SECTION 3.

EQUILIBRIUM CONSTANTS

Table of Contents
SECTION 3. EQUILIBRIUM CONSTANTS .......................................................................................................... 3-1
3.1 Format ......................................................................................................................................................... 3-1
3.2 Definitions................................................................................................................................................... 3-1
3.3 Notes to Table 3 .......................................................................................................................................... 3-3
3.4 References................................................................................................................................................... 3-6

Tables
Table 3-1. Equilibrium Constants............................................................................................................................. 3-2

3.1 Format
Some of the three-body reactions in Table 2 form products that are thermally unstable at atmospheric
temperatures. In such cases the thermal decomposition reaction may compete with other loss processes, such as
photodissociation or radical attack. Table 3 lists the equilibrium constants, K(T), for several reactions which may
fall into this category. The table has three column entries, the first two being the parameters A and B which can be
used to express K(T):
K(T)/cm3 molecule–1 = A exp(B/T) (200 < T < 300 K)
The third column entry in Table 3 is the calculated value of K at 298 K.
The data sources for K(T) are described in the individual notes to Table 3.

3.2 Definitions
When values of the heats of formation and entropies of all species are known at the temperature T, we
note that:
ΔSoT ΔHoT
log10 ⎡⎣ K(T) / cm3molecule-1 ⎤⎦ = − + log10 (T) - 21.87
2.303R 2.303RT

Where the superscript “o” refers to a standard state of one atmosphere. In some cases K values were
calculated from this equation, using thermochemical data. In other cases the K values were calculated directly from
kinetic data for the forward and reverse reactions. When available, JANAF values were used for the equilibrium
constants. The following equations were then used to calculate the parameters A and B:

The relationships between the parameters A and B and the quantities ΔSo(298 K) and ΔHo(298 K) are:
eR ′ T ⎛ ΔSo ⎞ −22 ⎛ ΔSo ⎞
A= exp ⎜ ⎟ = 3.7x10 T exp ⎜ ⎟
N av ⎝ R ⎠ ⎝ R ⎠

where R′ = 82.1 cm3 atm mole–1K–1, and Nav = 6.02 × 1023 molecule mole–1 and
⎡ ΔH o + RT ⎤
B/ o K = − ⎢ ⎥
⎣ R ⎦

3-1
 Table 3-1. Equilibrium Constants
A/cm3
Reaction B/°K Keq(298 K) f(298 K)a g Note
molecule–1
HO + NO2 → HOONO 3.9×10–27 10125 2.2×10–12 2 -400 1

HO2 + NO2 → HO2NO2 2.1×10–27 10900 1.6×10–11 1.3 100 2

NO + NO2 → N2O3 3.3×10–27 4667 2.1×10–20 2 100 3

NO2 + NO2 → N2O4 5.9×10–29 6643 2.8×10–19 1.4 100 4

NO2 + NO3 → N2O5 2.7×10–27 11000 2.9×10–11 1.2 100 5

CH3O2 + NO2 → 3CH3O2NO2 9.5×10–29 11234 2.2×10–12 1.3 500 6

CH3C(O)O2 + NO2 →
9.0×10–29 14000 2.3×10–8 1.2 200 7
CH3C(O)O2NO2
CH3CH2C(O)O2 + NO2 →
9.0×10–29 14000 2.3×10–8 10 800 8
CH3CH2C(O)O2NO2
CH3C(O)CH2 + O2 →
7×10–27 13000 6×10–8 10 800 9
CH3C(O)CH2O2
F + O2 → FOO 4.5×10–25 6118 3.7×10–16 1.5 300 10

