively how far reactions are from chemical equilibrium over the full space
of a two-dimensional atmospheric model. This method could be used with data where an instrument-equipped
aircraft measures numerous species simultaneously. An atmospheric reaction is displaced from equilibrium
by solar radiation and relocation of species by atmospheric motions. One purpose of this study is to seek
additional stratospheric or tropospheric gas-phase chemical reactions that might undergo heterogeneous catalysis.
Hypothetical cases can be rapidly screened in terms of their thermodynamic potential to react under measured
or modeled atmospheric conditions of temperature and local species concentrations. If a reaction is interesting,
is slow in the gas phase, and has a high thermodynamic tendency to react, it is a good candidate for a laboratory
study to seek a heterogeneous catalyst. If the reaction is thermodynamically unfavorable, there is no catalyst
that can cause the reaction to occur. If a reaction is thermodynamically favored to occur but also endothermic,
it will tend to be slow at stratospheric temperatures. We find, as expected, that four heterogeneous reactions
important in causing the Antarctic “ozone hole” have high thermodynamic tendencies to occur under
atmospheric conditions, but one of these is only weakly thermodynamically allowed in some regions of the
atmosphere. The reaction of SO2 and HNO3 to form HONO has a high thermodynamic potential to occur,
is a well-known laboratory reaction at ice temperature, and may occur in nitric acid-rich sulfate aerosols.
Throughout the troposphere and stratosphere, we find that formaldehyde has an extremely high thermodynamic
potential to reduce nitric acid. Formaldehyde is known to stick to and remain in sulfuric acid solution, where
it adds water to form H2C(OH)2. Near room-temperature H2C(OH)2 reacts with nitric acid in a two-step
mechanism to form two molecules of HONO, but the rate of this process under conditions of stratospheric
sulfuric acid aerosols is unknown.
Introduction
chemical potential of a substance, µ, is a fundamental property
derived from the laws of thermodynamics and observed physical
properties, and it represents the criterion for chemical equilib-
rium and the direction for spontaneous change. Chemical
potential, µ, decreases when a substance undergoes spontaneous
change, remains the same for small perturbations about equi-
librium, and increases when reversible work is applied.4 Since
this article is concerned primarily with gases at low concentra-
tions in the atmosphere, we use the ideal-gas approximation
throughout. The derivation starts with the statement “The
chemical potential of a substance A in any actual state, µA, is
the chemical potential of A in its defined standard state, µA°,
plus the change in chemical potential in going from the standard
state to the actual state.” For an ideal gas the change of
chemical potential per mole in going from its standard partial
pressure p° to its actual partial pressure p is given by RT ln(p/
p°). This leads to the following equation:
In this paper we present a method, an extension of the (K/Q)
method of Burley and Johnston,1 for identifying the thermody-
namic feasibility of gas-phase reactions to undergo heteroge-
neous catalysis in the atmosphere. Our analysis is limited by
the available concentration data in the Lawrence Livermore
National Laboratory (LLNL) model, which extends from pole
to pole and altitudes of 0 to 60 km, and by accessible
thermodynamic data for atmospheric species.2 Seasonal and
daytime effects are assessed using the LLNL model concentra-
tions at midnight and noon both in June and September. In
most cases, we examine gaseous reactants and products to find
the degree to which thermodynamics favors or forbids the
overall reaction to occur. If a reaction is thermodynamically
favorable but does not occur in the gas phase, it is reasonable
to inquire whether it might be made to occur by way of
heterogeneous catalysis. If a reaction is thermodynamically
unfavorable, no catalyst can cause it to proceed from reactants
to products, although it can be driven by photochemistry. The
procedure outlined in this paper does not consider the chemical
thermodynamics or physics of the processes that occur between
gas-phase and condensed-phase species or inside the condensed
phase (see Molina et al., 1996).3
µA ) µA° + RT ln(p/p°)
(1)
where the value of µA° depends on the standard state, which is
usually 1 atm or 1 bar in tables of thermodynamic data.
Consider the balanced chemical equation of the general form
Methodology
xA + yB ) zC + wD
(2)
The derivation is straightforward,4 but it is presented here
for the definition of terms and as a point of reference. The
where A, B, C, and D are four ideal gases mixed in any amounts
and x, y, z, and w are the stoichiometric integers required to
balance the equation. With each reactant and product expressed
in the form shown in eq 1, the difference in chemical potential
between the standard state and actual state is
† Present Address: Philips Semiconductors, 811E Arques Avenue M/S
65, Sunnyvale, CA 94088.
X Abstract published in AdVance ACS Abstracts, September 1, 1997.
