EPA-600/2-75-019
August 1975
THE KINETICS OF COM
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EPA-600/2-75-019
ESTIMATING
THE KINETICS OF COMBUSTION
INCLUDING REACTIONS
INVOLVING OXIDES OF NITROGEN AND SULFUR
by
S. W. Benson, D. M. Golden, R. W. Lawrence,
Robert Shaw, and R. W. Woolfolk
Stanford Research Institute
333 Ravenswoocl Avenue
Menlo Park, California 94025
Grant No. R-800798
ROAP No. 21BCC-019
Program Element No. 1AB014
EPA Project Officer: W. Steven Lanier
Industrial Environmental Research Laboratory
Office of Energy , Minerals, and Industry
Research Triangle Park, North Carolina 27711
Prepared for
U. S. ENVIRONMENTAL PROTECTION AGENCY ^
Office of Research and Development^ T5ronmentslPratecUDnAgOT' *
Washington, D. C. 20460 " ' -
August 1975
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EPA REVIEW NOTICE
This report has been reviewed by the National Environmental Research
Center Research Triangle Park, Office of Research and Development,
EPA, and approved for publication. Approval does not signify that the
tontenLs necessarily reflect the views and policies of the Environmental
Protection Agency, nor does mention of trade names or commercial
products constitute endorsement or recommendation for use.
RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U.S. Environ-
mental Protection Agency, have been grouped into series. These broad
categories were established to facilitate further development and applica-
tion of environmental technology. Elimination of traditional grouping was
consciously planned to foster technology transfer and maximum interface
in related fields. These series are:
1 . ENVIRONMENTAL HEALTH EFFECTS RESEARCH
2 . ENVIRONMENTAL PROTECTION TECHNOLOGY
•}. ECOLOGICAL RESEARCH
4. ENVIRONMENTAL MONITORING
5. SOCIOECONOMIC ENVIRONMENTAL STUDIES
6. SCIENTIFIC AND TECHNICAL ASSESSMENT REPORTS
9. MISCELLANEOUS
This report has been assigned to the ENVIRONMENTAL PROTECTION
TECHNOLOGY series. This series describes research performed to
develop and demonstrate instrumentation, equipment and methodology
to repair or prevent environmental degradation from point and non-
point sources of pollution. This work provides the new or improved
technology required for the control and treatment of pollution sources
to meet environmental quality standards.
This document is available to the public for sale through the National
Technical Information Service, Springfield, Virginia 22161.
Publication No. EPA-600/2-75-019
11
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CONTENTS
Page
List of Figures 1V
List of Tables Vi
Acknowledgments VH
Sections
I Conclusions 1
II Recommendations 4
III Introduction 5
IV Estimates of Rate Constants for the Reactions
X + YZ ;± XY + Z 6
V Estimates of Rate Constants for Specific Reactions
S* Requested by EPA and its Contractors 31
1
s VI The Computer Program 33
gr\
(/\ VII Estimates of Rate Constants for Combination
Cs^ and Dissociation Reactions 34
fV
,-_. VIII Variation of Equilibrium Constant with Temperature 35
IX References 37
X Appendices 39
111
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FIGURES
No.
A-3 H + OH -+ H2 + O
' 2
1 Heat changes for reactions having transition states
preceded by an intermediate that is stable with respect
to the reactants 8
2 Heat changes for reactions that are concerted or that
have a transition state that is preceded by an inter-
mediate that is unstable with respect to the reactants 9
3 Comparison of measured and estimated rate constants for
reactions of oxygen atoms 23
4 Comparison of measured and estimated rate constants for
the reaction H + ON -> HO + N 24
5 Comparison of measured and estimated rate constants for 26
reactions of sulfur atoms
6 Comparison of measured and estimated rate constants for
the reaction H + HS -» H2 + S 27
7 Comparison of measured and estimated rate constants for
>2
47
the reaction 0 + ON -> 02 + N 28
A-l 0 + OH -» 02 + H
A-2 H + 02 -4 HO + O 48
49
A-4 O + H2 -» OH + II 50
A-5 N + NO -> N0 + O 51
A-6 0 + N2 -> ON + N 52
A-7 N + 02 -> NO + O 53
A-8 0 + ON -> 02 + N 54
A-9 Heat changes for reactions having transition states
preceded by an intermediate that is stable with respect
to the reactants. In such cases AHg00 = -1 kcal/mole. 61
lv
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Figures (Continued) Page
A-10 Heat changes lor reactions that are concerted or that have i
transition state that is preceded by an intermediate that i.-j
unstable with respect to the reactants. In such cases
AH°00 = 7 kcal/mole. 62
A-11 N + OH -» NO + H 66
A-12 1) + II2 -+ DH + H .68
A-13 N(2D) + 02 -> NO + 0(3P) 69
A-14 NO + M -» N + O + M 76
A-1ft N + O i- M --» NO + M 77
A-16 Oil + M -> O + H + M 78
A-17 II + O + M -> HO + M 79
A-18 H2 -t- M -> II + H + M 80
A-19 II + II + M -> H2 -)• M 81
A-20 H2O + M -* II + OH + M 83
A-21 H + OH + M -» H2O + M 84
A-22 N02 + M -* NO + O + M 87
A-23 NO + O + M -4 N02 + M 88
A-24 H + 02 + M -> HO2 + M 89
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TABLES
No. Page
1 Parameters used in calculating rate constants 2
2 Hydrogen transfer reactions 12
3 Atom transfer reactions 13
4 Values used in calculating rate constants 16
5 Estimated rate parameters and rate constants 22
6 Heats of reaction and estimated Arrhenius parameters
for some requested reactions 32
A-l Thermodynamic properties of monatomic and diatomic
species in the H, N, O system 55
A-2 Overall entropies and heats for all chemical reaction
pairs 56
A-3 Values of A, B, and C used to calculate rate
constants 57
A-4 Calculation of the rate constant as a function of
temperature for O + H2 -» OH + H 58
i
A-5 Determination of values of AH°00 used to calculate
rate constants of atom-transfer reactions in the
II, N, O system 65
A-6 Modified Arrhenius parameters for the reaction
XY + M ^ X + Y + M 73
A-7 Calculation of rate constants for NO+Mi±N+O+M 75
A-8 Modified Arrhenius parameters for the reaction
XYZ +M^XY+Z+M 86
B-l Heats of formation of monatomic, diatomic, and
polyatomic species used to establish heats of
formation of triatomic species 93
VI
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ACKNOWLEDGMENTS
Thanks arc due to W. Steven Lanier and Blair Martin of EPA and
to David W. Pershing and J. Wondt of the University of Arizona, Victor
S. Engleman oE Exxon Research and Engineering Company, and C. Tom
Bowman of United Aircraft, The research was made very much easier by
the critical reviewing efforts of the Leeds group (1). L. Baulch,
D, D. Drysdale, and D. G. Home of the University of Leeds, England,
and A. C. Lloyd of the University of California at Riverside).
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SECTION I
CONCLUSIONS
The simplest and most important conclusion from this research is
that all previously measured rate constants Tor atom transfer reactions
between atoms and diatomic molecules containing the elements carbon,
hydrogen, nitrogen, oxygen, and sulfur have the same value (I a factor
of three) in the exothermic direction at 2000 K. This rate constant
is 1013-° cm3 mol~1 s~1 „ The rate constants in the cndothci-mic direc-
tion arc readily obtained from the equilibrium constants, all of which
can tae calculated. The above conclusion is based on previously
published experimental work on about a quarter of the 75 possible pairs
of atom transfer reactions.
In more detail, previously measured and evaluated rate constants
for the reactions X + YZ <;> XY + %, X + Y + M *•- XY + M, and X I YZ + M
L- v i- i , - • '
•f*/ '
*-: XYZ f M, where X, Y, and Z arc any of the atoms C, H, N, O, and S,
have been shown to fit the form:
B
k = AT exp(-C/RT) (1)
where k = the rate constant. For a second-order rate
constant, the units of k are cm3 mol~1 s~l.
For a third-order rate constant, the units
are cm<; mol~2 s~ l.
A, B, and C - constants
T = absolute temperature in Kelvins
R = the gas constant.
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The values of the constants A, B, and C are listed in Table 1.
Other symbols used in the table are defined as follows:
4.
AS°00 = the entropy of activation at 300 K
+
= the heat of activation at 300 K.
4;
The entropy of activation, AS^g, is equal to -22 cal/(mol K) in
the exothermic direction and -22 + AS°00 cal/(mol K) in the endothermic
+
direction; AH°00 is equal to either -1 kcal/mol for exothermic (-1 +
AH°00 kcal/mol for endothermic) reactions that have a transition state
preceded by an intermediate that is stable with respect to the reactants
or 7 kcal/mol for exothermic (7 + AH§00 kcal/mol for endothermic) reac-
tions that are concerted or that have a transition state preceded by an
intermediate that is unstable with respect to the reactants. The
criterion for a stable intermediate is that its heat of formation must,
be less than the sum of the heats of formation of the reactants.
Table 1. PARAMETERS USED IN CALCULATING RATE CONSTANTS
Elements •
X, Y, and Z
C, H, N, 0
and S
H, N, and O
H, N, and 0
H, N, and O
H, N, and O
H, N, and 0
H, N, and O
Reaction
X + YZ - XY 4 Z
X -t- Y + M -* XY + M
XY + M - X + Y + M
X + YZ + M - XYZ + M
(X and Z are both
hydrogen atoms)
XYZ + M - X+YZ+M
X + YZ + M - XYZ + M
(X and Z are not both
hydrogen atoms)
XYZ + M - X H- YZ + M
log,0A
16.6 + [AS°00/(2.3R)]
18
16.1 + [AS?500/(2.3R)]
19
17.1 + [As;500/(2.3R)]
20.2
18.3 + [AS?500/(2.3R)]
B
0.5
-1
-2
-1
-2
-1.5
-2.5
C
^"300 + 1
0
AH?500
0
AH?500
0
A»?500
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It is suggested that the rate constants listed in Table 1 may be
useful in estimating rate constants for reactions that have not been
studied experimentally, especially at temperatures above 1000 K.
A convenient form of the equilibrium constant, suitable for
combustion reactions, is:
" (2)
where K = the equilibrium constant
c
An = the mole change in the reaction
A^I'-JOO = tne standard entropy change at 1500 Kelvin
R = the gas constant
T - the absolute temperature
standard enthalpy change at 1500 Kelvin.
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SECTION II
RECOMMENDATIONS
We recommend that the estimating techniques developed for the
atom plus diatomic molecule reactions be extended to larger species,
for example, diatomic plus diatomic molecule reactions such as
CH + N2 -» HCN + N. As the species become bigger, more reactions will
be possible, so the estimating techniques will have to become more
widely applicable and less detailed than for the atom plus diatomic
molecule reactions. Furthermore, spin considerations will become
important, as in the example above, and experimental work will be
required to provide a firmer foundation for the estimates.
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SECTION III
INTRODUCTION
The aim of this research was to provide estimates of rate constants
of elementary chemical reactions for use in mathematical models of
combustion processes. The models are being developed by the Combustion
Research Section of the Environmental Protection Agency as tools to
reduce air pollution and improve the efficiency of utility boilers.
The chemical elements considered were carbon, hydrogen, nitrogen,
oxygenj and sulfur. The results and ideas developed on this project
arc also applicable to a wide range of other problems involving chemical
kinetics, such as atmospheric reactions that cause pollution. Initially,
the reactions of the atomic and diatomic species of hydrogen, nitrogen,
and oxygen were selected for their simplicity and because of the widely
praised critical reviews by Baulch et al.J'2 As the research progressed,
the elements under consideration were extended to include carbon and
sulfur. The temperature range was 200 to 3000 K.
The approach was to develop equations that would account for rate
constants that have been measured and then use these equations to
predict rate constants of reactions that have not been studied experi-
mentally.
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SECTION IV
ESTIMATES OF RATE CONSTANTS
FOR THE REACTIONS X + YZ ;± XY + Z
There are 75 possible pairs of reactions of the type
X + YZ ^ XY + Z (3)
where X, Y, and Z are atoms of the elements carbon, hydrogen, nitrogen,
oxygen, and sulfur. The problem of dealing with so many reactions was
simplified by tackling it in three stages. The first stage was to con-
sider only the four pairs of reactions in the H2/02 and N2/O2 systems.
The second stage was to consider only the 18 pairs of reactions in the
H2/N2/02 systems. The details of the estimation technique and results
of the first and second stages are documented in letter, quarterly, and
annual reports3"5 submitted to EPA under the first year's effort of this
grant. All the methodology and results described in these reports were
compiled and systematized in a paper presented at the Symposium on Chemical
Kinetics Data for the Upper and Lower Atmospheres, Airlie House, Warrenton,
Virginia.0 For completeness in reporting the findings under this grant,
the first year's effort is documented by the inclusion of the Airlie
House paper as Appendix A. The remainder of this section documents the
third stage of this study, which was to consider all 75 possible pairs
of reactions.
From transition state theory7 and from estimates of the heat capac-
ity of activation for atom transfer reactions between atoms and diatomic
molecules, it has been shown3"5 that the form of the rate constant is:
k/(cm3 mol"1 s"1) = 1016-G exp(AS°Q0/R)T0•5 exp[-(AH°*0 + 1)/RT] (4)
-------
For all reactions such as reaction (3), AS°00 = 22 cal/(mol K) in the
exothermic direction. Thus, equation (4) reduces to
k/(cm3 mol-1 s-1)^ 1011-8 T°'5 exp [-(AHgoo + D/RT] (5)
From equation (5) it is clear that the only unknown is the value of
a*
AHg^0. It has been shown3"5 that all the previous experimental data on
the II/N/O system evaluated by the Leeds group4 can be fitted by two values
$
of AHsoo, namely, -1 or 7 kcal/mol .
If there is no way to determine which of the two possible values
of Align 0 is appropriate for a given reaction, an average value of
3 -t 4 kcal/mol can be used. From equation (5), the rate constant is:
k/(cm3 mol"1 s~ 1 ) = 10 : ' • 8 T° • 5 exp[(-4 ± 4)/RT] (6)
At the high temperatures of combustion reactions, the uncertainty
in the activation energy becomes less important than at lower tempera-
tures. For example, at 2000 K, the rate constant from equation (6)
becomes
k/(cm3 mol"1 s"1) = iQii.8+i.7-o.5±o.s at 2000 K
= 10i3.o±o.r> at 200() K (7)
To a first approximation (± half a power of ten, i.e., ± a factor of
three), the rate constants of all atom transfer reactions such as
equation (3) have the same rate constant in the exothermic direction,
namely, 1013'° cm3 mol"1 s~ ] .
^
It has been suggested3"0 that the value of AHg,,,, is determined by
the stability of the triatomic transition state XYZ with respect to the
j-
reactants. The basic postulates arc (1) that AH(300 = -1 kcal/mol for
reactions that have a transition state preceded by an intermediate
that is stable with respect to the reactants (see Figure 1) and (2) that
Jr
AHg00 = 7 kcal/mol for reactions that are concerted or have a transition
state preceded by an intermediate that is unstable with respect to the
reactants (see Figure 2).
-------
o
o
o n
X
•1
REACTANTS
X ^ YZ
TRANSITION
STATE
1 kcal/mol
STABLE
INTERMEDIATE
XYZ
PRODUCTS
XY + Z
REACTION
SA 2008-3
FIGURE 1
HEAT CHANGES FOR REACTIONS HAVING TRANSITION STATES
PRECEDED BY AN INTERMEDIATE THAT IS STABLE WITH RESPECT
TO THE REACTANTS
jOI
In such cases AH
300
--1 kcal/mol.
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TRANSITION
STATE
o n
X
CONCERTED V
PATH \
REACTANTS
X + YZ
PRODUCTS
XY + Z
REACTION
SA 2008-4
FIGURE 2 HEAT CHANGES FOR REACTIONS THAT ARE CONCERTED
OR THAT HAVE A TRANSITION STATE THAT IS PRECEDED
BY AN INTERMEDIATE THAT IS UNSTABLE WITH RESPECT
TO THE REACTANTS
In such cases
^...