Cl + O2 → ClOO 6.6×10–25 2502 2.9×10–21 1.7 100 11

Cl + CO → ClCO 3.5×10–25 3730 9.6×10–20 1.2 200 12

ClO + O2 → ClO.O2 2.9×10–26 <3700 <7.2×10–21 13

ClO + ClO → Cl2O2 9.3×10–28 8835 7.0×10–15 1.2 300 14

ClO + OClO → Cl2O3 1.6×10–27 7155 4.3×10–17 1.3 300 15

OClO + NO3 → O2ClONO2 6.6×10–29 3971 4.0×10–23 5.5 500 16

OH + CS2 → CS2OH 4.5×10–25 5140 1.4×10–17 1.4 300 17

CH3S + O2 → CH3SO2 1.8×10–27 5545 2.2×10–19 1.4 300 18

Cl + CS2 → Cl---CS2 1.8×10–25 4982 3.3×10–18 1.3 150 19

Br+CH3SCH3→Br---(CH3)2 S 3.4×10–25 3021 4.6×10–15 1.2 100 20

K/cm3 molecule–1 = A exp (B/T) [200 < T/K < 300] – shaded areas indicate changes or additions since JPL02-25
a f(298 K) is the uncertainty factor at 298 K, and g is a measure of the uncertainty in the quantity B. To calculate
the uncertainty at temperatures other than 298 K, use the expression:
⎡ ⎛1 1 ⎞⎤
f ( T ) = f ( 298 K ) exp ⎢g ⎜ − ⎟⎥
⎣ ⎝ T 298 ⎠ ⎦

3-2
3.3 Notes to Table 3

JPL Publication numbers for the most recent revision of the table entry and note are given at the
end of each note.

1. HO + NO2. This value is for the HOONO product channel. Using the data from Hippler et al. [37], Golden et
al. [30] performed a third law analysis using structures and frequencies from an ab initio quantum calculation at
the QCISD(T)/cc-pVDZ level to extract the heat of formation of cis-cis HOONO at 0K of -9.28 kJ mol-1. The
value at 298K is -15.7 kJ mole-1. (A small error in the entropy of HOONO caused Golden et al. [29] to suggest
– 8.60 kJ mole-1.) The data covers 430<T/K<475 with 30% uncertainties. The error limits reflect the fact that
the uncertainty is greater at 298 K than in the temperature range where the data were taken. NEW ENTRY
Back to table
2. HO2 + NO2. The value was obtained by combining the expression from Table 2-1 for the rate constant of the
reaction as written with that from an average of the expressions from Graham et al. [33] and Zabel [72] for the
reverse reaction. Values for the entropy and heat of formation of pernitric acid may be extracted. These values
are: S(298 K) = 71.7 cal mole–1 K–1 and ΔHf(298 K) = –12.9 kcal mole–1. If the entropy is calculated from the
frequencies and moments of inertia given by Chen and Hamilton [16], the value becomes 71.0 and the heat is –
13.1. The values in the Appendix to this report reflect these results. A study of the thermal decomposition of
HO2NO2 by Gierczak et al. [27] combined with values for the association reaction are in agreement. (Table:
JPL06, Note: JPL06) Back to table
3. NO + NO2. The data are from JANAF [41] and Chao et al. [14]. This process is included because a
measurement of the rate constant by Smith and Yarwood [63] and Markwalder et al. [44] shows that it is too
slow to be an important process in most atmospheric and laboratory systems. (Table: 94-26, Note: 94-26) Back
to table
4. NO2 + NO2. The data are from JANAF [41] and Vosper [68], Chao et al. [15] and Amoruso et al. [1]. Rate
data for this process are reported by Brunning et al. [7], Borrell et al. [4] Gozel et al. [31] and Markwalder et al.
[44]. A direct study by Harwood and Jones [35] at low temperatures is in agreement with the recommendation.
Re-evaluation of the data suggests slightly different error limits than recommended in JPL 02-25. Estupiñán et
al. [23], Wollenhaupt and Crowley [71] and Tuchler et al. [65] deduce values that are in essential agreement,
within uncertainties, with the recommendation. (Table: 02-25, Note: 02-25) Back to table
5. NO2 + NO3. The recommendation is from Cantrell et al. [12]. They report rate constants for the
decomposition reaction, which they combine with the rate constants of Orlando et al. [53] to obtain the
equilibrium constant. Agreement is quite good with the data of Burrows et al. [9] and Cantrell et al. [11] and
the room temperature data of Tuazon et al. [64] Perner et al. [56] and Hjorth et al. [38]. An evaluation by
Pritchard [59] is also in excellent agreement with the recommendation. Pritchard [59] examined the data of
Cantrell et al. [11], Burrows et al. [9], Graham and Johnston [32], Wangberg et al [69], Schott and Davidson
[60], and the room temperature data of Tuazon et al. [64], Perner et al. [56] and Hjorth et al. [38]. He also
included the values given by Smith et al. [62], and Kircher et al. [42], who combined data on the forward
reaction, tabulated in Table 2-1, with decomposition data of by Connell and Johnston [18] and Viggiano et al.
[67]. The Pritchard [59] result was used as the basis for the value in JPL 00-3, but some uncertainties in the
entropies of NO3 and N2O5 justify the reversion to the JPL 97-4 recommendations. In JPL 02-25, the values of
the parameters were inadvertently left unchanged from those in JPL 00-3. The differences are very small. The
one sigma error limits are better described with f(298) = 1.2. (Table: JPL06, Note: JPL06) Back to table
6. CH3O2 + NO2. Zabel et al. [73] have measured k(dissociation) as a function of pressure (10<P/torr<800) and
temperature (253<T/K<272). Bahta et al. [3] have measured k(dissociation) at 263 K. Using the values of
k(recombination) suggested in this evaluation, (Table-2) Golden [28] has re-evaluated the equilibrium constant.
Bridier et al. [6] measure an equilibrium constant in good agreement with this recommendation, reducing the
uncertainty even further. (Table: JPL06, Note: JPL06) Back to table