S1089-5639(97)01250-4 CCC: $14.00 © 1997 American Chemical Society

Atmospheric Modeling
∆rµ ) zµC + wµD - xµA - yµB
J. Phys. Chem. A, Vol. 101, No. 40, 1997 7351
{RE1 + âE2 + γE3 + ... ) A }° in general (10)
{(1/2)H2 + 2O2 + (1/2)N2 ) HOONO2}° for example
(3)
z
x
y
[pC pDw/(pA pB )]ACTUAL
) ∆rµ° + RT ln
z
x
y
[pC pDw/(pA pB )]STANDARD
where R, â, γ are integers or ratios of integers. The equilibrium
constant for the reaction of formation, Kf, is
Since p° is equal to one standard state unit, p/p° ) p/1 ) p, eq
3 can be simplified, where each pressure is implicitly a
dimensionless quantity:
p(A)
Kf(A) )
(11)
R
â
γ
[
]
p(E1) p(E2) p(E3)
EQUIL
z
w
pC pD
Thermodynamic values of log Kf are tabulated as the last column
of data in the JANAF tables2 for a wide range of atmospheric
species and temperatures, including 200 and 300 K, which
encompass almost the total range of atmospheric temperatures
in this study. For the general reaction 2, the equilibrium
constant (eq 6) is related to Kf by
∆rµ ) ∆rµ° + RT ln
(4)
x
y
(
)
pA pB
ACTUAL
) ∆rµ° + RT ln Q(p)
where Q is defined as
z
w
y
log K ) z log Kf(C) + w log Kf(D) - x log Kf(A) -
y log Kf(B) (12)
pC pD
Q(p) )
(5)
x
(
)
pA pB
ACTUAL
In general, an equilibrium constant is a function of temperature.
To determine log K(T) values at temperatures between 190 and
300 K, we adopt the standard linear variation of log K(T) with
respect to 1/T and apply the following relationship:
The term p (actual) refers to the measured or modeled pressure
(LLNL model in this article) of each species at specified altitude,
latitude, season, and time of day. The chemical equilibrium
constant, K, is defined as
log K(T) ) log K(200) + [(log K(300) -
z
w
pC pD
log K(200))][(200-1 - T-1)/(200-1 - 300-1)] (13)
K(p) )
(6)
x
y
(
)
pA pB
EQUIL
This approximation has been checked for reactions considered
in this study for which formation constants at 250 K are given
in ref 2. Errors in log Kf values at 250 K are negligible, being
between -0.02 to + 0.01.
To ensure that K/Q is dimensionless, it is essential for K (from
tables of thermodynamic data) and Q (observed or modeled) to
have the same standard state, that is, be expressed in the same
units. In the LLNL model and in our study, the standard state
for gases is concentration c(A)° ) [A]° ) 1 molecule cm-3. Kf
values from the JANAF tables2 are quoted with a standard state
of 1 bar. Starting with pV ) nRT, we find c ) 7.24274 ×
1021p/T, where p is expressed in bars and the following
conversion is necessary:
At chemical equilibrium, the chemical potential of the reactants
equals the chemical potential of the products, that is, ∆rµ ) 0.
The pressures of reactants and products are at chemical
equilibrium values. Consequently, K ) QEQUIL. By substituting
∆rµ ) 0 and K ) QEQUIL into eq 4, we obtain for chemical
equilibrium
∆rµ° ) -RT ln K
(7)
Substituting eqs 5 and 7 into eq 4, we obtain the fundamental
expression for measuring the distance. An actual reaction is
from the chemical equilibrium state
-∆rµ
RT
log(K/molecules cm-3) ) log(K/bar) +
∆rn(21.860 - log T) (14)
K
Q
) ln
(8)
A reaction is thermodynamically favored to go from reactants
to products if ∆rµ < 0. It is thermodynamically favored to go
from products to reactants if ∆rµ > 0. When ∆rµ ) 0, the
reaction is at chemical equilibrium. In the context of eq 2 this
corresponds to the following.
∆rn ) z + w - x - y
(15)
In situations where the concentrations of all relevant species
are known, we use this procedure to prepare two-dimensional
contour plots of log(K/Q) as a function of altitude (y) and latitude
(x). At a glance, these contour plots show the extent of a
reaction’s displacement from chemical equilibrium at all
latitudes and altitudes.
The equilibrium constant at one temperature can be expressed
in terms of the change of enthalpy ∆rH° (“heat of reaction”)
and change of entropy ∆rS°:
If K/Q > 1 or log(K/Q) > 0, A + B f C + D
If K/Q < 1 or log(K/Q) < 0, A + B r C + D
If K/Q ) 1 or log(K/Q) ) 0,
(9)
A + B are in chemical equilibrium with C + D
∆rH° - T∆rS°
∆rH° ∆rS°
If log (K/Q) is between about -1 to + 1, the actual reactants
and products are close to chemical equilibrium. The expression
log(K/Q) is a quantitative indicator with continuous gradations
of the thermodynamic potential for a reaction to proceed from
reactants to products.
In chemical thermodynamics, the “reaction of formation” of
a substance A from its component elements, E1, E2, E3, ..., each
in its standard state, is
ln K ) -
) -
+
(16)
RT
RT
R
A large value of the equilibrium constant is favored by a
negative change of enthalpy (exothermic reaction) and a positive
change of entropy as reaction occurs. The change in enthalpy
in going from reactants to products, ∆rH°, averaged between
200 and 300 K, is

7352 J. Phys. Chem. A, Vol. 101, No. 40, 1997
Fairbrother et al.
by its exact reverse, and both proceed at the same rate, on
average, at chemical equilibrium. In the Chapman mechanism
for oxygen chemistry, photochemical steady state for reaction
#1 is obtained by the pumping action of two photochemical
reactions and two thermal chemical reactions:
[log K(300) - log K(200)]
[1/200 - 1/300]
2.303R
1000
∆rH°/kJ mol-1
)
(17)
A major factor in determining the change in entropy for a given
reaction is the change in number of gas molecules as reactants
go to products, ∆rn (eq 15). If a reaction is endothermic, ∆rH°
> 0, there is a general, useful relation between thermodynamics
and chemical kinetics: the kinetic activation energy E must be
equal to or greater than ∆rH°, where activation energy is defined
as E in the Arrhenius rate constant expression
j1: O2 + hν (l < 242 nm) ) O + O slow
k1: O + O2 + M ) O3 + M fast
j2: O3 + hν (vis and UV) ) O2 + O fast
k2: O + O3 ) 2O2 slow
k ) A e-E/(RT)
(18)
A reaction, which is thermodynamically favored by an increase
of entropy (∆rn > 0), may be kinetically limited by an activation
energy inferred from a positive ∆rH°.