300
= 7 kcal/mol.
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The simplest case is the concerted reaction, in which a hydrogen
atom is transferred. For example
-i-
II + HO - -(H- • •!!• • -O) - -H2 + O (8)
For reaction (8), AH°*0 - 7 kcal/mol. All reactions (involving C, H,
N, 0, S) of the type
+
X + YZ - -(X-.-Y---Z) - ~XY + Z (9)
4;
where Y is a hydrogen atom, have AH(300 = 7 kcal/mol.
For all the other reactions, the triatomic intermediate XYZ was
examined to determine whether it is stable or unstable with respect
to the reactants. The heats of formation of the reactants and some
of the intermediate are well known.8 An example is the reaction
t
N + NO - -(N- • -N- • -O)
+ 0 (10)
The intermediate in this case is N2O. The sum of the heats of forma-
tion of the reactants N + NO is 134.6 kcal/mol, compared with 19.6
kcal/mol for N2O; that is, N2O is 115 kcal/mol more stable than N + NO.
II it takes 60-80 kcal to form the triplet state N20, this intermediate
$
is still 40 :t 10 kcal more stable than reactants and AH°00 (reaction 10)
-1 kcal/mol.
Another example is
H + 02 - -(H. • -O- • -O)* - -HO + O (ID
In this case, the stable molecule intermediate is HO2. The reaction
II + 02 - -H02
is 63.9 kcal/mol exothermic; hence, AH°"00 (reaction 11) •= 1 kcal/mol.
10
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If the heat of formation of the intermediate XYZ is not known,
it must be estimated. For example, consider the reaction
N + O2 - - (N- • -O. . .O) - — ~NO + O (13)
The intermediate is NOO produced by the reaction
N + 02 - -NOO (14)
It has been estimated (see later) that AH°,nn(NOO) is 136 ± 7 kcal/mol.
.p O U U
Since the sum of the heats of formation of the reactants is 113 ± 1
kcal/mol, NOO is unstable with respect to NO + O2, and AH°00 (reaction 13)
- 7 kcal/mol,
In general, the estimating technique was to take the fully hydro-
genated species and estimate the strengths of the bonds to the hydrogens.
For example, the heat of formation of HNN was estimated from AH°300
(II2NNH2), assuming each N-II bond strength to be 95 kcal/mol. The details
of the estimation are given in Appendix B, which considers the triatomic
species in the complete C, H, N, O, S system,
t
The values assigned to AIIC300 for the 75 exothermic or thermoneutral
reaction are given in Tables 2 and 3. The hydrogen transfer reactions
(all have 7 kcal/mol for AH°300) are in Table 2; the other reactions
are in Table 3.
Equation (4) has the form
k/(cm3 mol"1 sec"1) -AT0-5 exp(-C/RT) (15)
±
where A = 101G-G exp(AS°00/R) cm3 mol"1 s~ 1
%
C = -(AHgoo + 1) kcal/mol
$ $
The appropriate values of AS°OQ and AH°0() have been substituted in
equation (15) for all reactions of the type X + YZ «-> XY + Z, where X,
Y, and Z are atoms of the elements carbon, hydrogen, nitrogen, oxygen,
and sulfur. The values of log10A, C, and Iog10k at 1000 K for these
reactions are given in Table 4.
1]
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Table 2. HYDROGEN TRANSFER REACTIONS
a
•"orrnula of Triatomic Transition State XYZ
Empirical
CHN
CHO
CHS
CH2
C2H
HNO
HNS
UN 2
HOS
H02
IIS 2
H2N
H2O
II 2S
H3
Structural
CHN
OHN
SHC
HHC
cue
OHN
SHN
NUN
OIIS
OHO
SHS
HHN
IIHO
HHS
IIHII
Reaction
C + NH -4 CH + N
O + HC -4 OH + C
S + HC -4 SH + C
H + HC -4 H2 + C
C + HC -4 CH + C
O + HN -4 OH + N
S + HN -* SH -f N
N + HN -4 NH + N
O + HS 4 OH + S
0 + HO -4 OH + 0
S + IIS -> SH + S
II + HN -4 H2 + N
II + HO -> H2 + O
II + HS -4 H2 + 0
II + H2 -4 II 2 + II
Reactions X + HZ -4 XII + Z where X and Z are atoms of the elements
carbon, hydrogen, nitrogen, oxygen, and sulfur. The rate constant
for every reaction is: k/(cm3 mol"1 s~1) = lo11-^0-5 exp(-8/RT).
Reactions are in the exothermic direction.
12
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Table 3. ATOM TRANSFER REACTIONS
Formula of Triatomic
Intermediate XYZ
Empirical
CIIN
C1IN
CIIO
CHO
CHS
CHS
CIJ2
CNO
CNO
CNO
CNS
CNS
CNS
CN2
;
CN2
Structural
CNII
NCII
OCH
COH
CSH
sen
1ICH
CNO
CON
OCN
CNS
CSN
SCN
NCN
NNC
Reaction
C + Nil > NC 1 H
N 4 CH * NC 4 H
O 4 CII -» OC 4 II
C 4 OH > CO I- H
C 4 SH ••• CS H- H
S 4 CH -> SC 4 H
II + CH ' IIC 4 H
C + NO •• CN 4 O
C 4- ON • CO -i- N
0 H- CN - OC I- N
C + NS > CN 4 S
C 4 SN > CS 4 N
S + CN -• SC 4 N
N 4 CN •• NC 4 N
N 4 NC • N2 4 C
[AH°(X) 4 AHj(YZ)]
155 t 5
255 ± 1
201 .6 4 0.1
180 1: 1
203 1. 1
208.3 ± 0.1
194.1 h 0.1
192.5 ! 0.5
192.5 1 0.5
164 \ 3
234 t 10
234 A 10
1 70 J 3
217 t 4
217 i 4
AH°(XYZ)
b
110 i- 3
32.3 4 2°
( 7.2C
(10.4 i 2°
81 f 15b
123 ]• 15b
b
92 i 8
92.4 :|- 1°
b
145 -t 17
b
220 4 29
38 4 3°
186 4 25
b
250 1 29
b
73 4: 3
113 4. 5°
140 | 30°
A 3 00
-1
-1
_1
-1
-1
-1
-1
-1
7
-1
-1
7
-1
-1
-1
Reactions X + YZ -» XY + Z where Y is not a hydrogen atom and where X
and Z are atoms of the elements carbon, hydrogen, nitrogen, oxygen
and sulfur. IT the heat of formation of the intermediate XYZ is less
than the sum of the heats of formation of X and YZ, then AH°00 = -1
kcal/mol in the equation for the rate constant: k/(cm3 mol~] s-1) -
"Inll.^T^S ~^« f /ATtO , -l\/r>Tll TP J_l__ 1_ _J f r.
10
To.r, exp [_(AnO()o + D/RT], If the heat of formation of the
intermediate XYZ is greater than the sum of the heats of formation
of X and YZ, then AH"00 ^ 7 kcal/mol. All units are kcal/mol. Reactions
are in the exothermic direction.
Estimated value for AH°(XYZ). See Appendix B.
Reference 8.
Reference 7.
b
d
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Table 3 (continued). ATOM TRANSFER REACTIONS
Formula of Triatomic
Intermediate XYZ
Empirical
COS
COS
COS
C°2
C°2
CS2
cs2
c2n
C2N
C2N
c2o
c2o
C2S
C2S
C3
UNO
HNO
HNS
HNS
HN2
HOS
Structural
COS
OCS
CSO
COO
OCO
CSS
scs
CCH
NCC
CNC
OCC
COC
sec
CSC
ccc
ONH
NOH
SNH
NSH
IIHH
SOH
Reaction
C + OS -> CO + S
0 + CS --> OC + S
C + SO - CS + O
C + 02 - CO + 0
O + CO -- OC + O
C + S2 -* CS + S
S + CS > SC + S
C + CH --» C2 + H
N + C2 -» NC + C
C + NC -» CN + C
0 + C2 ^ OC + C
C + OC .-» CO + C
S + CC -> SC + C
C + SC -, CS + C
*— ' "T" \^s r\ • "* *— ' O ~*~ ^
O + NH -» ON + H
N + OH -NO + H
S + Nil -, SN + H
N + SH -. NS + H
N + NH --, N2 + H
S + OH .., SO + H
[iHj(X) + AH°(YZ)]
172.1 ± 0.8
115 1: 5
172.1 1 0.8
170.9 ± 0.5
33.2 i 0,6
201.7 i. 0.7
121 i 5
312.9 ± 0.6
313 t: 2
275 t 4
259.7 t 0 .9
144.5 t 1.1
266.5 ± 0.9
266 i- 5
371 + 1
150 ± 4
122 ± 1
156 .+. 4
146 f 2
203 i 5
75.6 + 0.3
AH°(XYZ)
b
161 i 36
-33.1 i 0.3a
b
164 .-t 19
b
135 ± 22
-94.05 I 0.01
b
164 + 19
28.0 i 0.2°
c
114 d- 7
b
146 1 16
133 i 30°
69 -t 15°
b
213 ± 30
b
130 d- 15
b
248 ± 30
b
196 i 4
b
23.8
b
77 ± 11
b
65 + 11
b
112 d- 11
b
152 + 16
b
11 ± 13
AH?l'
-1
-1
-1
— 1
-1
-1
-1
-1
-1
-1
-1
7
-1
7
-1
-1
-1
-1
-1
-1
-1
14
-------
Table 3 (concluded). ATOM TRANSFER REACTIONS
Formula of Triatomic
Intermediate XYZ
Empirical
HOS
H02
HS2
H2N
H2°
H2S
NOS
NOS
NOS
NO2
N02
NS2
NS2
N20
N20
N2S
N2S
N3
S20
S2°
so2
s°2
°3
S3
Structural
OSH
OOH
SSH
HNH
HOH
HSH
NOS
OSN
ONS
NOO
ONO
NSS
SNS
NNO
NON
NNS
NSN
NNN
OSS
SOS
soo
oso
ooo
sss
Reaction
O + SH _* OS + H
0 + OH _ O2 + H
S + SH ... S2 + H
H + NH .-, HN + H
II + OH ^ HO + H
H + SH ..-, HS + H
N + OS .-> NO + S
O + SN -. OS + N
O + NS -, ON + S
N + 02 _ NO + O
0 + NO -. ON 4 0
N + S2 :, NS + S
S + NS -> SN + S
N + NO .-, N2 + 0
N + ON -„ NO + N
N + NS -, N2 + S
N + SN ~, NS -I N
N + N2 ... N2 + N
0 + S2 -> OS + S
S 4 OS -> SO + S
S f 02 _, SO 4 0
o + so os + o
o + o2 ., o2 4 o
S + S2 ., S2 + 0
f/\H°(X) + AH°(YZ)"
- £ f
93 ± I
69.9 ± 0.3
99.6 ± 1.2
142 i 4
61.4 +- 0.3
85.4 4- 1.2
114 ± 1
123 4- 10
123 -t 10
113 4- 1
81.1 -t 0.4
144 -t 1
129 ± 10
135 4- 1
135 .h l
176 4 11
176 :|- 11
113 4- 1
90.4 :h o.2
67.5 i_ 0.3
66.29-;- 0.01
60.8 j 0.3
53,554 0.02
97.1 j- 0 .2
AH°(XYZ)
b
23 ± 10
c
5 ± 2
33 ± 5 3
46 ± 2°
-57.8 ± 0.001
-4.9 ± 0.2°
149 ± 21
b
166 ± 39
b
49 4- 10
136 ±17
7.9 ± 0.2°
164 ± 32b
b
90 ± 20
19.6 ±0.1°
209 ± 27
61 ± 10
b
244 ± 31
b. c, e
171 ± 13 ' '
-14 ± 8°
b
36.5 ± 1.0
35.3 ± 0.7
70.95 4 0.05
34.1 i 0.4
b
65 ± 1
H°*
-1
-1
-1
-1
-1
-1
7
7
-1
7
-1
7
-1
-1
7
-1
7
7
-1
-1
-1
-1
-1
-1
"The AH°(XYZ) includes an
reaction.
additional 60 ± 6 kcal/mol for spin forbidden
15
-------
Table 4. VALUES USED IN CALCULATING RATE CONSTANTS'
Empirical Formula
oC Triatomic
Intermediate XYZ
CI1N
CHO
CHS
CH2
CNO
Reaction
C + UN > CH + N
N + IIC -> Nil H C
H + CN ~> IIC + N
N + CII -, NC -I- 11
II + NC .-> HN + C
C + NH -» CN + II
C + HO _> CH + O
0 + HC .-, OH + C
C + OH > CO + H
II + OC , HO + C
H + CO > IIC + 0
0 + CH .- OC + II
C + HS .-> CH + S
S + IIC .. SH + C
C + SH ...» CS + II
II + SC --> IIS + C
H +-CS -> IIC + S
S + CH * SC + 11
C + H2 -, CH + H
H 4 HC -.» H2 + C
H + CH -., IIC + II
C + NO -, CN + O
0 + NC -. ON + C
C + ON -> CO + N
log 10 A/
[cm3 mol-1 s-1]
11.8
12.0
12.8
11.8
13.0
11.8
11.9
11.8
11.8
13.3
13.4
11.8
11.6
11.8
11.8
13.3
13.1
11.8
12.2
11.8
11.8
11.8
12.1
11.8
1
C/(kcal/mol)
8.0
13.9
12.8
0
104.8
0
29.4
8U0
0
154.5
174.9
0
12.1
8.0
0
97.1
101,, 2
0.8
31 „ 2
8.0
0
0
28.9
Iog10k/[cm3
mol" * s~ 1 ]
at 1500 K
12.2
11.6
-0.1
13.4
-0.7
13.4
9.2
12.2
13.4
-7.6
-10.6
13.4
11.5
12.2
13.4
0.6
-0.1
13.4
9.3
12.2
13.4
13.4
9.5
8,0 I 12.2
Values of log10A, C, and Iog10k at 1500 K in the equation Iog10k/(cm mol s ) =
AT°'Gexp(-C/RT) for all the reactions of the type X + YZ -4 XY + Z where X, Y,
and Z are atoms of the elements carbon, hydrogen, nitrogen, oxygen and sulfur.