3-3
7. CH3C(O)O2 + NO2. The recommendation is derived from measurements of the rate constants in both directions
by Bridier et al. [5]. These authors used the values of the rate constants at 298K and a calculated value of the
entropy change to get a third law value of the equilibrium constant. Their value of the enthalpy is exactly
reproduced in a theoretical study by Miller et al. [46]. (Table: JPL06, Note: JPL06) Back to table
8. CH3CH2C(O)O2 + NO2. Assumed to be the same as for PAN (Note 7). Both sides of the of the reaction differ
from PAN by the group C–(C)(CO)(H)2. Error limits are estimated and expanded from those for PAN. (Table:
02-25, Note: 02-25) Back to table
9. CH3C(O)CH2 + O2. Estimated values of the entropy and enthalpy changes for the reaction are: ΔS = –33 e.u.
and ΔH = –26 kcal/mole. The entropy is from group additivity and the enthalpy from group additivity for the
hydroperoxide followed by assuming that the O–H bond dissociation energy is 88 kcal/mole. Error limits are
estimated from the uncertainties in this procedure. (Table: 02-25, Note: 02-25) Back to table
10. F + O2. Taken from Campuzano-Jost et al. [10]. There is good agreement with data from Pagsberg et al. [54].
This corresponds to a value for ΔHf,298(FO2) = 6.13 ± 0.5 kcal mol–1. There are several modern theoretical
computations [21, 24, 25]of this value, ranging from 6 to 9 kcal mol-1. (Table: JPL06, Note: JPL06) Back to
table
11. Cl + O2. Data are from Baer et al. [2], Nicovich et al. [50] and Mauldin et al. [45]. Zhu and Lin [75] have
reported structure and frequency calculations and a heat of formation for ClOO. Using known thermochemistry
for Cl and O2 and entropy values for ClOO computed from, ΔHf,0 (ClOO) = 23.85 ± 0.1 kcal mole–1 is obtained
by the third law method from the individual data points of the Nicovich et al. [50] data. The Baer et al. [2]
paper reports only one value at each temperature and only graphically, but yields essentially the same value as
Nicovich et al [50]. The third law value from Mauldin et al. [45] is less stable by 0.4 kcal mole-1. Earlier
values, both experimental and theoretical, of the structural parameters of ClOO are referenced in [75]. S°298
(ClOO) = 64.6 cal mole–1 K–1 and ΔHf,298 (ClOO) = 23.5 ± 0.5 kcal mole–1 are recommended. (Table: JPL06,
Note: JPL06) Back to table
12. Cl + CO. From fitting the data of Nicovich et al. [51] who measured both k and K between 185 and 260 K in
N2. They report ΔHf,298 (ClCO) = –5.2 ± 0.6 kcal mole–1. (Table: JPL06, Note: JPL06) Back to table
13. ClO + O2. DeMore [20] reports K < 4 × 10–18 cm3 molecule–1 at 197 K. His temperature dependence of the
equilibrium constant is estimated using S°298 (ClO·O2) = 73 cal mol–1K–1 and ΔH°298 <7.7 kcal mol–1. A higher
value of K has been proposed by Prasad [57], but it requires S°(ClO·O2) to be about 83 cal mol–1 K–1, which
seems unreasonably high. Carter and Andrews [13] found no experimental evidence for ClO·O2 in matrix
experiments. Prasad and Lee [58] discuss these issues and question the validity of the upper limit reported by
DeMore. (Table: 92-20, Note: 94-26) Back to table
14. ClO + ClO. The value is from a third-law calculation based on the data from Cox and Hayman [19] (except for
the two lowest temperature points) and Nickolaisen et al.[49]. The entropy of ClOOCl, the value of which is
71.9cal mol–1 K–1 at 300 K, is calculated from structures and frequencies calculated by Zhu and Lin [74]. The
heat of formation at 300 K is ΔH°f,300 = 30.4 kcal mol–1. A study of branching ratios of ClO + ClO channels in
Cl2/O2/O3 mixtures by Horowitz et al. [39] also finds the equilibrium constant in O2 at 285 K to be in agreement
with the recommendation. Avallone and Toohey used K = 1.99E-30Texp(8854/T) derived from in situ
experiments. (Table: JPL06, Note: JPL06) Back to table
15. ClO + OClO. Data are from Burkholder et al. [8], Hayman and Cox [36] and Green et al. [34]. The best van‘t
Hoff fit to all the data (except for the lowest temperature point of) yields K/cm3 molecule-1 = 2.5x10-
25
exp(5850/T) for {232<T/K<298}. A calculation of the entropy and heat capacity from the structure and
frequencies of ClOCl(O)O reported by Zhu and Lin [76] allows a “3rd Law” fit that yields the recommended
parameters. The 95% error limits encompass all the data. From the 3rd Law calculations S°298 (Cl2O3)=78.7 cal
mol–1 K–1 and ΔHf,0(Cl2O3) =33.6 kcal mol–1 and ΔHf,298(Cl2O3) =32.4 kcal mol–1. (This compares to a
calculated value of ΔHf,0(Cl2O3) =32.3 from [76] and 32.9 from a theoretical calculation by Sicre and Cobos
[61]. Burkholder et al. [8] claim that treating the lowest vibration as a free internal rotation increases the
entropy of ClOCl(O)O by almost 9 cal mol-1 K-1. This value, repeated by Green et al. [34], is not correct. Clark
and Francisco [17] calculated structure and frequencies and conclude that S°298 (Cl2O3)=78.5 cal mol–1 K–1 in
close agreement with the above, but they conclude that ΔHf,0(Cl2O3) =36.9 kcal mol–1 by fitting the data of [8]
and [36] including the lowest temperature point. Li et al. [43] have also reported theoretical calculations for