which sets up a steady-state concentration of atomic oxygen
and of ozone:
j2[O3]
Results with K/Q Method
[O]PHOTO STEADY STATE
)
k1[M][O2]
Chemical reactions discussed here are identified by a number
and the symbol #, and a single sequence of reactions numbered
#1-#33 runs through Tables 1-3. Results of log(K/Q) are
summarized in Table 1. For each of 14 reactions, the range of
log(K/Q) over the two-dimensional atmospheric model is given
for (i) September 21 noon, (ii) September 21 midnight, (iii) June
21 noon, and (iv) June 21 midnight. For each reaction there is
a brief comment concerning whether thermodynamics favors
the occurrence of the reaction, does not allow it to occur, or
gives a mixed result depending on altitude, latitude, time of
day, or season. Negative heat of reaction, -∆rH° (eq 17), and
increase of gas volume upon reaction, ∆rn (eq 15), are listed in
Tables 1 and 3.
1/2
j1k1[M]
[O3]PHOTO STEADY STATE
)
[O2]
(
)
j2k2
This photochemical steady-state concentration of ozone by the
Chapman mechanism exceeds the chemical thermodynamic
equilibrium concentration by many orders of magnitude,
comparable to those in Figure 1 and Table 1 (reaction #1).
Ozone is never at chemical equilibrium in the atmosphere.
Also, ozone undergoes thermal decomposition:
k3: O3 + M ) O2 + O + M
Difference between Chemical Equilibrium and Photo-
chemical Steady State. We carried out this procedure for a
case that is fundamental to atmospheric chemistry, the balance
between ozone and molecular oxygen (Chapman,5 1930):
However, the thermal decomposition of ozone is so slow as to
be negligible at tropospheric and stratospheric temperatures, but
the rate becomes very fast as the temperature rises above 100
°C.
Within the Chapman mechanism, the conversion of ozone to
oxygen is strongly thermodynamically favored, and the rate of
this conversion is slow. By satisfying these two conditions,
reaction #1 satisfies the necessary condition for being sped up
by catalysis; the sufficient condition is to find a suitable catalyst.
Indeed, the decomposition of ozone is well-known to be
catalyzed by free radical pairs (OH/HOO,6 NO/NO2,7,8 Cl/
ClO,9,10 and others) through homogeneous gas-phase catalytic
cycles, illustrated below with two examples:
2O3 ) 3O2
(#1)
The convention in all latitude-altitude plots is that -90, 0, and
90 latitudes correspond to the south pole, equator, and north
pole, respectively. Figure 1 shows values of log(K/Q) for #1
at all latitudes, altitudes 0-60 km, June, noon. We made similar
plots at June midnight, September noon, and September
midnight, and the four plots are so nearly alike that it is pointless
to show more than one. Ozone is thermodynamically unstable
with respect to oxygen. Reaction #1, 2O3 ) 3O2, is 286 kJ
OH + O3 ) HOO + O2
HOO + O3 ) OH + 2O2
-1
mol
exothermic (eq 17), and it occurs with a 50% increase
in number of gas molecules (eq 15). Since the concentration
of molecular oxygen is about a million-fold larger than that of
ozone, the concentration of oxygen is essentially constant as
ozone reacts according to reaction #1, and the actual and
equilibrium concentrations of O2 are essentially equal. Con-
sequently, K/Q is equal to ([O3]ACTUAL/[O3]EQUIL)2 and thus
net: 2O3 ) 3O2
NO + O3 ) NO2 + O2
NO2 + O ) NO + O2
net: O3 + O ) 2O2
(21a)
[O3]ACTUAL/[O3]EQUIL ) (K/Q)1/2
(19)
(21b)
log([O3]ACTUAL/[O3]EQUIL) ) (1/2)log(K/Q)
Two Illustrative Reactions in Table 1. Smith11 [1947]
observed reaction #2 to occur between 330 and 273K:
The actual concentration of ozone in the troposphere and
stratosphere exceeds the equilibrium concentration by 23-40
orders of magnitude (Figure 1 and eq 19).
NO + 2HNO3 ) 3NO2 + H2O all gases
(#2)
There is a difference between “chemical equilibrium” and
“photochemical steady state”, which is sometimes called
“photochemical equilibrium”. Chemical equilibrium is the
dynamic balance between reactants and products with no
external source of energy. Every molecular process is balanced
The results were interpreted, in part, on the basis of surface
adsorption and heterogeneous catalysis. The entries in Table 1
show a range of values of log(K/Q) from -1 to +12; the reaction
is thermodynamically unfavorable under some conditions and

Atmospheric Modeling
J. Phys. Chem. A, Vol. 101, No. 40, 1997 7353
TABLE 1: Thermodynamic Feasibility of Reactions with Gaseous Reactants and Productsa
Sept
noon
Sept
midnight
June
noon
June
midnight
no.