16
-------
Table 4 (continued). VALUES USED IN CALCULATING RATE CONSTANTS
Empirical Formula
of Triatomic
Intermediate XYZ
CNS
CN2
COS
c°2
cs2
c2n
— ___
Reaction
N 4 OC -, NO 4 C
N 4 CO _v NC + O
0 4 CN » OC + N
C 4 NS - > CN 4 S
S 4 NC .-> SN 4 C
C 4 SN _> CS 1 N
N 4 SC ._ NS 4 C
N 4 CS ... NC 4 S
S 4 CN -•, SC 4 N
C 4 N2 > CN 4 N
N 4 NC -, N2 4 C
C 4 NC ... CN 4 C
C 4 OS . CO 4 S
S 4 OC .., SO 4 C
C 4 SO * CS 4 0
O 4 SC -> OS 4 C
0 4 CS » OC 4 S
S 4 CO , SC 4 O
C 4 O2 . » CO i O
O 4 OC ._ 02 4 C
O 4 CO ..» OC 4 O
C 4 S2 -> CS 4 S
S 4 SC , S,, 4 C
S 4 CS .,, SC 4 S
C 4 C1I .., C2 4 H
H 4 C2 » HC 4 C
C 4 HC -, CH 4 C
log10A/
[ cm3 mol~ 1 s~1~\
12,7
12.5
11 .8
11.8
12.3
11.8
12.6
12.1
11.8
12.1
11,8
11.8
11.8
12.6
11.8
12.2
11.8
12.1
11.8
12.0
11.8
11.8
12.2
11.8
11 .8
13.2
11.8
C/(kcal/mol)
113.9
77.1
0
0
63.6
8.0
73.9
2.3
0
45.2
0
0
0
132.2
0
57.5
0
74.7
0
137.7
0
0
80.4
0
0
60.5
8.0
Iog10k/[cm3
mol'1 s"1]
at 1500 K
-2.3
2.8
13,4
13.4
4.6
12.2
3.5
13.4
13.4
7.1
13.4
13.4
1304
-5.1
13..4
5.4
13.4
2»8
13.4
-6.4
13.4
13.4
2.1
13,4
13.4
6.0
12.2
17
-------
Table 4 (continued). VALUES USED IN CALCULATING RATE CONSTANTS
Empirical Formula
of Triatomic
Intermediate XYZ
C2N
C2°
C2S
C3
UNO
HNS
HN2
1IOS
Reaction
C + CN --> C2 + N
N + C2 _, NC + C
C + NC _> CN + C
C + CO _ C2 + 0
0 + C2 _> CO + C
0 + CO .-., OC + O
C + CS _ C2 + S
S + C2 -, SC + C
C + SC ^ CS + C
C + C2 -. C2 + C
H + NO -* HN + O
O + NH _, ON + H
H -',- ON _ HO + N
N + OH _> NO + H
N + HO _ NH + O
0 + UN --> OH + N
H + NS .-» HN + S
S + NH _* SN + H
H + SN -* HS + N
N + SH .-* NS + H
N + HS -» NH + S
S + HN _» SH + N
H + N2 -».HN + N
N + NH _, N2 + II
N + HN -, NH + N
H + OS -* HO + S
S + OH _ SO + H
H + SO _> HS +0
log10A/
[cm3 mol~ * s~ 1 ]
11.4
11.8
11.8
12.0
11.8
11.8
11.7
11.8
11.8
11.8
12.7
11.8
12.4
11.8
12.1
11.8
12.4
11.8
12.4
11.8
11.8
11.8
13.3
11.8
11.8
12.6
11.8
12.8
C/(kcal/mol)
38.3
0
0
115.3
0
0
40.6
0
0
0
75.9
0
48.6
0
35.3
8.0
41.2
0
31.2
0.8
18.0
8.0
150.9
0
8.0
22.3
0
39.6
Iog10k/[cm3
mol"1 s-1]
at 1500 K
7.4
13.4
13.4
*J a £i
13.4
13.4
704
13.4
13.4
13.4
3o2
13.4
6.9
13.4
8.5
12.2
8.0
13.4
9.5
13.4
10.8
12.2
-7.2
1304
12.2
10.9
13.4
8.6
_ : __ ___
18
-------
Table 4 (continued). VALUES USED IN CALCULATING RATE CONSTANTS
Empirical Formula
of Tri atomic
Intermediate XYZ
II02
HS2
H2N
"2°
H2S
«3
NOS
4
N02
Reaction
0 + SH -, OS + H
0 + HS -> OH + S
S + HO -, SH + O
H + O2 ~, HO + O
0 + OH -» O2 + H
O + HO _ OH + O
H + S2 .--, HS + S
S + SH _» S2 + H
S + IIS -* SH + S
II + HN -* H2 + N
N + H2 _, NH f H
H + NH ._> HN + H
H + HO _ H2 + O
0 f H2 .., OH + H
II + OH ._» HO + H
H + HS -» II2 + S
S + H2 , SH + H
H + SH -> IIS + H
H + H2 _., H2 + H
N + OS _ NO + S
S + ON -> SO + N
S + NO ... SN H- 0
0 + NS ...., ON + S
0 + SN . OS + N
N + SO _, NS + 0
N + O2 ., NO + O
O + ON -, O2 + N
0 + NO » ON + O
log10A/
[cm3 mol 1 s~ l ]
11.8
11.8
12.1
13.1
11.8 '
11.8
12.9
11.8
11.8
11.8
12.4
11.8
11.8
12.1
11.8
11.8
12.4
11.8
11.8
11.8
11.6
12.0
11.8
11.8
12.2
11.8
11.1
11.8
C/(kcal/mol)
0
8.0
25.2
16.8
0
8.0
16.6
0
8.0
8.0
37.2
0
8.0
9,9
0
8.0
27.1
0
8.0
8.0
34.3
34.7
0
8.0
16.4
8.0
39.8
0
Iog10k/[cm3
mol-1 s-1]
at 1500 K
13.4
12.2
10.0
12.2
13.4
12.2
12.0
13.4
12.2
12.2
8.6
13.4
12.2
12.3
13.4
12.2
10.0
13.4
12.2
12.2
8.2
8.6
13.4
12.2
11.4
12.2
6.9
13.4
19
-------
Table 4 (concluded). VALUES USED IN CALCULATING RATE CONSTANTS
Empirical Formula
of Triatomic
Intermediate XYZ
NS2
N20
N2S
N3
os2
°2S
°3
S3
Reaction
N + S2 --> NS + S
S + SN _> S2 + N
S + NS _> SN + S
N + NO .» N2 + O
O + N2 _> ON + N
N + ON _4 NO + N
N + NS -» N2 + S
S + N2 -> SN + N
N + SN -* NS + N
N + N2 _* N2 + N
O + S2 -> OS + S
S + SO -> S2 + 0
S + OS -» SO + S
O + OS _» 02 + S
S + O2 , SO + O
O + SO .., OS + 0
O H- O2 _> O2 + O
S + S2 -, S2 + S
log10A/
[cm3 rnol" J S~ 1 ]
11.8
11.3
11.8
11.8
12o4
11.8
11.8
12.6
11.8
11.8
11.8
11.8
11.8
11.3
11.8
11.8
11.8
11.8
C/(kcal/mol)
8.0
21.6
0
0
75.0
8.0
0
109.7
8.0
8.0
0
22.9
0
5.5
0
0
0
0
Iog10k/[cm3
mol"1 s-1]
at 1500 K
12.2
9.8
13.4
13.4
3.0
12.2
13.4
-1.8
12.2
12.2
13.4
10.0
13.4
12.0
13.4
13.4
13,4
13.4
20
-------
For the reactions in the II/N/0 system, the experimental rate
constants evaluated by the Leeds group1'2 and the estimated rate
constants are compared in Appendix A. The rest of this section compares
the estimated rate constants with experimental data for reactions
involving carbon and sulfur atoms that were not covered previously and
with more recent data for the reaction of hydrogen atoms with nitric
oxide and oxygen atoms with nitric oxide. The reactions of interest
and the estimated rate parameters arc given in Table 5.
For each reaction in Table 5, the experimental and estimated
results have been compared. Boden and Thrush9 have measured the rate
of reaction (16)
O + CN OC + N (16)
between 570 and 687 K. The only rate constant reported by Boden and
Thrush was 1013-° cm3 mol"J s~1 at 687 K. Albens, Schmatjko, Wagner,
and Wolfrum10 recently reported a rate constant of 1013-1 cm3 mol~1 s~a
independent of temperature at 298, 400, and 500 K. The experimental
and estimated values are compared in Figure 3.
Hancock and Smith11 have studied reaction (17).
0 + CS OC + S (17)
They measured a rate constant of 1012-8 cm3 mol~l s~1 at 298 K and
reported a previous measurement of 101*'1 cm3 mol~1 s'1 at 1100 K by
Ilomann, Kromc, and Wagner,12 The experimental results are compared
with estimated values in Figure 3.
Flower, Hanson, and Kruger13 recently completed a study of
reaction (18) in a shock tube between 2400 and 4500 K.
II + ON HO + N (18)
The experimental and estimated results are compared in Figure 4.
21
-------
Table 5. ESTIMATED RATE PARAMETERS AND RATE CONSTANTS
CO
CO
Empirical
formula of
XYZ
CNO
COS
HNO
HOS
HS2
H2S
NO 2
S02
Reaction
0 + CN -4 OC + N
0 + CS -4 OC + S
H + ON -> HO + N
0 + SH -> OS + H
S + SH -> S2 + H
H + HS -> H2 + S
0 + ON -> 02 + N
S + 02 -» SO + 0
log [A/ (cm3 mol"1 s'1)]
11.8
11.8
12.4
11.8
11.8
11.8
11.1
11.8
C/(kcal/mol)
0
0
48.6
0
0
8.0
40.1
0
log [k/(cm3 mol"1 s"1)]
at 1000 K
13.4
13.4
6.9
13.4
13.4
12.2
6.9
13.4
Estimated rate parameters of the equation k = AT0'5 exp(-C/RT) and rate constants at 1000 K
for some reactions of the type X + YZ -» XY + Z, where X, Y, and Z are atoms of the elements
carbon, hydrogen, nitrogen, oxygen, and sulfur.
-------
13.0
2000
1000
T/K
500
300
y 12.0
~ 11-0
O O + CN -> OC + N, BT [9]
| 0 + CN -> OC + N, ASWW [10]
/\ O + CS -» OC + S, HKW [12]
O + CS -» OC + S, HS [11]
O + SH -» OS + H, CG [14]
Estimated, This Work
A
10.0
103K/T
FIGURE 3 COMPARISON OF MEASURED AND ESTIMATED RATE CONSTANTS
FOR REACTIONS OF OXYGEN ATOMS
4.0
SA-2008-5R
23
-------
10.00
7 8.00
° 6.00
4.00
10,000
5000
T/"
3000
2000
1500
O FHK [13]
—_ Estimated This Work
0.2
0.4
103K/T
0.6
SA-2008-6R
FIGURE 4 COMPARISON OF MEASURED AND ESTIMATED RATE CONSTANTS
FOR THE REACTION H + ON -> HO + N
24
-------
Cupitt and Glass14 have studied the reaction of atomic oxygen
with hydrogen sulfidc by csr spectroscopy. The variation in the con-
centration of free radicals was measured, and the results were inter-
preted in terms of a mechanism consisting of seven elementary reactions.
One of the reactions was
0 4 SH OS + H (19)
The experimental results were consistent with a rate constant of 1014-5
cm'5 mol"1 s-1 at 295 K for reaction (19). This rate constant is compared
with the estimated one in Figure 3.
Mihclcic and Schindlcr15 have studied the sulfur analog of reaction
(19)
S + SH "~^2 + H (20)
by the same method as Cupitt and Glass. The rate constant of reaction
(20) at 300 K was found to be 10'3•" cm3 mol"» s~ ' . This rate constant
is compared with the estimated one in Figure 5.
Using the same system as was used to study reaction (19), Cupitt
and Glass measured the. rate constant at 295 K for reaction (21)
II t US H2 + S (21)
to be 1013-» cm3 mol"1 s~'. This rate constant is compared with the
estimated one in Figure G.
Hanson, Flower, and Krugcr17 recently investigated the decomposi-
tion of nitric oxide in a shock tube in the range of 2500 to 4100 K.
From their rate measurements, they derived the rate constants for
reaction (22)
O + ON O2 i- N (22)
shown in Figure 7 with rate constants measured by other workers18""21
and with the estimated rate constants.
25
-------
12.0
2000
1000
T/K
500
300
11.0
10.0
O S + O2 - SO + O, FT [16]
^1 S + O_ -> SO + O, CG [14]
A
S + SH - S2 + H, MS [151
. Estimated, This Work
A
O
9.0
1.0
2.0
103K/T
3.0
4.0
SA-2008-7R
FIGURE 5 COMPARISON OF MEASURED AND ESTIMATED RATE CONSTANTS
FOR REACTIONS OF SULFUR ATOMS
26
-------
12.0
2000 1000
T/K
500
300
11.0
4
6.0
5.0
4.0
O CG [14]
Estimated This Work
o
4
1.0
2.0
103K/T
3.0
SA-2008-8R
FIGURE 6 COMPARISON OF MEASURED AND ESTIMATED RATE CONSTANTS
FOR THE REACTION H + HS ->• H2 + S
27
-------
T/K
8.00
6.00
4.00
2.00
10,000
I
5000
3000
2000
1500
HFK [17]
WT [20]
/\ KD [19]
KK [18]
CGK [21]
Estimated This Work
0.2
0.4
103K/T
0.6
0.8
SA-2O08-9R
FIGURE 7 COMPARISON OF MEASURED AND ESTIMATED RATE CONSTANTS
FOR THE REACTION O + ON -> O0 + N
28
-------
Reaction (23)
S + 02 SO + 0 (23)
.,3
has been studied by Cupitt and Glass,14 who found k23 = 1011'9 crrr
mol~l s"1 at 295 K, and by Fair and Thrush,16 who found k23 = 1012'1
cm3 mol"1 s~1 at 298 K. The experimentally determined rate constants
are compared with the estimated ones in Figure 5.
The agreement between measured and estimated rate constants for
H, N, O reactions is excellent, as shown in Figures 4 and 7. For
reactions involving carbon and sulfur atoms, there is enough experi-
mental evidence to suggest that the method of estimation is at least
a good first approximation.
Consider reactions of the type
O + YZ OY + Z (24)
shown in Figure 3. At first sight it appears that the worst agreement
between measured and estimated values is for reaction (19)
OS + H (19)
However, if all the difference between measured and estimated rate
constants is attributed to activation energy, as is likely, then the
difference between observed and calculated rate constants for reaction
(19) corresponds to less than 2 kcal/mol, whereas the difference is
3 kcal/mol for reaction (17)
0 + CS -— CO + S (17)
These differences are not large for combustion reactions.
Similarly, for reactions of the type
S + YZ - SY + Z (25)
where Y is an sulfur or an oxygen atom, the difference between estimated
29
-------
and observed rate constants at 300 K corresponds to a difference of
about 2 kcal/mol, as shown in Figure 5. However, when Y is a hydrogen
atom, as in reaction (-21)
S + H2 SH + H (-21)
H + HS h2 + S (21)
there is a big discrepancy (about 7 powers of 10) between the rate
constants at 300 K. This discrepancy in the rate constants for reaction
(21) corresponds to about 10 kcal/mol in the activation energies. There
is only one experimental value for reaction (21), but the other two rate
constants in the same experiment, namely, for reactions (19) and (23)
O + SH OS + H (19)
S + 02 SO + O (23)
are in good agreement with other experimental work and with the estimates,
On the other hand, this one value for reaction (21) is the only example,
out of all available experimental data for the CHNOS system, whers the
estimated and experimental data are not in agreement. There is no room
for adjusting the estimated value, because the thermochemistry is too
well known for reaction (21) to be anything other than exothermic.
Furthermore, since the atom being transferred is a hydrogen atom, there
is no need to estimate the heat of formation of the transition state.
Clearly, more work is required on this reaction.
30
-------
SECTION V
ESTIMATES OF RATE CONSTANTS FOR SPECIFIC REACTIONS
REQUESTED BY EPA AND ITS CONTRACTORS
During the course of this research, estimates of rate constants
for reactions outside the limits of Table 1 were made by telephone, by
letter, and during visits in response to requests on specific reactions
by EPA and its contractors. The estimating techniques have been des-
cribed previously.7 The most recent estimates are given in Table 6.
The other estimates have been published as part of a final report to
EPA on a related project by Exxon.22
31
-------
Table 6. HEATS OF REACTION AND ESTIMATED ARHHENIIIS PARAMETERS FOR SOME REQUESTED REACTIONS
Ruact, ion
IICN 4 N - CII 4 N.,
HCO 4 N - CH 4 NO
CII., 4 CN - CII + IICN
IICN 4 0 - CH 4 NO
CN 4 Nil - CH 4 N2
CllO I HO -» H20 4 CO
CII, 4 N,, - IICN 4 Nil
HCO 4 N - HCN 4 0
CO., 4 li — HCO 4 O
co 4 no., - HCO i- o..