3-4
 ClOCl(O)O. Their structure and frequencies are in general agreement with [76] and [17], but their energetics
are quite different. (Table: JPL06, Note: JPL06) Back to table
16. OClO + NO3. Theoretical calculations of Parthiban et al. [55]. This value replaces the value in 02-25 that was
deduced by Friedl et al. [26]. Uncertainties are based on ±1 kcal mole-1 uncertainty in calculated heat of
formation. (Table: JPL06, Note: JPL06) Back to table
17. OH + CS2. Fit to the data of Murrells et al. [47], Hynes et al. [40] and Diau and Lee [22] between 246 and 318
K. Re-analysis of errors led to lower value of g than in JPL-02-25. (Table: JPL06, Note: JPL06) Back to table
18. CH3S + O2. Turnipseed et al. [66] report the equilibrium constant for 216 ≤ T/K ≤ 258. From a third law
analysis using ΔS°237 = –36.8 ± 2.6 eu, they obtain ΔHo237 = –11.5 ± 0.9 kcal/mole. (Table: 94-26, Note: 94-26)
Back to table
19. Cl + CS2. Fit to the data of Nicovich et al. [52] between 193 and 258 K. NEW ENTRY Back to table
20. Br + CH3SCH3. Second Law fit to data of Wine et al. [70] and Nakano et al. [48]. This corresponds to a bond
dissociation energy in the adduct of 13.84 kcal mole-1. NEW ENTRY Back to table

3-5
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