reaction
2O3 ) 3O2 (Figure 1)
NO + 2HNO3 ) 3NO2 + H2O (Figure 2)
ClO + H2O ) HCl + HOO
-∆rH°
∆rn
comment
#1
#2
#3
48 to 72
4 to 11
-8 to -4
48 to 72
-1 to 14
-9 to -3
48 to 80
0 to 12
-8 to -3
46 to 78
0 to 12
-9 to -3
+286
-35.1
-50.4
+1
+1
0
favored
mixed
forbidden
Antarctic Reactions
#4
#5
#6
#7
ClONO2 + HCl ) Cl2 + HNO3
HOCl + HCl ) H2O + Cl2
17 to 20
17 to 21
10 to 16
9 to 15
2 to 8
16 to 22
9 to 18
7 to 15
1 to 8
16 to 22
9 to 17
7 to 15
1 to 8
+67.9
+75.1
+36.7
-7.2
0
0
0
0
favored
favored
favored
mixed
9 to 17
9 to 15
2 to 8
N2O5 + H2O ) 2HNO3
ClONO2 + H2O ) HOCl + HNO3 (Figure 3)
Miscellaneous Reactions
#8
#9
#10
#11
#12
#13
#14
2HNO3 + H2CO ) CO2 + NO + NO2 + 2H2O
HOBr + HBr ) H2O + Br2
72 to 106
15 to 34
11 to 17
0 to 6
-2 to 12
-6 to 0
78 to 109
15 to 34
14 to 17
0 to 6
5 to 18
-3 to 4
72 to 114
15 to 37
11 to 19
0 to 7
76 to 114
15 to 37
10 to 18
2 to 7
+486
+156
+79.0
+42.3
-93.5
100.7
-108
+2
0
0
favored
favored
favored
mixed
mixed
mixed
N2O5 + H2O2 ) HNO3 + HOONO2
HNO3 + H2O2 ) H2O + HOONO2
N2O5 ) NO3 + NO2
0
-4 to 14
-4 to 18
+1
+1
0
HOONO2 ) HO2 + NO2
ClONO2 + H2O ) HCl + HOONO2
-6 to 3
-3 to 4
-11 to -3
-11 to -2
-11 to -1
-12 to -3
forbidden
a The numbers in each cell represent the range of log(K/Q) encountered for that reaction at the specified time and season. -∆rHo in units of
kJ/mol.
TABLE 2: Thermodynamic Feasibility for Atmospheric Reactions Producing Photolytically Active Intermediates As Measured
by the Range of log[X], When X Is at Chemical Equilibrium with Ambient Reactants and Productsa
Sept
Sept
June
June
no.
reaction
noon
midnight
moon
midnight
comments
HONO-Producing Reactions
#15
#16
#17
#18
#19
#20
#21
#22
H2CO + 2HNO3 ) CO2 + 2HONO + H2O
CO + HNO3 ) CO2 + HONO
H2CO + 2NO2 ) 2HONO + CO
HO2 + NO2 ) HONO + O2
47 to 67
44 to 64
27 to 36
22 to 34
16 to 21
7 to 11
47 to 67
44 to 64
25 to 35
22 to 38
15 to 21
0 to 9
47 to 73
44 to 68
25 to 39
20 to 41
15 to 22
2 to 11
47 to 73
44 to 68
25 to 30
24 to 40
15 to 22
0 to 9
always favored
always favored
always favored
always favored
always favored
favored, Figure 5
mixed, Figure 5
not favored, Figure 5
HOONO2 ) HONO + O2
NO + HNO3 ) NO2 + HONO
NO + NO2 + H2O ) 2HONO
2NO2 + H2O ) HONO + HNO3
3 to 8
2 to 6
3 to 8
-4 to 6
2 to 7
-4 to 6
-2 to 6
-4 to 6
ClNO2 and Br2 Reactions
#23
#24
#25
N2O5 + HCl ) HNO3 + ClNO2
HNO3 + HCl ) H2O + ClNO2
HOBr + HBr ) H2O + Br2
10 to 18
1 to 7
5 to 18
2 to 7
15 to 34
7 to 15
1 to 7
15 to 37
9 to 19
1 to 7
15 to 37
always favored
weakly favored
always favored
15 to 34
a All thermochemical data are obtained from ref 2 except Kf(HOBr), which is taken from ref 23. [X] ) HONO, ClNO2 or Br2.
TABLE 3: Thermodynamic Feasibility According to Different Dimensionless Ratios (See Text)a
no.
reaction
thermodynamic test
value range
-∆rH°
∆Rn
comment
Complex Mechanisms
log K26/[H2O]
log K26/[H2O]
#26
#27
#28
HNO3 + H2CO ) HONO + CO + H2O
2HONO ) NO + NO2 + H2O
2HNO3 + 2H2CO ) NO + NO2 + 2CO + 3H2O
#28 ) 2 × #26 + #27
59 to 80
1.8 to 8.5
81 to 140
+297.3
-38.5
+1
+1
+3
strongly favored
endothermic
strongly favored
log(K28/Q28)
+556.0
#20
#2
HNO3 + NO ) HONO + NO2
#2 ) 2 × #20 + #27
K20 (not log K20)
log(K2/Q2)
8.5 to 14
0 to 12
+1.7
-35.1
0
+1
weakly favored
mixed, Figure 2
Nitric and Sulfuric Acid Reduction
log(K/[H2O])
#29
#30
#31
#24
#32
#33
2HNO3+CH4 ) 2HONO+H2CO+H2O
HNO3 + H2O2 ) HONO + H2O + O2
HNO3 + SO2 + H2O ) H2SO4 (liq) + HONO
HNO3 + HCl ) ClNO2 + H2O
H2SO4 (liq) + H2CO ) SO2 + CO + 2H2O
H2SO4 (liq) + 2HCl ) SO2 + Cl2 + 2H2O
42 to 67
17 to 25
1.7 to 32
8.8 to 21
25 to 45
-15 to +5
+59.0
+6.7
+1
+1
-2
0
+3
+2
strongly favored
strongly favored
favored, Figure 6
weakly favored
endothermic
log(K/[O2]
log[HONO]/[SO2]
K24 (not log K24)
+220.5
+3.4
log([SO2/[H2CO]
-38.2
-218.6
log[SO2][Cl2]/[HCl]2
not allowed
a Nitric acid reduction and sulfuric acid reduction. The range of values is based on profiles at 6, 42, and 71 °N, June noon.