CIIO ^ 0 -t CO 4 110
CII., + O2 - CH, 4 HO.,
CH., -1- 0., - CII-,O 1- O
CII.^O 4 N - CII,, 4 NO
CH,O i- M -< CII2O 4 II + M
CII.,0 4 N -* CII.,0 4 Nil
CH.,O 4 0 - CII.,0 h HO
CII.,0 4 0., - CII.,0 4 110.,
CH.,O 1- II - CII.,0 4 H2
CII.,0 4 Oil - CH..O 4 II., 0
CII., ^ CII.,0 - CII., 4 CIIO
CII., 4 CII.,0 - CII, 4 CIIO
CN -1- II., ' IICN 4 II
CN 4 11O - IICN 4 0
O 4 CH 4 M " CIIO 4 M
(kcal/mol)
- 3.30
41.58
-22.70
71 .72
—52 .00
2!). 30
-30.14
110.5
30.1
G2.53
27 .8
2H.88
-51 .95
-79 .21
-23 .95
-81 .05
— 9(i .05
-22 .1)5
-17 .75
_1D.()
-192. (i
CIIO 4 HO., - CH.,0 4 0,, ; -40.0
CH., 4 H2 - CH., + H
CII -1 CII., - 2 CH2
CH •>• CII,, _, C1I2 -1 CII.,
-5.5
8.0
3.1
(A/(cntlmol"1s '))
11.7
14
12 .5
14
M
1(1.5 4 loK,()(T/K)
14
11
14
12.5
11.5 1 1<>K1()(T/K)
12.5
12 .5
14
10.fi - 7.5 I.,,;,,,
(T/K)
14
14
12
M
13.5
11 .3
11.3
12 .5
12.5
b
14
12.5
12.5
12
K/( kcal/mol)
[1G ± G]*
4 8 . (i
5
[72 1 2]
[40 ±20]
0
[70 -!• 20]
[0 ± 2]
P1±S1
37 . 1
0.5
G9 .53
30
[31 -fr 4 1
22.fi
()
0
(j
o
11
0 .T>
«.s
5
3
0
:*
7
8.0
17.1
C omme n t s
Spin retarded .
Based on an estimate of E = 7 j: 3
kcal/mol .for | ]\c buck reaction.
Based on an estimate of K = 0 +. 2
kcal/mol for Lhe back rtiact urn .
•'our-centor .
Based on an estimate of K - 40 i 20
kcal/mol for Hie bac-.k read: i on .
No spin problem .
Based on an estimate of K --=0+2
-------
SECTION VI
THE COMPUTER PROGRAM
A computer program was written to calculate the rate constant at
any temperature of any of the 75 reactions of the type X + YZ ^ XY + Z,
where X, Y, and Z are atoms of the elements carbon, hydrogen, nitrogen,
oxygen, and sulfur. The program, written in FORTRAN IV, is named
CRATES for Chemical Reaction Rate Constants, Complete documentation
for the program is inline in the form of FORTRAN comment cards. These
cards are fully prepared to run on the UNIVAC 1108 computer under the
EXEC-8 operating system. Only the RUN card needs to be changed to
run the deck on the EPA installation.
A printout of the program and the deck of cards, containing the
source deck for program CRATES and the data files, have been submitted
to EPA. A 7-track, 556 bpi, unlabelled, BCD tape with one file was also
submitted as a backup. This file has 84 characters per physical
record (the last 4 characters are blanks) and is the source deck and
data files for program CRATES but with no control cards. The tape can
be converted to cards and the appropriate EXEC-8 control cards inserted
by hand before executing the program.
Requests for copies of the program should be addressed to the
Project Officer.
33
-------
SECTION VTT
ESTIMATES OF RATE CONSTANTS FOR COMBINATION AND DISSOCIATION REACTIONS
Rate constants have been estimated for some of the combination
and dissociation reactions of the type
X + Y + M J± XY + M (26)
and
XY + Z + M ?i XYZ + M (27)
where X, Y, and Z are atoms of the elements hydrogen, nitrogen, and
oxygen and M is N2. The results are summarized in Section I, Conclusions,
and are discussed in detail in the interim annual report5 and in the
Airlie House paper,6 which is included as Appendix A.
34
-------
SECTION VIII
VARIATION OF EQUILIBRIUM CONSTANT WITH TEMPERATURE
It has been pointed out5'6'22 how useful it would be to have in
analytical form the variation of the equilibrium constant with tempera-
ture. Rigorously,7 the variation of the equilibrium constant with
temperature is given by:
RT In K = -AGJ (28)
where
AG« = All0 - TAS° (29)
/-
•3oo
AC°dT
-T r AC°d In T
./TOO P (30)
However, for estimating the equilibrium constants of the elementary
reactions that are important in combustion systems, it is a very good
approximation to use:
AC J ~ AH° 50„ - TAS ° 50 Q (31)
For reactions in which there is a change in the number of moles,
for example, N + O + M -> NO + M, the equilibrium constant in units of
concentration K is related to that in pressure units K by
c P
K -- K (R'T)~An (32)
c p
35
-------
where R is 82.057 cm3 atm/(mol K) and An is the mole change in the
reaction. For compatibility with the modified Arrhenius equation,
which is;
B
k = AT exp(-C/RT) (33)
equation (32) can be put in the form:
K /(mol/cm3)An = (82)""An[exp(AS°500/R) ]T~An exp[-AH°500/(RT) ]
c
= A'T exp[-c'/(RT)] (34)
where:
log10A' = -1.9An + [AS°500/(2.3R)]
B' = An
C' - AH°
^ ~ ani5oo-
36
-------
SECTION IX
REFERENCES
1. Baulch, D. L., D. D. Drysdale, D. G. Home, and A. C. Lloyd. High
Temperature Reaction Rate Data No. 4. Department of Physical
Chemistry, The University, Leeds 2, England. December 1969.
2. Baulch, D. L., D. D. Drysdale, D. G. Home, and A. C. Lloyd. Eval-
uated Kinetic Data for High Temperature Reactions. Volumes 1 and 2.
London, Bu.tterworths, 1972.
3. Shaw, R. Estimation of Combustion and Nitric Oxide Kinetics. SRI
Informal Letter Report to David W. Pershing, EPA. EPA Grant No.
R-800798, SRI Project 2008. October 18, 1972.
4. Benson, S.W., D. M. Golden, R. W. Lawrence, and Robert Shaw.
Estimation of Combustion and Nitric Oxide Kinetics. Quarterly
Progress Report No. 2, EPA Grant No. R-800798, SRI Project 2008.
February 15, 1973.
5. Benson, S. W., D. M. Golden, and Robert Shaw. Estimation of Com-
bustion and Nitric Oxide Kinetics. Interim Annual Report, EPA
Grant No. R-800798, SRI Project 2008. August 30, 1973.
6. Benson, S. W., D. M. Golden, R. W, Lawrence, R. Shaw, and R. W.
Wool folk. Estimation of Rate Constants as a Function of Temperature
X -i YZ ii XY + Z, X + Y + M «=t XY + M, and X + YZ + M rf XYZ + M, where
X, Y, and Z are atoms II, N, and O. Symposium on Chemical Kinetics
Data for the Upper and Lower Atmospheres, September 16-18, 1974,
Arlie House, Warrenton, Virginia. In press, New York, John Wiley
and Sons, Inc., 1975.
7. Benson, S. W. Thermochemical Kinetics. New York, John Wiley and
Sons, Inc., 1968.
8. JANAF Thermochemical Tables. Dow Chemical Company, Midland,
Michigan, 1975.
37
-------
9. Boden, J. C., and B. A. Thrush. Proc. Roy. Soc. (London). 305A:107,
1968.
10. Albers, E. A., K. J. Schmatjko, H. Gg. Wagner, and J. Wolfrum.
15th Symposium (International) on Combustion. The Combustion
Institute, Pittsburgh, Pa. Paper No. 73.
11. Hancock, G., and I. W. M. Smith. Trans. Faraday Soc. ^7:2586, 1971.
12. Homann, K. H., G. Krome, and H. Gg. Wagner. Ber. Bunsenges Phys.
Chem. T2:998, 1968.
13. Flower, W. L., R. K. Hanson, and C. H. Kruger. 15th Symposium
(International) on Combustion. The Combustion Institute, Pittsburgh,
Pa. Paper No. 78.
14. Cupitt, L. T. , and G. P. Glass. Trans. Faraday Soc. e>6:3007, 1970.
15. Mihelcic, De, and R. N. Schindlcr. Ber. Bunsenges Phys. Chem.
^74:1280, 1970.
16. Fair, R. W., and B. A. Thrush. Trans. Faraday Soc. £>5:1557, 1969.
17. Hanson, R. K., W. L. Flower, and C. H. Kruger. Combustion Sci.
Tech., in press.
18. Kaufman, F., and J. R. Kelso. J. Chem. Phys. ,23:1702, 1955.
19. Kaufman. F., and L. J. Decker. 7th Symposium (International) on
Combustion. The Combustion Institute, Pittsburgh, Pa., 1959. p. 57.
20. Wray, K. L. , and J. D. Teare. J. Chem. Phys. 3>6:2582, 1962.
21. Clark. T. C., S. H. Garnett, and G. B. Kistiakowsky. J. Chem.
Phys. 51_:2885, 1969.
22. Englcman, V. S. Summary and Evaluation of Kinetic Data on Reactions
in Methane-Air Combustion. Final Report. EPA Contract No.
68-02-0224. May 15, 1975.
38
-------
SECTION X
APPENDICES
Page
A. Estimation of Rate Constants as a Function of Temperature
for Reactions X + YZ ;± XY + Z, X + Y + M^XY + M, and
X + YZ + M -fi XYZ + M, Where X, Y, and Z are Atoms
H, N, 0 40
B. Estimation of Heats of Formation at 300 K of some Triatomic
Species Containing Atoms of the Elements Carbon, Hydrogen,
Nitrogen, Oxygen, and Sulfur 92
39
-------
Appendix A
ESTIMATION OF RATE CONSTANTS AS A FUNCTION OF TEMPERATURE
FOR REACTIONS X + YZ ^ XY + Z, X + Y + M ^ XY + M, AND
X + YZ + M S XYZ + M, WHERE X., Y, AND Z ARE ATOMS H, N, 0
S. W. Benson, D. M. Golden, R. W. Lawrence, R. Shaw, and R. W. Woolfolk
Physical Sciences Division, Stanford Research Institute
Menlo Park, California 94025
Presented at the Symposium on Chemical Kinetics Data for the Lower and
Upper Atmosphere, September 16-18, 1974, Airlie House, Warranton,
Virginia, U.S.A. To be published in a special issue of the
INTERNATIONAL JOURNAL OF CHEMICAL KINETICS, 1975.
40
-------
ABSTRACT
Previously measured and evaluated rate constants for the reactions
X + YZ ^ XY + Z, X + Y + Jjl - XY + M, and X + YZ + M ^ XYZ = M,
where X, Y; and Z are the atoms H, N. and 0; have been shown to fit the
form k = AT exp(-C/RT), where k is in mole, cm3, sec units,, and the
constants A, B,, and C have the values listed below.
1
Reaction
X + YZ r
X + Y + M -
XY + M -
X + YZ + M ->
(X and Z are
hydrogen
XYZ + M -
X + YZ + M --
(x and Z are
- XY + Z
XY + M
X + Y + M
log10A
l.j.6 + [iS«*01>/(2.3H)]
18
16;. 1 + [AS°too/(2.3R)]
'
XYZ + M 1 19
both i
atoms) i
X + YZ + M 17|.l + [AS°500/(2.3R)]
XYZ + M • 20.2
not both '
hydrogen atoms)
1 XYZ + M -'
B
0.5
-1
-2
-1
_2
-1.5
X + YZ + M 181 3 + [AS(1'500/(2.3R)] -2.5
C
^o - 1
0
AH?SOO
0
*«?.„„
0
A TrO
UH1500
AS300 is the entropy of activation at 300 K and is/equal to -22
cal/(mole K) in the exothermic direction (-22 + AS^,, cal/(mole K) in
the endothermic direction). AH°00 is the heat of activation at 300 K
41
-------
and is equal to either (a) -1 kcal/mole for exothermic (-1 + ^Hg00 kcal/
mole for endothermic) reactions that have a transition state preceded
by an intermediate that is stable with respect to the reactants, or
(b) 7 kcal/mole for exothermic (7 + AH300 kcal/mole for endothermic)
reactions that are concerted or that have a transition state preceded
by an intermediate that is unstable with respect to the reactants. The
criterion for a stable intermediate is that its heat of formation must
be at least 3 kcal/mole less than the sum of the heats of formation of
the reactants.
It is suggested that the rate constants listed above may be useful
in estimating rate constants for reactions that have not been studied
experimentally, especially at temperatures above 1000 K.
A convenient form of the equilibrium constant, suitable for
combustion reactions, is K/(cm3/mole) = 101-9(exp AS°500/R) T exp(-&H°500/RT)
42
-------
INTRODUCTION
The aim of this research is to provide a computer program that
will estimate rate constants of elementary chemical reactions for
mathematical models of combustion processes. The models are being
developed by the Combustion Research Section of the United States Environ-
mental Protection Agency as tools to reduce air pollution and improve
efficiency of utility burners. The chemical elements to be considered
are carbon, hydrogen, nitrogen, oxygen, and sulfur. In the beginning,
we selected the reactions of the atomic and diatomic species of hydrogen,
nitrogen, and oxygen for their simplicity and because of the widely
•Si-
praised critical reviews by Baulch, Drysdale, Home, and Lloyd. l >z The
species under consideration are H, N, O, H2, N2, O2, HN, NO, and OH.
For combinations, the "third body" M, is taken as N2. The temperature
range is 200 to 3000 K. The approach is to develop equations that will
account for rate constants that have been measured and then use these
equations to predict rate constants of reactions that have not been
studied experimentally.
References are listed at the end of Appendix A,
43
-------
TRANSFER REACTIONS
Transfer reactions were considered in this study first because
they are simple and because of inspiration from Dryer, Naegeli, and
Classman's work3 on the transfer reaction CO + Oil -» C02 + II. The
simplest transfer reactions are those between atoms and diatomics:
X + YZ -.-* XY + Z (1 )
From transition state theory,4 the rate constant, k, is given by:
QOI/-rp2 -j-
k/[cm3 /(mole sec)] = ~~ exp(-AG° /R'f) (2)
where K is Boltzmann's constant, h is Planck's constant, AG° is the
standard free energy change (standard state of 1 atmosphere) at. temper-
ature T, going from the initial state to the transition state., R is the
gas constant, and 82T is to express the rate constant in cm3/(mole sec).
rj: $ $
AG° = AH° - TAS° (3)
T T T V
A * *
where ^11" and ASr' are the enthalpy and entropy changes from the
rcactants to the transition state, and:
A <>* - t °* f A^l" -A o* „ f A o*,! ,
3 OO P 3 O O P
where AC0 is the heat capacity change from the initial state to the
P
transition state.
The heat capacity correction AC0 is given by AC° =-311 calf
P " P
(mole K). The reasoning is as follows: in a reaction X + YZ going to a
transition state X---Y---Z. we can estimate the heat capacities of the
44
-------
species X, YZ, and X-'-Y-'-Z (neglecting electronic heat capacities)
as follows:
C° (X) = 5R/2
C° (YZ) = C° (translation) + C° (rotation) + C°(vibration)
P P P p '
= 5R/2 + R + C°(vib)
= 7R/2 + C°(vib)
P
j-
C° (X--.Y---Z) = C°(translation) + C°(rotatioii) + C°(vibration)
P P P P
- 5R/2 + 3R/2 (nonlinear) + C°(vib)
* p ±
. . Ac° (X + YZ -> X---Y---Z) = 8R/2 + C° (X---Y. --Z)' - 12R/2 - C° (YZ)
P p,vib ' p,vib
X-..Y---Z has 3n - 6 = 3 frequencies, one of which is the reaction frequency;
one of which can be assumed equal to the Y-Z stretch in YZ; and the remain-
ing one is the X---Y'-'Z bend.
.'. AC0 (X + YZ - X---Y---Z) = -2 R + C°(X...Y---Z bend)
The C° bend must lie between 0 and R and, therefore, has the value
R/2 ± R/2:
.'. AC0' = -3R/2 ± 1R/2
P
= -3 ± 1 cal/(mole K)
Equation (4) can now be integrated directly, giving:
AG« = AII°00 - TAS°00 + AC0 [(T - 300) - Tln(T/300)] (5)
where AC0 is -3 cal/(mole K).
p '
Summarizing,
p QO^'rp2 -f
k/Lcm3/(mole sec)] = —— exp (-AG° /RT) (2)
Engleman5 has pointed out that it would be more convenient to
transpose equation (2) to the modified Arrhenius equation:
k = AT exp(-C/RT) (6)
The results follow.
45
-------
In general,
op if i i
A/(cms/(niole sec) = — —, exp[AsJ*0 - (AC° /R)] (7)
InW^ /"'
B = 2 + (AC° /R) (s)
£ P j.
C/(kcal/mole) - AH°00 - .3 AC° (9)
t
where Ac0 is in units of cal/(mole k).
Inserting the value of AC° = -3 cal/(mole K), equations (?), (8), and
(9) become:
A = 1016-6 exp(As°*0/R) (10)
B = 0.5 (11)
c = AH°L +
That is,
k/[cm3/(mole sec)] = 1016.6 exp(As°*0/R)T0- 5 exp[-(AH°*0 + 1/RT] (is)
We have found empirically (Figures A-l to A-8) that all the Leeds
critically evaluated data1*2 could be fitted by substituting the following-
values in equation (13). In the exothermic direction, AS300 - -22 cal/mole K) ,
and AHgoo = -1 or 7 kcal/mole. In the endothermic direction, A
$
-22 + AS^oo cal/(mole K), and AH°00 = (-1 + AH°00) or (7 + AH°00) kcal/mole.
References in the figures refer to the original compilation.
JANAF values6 for the three atoms and six diatomic species in the H, N,
0 system are listed in Table A-l, and were used to calculate AS300 and
AH°00 for the nine reaction pairs of the H, N, 0 system in Table A-2.
Unless otherwise noted, JANAF values are used throughout this paper. The
values of A, B, and C used to calculate the rate constants in Figures A-l
to A-8 are given in Table A-3. The rate constants were calculated at
200 K, 300 K, 400 K, 500 K, 700 K, 1000 K, 2000 K, 3000 K, and 4000 K. A
typical calculation for the reaction 0 + H2 -» OH + H is shown in Table A-4 .
46
-------
QtOH
-Qs-4-H-
1000
500
T/K
300
200
14.0
E
-------
2000
14.0
700
500
(84)
(140)
13.0
^ 12.0
o
E
o
en
o
11.0
10.0
9.0
EXPERIMENTAL DATA
Semenov 1945 (11)
Baldwin 1956 (27)
Fenimore and Jones 1958 (33)
Karmilova et a_K 1958 (34)
Schott andTinsey 1958 (35)
Fenimore and Jones 1959 (36)
Just and Wagner 1960.(42)
Azatyan et al. 1961 (45)
Azatyan et aT. 1962 (57)
Lovachev"T9¥3 (84)
Azatyan et al. 1964 (93)
Hirsch e"nZ TTyason 1964 (103)
Aganesyan and Nalbandyan 1965
Dixon-Lewis e_t a_K 1965 (119)
Balakhnin et a_K 1966 (132)
Ripley and~Gardiner 1966 (140)
Azatyan et al. 1967 (147)
Gutman eF'aTT 1967 (152)
Gutman and~S~chott 1967 (153)
Jenkins et al. 1967 (157)
Kurzius andToudart 1968 (171)
Myerson and Watt 1968 (172)
Browne et al. 1S69 (179)
Buneva el aT. 1969 (180)
Schott T9"6?"~(187)
Brabbs et al. 1971 (203)
Eberius~£t~jTK 1971 (204)
This evaluation.
(113)
(171)
O
Estimated, this work
1.0
103T"1/K"1
2.0
FIGURE A-2 H + 0
HO + O
48
-------
2000
1000
500
300
10.0 -
9.0
o
E
en
O
8.0
7.0
6.0
CALCULATED EXPRESSIONS
Fowler 1962 (9)
Kaufman and Del Greco 1963 (14)
Kaskan and Browne 1964 (17)
e Mayer e_t al . 1966, 1968 (28,45)
_ __ Heicklen T967 (36)
Jenkins et al. 1967 (38)
SchofielcTlI£7 (39)
Baulch e_t al . 1968 (42)
Browne et aT. 1969 (46)
Nicolet~T970 (53)
This evaluation
Estimated, this work
Note. The ordinate of this
figure is log(kT"1).
5.0
1 .0
2.0
3.0
4.0
FIGURE A-3 H + OH -» H2 + O
49
-------
2000
1000
500
300
(14)
10.0
9.0
8.0
o
E
f
•••HOI
I
(83)
7.0
en
o
EXPERIMENTAL DATA
Schumacher 1930 (2)
Baldwin 1956 (7)
H Fenimore and Jones 1958 (9)
Kaufman 1958 (11 )
Schott 1960 (14)
Azatyan et al. 1961 (15)
Fenimore ancT~Jones 1961 (18)
Clyne and Thrush 1963 (25)
Wong and Potter 1965 (50)
Balakhnin et al . 1966 (51)
Ripley and GaFJiner 1966 (57)
Gutman and Schott 1967 (64)
Gutman e_t aj_. 1967 (65)
Hoyermann e_t al . 1967 (69)
Westenberg aricfde Haas 1967 (74)
Westenberg and de Haas 1967 (75)
Balakhnin et a±. 1968 (77)
Campbell an"d" Thrush 1968 (79)
Kurzius 1968 (83)
Mayer and Schieler 19-68 (84)
Browne et al. 1969 (88)
Schott T9"69~(96)
Wakefield 1969 (98)
Westenberg and de Haas 1969 (100)
Balakhnin e_t al. 1970 (102)
Dean and Kistiakowsky 1970 (107)
Jachimowski and Houg'hton 1970 (112
Brabbs e_t a_K 1971 (117)
This evaluation
6.0
Note. The ordinate of this
figure 1s
5.0
O
Estimated, this work
1
4.0
1.0
2.0
3.0
103T"1/K"1
FIGURE A-4 0 + Ha ->, OH + H
50
-------
NO-f-N
December
N2+O
1969
2000 1000
T(°K)
500
30O
14
Fenimore and Jones 1957 (6)
Harteck and Dondes 1957 (8)
Kistiakowsky and Volpi 1958 (12)
Kaufman and Decker 1959 (13)
Verbeke and Winkler 1960 (15)
U
-------
December 1969
12.0
10000
T(°K)
5000 4000
3000
—I
11.0
10.0
9.0
O)
o
8.0
Dufl and Davidson 1959 (4)
WrayandTeare 196Z (16)
This Evaluation
O
Estimated, this work
7.0
0
FIGURE A-6 0 + N -» ON + N
52
-------
December 1969
u
0)
_
o
n
10-00
h-
D)
O
9-00 -
8-00 -
7-00 -
6 OO -
5-00
2000 1000
Kistiakowsky and Volpi 1957 (3)
Kaufman and Decker 1959 (7)
dyne and Thrush 1961 (14)
Mavroyannis and Winkler 1961 (18)
Kretschmer and Petersen 1963 (27)
Vlastaras and Winkler 1967 (62)
Wilson 1967 (64)
Miyazahi and Takahashi 1968 (67)
Becker, Groth and Kley 1969 (68)
^^^ Estimated, this
\) work
1 OO
2-00
3-OO
FIGURE A-7 N + 09
NO + O
53
-------
10-00
s-oo
i.
o
en
BOO
E
o
4-00
0)
O
2-00
00
NO+O- >>O2+
December 1969
10000 5000 300O
20OO
1500
0-2
* Kaufman and Kelso 1955 (6)
V Kaufman and Decker 1959 (8)
O !WrayandTeare 1962 (16)
This Evaluation
O
Estimated, this work
0-4
O-6
FIGURE A-8 0 + ON "* 0, + N
06
54
-------
Table A-l
THERMODYNAMIC PROPERTIES OF MONATOMIC
AND DIATOMIC SPECIES IN THE H, N, 0 SYSTEM5
Monatomic H
N
0
Diatomic HN
HO
H2
NO
N2
02
AH°300/(kcalA>°le)
52.1
113.0
59.6
90.0
9.3
0
21.6
0
0
S°00/[cal/(mole k)]
27.42
36.64
38.50
43.29
43.92
31.25
50.39
45.81
49.05
55
-------
Table A-2
OVERALL ENTROPIES AND HEATS FOR ALL CHEMICAL REACTION PAIRS
Reaction Pair
0 + NH 5± NO + H
0 + HN ?± HO + N
N + OH *± NO + H
N + NH ?± N2 + H
O + OH ^ 02 + H
H - + HN ^ H2 + N
H + HO 5i H2 +0
N + 02 ?2 NO + O
N + NO ^ N2 + 0
As°00/[cal/(mole K)]
4.0
1.2
2.8
6.7
6.0
2.8
1.6
-3.2
2.7
AH°00/[kcal/mple]
-75.9
-27.3
-48.6
-150.9
-16.8
-29.1
-1.8
-31.8
-75.0
56
-------
Table A-3
B
Values of A, B, and C in k/[cm3/(mole sec)] = AT exp(-C/RT) Used to Calculate Rate
Constants in Figures A-l to A-8
Figure
A-l
A-2
A-3
A-4
A-5
A-6
A-7
A-8
Reaction
0+OH •-> 02+H
H+02 -» HO+0
H+HO ~* H2-KD
0+H2 - OH+H
N+NO -" N2+0
0+N2 -> ON+N
N+02 -» NO+0
0+ON -* 02-fN
AS3°00/[cal/(inole K)]'
-22
-22+AS°00 = -1.6.0
-22
-22-^S°00 = -20.4..
-22
-22+AS°00 = -19.3
-22
-22+AS°00 = -25.2
log A/Lcm3/mole sec)]
11.8
13.1
11.8
12.1
11.8
12.4
11.8
11.1
B
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
AH°00/(kcal/mole)
-1
-HAH°00 = 15.8
7
7+AH°00 = 8.8
-1
-1+AH°00 = 74.0
7
7+AH300 = 38'8
C/(kcal/mole)
0
16.8
8
9.8
0
75.0
8
39.8
-------
Table A-4
Calculation of the Rate Constant as a Function.
of Temperature for O + H2 -* OH + H from
k/[cm3/Uole sec)] = 1012- lrr°- 5 exp(-9. 8/RT)
(See Figure A-4)
Temperature /K
200
300
400
500
700
1000
1500
2000
3000
4000
1000K/T
5.0
3.33
2.50
2.00
1.43
1.00
0.67
0.50
0.33
0.25
Iog10k/[cm3/(mole sec)]
2.5
6.2
8.0
9.2
10.5
11.5
12.3
12.7
13.2
13.4
M[ Kelvin 1
^T/|cma/(niole sec)J .
0.2
3.7
5.4
6.5
7.6
8.5
9.1
9.4
9.7
9.8
58
-------
The value of AS°g0 = -22 cal/(mole K) is very reasonable. Consider
for example the reaction,
H + Q2 -> (H...O-.-0) -> HO + O (14)
As a first approximation the triatomic transition state may be
approximated by the molecule H02. The entropy of activation of 300 K
is then given by the entropy change at 300 K for the reaction
H + 02 -+ H02 (15)
That is AS°oo (Reaction 14) = AS°00 (Reaction 15) = S°00(HO2) - S°00(H) -
S°00(02) = 54.4 - 27.4 - 49 - 0 = -22.0 cal/(mole K). The exact agree-
ment is fortuitous because in another example,
N + NO -> N- • -N- • -0 -» N2 + 0 (16)
the activation reaction is approximated by
N + NO -> N20 (17)
The entropy change for Reaction (17) is
AS°00(17) = S°00(N20) - S°00(N) - S°00(NO)
= 52.6 - 36.6 - 50.4
= -34.4 cal/(mole K)
However the point is that the "universal" value of AS300 = -22 cal/(mole K)
can be readily understood in terms of the entropy of the reactants and of
the transition state.
The two values for AHg00 in the exothermic direction require more
interpretation and discussion. The basic postulates are (a) that
-1 kcal/mole for reactions that have a transition state preceded by an
intermediate that is stable with respect to the reactants and (b) that
+
AH2!L = 7 kcal/mole for reactions that are concerted or have a transition
4J o U O
state preceded by an intermediate that is unstable with respect to the
reactants.
59
-------
For ttje genera^ reaction
±
X + YZ -» (X"-Y-"Z) -* XY + Z (1)
ponsider first the case where the transition state is preceded by a
stable molecule intermediate as shown in Figure A-9. An example is
the reaction
*
N + NO -> (N-..N---0) -* N2 + 0 (16)
The stable molecule intermediate in this case is N20. The sum of the
heats of formation of the reactants N + NO is 134.6 kcal/mole compared
to 19.6 kcal/mole for N2O. That is, N20 is 115 kcal/mole more stable
than N + NO. If we allow 60-80 kcal to form the triplet state N203 it
J.
is still 40 ± 10 kcal more stable than reactants and AH°Q0 (Reaction 16)
- -1 kcal/mole. Another example is
$
H + O2 -» (H-.-O-'-O) -» HO + 0 (18)
In this case, the stable molecule intermediate is H02. The reaction
H + 02 -> H02 (19)
is 63.9 kcal/mole exothermic, hence AH°00 (Reaction 18) = -1 kcal/mole.
Consider now the case where the reaction is concerted or has a
transition state preceded by an intermediate that is unstable with
respect to the reactants as shown in Figure A-10. An example of a
concerted reaction is
H + HO -> (H---H...O) -» H2 + 0 (20)
±
Therefore, in the case of Reaction (20), AH°00 = 7 kcal/mole.
60
-------
o n
I
•1
REACTANTS
X + YZ
3 kcal/mole
OR GREATER
TRANSITION
STATE
(X ... Y ... Z}:|
1 kcal/mole
STABLE
INTERMEDIATE
XYZ
PRODUCTS
XY t Z
REACTION
SA 2008 3
FIGURE A-9
HEAT CHANGES FOR REACTIONS HAVING TRANSITION STATES
PRECEDED BY AN INTERMEDIATE THAT IS STABLE WITH
RESPECT TO THE REACTANTS
In such cases -^ ~1 kcal/mole-
61
-------
o
o
o n
I
O
TRANSITION
STATE
(X . . . Y . . . 21*
/ UNSTABLE
INTERMEDIATE
CONCERTED^M
PATH \
PRODUCTS
XY + Z
FIGURE A-10
REACTION
SA-2008-4
HEAT CHANGES FOR REACTIONS THAT ARE CONCERTED
OR THAT HAVE A TRANSITION STATE THAT IS PRECEDED
BY AN INTERMEDIATE THAT IS UNSTABLE WITH RESPECT
TO THE REACTANTS
In such cases AH°*0 = 7 kcal/mole.
62
-------
An example of a reaction that has a transition state preceded by an
intermediate that is unstable with respect to the reactants is
4-
N + o2 -> (N--.O..-O) -* NO + o (21)
The intermediate is NOO produced by the reaction
N + 02 - NOO (22)
We have estimated (see later) that AH°0(NOO) is 136 ± 16 kcal/mole.
The sum of the heats of formation of the reactants is 113 ± 1 kcal/mole,
therefore NOO is unstable with respect to N + 02, and AH°00 (Reaction 22) ''
- 7 kcal/mole.