strongly favored under other conditions. In this case, it is
interesting to show two-dimensional altitude and latitude plots
of log(K/Q) for (a) September noon, (b) September midnight,
(c) June noon, and (d) June midnight in Figure 2. Above 30
km altitude in the sunlit atmosphere, including the June summer
pole, the reaction is thermodynamically favored to proceed by
8-9 orders of magnitude, but at midnight the modeled Q
approaches the equilibrium value. Below 30 km, log(K/Q) is
large and positive in the south polar region, day and night at
both seasons, and at equatorial and midlatitudes log(K/Q) is +1
at midnight and 5-9 at noon. The low midnight values mean
that the concentrations of NO, NO2, HNO3, and H2O are close
to their equilibrium values with respect to this reaction. Solar
radiation during the daytime increases the [NO]/[NO2] ratio
through ultraviolet photolysis of NO2 and drives this reaction
away from its nighttime near-equilibrium state. Thus, the
changes in Figure 2 are not driven by this reaction itself but
rather by other chemical and photochemical processes that
control the [NO]/[NO2] ratio. The ambient values of reactants
and products are such that this reaction has a strong thermo-

7354 J. Phys. Chem. A, Vol. 101, No. 40, 1997
Fairbrother et al.
than in the reactants. The values of log(K/Q) vary between 72
and 114, which means that at chemical equilibrium the
concentration of at least one of the reactants must approach zero.
Reactions #3-#7, #9-#11, and #14) have ∆rn of zero, their
average values of log(K/Q) are plotted against -∆rH° in Figure
4, and there is a strong correlation, which shows that the value
of -∆rH° alone could be used as a qualitative guide to their
thermodynamic viability. Reactions in Table 1 that have ∆n
) 1, have values of log(K/Q) about 5-10 units higher than
those with comparable -∆rH° and with ∆n ) 0.
Results with Other Thermodynamic Tests
Thermodynamic Assessment for Species Not Included in
LLNL Model. The LLNL model does not include HONO,
ClNO2, and Br2, and Table 2 presents a series of reactions
involving these species. In cases such as these where only one
species is unobserved, a modified version of the log(K/Q)
method can still provide valuable insight into the thermodynamic
viability of a particular process. For example, consider the
reaction
Figure 1. Latitude-altitude plot of logl0(K/Q) for the gas-phase
reaction 2O3 ) 3O2, modeled at June noon, as a function of altitude
and latitude (reaction #1 in Table 1). Over the troposphere and
stratosphere, the reaction has an exceedingly strong thermodynamic
potential to react at all latitudes, altitudes, times of day, and season.
The reaction is strongly exothermic with an average enthalpy of reaction
of -286 kJ mol-1 between 200 and 300 K.
H2CO + 2HNO3 ) CO2 + 2HONO + H2O (#15)
In this case, define Q′ as
dynamic potential to occur under sunlit conditions everywhere
and at south polar winter and fall conditions, and it has a weak
but nonzero thermodynamic potential to occur at night below
30 km altitude.
One use for this method is illustrated with respect to the
potential deactivation of atmospheric ClO by heterogeneous
catalysis according to reaction #3 of Table 1:
Q ) Q′[HONO]2
(22)
When the reaction is at thermodynamic equilibrium, K ) Q,
and the concentration of HONO that would, according to this
reaction, be in chemical equilibrium with ambient observed or
modeled H2CO, HNO3, CO2, and H2O is
ClO + H2O ) HCl + HOO
(#3)
[HONOlEQUIL ) (K/Q′)1/2
)
K15([H2CO][HNO3]2
1/2
If this reaction is subjected to the method of this article, it is
found to be thermodynamically unfavorable by 3-9 orders of
magnitude over the entire troposphere and stratosphere. On this
basis, one would reject this reaction with no loss of time and
effort in looking for a suitable catalyst.
(23)
{
)
[CO2][H2O]
ACTUAL
The values of [HONO]EQUIL can be plotted as either a vertical
profile or as latitude-altitude contours. We apply this procedure
to three species, X ) HONO, ClNO2, Br2, and give results in
Table 2.
To decide whether a reaction for these transients is thermo-
dynamically “favored”, we compare the calculated [XlEQUIL
against what we regard as an atmospherically important value,
which depends on its reactivity and potential for forming active
photolytic products, which for [HONO], [ClNO2], or [Br2] are
HO + NO, Cl + NO2, and Br + Br, respectively. On this basis,
we take thermodynamically favored values of [X] to be
Catalysts Associated with Antarctic Ozone Loss. For four
gas-phase reactions (#4-#7), which are associated with the
Antarctic ozone hole, Table 1 summarizes the range of log(K/
Q) in decreasing order of the values of log(K/Q). For the first
three cases, the reactions have a strong thermodynamic tendency
to occur at all latitudes, altitudes, and seasons, and yet these
reactions do not occur at a measurable rate in the gas phase.
As is now well-known,12-16 these reactions occur at a significant
rate by heterogeneous catalysis on atmospheric particles in the
south polar winter and spring. The fourth reaction in this group
in Table 1, the hydrolysis of chlorine nitrate, has values of log-
(K/Q) between 1 and 8, that is, from very weak to strong
thermodynamic tendency to occur, and it is interesting to
examine the full two-dimensional plots, which are given as
Figure 3. The low values occur only in the Austral winter and
spring south polar stratosphere, and under some Antarctic
conditions, the hydrolysis of chlorine nitrate may be thermo-
dynamically limited. The K/Q values are at least 1000 over
the rest of the troposphere and stratosphere.
Other Atmospheric Processes. Table 1 illustrates the range
of log(K/Q) values for a variety of reactions determined as a
function of both daytime and seasonal variations. The additional
stratospheric processes in Table 1 are listed in decreasing order
of their molar heats of reaction, -∆rH° (eq 17). It is interesting
to note the relative role of -∆rH° and ∆rn on the magnitude of
the thermodynamic tendency to react. The reduction of nitric
acid by formaldehyde (reaction #8) is exothermic by 486 kJ
mol-1, and there are two more moles of gas in the products
log[HONO] g 7
log[ClNO2] g 7
log[Br2] g 5
(in molecules cm-3) for the proposed reaction to represent a
significant potential source of radical species. Results from this
type of analysis, evaluated for log([HONO]), log([ClNO2]), or
log([Br2]) are shown in Table 2.
HONO-Producing Reactions. For five of the reactions
(#15-#19) in Table 2, the calculated concentrations of [HO-
NOEQUIL] are much larger than the atmospheric source material,
and thus, we obtain only the qualitative result that these reactions
are strongly thermodynamically favored to produce HONO and
its photolysis products; the numbers and plots of these cases
are not significant. Cases that are weakly favored or are favored
in some regions but not in others are plotted as vertical profiles

Atmospheric Modeling
J. Phys. Chem. A, Vol. 101, No. 40, 1997 7355
Figure 2. Latitude-altitude plot of logl0(K/Q) for the gas-phase reaction NO + 2HNO3 ) 3NO2 + H2O modeled at (a) September noon, (b)
September midnight, (c) June noon, and (d) June midnight (reaction #2 in Table 1).
at three representative latitudes for the daytime log([HO-
NO]EQUIL) in Figure 5. Reaction #20, NO + HNO3 ) HONO
+ NO2, would be a strong source of HONO and thus of OH, if
it had a suitable catalyst (Figure 5, right trio of profiles). The
formation of HONO by heterogeneous catalysis of reaction #21,
NO + NO2 + H2O ) 2HONO, could be important in the
boundary layer, but from thermodynamics alone (and in
agreement with ref 1 and laboratory results by Saastad et al.17),
it is seen to be a weak source of OH in the rest of the atmosphere
(Figure 5, center trio of profiles). The formation of HONO by
heterogeneous catalysis of reaction #22, 2NO2 + H2O ) HONO
+ HNO3, might be important overnight in heavy urban smog,
but from thermodynamics alone, it is seen to be a negligible
source of OH in the rest of the atmosphere (Figure 5, left trio
of profiles).
Other Thermodynamic Tests. For a reaction with ∆rn of
zero, the equilibrium constant is dimensionless; it gives the
relative probability of products and reactants, and K or log K is
a rough measure of the thermodynamic reaction potential. If
log K is very large, the qualitative evaluation of “strongly
favored” is obtained by this simple method. This test would
be adequate in making a qualitative judgment of thermodynamic
feasibility of reactions #4-#6, #9, #10, #16, #18, #23), all of
which have zero ∆rn and very large equilibrium constants. An
extension of this use of dimensionless ratios is made for some
reactions that involve a unit change of ∆rn. In the troposphere
and stratosphere, H2O is present at concentrations 2 or more
orders of magnitude larger than those of NOy, HOy, or Cly, and
[H2O] will not change significantly upon reaction with these
trace species. The essentially constant value of [H2O] is
incorporated in the equilibrium constant. Reaction #26, the first
entry in Table 3, is an example:
K26
[HONO][CO]
)
, dimensionless
(
)
[H2O]ACTUAL
[HNO3][H2CO]
EQUIL
This procedure would identify reactions #15, #26, #29 as
strongly favored. Since molecular oxygen is in great excess
over the trace atmospheric species, an analogous procedure to
that used for H2O can also be employed for reactions involving
O2. Application of this approach with O2 demonstrates that
reaction #30 in Table 3 is strongly favored.
Reaction #31 in Table 3, the formation of HONO from sulfur
dioxide and nitric acid, involves two species not included in
the LLNL model: HONO and SO2 . Since HONO is a product
and SO2 a reactant, the equilibrium constant expression can be
solved for the ratio of the two unknown species, which gives a
measure of the local thermodynamic feasibility of the reaction:
[HNO3]
31 [ H2O]
[HONO]
[SO2]
) K
(24)
We evaluate the equilibrium ratio over the two-dimensional
space of the model and show vertical profiles of this ratio in
Figure 6. This reaction is very strongly favored by thermody-

7356 J. Phys. Chem. A, Vol. 101, No. 40, 1997
Fairbrother et al.