For a system of three elements, there are 18 ways to arrange linearly
the atoms. For example the empirical formula HNO can be HNO, HON, or
NHO. Thus there are 18 pairs of reactions: 9 pairs are chemical
reactions, for example
O + OH ^ 02 + H (23)
and 9 pairs are exchange reactions, for example
O18 + 01601S & 018016 + O16 (24)
In order to estimate the rate constants of all 18 pairs of reactions,
$ .
it is necessary to assign values of AH°OO of either -1 or 7 kcal/mole
to the reaction in the exothermic direction. (The exchange reactions
are all thermoneutral, which is taken as exothermic for the purpose of
assigning a value of AHg00.) All reactions that involve transfer of a
4-
hydrogen atom are concerted and have AH°00 =7 kcal/mole. For the other
reactions it is necessary to know the heat of formation of the triatomic
intermediate and determine whether it is stable or unstable with respect
to the reactants. In some cases the heat of formation of the triatomic
is well known, for example HOH, OCO, HNO, and HO2. In other cases the
63
-------
of formation fyad to be estimated. In general the main estimating
technique was to take the fully hydrogenated species and estimate the
Strengths Qf the bonds to the hydrogens. For example, the heat of
formation of HNN was estimated from AH°300 (H2NNH2) assuming each N-H
bond strength to be 95 kcal/mole. The details of the estimation are
given in a separate paper7 that considers the 75 triatomic species in
the complete C, H, N, 0, system but the results relevant to the present
vfork are summarized in Table A-5.
It is interesting to compare the rate constants predicted by the
above considerations with some experimental results not given as
figures in the Leeds compilation. Reaction (25)
N + OH -+ NO + H (25)
has been studied by Campbell and Thrush,8 and by Garvin and Broida.9
Their results are shown in Figure A-ll along with some estimates by
Tunder, Mayer, Cook, and Schieler.10
The exchange reactions are of limited practical importance, but
their primary purpose here is to test the model described above with
the available experimental data on isotoplc exchange reactions. For
example, Klein and Herron11 and later Jaffe and Klein12 showed that
oxygen.atoms will exchange with O2 and NO at rate constants plose to
10s M""1 sec"1 at 300 to 400 K, in fair agreement with our predicted values
of 1010 M-1 sec"1 based on AH°*0 = -1 kcal/mole, AS°*0 = -22 cal/(mole K),
and AC° 300 = -3 cal/(mole K). In the case of H/H2 exchange, Ridley,
Schultz, and LeRoy13 and Westenberg and de Haas14 measured rate constants
64
-------
Table A-5. Determination of values of AH°00 used to calculate rate constants
of atom-transfer reactions in the H, N, 0 system
Reaction pair in
exothermic direction
except when thermoneutral
0 + NH ~ ON + H
0 + HN ^ OH + N
N + OH * NO + H
N + NH - N2 + H
N + HN ~ NH + N
0 + OH ^ 02 + H
0 + HO ~ OH + O
H + HN - H, + N
A
H + NH ^ HN + H
H + OH ^ HO + H
H + HO ~ H, +0
2
N + O2 ~ NO + 0
0 + NO - ON + 0
N + NO - N2 +0
N + ON 5s NO + N
H + H2 - H2 + H
N + N2 - N2 + N
0 + 02 ^ 02 +0
Triatomic Intermediate
structure
HNO
concerted
NOH
HNN
concerted
OOH
concerted
concerted
HNH
HOH
concerted
NOO
ONO
NNO
NON
concerted
NNN
000
AH°300/(kcal/mole)
23. 85
77 ± 11
152 ± 16
5 ± 25
4.5 ± 1 .55
57.8s
136 ± 16
7.9 ± 0.2s
19.6 ± O.I5
209 ± 26
111 ± 5
34.1 ± 0.4
Keactants
species
0 + NH
N. + OH
H + N2
0 + OH
H + NH
H + OH
N + 02
0 + NO
N + NO
N + ON
N + N2
0 + 02
AB°300/(kcal/mple)
149.5 ± 4
122.3 ±1.3
203 ± 5
68.9 ± 0.3
142 ± 4
61 .4 ±0.3
113 ± 1
81 .9 ±0.4
134.6 ±1.4
134.6 ±1.4
' 113 ± 1
59 .55 ± 0.02
AHjoodntermediate -
reactants)/(kcal/mole)
126 ± 5
45 ± 12
51 ± 21
64 ± 3
96 ± 6
119 ± 1
-23 ± 17
73 ± 1
115 ± 2
-74 ± 28
2 ± 6
26 ± 1
AH°*d/
(kcal/mole)
-1
7
-1
-1
7
-1
7
7
-1
-1
7
7
-1
-1
7
7
7
-1
-------
10.0
9.0
8.0
o
£
E
O
2000 1000
0°
T
o
A
A
500
o
A
o
A
300
6
o
je
D
7.0
A
6.0
5.0
A
O
Calculated by Tunder, Mayer,
Cook, and Schieler, 1967
Estimated, this work
Measured by Campbell and Thrush, 1968
O
Measured by Garvin and Broida, 1963
4.0
1.0
2.0
66
3.0
FIGURE A-ll NO + OH -* NO + H
-------
for D + H2 -> DH + H. As shown in Figure A-12, their rate constants
agree well with estimated values.
Another interesting test of the model is given by Reactions (26)
and (27)
N(4S) + 02 -> NO + 0(3P) (26)
N(2D) + 02 -> NO + 0(3P) (27)
When ground state nitrogen atoms react with molecular oxygen as in
Reaction (26), the intermediate NOO is unstable with respect to the
reactants and AH°*0 = 7 kcal/mole (see Table A-5 and Figure A-7). However,
when the nitrogen atom is in its upper excited state, N(2D), which is
55 kcal/mole above the ground state, the sum of the heats of formation
of the reactants is now 163 kcal/mole compared with 136 ± 16 for the
intermediate NOO so that intermediate is now stable with respect to the
reactants, and AH§oo = -1 kcal/mole. Slanger, Wood, and Black15 have
measured rate constants for Reaction (27) as shown in Figure A-13.
The good agreement between estimated and measured data suggests
that equation (13) is a good approximation for reactions of the type
X + YZ -4 XY + Z that have not been studied experimentally.
A computer program has been written in FORTRAN IV to estimate rate
constants for the eight transfer reactions in the H2/O2 and N2/O2 systems.
This program has been tested and is working in both batch and conversa-
tional modes on Stanford Research Institute's CDC 6400 computer. Requests
for copies of the program should be addressed to W. Steven Lanier, Combus-
tion Research Section, Clean Fuels and Energy Branch, U. S. Environmental
Protection Agency, Research Triangle Park, North Carolina 27711.
67
-------
2000
1000
500
300
10.0
A
O
Experiments by Ridley,
Schulz, and LeRoy, 1966
Experiments by Westenberg,
and de Haas, 1967
Estimated, this work
9.0
8.0
E
u
o>
O
7.0
6.0
5.0
D
O A
D A
O A
A
D
D
4.0
1.0
2.0
3.0
FIGURE A-12 D + H2 -» DH + H
68
-------
2000 1000
T/K
500
300
10.0
I
o
o
o
n
9.0
8.0
A
A
E
u
7.0
A
6.0
5.0
D Measured by Slanger,
Wood and Black, 1971
O
A
Estimated, this work
N(4S) + O2 -» NO + O(3P)
A
4.0
1.0
2.0
3.0
4.0
FIGURE A-13 N(2D) + 02
69
NO + O(3P>
-------
Variation of Equilibrium Constant with Temperature
V. Engleman5 has pointed out how useful it would be to have in
analytical form the variation of the equilibrium constant with tempera-
ture. Rigorously,4 the variation of the equilibrium constant with
temperature is given by:
RTlnK = - AG° (28)
where
AG° = AH° - TAS° (29)
rn rp rp \ /
- T
AG° = AH° + /Ac°dT - TAS°
rp 3 OOrri »/ j, 3OO
» 3 0 O "
Ac° dlnT (30)
oo P
However, for the purpose of estimating the equilibrium constants of the
elementary reactions that are important in combustion systems, it is a
very good approximation to use:
500 »TAS»500 (31)
For reactions in which there is a change in the number of moles,
for example, N + O + M ~» NO + M, the equilibrium constant in units of
concentration K is related to that in pressure units K by:
c p
K = K (R'T)"An (32)
c p ^
where R' is 82.057 cm3 atm/(mole K) and An is the mole change in the
reaction. For compatibility with the modified Arrhenius equation, which
is:
k = AT exp(-C/RT) (6)
equation (32) can be put in the form:
Kc/(mole/cm3) - (82) ~An[exp(AS°500/R)]T~An exp[-AH»500/(RT) ] (33)
= A'T exp[-c' /(RT)]
70
-------
where
Iog10 A' = -1.9 An + [AS?500/(2.3R)]
B' = An
C = AHisoo
Reactions of the Type XY + M -^ X+Y+M
In air-oxidized combustion, N2 is by far the most abundant species.
It is therefore a good first approximation to take N2 as M. In all the
following, M and N2 may be used interchangeably:
XY+M - X+Y+M (34)
According to Benson,4 most atom recombinations, back reaction (-34), have
rate constants in the range io15-5±0'5 cms/(mole2 sec) at 300 K. The
rate constants are slightly more than a power of ten slower at 3000 K.
We have empirically derived the following rate equation for reaction
(-34) over the temperature range 200 K to 4000 K:
k_23/[cms/mole2 sec)] = 1018 T-1 (35)
That is,
r>
k_34/[cm6/(mole2 sec)] = A_34T ~34 exp(-C_34/RT) (36)
where
Iog10 A-34 = 18
B-,
34 _
= -1
P- — 0
C 34 U
and where the subscript -34 denotes the reverse of Reaction (34).
71
-------
The rate constant of the forward Reaction (34) is related to k_
the rate constant of the reverse reaction (-34) by the equilibrium
constant K0, :
34
k34
— = K34 (37)
K-34
that is,
k34 = K34k-34 <38)
As discussed previously, for high-temperature combustion., a good
approximation for K34 is:
K34/(cm3/mole) = KT1. 9 [exp(AS°5OO/R) ]T-1[exp(-4H°50o/RT) ] (39)
. ' . k34/Lcm3/(mole sec)] = 1018 T'1 KT1-9 [exp(AS°500/R)] T-1[exp(-^H°500/RT)
= lO^-i [exp(AS°500/R)T-2[exp(^H°500/RT))] (40)
where As°500 and AH°SOO are the entropy and heat changes in reaction
(34) as written. In the modified Arrhenius form
k34/[cc/mole sec)] = A34T 34 exp (- C34/RT) (4l)
where
log10 A34 = 16.1 + [AS°500/(2.3R)]
B34 = -2
AH°
"nl
500
The Leeds group 1'2 has critically evaluated rate data for three
reactions of the type XY+M^ X+Y+M; namely, where XY is NO,
R2, or HO. The relevant data for calculating the rate constant from
equations (35) and (41) are given in Table A-6.
72
-------
Table A-6
MODIFIED ARRHENIUS PARAMETERS [k = AT8 exp(-C/RT)] FOR THE REACTION XY + M s± X + Y + M (34)
AB
NO
H2
HO
*S°15oo
28.52
28.12
26.49
AH°150o
154,5
107.4
105.4
log10[A33
22.32
22.24
21.88
B34
-2
-2
-2
b
C34
154.5
107.4
105.4
c
log10[A-34]
18.0
18.0
18.0
B-34
-1
-1
-1
b
C-34
0
0
0
Units are;
cal/(mole K)
kcal/taole
cra3deg2/(mole sec).
oo
-------
Examples of rate constant calculations for NO+M-»N+0+M
are givep. in Table A-7.
The calculated rate constants for reaction (34) where XY is NO,
H2, or HO are plotted on copies of the Leeds evaluations in Figures
A-14 to A-19.
The good agreement between estimated and measured data suggests
that equations (35) and (41) are good approximations for reactions of
the type XY+M-+X+Y+M that have not been studied experimentally.
Reactions of the Type XYZ + M -* XY + Z + M
As in the previous case of XY + M ~* X + Y + M, M can be taken
as N2. For most reactions4 of the type:
. XYZ + M -> XY + Z, + M' (42)
the rate constant k_42 is of the order of 1016-5 cc2/(mole2 sec) at
300 K. When X and Z are hydrogen atoms, for example, H20 + M - HO + H + M,
the temperature dependence is close to T"1, which is the same as for the
diatomic series XY + M ^ X + Y + M. In the modified Arrhenius form of
the rate constant:
k_42/[cme/(mole2 sec)] = A_42 TB~4 2 exp(-C4.2/RT) (43) .
where
log10(A_42/[cms/(mole2 sec)]) =19'
B-42 = -1
C_42/(kcal/mole) = 0 .
74
-------
Table A-7
CALCULATION OF RATE CONSTANTS FOR NO + M
N + 0 + M (1)
T
200
300
400
500
700
1000
1500
2000
3000
4000
Iog10 Aj
22.32
22.32
22.32
6.60
154.5/9
16.88
1
6.96
11.26
7.20 8.44
Iog10 k±
-1.16
l..MT*
1.15
1.24
1.30
1.35
1.42
1.50
1.59
1.65
I
4.10
6.68
1.74
1.80
log k±
T1/2
0.49
5.84
8.48
Iog10
18.0
18.0
18.0
18.0
18.0
18.0
18.0
18.0
18.0
18.0
Iog10 T
2.30
2.48
2.60
2.70
2.84
3.00
3.18
3.30
3.48
3.60
'k!*0
15.70
15.52
15.40
15.30
15.16
15.00
14.82
14.70
14.52
14.40
k_j T*%
16 . 85
16.76
16.70
16.65
16.58
16.50
16.41
16.35
16.26
16.20
1OOO/T
5.0
3.33
2.5
2.0
1.43
1.00
0.67
0.50
0.33
0.25
Ol
Units are: T, Kelvins
A±, cm3cleg2/(mole sec)
6, kcal/mole
k, cra^Cmole sec)
A-j, cm6 deg/(mole2 sec)
k-lt cm6/(mole2 sec).
-------
December 1969
12
10
I
(f)
8
'«
O
ro
0)
O
O
10000
T(°K)
5000 4000
T
30OO 25OO
T
M.Na.Oa.Ar
M= all species
Freedman and Daiber 1961 (2) (M = Ar)
Vincent! 1961 (3)
Wray and Teare 1962 (4)
McKenzie 1966 (13)
Caraac and Feinberg 1967 (17)
This Evaluation
\
\
\
O
Estimated, this work
2000
FIGURE A-14 NO+M^N+0+M
76
-------
M
December 1969
T(°K)
18
M
§ •
50 U
1 CM
5 '„
a 0
+ £ 17
O (0
+ E
g O
4 C
§ i
g "h-
^ 16
D)
_O
15
5000 2000 1000 500 4OO 300 200
' ' i i i "-- • r 1
Wray et al. 1960 (8) (M = NO. 0,N,0 , N )
2 2
+ Harleck, Reeves and Manella 1961 (12) (M unspecified) ^^ Estimated, this Work
• Mavroyannis and Winkler 1961 (15)*
^ Kretschmer and Petersen 1963 (21)"
T Barlh 1964 (26)*
0 Campbell and Thrush 1966 (36)
A A Campbell and Thrush 1967 (39)*
O Campbell and Thrush 1968 (42) 2
V Campbell and Thrush 1968 (43)
• Takahashi 1968 (47)* = 2
/ M = Ho — »0> M=N->O
_/ Th-SE i r A--M=co2 9— M,co2
' Black poiotirepresent M fN\ (3 >>^A — M = Ar ^^ M = Ar
' r\ O . -t •
x-vO ^
x-vV^A^ A* — M=He
(y
1 i i i i
0 12 3 4 5 6
103(°K~1)
T
-------
10.0
5.0
O
E
S
O
-5.0
-10.0
\
O %
unspecified—f\\ •>•
OkN.