Figure 3. Latitude-altitude plot of logl0(K/Q) for the gas-phase reaction ClONO2 + H2O ) HOCl + HNO3 modeled at (a) September noon, (b)
September midnight, (c) June noon, and (d) June midnight (reaction #7 in Table 1).
Figure 5. Vertical profiles, triplets at 6, 42, and 71 °N, for each
reaction, of the concentration of HONO that would exist if reactions
#20, #21, and #22 of Table 2 were in chemical equilibrium with ambient
reactants and products of reactions: (left) 2NO2 + H2O ) HONO )
HNO3; (middle) NO + NO2 + H2O ) 2HONO; (right) HNO3 + NO
) HONO + NO2.
Figure 4. Plot of log(K/Q) as a function of negative heat of reaction
(-∆rH°/kJ mol-1) for the nine reactions in Table 1 with no change in
number of gas molecules between reactants and products (∆rn ) 0).
namics. It is known to occur at room temperature,18 and it may
be important after volcanoes, which eject SO2 high into the
atmosphere.
by heterogeneous catalysis, has one of the strongest thermody-
namic potentials of all the reactions studied here: the log(K/Q)
range is 72-114; it is exothermic by 486 kJ mol-1; the number
of moles of gas increases by 2. As written, the reaction would
require a three-body collision, and it is therefore more reasonable
Discussion
Proposed Mechanisms for Complex Reactions. The reduc-
tion of nitric acid by formaldehyde (reaction #8), presumably

Atmospheric Modeling
J. Phys. Chem. A, Vol. 101, No. 40, 1997 7357
troposphere. When the settling aerosol particles take on extra
water, positive ionic forms of nitrous acid turn into molecular
HONO and evaporate into the atmosphere, where they ac-
cumulate overnight and photolyze to OH and NO at sunrise
and during the day. This source of HONO would add to the
HONO locally formed in the lower stratosphere and upper
troposphere, and it might contribute to the extra OH ob-
served.21,22
Similarly, reaction #2 can be represented by the sum of
bimolecular steps:
twice HNO3 + NO ) HONO + NO2
plus 2HONO ) NO + NO2 + H2O
net: 2HNO3 + NO ) 3NO2 + H2O
(#20)
(#27)
(#2)
Figure 6. Thermodynamic potential for forming HONO from HNO3,
SO2, and H2O (reaction #31 in Table 3). The vertical profiles are the
ratio of HONO over SO2 if there was chemical equilibrium between
these two species and ambient HNO3 and H2O.
This reaction has its best chance of occurring in nitric acid-rich
sulfate aerosols. Since #27 is 38.5 kJ mol-1 endothermic, the
reduction of nitric acid by nitric oxide in the stratosphere is
expected to be given by reaction #20 rather than by reaction
#2. Figure 5 shows that reaction #20 is mildly favored by
thermodynamics at altitudes below the middle stratosphere.
Reduction of Nitric Acid and of Sulfuric Acid. There is
strong thermodynamic potential for reducing nitric acid through
heterogeneous catalysis by methane (reaction #29), formalde-
hyde (reactions # 8, #15, #26), carbon monoxide (reaction #16),
sulfur dioxide (reaction #31, Figure 6), and hydrogen peroxide
(reaction #30). Nitric acid is weakly reduced by nitric oxide
(reaction #20, Figure 5) but not by hydrogen chloride (reaction
#24). Sulfuric acid has a strong thermodynamic tendency to
be reduced by formaldehyde (reaction #32) but not by HCl
(reaction #33). The possible atmospheric importance of some
of these reactions is discussed below.
on kinetic grounds to expect that it requires a set of elementary
bimolecular steps. Formaldehyde is known to stick to and
remain indefinitely in sulfuric acid.19,20 Jayne et al.20 suggest
a condensed-phase mechanism for the reaction of nitric acid
with formaldehyde in sulfuric acid solution, based on room
temperature observations, which involves formic acid (HCOOH)
as an intermediate. These two steps plus reaction #27 is a
mechanism for reaction #8:
HNO3 + H2CO ) HONO + HCOOH
all in sulfuric acid solution (25a)
HNO3 + HCOOH ) HONO + CO2 + H2O (25b)
Methane (reaction #29) and carbon monoxide (reaction #16)
have exceedingly strong thermodynamic potentials for reducing
nitric acid to HONO. Since methane and carbon monoxide are
present in the atmosphere at concentrations many orders of
magnitude greater than those of other possible significant
reducers of HNO3 (H2CO, SO2, H2O2, NO), heterogeneous
catalytic reduction of nitric acid by CO or CH4 might be
important, even with a low value of γ, the reaction probability
per collision, with nitric acid-rich sulfuric acid aerosols.
Reaction #31, HNO3 + SO2 + H2O ) H2SO4(liq) + HONO,
is known to occur readily at ice temperature,18 but the products
are ionic species H2ONO+HSO4- (solid or in solution). Upon
addition of water, HONO is evolved as a gas. Figure 6 shows
the reaction to be strongly thermodynamically allowed from the
earth surface to the middle stratosphere. The reaction is
exothermic, and thus, it could have no activation energy. The
rate of this reaction under atmospheric conditions is not known.
If reaction #31 occurs on sulfuric acid aerosols, it might be
important after large volcanoes and also at night. The reduction
of nitric acid by hydrogen peroxide, HNO3 + H2O2 ) HONO
+ H2O + O2 (reaction #30), is strongly thermodynamically
2HONO ) NO + NO2 + H2O
(#27, 25c)
net: 2HNO3 + H2CO ) CO2 + 2H2O + NO + NO2 (#8)
The sum of the first two steps is strongly exothermic, but the
third step is endothermic, ∆rH ) 38.5 kJ mol-1, which implies
a significant activation energy (eq 18) and a slow rate for the
third step at stratospheric temperatures. According to these
considerations, the reaction between nitric acid and formalde-
hyde to form carbon dioxide does not occur as reaction #8 but
rather as
2HNO3 (gas) + H2CO (solvated) ) 2HONO (solvated) +
CO2 (gas) + H2O (gas) (26)
Like reaction 26, reactions #15- #22 are shown as producing
HONO in sulfuric acid aerosols, and thus, the interaction
between HONO and sulfuric acid needs to be considered.1 In
highly concentrated sulfuric acid, HONO exists in solution as
nonvolatile nitronium bisulfate ions, NO+ and HSO4-, and at
high concentrations of these ions, they precipitate out as the
ionic crystal nitrosyl sulfuric acid. At somewhat lower con-
centration of sulfuric acid, nitrous acid exists in solution as a
hydrated nitronium ion, H2ONO+. At still lower concentrations
of sulfuric acid it exists as molecular HONO and tends to
evaporate out of the sulfuric acid solution. If HONO is formed
in the 20-25 km altitude range, where the sulfuric acid
percentage is high, the nonvolatile dissolved or precipitated
nitronium bisulfate form of nitrous acid could accumulate in
sulfuric acid aerosols, and when the particles grow big enough,
they begin to settle out into the lower stratosphere and upper
allowed, and the reaction is exothermic by 6.7 kJ mol-1
.
We examine the thermodynamics of the reduction of super-
cooled liquid sulfuric acid by HCl and by formaldehyde:
H2SO4 (liq) + 2HCl ) SO2 + Cl2 + 2H2O (#33)
H2SO4(liq) + H2CO ) SO2 + CO + 2H2O (#32)
Reduction by HCl is thermodynamically unfavorable in most
of the atmosphere, and in addition, the rate must be slow at
stratospheric temperatures, since the reaction is endothermic by

7358 J. Phys. Chem. A, Vol. 101, No. 40, 1997
Fairbrother et al.
219 kJ mol-1. Reduction of sulfuric acid by HCl is thus ther-
modynamically and kinetically unfavorable. Sulfuric acid has
a strong thermodynamic tendency to be reduced by formalde-
hyde (reaction #32) largely by virtue of the large increase of
entropy as one volume of gas goes to four, but the reaction is
endothermic by 38 kJ mol-1 and probably slow at stratospheric
temperatures.
products: ionic forms in sulfuric solution and NO and NO2 in
the gas phase.
By use of standard chemical thermodynamics, this article
presents a full derivation and extensive use of a relatively new1
method of interpreting global atmospheric data. As an example
of its use, we take a global look at the departure of atmospheric
reactions from chemical equilibrium, seeking possible new
heterogeneous reactions and demonstrating that some reactions
cannot be made to go from reactants to products by catalysis.
Summary
A purpose of this study is to see if there are additional
stratospheric or tropospheric gas-phase chemical reactions that
might undergo heterogeneous catalysis. On the basis of their
thermodynamic and kinetic characteristics, we regard the
following reactions as being reasonable candidates for further
laboratory study to see if they undergo heterogeneous catalysis
under atmospheric conditions.
Acknowledgment. The authors acknowledge support of this
work by the National Science Foundation under Grant No.
ATM-9412445 and the U.S. Department of Energy under
Contract No. DE-AC03-76SF00098. We are grateful to Dr.
Douglas Kinnison for providing concentrations of atmospheric
species as calculated by the LLNL two-dimensional model.
References and Notes
on H2SO4 aerosols preloaded with H2CO:
HNO3 + 2H2CO ) 2HONO + CO2 + H2O
on H2SO4 or HNO3-rich aerosols:
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HNO3 + SO2 + H2O ) H2SO4 (liq) + HONO
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HNO3 + CO ) HONO + CO2
(8) Johnston, H. S. Science 1971, 173, 522.
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2HNO3 + CH4 ) 2HONO + H2CO + H2O
HNO3 + H2O2 ) HONO + H2O + O2
HNO3 + NO ) HONO + NO2
on cold ice surfaces:
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1987, 1258.
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N2O5 + H2O2 ) HNO3 + HOONO2
Formaldehyde H2CO has an extremely strong thermodynamic
tendency to reduce nitric acid to HONO. Formaldehyde is
captured and held by sulfuric acid aerosols,19,20 and conse-
quently, aerosols loaded with H2CO might react upon collision
with nitric acid. Reactions just among NO, NO2, and H2O have
weak or highly localized thermodynamic potential of forming
HONO, and these reactions are not good candidates for
heterogeneous catalysis. Where HONO is a product in the cases
above, laboratory studies should look for HONO or its reaction
(23) McGrath, M. P.; Rowland, F. S. J. Phys. Chem. 1994, 98, L4773.