\
• unspeci fied
\
\
\
\
\
\\\
\
»*• x
%x
I UUU
\
\
\\\
\
\
\
\
\
Vx'
REVIEW ARTICLES
Duff 1958 (1)
— Pergament, expression (a) 1963 (6)
Kaskan and Browne 1964 (8)
Tamagno et al. 1966 (16)
. Bortner T9~6~7~(18)
Jenkins e_t aJL 1967 (19)
\
\
Estimated, this work
2.0
4.0
6.0
8.0
10.0
FIGURE A-IG OH+M->O+H+M
78
-------
H+O+M > OH4M
3000
1000
T/K
500
300
~T
T
EXPERIMENTAL DATA
Schott 1960 (9)
1 Getzinger and Schott 1965 (23)
Jenkins et aj_. 1967 (36)
18.0
— X * —
X It XX-
REVIEW ARTICLES
Bates and Nicolet 1950 (3)
Kushida 1960 (8)
Franciscus and Lezberg 1963 (14)
Westenberg and Favin 1963 (15)
Kaskan and Browne 1964 (18)
Kurzius, unpublished
Chinitz and Baurer 1966 (30)
Tunder et al. 1966 (33)
Bortner~T967 (34)
Bahn et al. 1969 (42)
unspeci fied
17.0
o
OH,H20
02,H20
Estimated, this work
— — » « — unspecified
o
£
E
0
-X
C71
O
16.0
15.0
Ar
H,,
fi ed
o
unspeci fi ed
O
unspeci fied
14.0
1.0
2.0
103T"1/K"1
3.0
4.0
FIGURE A-17 H+0+M-*HO+M
-------
H
H+M
T/K
13.0
10 OOP
I
5000
3000
2000
12.0
o
E
u
D>
O
11.0
10.0
9.0
8.0
7.0
6.0
5.0
REVIEW ARTICLES
M = H
_^M U U
•— PI _ [-J
M = Ar
M = H20
M = N
M = unspeci
(26)
O
I
Duff 1958 (17)
Libby et al. 19
Fowler~T96~2" (26
Ski nner et. al.
Kaskan and Browne
Bascombe 1965 (52)
Chinitz and Baurer
Khan (72)
Newhall 1969 (82)
•This evaluation (M=Ar,H2 and H)
Estimated, this work
i .0
2.0
3.0
4.0
5.0
TO4!"1/*"1
FIGURE A-18 H2 +M-*H+H+M
80
-------
H + H + M
T/K
50
100
300
H2 + M
500 1000
2000
5000
17.0
16.0
REVIEW ARTICLES
Ho
oo
o
E
E
(J
Dl
O
15.0
— M
— M = H*
— M = Ar
--- M = N
M unspecified
14.0
O
13.0
1 .0
Bates and Nicolet 1950 (24)
Careri 1953 (29)
Campbell and Fristrom 1958
Westenberg and Favin 1963 (
Kaskan and Browne 1964 (92)
Nicolet 1964 (98)
Bascombe 1965 (107)
Wilde 1965 (127)
Bortner 1967 (149)
Heicklen 1967 (152)
Khan (158)
Newhall 1969 (187)
This evaluation
(M = H2)
(98)
H)
(32)
84)
(107
(152)
(M = Ar)
Estimated, this work
2.0
3.0
4.0
log(T/K)
FIGURE A-19 H +' H + M •* H2 +M
-------
As discussed previously in the case of 'XY + M *± X + Y + M, the
equilibrium constant is given by:
k42/(cmVmole) = 10-J-9Cexp(AsJ500/R)]T-i(^05oo/(RT) )]
/. k42/[cm3/(mole sec)] = 1017- 1[eXp(As?500/R)]T-2[exp(^ °500/(RT) ) ] (45)
In the modified Arrhenius form:
k42/[cm3/(mole sec)] = A42TE*2 exp(-C42/RT) (46)
where
los10(A^2/(cm3/(mole sec)]) = 17.1 + [As°500/(2. 3R)]
B42 = -2
C42/(kca I/mole) - ^°1500
The calculated results for H20 + M tf HO + H + M are compared in Figures
A-20 and A-21 with the Leeds critically evaluated data.1'2
When X and Z are not both hydrogen atoms (for example, N02 or
H02), the temperature variation of the combination rate constant is more
nearly T'1-5 than T'1. So k_42 is given by:
k_42/[cme/(mole2 sec)] = 102o.2 T-i.s ^^
In the modified Arrhenius form
k_42/[cm6/(mole2 sec)] = A_42 TB-42 exp(-C_42/RT) (48)
where
log10(A_42/[cm6/(mole2 sec)] = 20.2
C_42 = -1.5
C_42/(kcal/mole) = 0
and for the forward reaction:
k42/[cm3/(mole sec)] = A42TB42 exp(-C42/RT)
(49)
82
-------
I / N
5000
3000
2000
1500
EXPERIMENTAL DATA
Jenkins et aj[. 1967 (27)
OlschewsFT ^t al. 1967 (28)
•• Homer and Hurle 1970 (36)
REVIEW ARTICLES
14.0 —
12.0
10.0
8.0
6.0
4.0
2.0
Duff 1962 (3)
-- Skinner et al.1962 (10)
Kaskan arT3 Frowne 1964 (14)
Bascombe 1965 (19)
• Baulch e_t al . 1968 (31 )
Calculated from k
-1
Estimated, this work
H0,0 \\ \
•
2,
e. t.
0.2 0.4
0.6
103T"1/K"T
FIGURE A-20 H,,0 +M-+H+OH+M
0.8
83
-------
H+OH+M
H2O-+M
300
19.
500
18.0
oo
17.0
E
u
C71
O
16.0
15.0
T/K
1000
2000
3000
EXPERIMENTAL DATA
Prost and Oldenberg 1936 (1)
Oldenberg and Rieke 1939 (2)
Padley and Sugden 1958 (5)
Schott 1960 (6)
Black and Porter 1962 (9)
Dixon-Lewis et al. 1962 (11)
McAndrew and~TJheeler 1962 (13)
Rosenfeld and Sugden 1964 (24)
Schott and Bird 1964 (25)
Dixon-Lewis et aj_. 1965 (30)
Zeegers and ATkemade 1965 (40)
Zeegers and Alkemade 1965 (41)
Getzinger 1967 (51)
SO
He
Estimated, this work
- XeO
Xe
Ar
He
o
0
\~S
A t
Y f
*
Getzinger and Blair 1967,
Jenki ns e_t aj_. 1967 (55)
Macfarlane and Topps 1967
Browne ejb ^1_. 1969 (64)
Gay and Pratt 1969 (66)
Halstead and Jenkins 1970
This evaluation
(56)
(79)
2.5
3.0
3.5
1og(T/K)
-------
where
log10(A42/[cm3/(mole sec)]) = 18.3 + [AS1500/(2.3R) ]
B42 '
C42/(kcal/mole) = ^.H°500
The data for calculating rate constants for XYZ + M -> XY + Z + M
are summarized in Table A-8. (There was no Leeds figure for
H02 + M -> H + 02 + M, so rate constants were not calculated for the
forward reaction.)
The calculated rate constants are compared with the Leeds
critically evaluated experimental data1.2 for XYZ = NO2 in Figures A-22
and A-23, and for the reaction H + 02 + M -4 HO2 + M in Figure A-24.
The good agreement between estimated and measured data suggests that
equations (43) and (49) are good approximations for reactions of the
type XYZ +M?±X + YZ + M that have not been studied experimentally.
A final warning is in order. Not all atom-metathesis reactions
will have activation energies of either 7 or -1 kcal/mole. Many such as
H + C12 or F + H2 will have each of the order of 2 or 3 kcal/mole. At
300 K, an extension of our scheme for these reactions will yield serious
discrepancies of many powers of 10. However, in flame systems at a
4-
temperature of 2000 K, an error of 4 kcal/mole in estimating AH will
lead to an error of about a factor of 2 in a rate constant. This value
is crude but useful.
As regards extending the technique to species larger than atoms and
diatomic molecules, there appears to be no reason why the principles used
in the present work cannot be developed further. The form of the rate
85
-------
oo
05
Table A-8
MODIFIED ARRHENIUS PARAMETERS [k = AT8 exp(-C/RT)] FOR THE REACTION XYZ +M-XY+Z+M (42)
Units are:
cal/(raole K)0
kcal /mole .
cm3deg /(mole sec) .
ABC
H20
N02
H02
AS°BOO
31.13
33.97
AH°1500
122.6
74.6
c
log10[A42]
23.89
24.51
B4 2
-2
-2.5
-— F
^4 2
154.5
74.6
log10[A_42j
19.0
20.2
20.2
B-4 2
-1
-1.5
-1.5
b
C_ 4 2
0
0
0
cm6 deg-B/(mole2 sec)
-------
5000
NO2+M
3000
July 1970
T(°K)
2000
1500
1000
11-0
10-0
-------
D)
O
18
u
)
1368 (70)
^(36)
,(15)
(61 ^
(3)
Q:
3 1
Bortnor
" — Heicklen
Newhall
•™— — — This evolu
i
2
103
T
1963 (33) M unspecified
1964 (48) M unspecified
1965 (52) M =* 0,
1967 (61) M - 02, N2
1969 (72) M unspecified
1tl0". M - Or Ar
QJ) Estimated, this work
(°K-1)
O M = 02 data from Clyne and Thrush 1962 (29)
D M-Nj
H M = N2 data from Klein and Herron 1964(47)
T M = Ar
A M-CO2
« M =• N2 0
$ M = NO
FIGURE A-23 NO A- n
M
-------
18-
O2 + H + M
HO + M
(April 1969)
CD—(GD
, 1—(28) (M=H2)
A—(29)
El—(45)
O
O
(45)^
Q-(54) O <>-(45)
Von Elbe and Lewis 1939 (5)
A—(35)
cn
O
14-
13-
11
Burivss and Robb 1957 (23)
lloi're .mj*alsh 1957(29)
R.i;j.iaei3l mO(W)
A vcamcrAo and
Kulcsnikova 1961(35)
Paid.. in and Doran 1961 (36)
Eakl> metal 196 2 (-10)
Clyne 1%3 (44)
Clyne and Thrush 1963(15)
Kiimus 1964 (53)
Larkin and Thrush 1964 (54)
Fenixerc and Jones 1965 (6!)
Ccra.iiicr and SchotI 1965 (63)
Skinner and Ringrose 1965 (65)
Gct'infter and Blair 1966 (69)
Stciiukhnvich and
Uman^y 1966 (71)
Di'on-Leftis and
Billiatns 1967(75)
12 , __, £
0 1 2
103(°K"1
Gu.raan ec al 1967 (77)
13ro*ne ct al 1968 (86)
P M - II20
A M - 11 2
O M - Noble Gas
• This evaluation
A*-(5)
O Estimated, this work
345
)
T
FIGURE A-24 H + 0, + M
H02 + M
89
-------
constant for reactions of larger species should be similar to equation (2)
although the values of AH°*0, AS°*0, and AC°* may be different.
P
ACKNOWLEDGMENTS
We thank N. A. Kirshen for preliminary work, V. S. Engleman and
C. T. Bowman for many helpful and constructive suggestions, and D. Pershing
and S. W. Lanier of the Combustion Research Section of the U.S. Environ-
mental Protection Agency for supporting this work. We are indebted to
D. L. Baulch, D. D. Drysdale, D. G. Home, and A. C. Lloyd for permission
to use their figures.
90
-------
REFERENCES TO APPENDIX A
1. Eaulch, D. L., D. D. Drysdale, D. G. Home, and A. C. Lloyd. High
Temperature Reaction Rate Data No. 4. Department of Physical
Chemistry, The University, Leeds 2, England. December 1969.
2. Baulch, D. L., D. D. Drysdale, D. G. Home and A. C. Lloyd. Evalu-
ated Kinetic Data for High Temperature Reactions, Vol. 4. Butter-
worths, London, 1972.
3. Dryer, F., D. Naegeli, and I. Classman. Combustion and Flame.
1/7: 270, 1971.
4. Benson, S. W. Thermochemical Kinetics. John Wiley and Sons, Inc.,
New York, 1968.
5. V. S. Engleman. Private communication, 1973.
6. JANAF Thermochemical Tables. Dow Chemical Company, Midland, Michigan, 1974,
7. Benson, S. W., D. M. Golden, R. W. Lawrence, R. Shaw, and R. W. Woolfolk,
to be published.
8. Campbell, I. M., and B. A. Thrush. Trans. Faraday Soc. 64: 1265, 1968.
9. Garvin, D., and H. P. Broida. Ninth Symposium (international) on
Combustion. Academic Press, New York, 1963. pp. 678-688.
10. Tunder, R., S. Mayer, E. Cook, and L. Schieler. Aerospace Corporation
Report No. TR-100K9210-02)-!. January 1967.
11. Klein, F. S., and J. T. Herron. J. Chem. Phys., 41: 1285, 1964.
12. Jaffe, S., and F. S. Klein. Trans. Faraday Soc. 62: 3135, 1966.
13. Ridley, B. A., W. R. Schulz, and D. J. LeRoy. J. Chem. Phys. 44: 3344,
1966.
14. Westenberg, A. A., and N. de Haas. J. Chem. Phys. 47: 1393, 1967.
15. Slanger, T. G., B. J. Wood, and G. Black. J. Geophysical Res. 7£:
8430, 1971.
91
-------
Appendix B
ESTIMATION OF HEATS OF FORMATION AT 300 K OF SOME TRIATOMIC
SPECIES CONTAINING ATOMS OF THE ELEMENTS CARBON, HYDROGEN,
NITROGEN, OXYGEN, AND SULFUR
As discussed in the main body of the report, to determine whether
AH300 i-s -1 or 7 kcal/mol, it is often necessa^ to know the heat of
formation at 300 K of the triatomic intermediate XYZ in the reaction
X + YZ -4 XY + Z. In some cases, XYZ is a molecule whose heat of
formation is well known; for example, AH° 0 (H20) = -57.8 kcal/mol.
In other cases, no data are available in the literature and an estimate
is necessary. Table B-l lists the known heats of formation of some
molecules that were used in the estimates. The following estimates of
bond dissociation energies were used: D(N-H) = 95 ± 5, D(C-H) =
95 ± 5, D(H-O) = 90 ± 5, and D(H-S) = 82 kcal/mol. All heats of forma-
tion are for a temperature of 300 K; the units are kcal/mol. Each
estimate is discussed in detail below.
CNH
The method of estimation for AH°(CHN) involved estimating the
AH° of CH2=NH from the dehydrogenation of CH3-NH2 and removing two
H-atoms to get AH° (CNH).
CH3-NH2 -H2 + CH2=NH AH = 21.5 ± 1 (Reference 7)
AH°(CH2=NH) = 21.5 + AHj(CH3-NH2) =16.0 ± 1
92
-------
Table B-l HEATS OF FORMATION OF MONATOMIC, DIATOMIC, AND POLYATOMIC
SPECIES'USED TO ESTIMATE HEATS OF FORMATION OF TRIATOMIC SPECIES
(all values have units of kcal/mol)
Species
Monatomic
C
H
N
o
s
Diatomic
C2
CH
CN
CO
cs
H2
NH
HO
HS
N2
NO
NS
02
SO
S3 '_ - .
Polyatomic
CH3NH2
CH2CH2
. CHgOH
CHgSH
CH3NO
CH3ONH2 (liquid)
CHgOCHg
CHgSCHg
HNCS
CHgSSCHg
CHgCN
(CN)a
*f
170.89 ± 0.45
52.10 ± 0.001
113.0 ± 1
59.55 ± 0.02
66.29 ± 0.0.1
200.2 ± 0,9
142.0 ± 0.1
104.0 ± 2.5
-26.4 ± 0.6
55.0 ± 5.0
0
90.0 ± 4.0
9.49 ± 0.04
34.6 ± 4.0
21.58 ±0.04
63.0 ± 10
0
1.2 ± 0.3
30.8 ± 0.2
-5.5 ± 0.1
12.5 ± 0.1
-48.1 ±0.05
-5.4 ± 0.1
16.0 ± 2
-13.0 ± 2b
-44.0 ± 0,1
-8.9 ± 0.1
30.0 ± 2b
-5.6 ± 0.2
21.0 ± 1
73.9 ±0.4
a
Reference
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1 .
2
2
2
2
3
1
2
2
3
2
4
1
93
-------
Table B-l (Concluded). HEATS OF FORMATION OF MONATOMIC, DIATOMIC, AND
POLYATOMIC SPECIES USED TO ESTIMATE HEATS OF FORMATION OF TRIATOMIC
SPECIES
(all values have units of kcal/mol)
Species
OCO
OCS
HNO
SCS
ceo
NH2OH
NH2NH2
CH3OOCH3
HOO-
CH30-
CH3S-
HOOH
HSSH
ONO
HOH
HSH
CH3OOH
HOOOH
NNO
HNNN
03
HCO-
CH3-
AH°
f
-94.05 ± 0.01
-33.1 ± 0.3
23.8 ± lb
27.98 ± 0.19
68.5 ± 15.0
-9.0 ± lb
22.8 ± lb
-30.0 ± 2b
5.0 ± 2b
3.5 ± 1
29.0 ±2
-32.5 ± lb
+2.5 ± 2b
7.9 ± 0.2
-57.8 ± 0.001
-4.9 ±0.2
-31.5 ± 2b
-13.5 ± lb
19.6 ± 0.1
70.3 ± 2b
34.1 ± 0.4
10.4 ± 2.0
34.81 ± 0.2
a
Reference
1
1
1
1
1
3
3
3
1,3
3
5
1,3,4
6
1
1
1
3
3
1
3
1
1
1
n
References are listed at the end of Appendix B,
Errors estimated for this report.
94
-------
CNO
The AH°(CNO) was estimated by removing three H»atoms from CH3NO.
CH,NO - -3H- + CNO AH = 285 ± 15
o
AH°(CNO) •= 285 ± 15 + AH°(CH3NO) - 3[AH°(H-)] - 145 ± 17
CON'
The AH°(CON) was estimated by removing five H- atoms from CH3ONH2
where the AH°(CH3ONH2) was obtained from the liquid value and from an
estimated AH (CH3ONH2) of 8 ± 1.
CH3ONH2(^) - «-CH3ONH3(g) AH = 8 ± 1
AH°(CH3ONH2) = 13 - AH° (CH3ONH2) g = 5 ± 3
-L ^ <-'
CH,ONH, - — 5H- + CON AH = 475 ± 25
i5 £
°(CON) = 475 ± 25 + AH°(CHgONH2) - 5[AH°
AH°(CON) = 475 ± 25 + AH°(CHgONH2) - 5[AH°(H-)] = 220 ± 2.9
CNS
The AH°(CNS) was estimated by noting that the difference between
AH°(NO) and AH°(NS) was 41 ± 10. This value was added to the AH° (CNO) .
AH°(NS) - AH°(NO) = 41 ± 10
AH°(CNS) = AH°(CNO) +. 41 = 186 ± 25
CSN
The AH°(CSN) was estimated from AH°(CON) by noting that the substi-
tution of an S-atom for an O-atom adds 35 to the heat of formation of
methyl ether.
AH°(CH3SCH3) - AH°(CH3OCH3) = 35.1 ± 0.2
AH°(CSN) - AH°(CON) + 35 = 250 ± 29
95
-------
C2 + C2H4 ^2C-CH2 AH = 0 ± 1 (assumed)
AH°(C-CH2) a [0 + AH°(C2) + AH°(C2H4)]/2 = 106.4 ± 2
C2H4 C-CH2 + 2H
AH = AH°(C-CH2) + 2 [AH°(H •>] - AH°(C2H4) = 198.1 ± 2
CH2=NH — 2H + CNH AH = 198 ± 2
AH°(CNH) = 198 + AH°(CH2=NH) - 2[AH°(H.)] = 110 ± 3
COH
The AH°(COH) was estimated by removing three H-atoms from CH3OH.
CH3OH -3H- + COH AH = 285 ± 15
AH°(COH) = 285 ± 15 + AH°(CH3OH) - 3[AH°(H.)] = 81 ± 15
CSH
The AH°(CSH) was estimated by removing three H-atoms from CH3SH.
CH3SH — 3H- + CSH AH = 285 ± 15
AH°(CSH) = 285 ± 5 + AH°(CH3SH) - 3[AH°(H-)] -= 123 ± 15
HCS
The AH°(HCS) was estimated by assuming that the bond dissociation
energy D(H-CS) was equal to D(H-CO).
HCO —H- + CO
AH = D(H-CO) = AH°(H-) + AH°(HCO) = 15.3 ± 2.6
D(H-CS) = D(H-CO) = 15.3 ±2.6
HCS -H- + CS AH = 15.3 ± 2.6
AH°(HCS) = AH°(H-) + AH°(CS) - 15.3 = 91.8 ± 8
96
-------
NCS
The AH°(NCS) was estimated by removing an H-atom from HNCS.
HNCS -NCS + H- AH = 95 ± 5
K
AH°(NCS) = 95 + AH°(HNCS) - AH°(H-) - 73 ± 7
Note: A value of 75 ± 5 kcal/mol for AH°(NCS) has been estimated by
N. Barroeta.8
COS
Method I—The AH°(COS) was estimated by adding 35.1 ±0.2 for
S-atom substitution (see CSN) to the AH°(COO) (see COO).
AH°(COS) = AH°(COO) + 35 = 170 ± 22
Method II—The AH°(COS) was estimated by subtracting 12 ± 11
from AH°(CSO) (See CSO).
11 ± 10 is the difference between AH°(HOS) and AH°(HSO)
AH°(COS) = AH°(CSO) - 12 = 152 ± 30
Taking the average of methods I and II, AH°(COS) - [170 + 152]/2 = 161 ± 36.
CSO
COO
The AH°(CSO) was assumed to be equal to the AH°(CSS) (See CSS).
f ±
AH°(CSO) = AH°(CSS) = 164 ± 19
The AH°(COO) was estimated by removing four H-atoms from CH3OOH.
CH3OOH -COO + 4H- AH = 375 ± 20
AH°(COO) = 375 + AH°(CH3OOH) - 4[AH°(H-)] = 135 ± 22
97
-------
CSS
The AH°(CSS) was estimated by removing three H-atoms and a CH
f
from CH3-S-S-CH3.
CH3SH -~CH3- + HS-
AH = AH°(CH3-) + AH°(HS-) - AH°(CH3SH)
D(CH3-SH) = AH = 74.8 ± 4
CH3SSCH3 -CSS + CH3- + 3H- AH = 360 ± 19
AH°(CSS) - 360 + AH°(CH3SSCH3) - AH°(CH3•) - 3[AH°(H-)]
AH°(CSS) = 164 ± 19
CCN
Method I — The AH°(CCN) was estimated by removing three H~atoms
from CH3CN.
CH3CN - -CCN + 3H- AH°(CH3CN) - 3[AH°(H-)]
AH°(CCN) = 150 ± 16
f
Method II — The AH°(CCN) was estimated by removing an N-atom from
(CN)2 using a value for D(C-N) = 180 ± 4 kcal/mol.
•CN - -C + N
DC_N = AH°(C) + AH°(N) - AH^(-CN) = 180 ± 4
NCCN - -N + CCN AH = 180 ± 4
AH°(CCN) = 180 + AH°(CN)2 - AH° (N)
AH" (CCN) = 141.0 ±3.4
was taken as the average of methods I and II.
AH°(CCN) = 146 ± 16
98
-------
COG
The AH°(COC) was estimated by removing six H-atoms from CH3OCH3.
CH,OCH, -COC + 6H- AH = 570 ± 30
J o
AH°(COC) - 570 + AH°(CH3OCH3) - 6[AH°(H->] = 213 ± 30
CCS
The AH°(CCS) was estimated by adding 61 to AH°(CCO). 61 ± 0.4 is
the difference between AH°(CS2) and AH°(SCO) and also the difference
between AH°(SCO) and AH°(C02).
AH°(CS2) - AH°(SCO) = 61.1 ± 0.5
AH°(SCO) - AH°(C02) = 61.0 ±0.3
.'. AH°(CCS) = AH°(CCO) + 61 = 30 ± 15
CSC
The AH°(CSC) was estimated by adding the difference [AH°(CH3SCH3)
AH°(CH3OCH3)] to AH°(COC) (See COC).
AH°(CH3SCH3) - AH°(CH3OCH3) = 35.1 ± 0.2
AH°(CSC) = AH°(COC) + 35 = 248 ± 30
This is equivalent to removing 6 H-atoms from CH3SCH3.
HON
The AH°(HON) was estimated by removing two H-atoms from NH2OH.
H2NOH - -NOH + 2H- AH = 190 ± 10
AH°(NOH) = 190 + AH°(NB2OH) - 2[AH°(H-)] = 77 ± 11
The AH°(HNS) was estimated by adding 41 ±10, the difference between
AH°(NO) and AH°(NS), to AH°(HNO) (See CNS) .
99
-------
AH°(NS) - AH°(NO) = 41 ± 10
AH°(HNS) = AH°(HNO) + 41 = 65 ± 11
HSN
The AH°(HSN) was estimated by adding 35.1 ±0.2, the increase in
the AH° of CH3OCH3 when an S-atom is substituted for an 0-atom, to
AH°(HON).
AHj(CH3SCH3) - AH°(CH3OCH3) = 35.1 ± 0.2 (See CSN)
AH°(HSN) = AH°(HON) + 35 - 112 ± 11 (See HON)
HKN
The AH°(HNN) was estimated by removing three H-atoms from H2NNH2.
H2N-NH2 HNN + 3H- AH = 285 ± 15
AH°(HNN) = 285 + AH°(N2H4) -
AH°(HNN) = 152 ± 16
HOS
Method I—The AH°(HOS) was estimated by obtaining D(S-OH) from
D(CH3S-SCH3) and D(CH30-OCH3) . These were averaged (50.5), and 14.5
was added as the difference between D(HO-OH) and D(CH30-GCH3) .
CH3S-SCH3 -- -2CH3S-
D(CH3S-SCH3) = AH = 2[AH°(CH3S-)] - AH° (CH3SSCH3) = 64 ±4
CH3OOCH3 - —2 CH3O-
D(CH30-OCH3) •= AH = 2[AH° (CH30- ) ] - AH° (CH3OOCH3) - 37 ± 4
D(CH3S-OCH3) = [D(CH3S-SCH3) + D(CH30-OCH3 ]/2 = 50.5 ± 6
D(HO-OH) - CH30-OCH3 = 14.5 ± 5
100
-------
.'. D(HS-OH) = D(CH3S-OCH3)
HOS HO- + S AH = 65 ± 11
AH°(HOS) = AH°(-OH) + AH°(S) - 65 = 11 ± 11
Method II—The AH°(HOS) was estimated fromD(H-OS), which was
obtained from D(H-02).
HO2 -» H- + 02
D(H-02) = AH = AH°(H.) + AH°(O2) - AH°(H02) - 47.1 ± 2
HOS H + OS AH = 47.1 ± 2
AH°(HOS) = AH°(H-) + AH°(SO) - 47.1 = 6.2 ± 2
Method III—The AH°(HOS) was estimated by estimating AH°(HOSH)
from AH°(HOOH) and AH°(HSSH) and then estimating D(H-SOH).
AH°(HOSH) = [AH°(HOOH) + AH°(HSSH)]/2 = -15 ± 5
Since D(H-OH) - D(H-OCH3) = D(H-OCH3) - D(H-OOH) . 14
and D(H-SH) - D(H-SCH3) = 5 ± 3
.'. D(H-SCH3) - D(H-SSH) = 5 ± 3
D(H-SSH) - D(H-SCH3) - 5 = 82 ± 5
HSOH HOS- + H- AH = 82 ± 5
AH°(HOS) = 82 + AH°(HSOH) - AH°(H-) = 15 ± 10
An average of methods I, II, and III gives
AH°(HOS) = 11 ± 13
101
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HSO
The AH°(HSO) was estimated by first estimating the AH°(HSOH) as
an average of AH°(HOOH) and AH°(HSSH) and removing an H-atom from
HSO-H.
AH°(HOSH) - [AH°(HSSH) + AH° (HOOH) ]/2 = -15 ± 5
D(H-OSH) = 90 ± 5
HOSH - -H- + OSH AH = 90 ± 5
AH°(OSH) =90 + AH°(HOSH) - AH°(H-) = 23 ± 10
HSS
The AH°(HSS) was estimated by removing an H-atom from HSSH.
HSSH - - H + SSH AH = 82 ± 5
AH°(SSH) = 82 - AH°(H.) + AH° (HSSH) = 33 ± 5
NOS
The AH°(NOS) was estimated by estimating the AH°(H,NOSH) and
-L £ £ •
removing three H-atoms. AH°(H2NOSH) was estimated by inserting an
S-atom in H2NO-H using a value of 42, which was obtained from the
difference between AH°(HOH) and AH° (HOSH) (See HOS).
-L \_ ' ' -
AH°(HOH) - AH°(HOSH) = 42 ± 5
AH°(H2NOSH) - AH°(H2NOH) + 42 = 33 ± 6
H2NOSH - -NOS + 3H. AH = 272 ± 15
AH°(NOS) = 272 + AH°(H2NOSH) - 3[AH°(H-)]
AH°(NOS) ^ 149 ± 21
102
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NSO
Method I—The AH° (NSO) was estimated by adding 35 to AH°(NOO).
The 35 factor was obtained from the difference between AH°(ROR) and
AH°(RSR). Note: also close to AH°(NS) - AH°(NO) = 41 and AH°(RSH) -
AH°(ROH) = 43.
AH°(NSO) = AH°(NOO) + 35 = 171 ± 20
Note: See NOO for estimates of AH°(NOO).
- -J --1 • ' I
Method II—The AH°(NSO) was estimated by comparing AH° of XSO and
XOS
AH°(HSO) - AH°(HOS) = 11 ± 10
.'. AH°(NSO) - AH°(NOS) = 11 ± 10
AH°(NSO) = AH°(NOS) + 11 = 160 ± 31
The average of the two methods is
AH°(NSO) = 166 ±39
ONS
Method I—The AH°(ONS) was estimated by adding 41, the difference
between AH°(NS) and AH°(NO), to AH°(ONO)
AH°(NS) - AH°(NO) = 41 ± 10
AH°(ONS) -= AH°(ONO)'+ 41 = 49 ± 10
Method II—The AH°(ONS) was estimated by assuming D(O-NS) was
equal to D(O-NO) (73.3 ±0.6).
D(O-NS) - D(O-NO) = 73.3 ± 0.6
ONS -0 + NS AH = 73.3 ± 0.6
AH°(ONS) = AH°(0) + AH°(NS) - 73 = 49 ± 10
103
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Average of methods I and II: AH°(ONS) = 49,± 10.
NOO
The AH°(NOO) was estimated by inserting an 0-atom in H2NOH and
removing three H-atoms. The value for 0-atom insertion was determined
from AH°(HOOH) - AH°(HOH) and AH°(CH3OOH) - AH°(CH3OH).
AH°(HOOH) - AHj(HOH) = 25.3 ± 1
AH°(CH3OOH) - AHj(CH3OH) = 16.6 ± 2
Average value = 21 ± 2
AH°(H2NOOH) » AH°(H2NOH) + 21 = 12 ± 3
H2NOOH -NOO + 3H- AH = 280 ± 15
AH°(NOO) = 280 + AH°(H2NOOH) - 3[AH°(H-)] = 136 ± 17
AH°(NSS) was estimated by comparing the differences between XOO and
XSS compounds.
AH°(HSS) - AH°(HOO) = 28 ± 7
AH°(CSS) - AHj(COO) = 28 ± 41
The average is 28 ±15
.'. AH°(NSS) - AH°(NOO) •= 7 ± 15
AH°(NSS) = AH«(NOO) + 27 = 164 ± 32
SNS
Method I—The AH°(SNS) was estimated by using D(S-NO) and D(S-NS)
f
and calculating D(S-NO) from AH°(SNO).
SNO — S + NO
°S-NO = AHf(S) + ^Hf(NO) ~ AH°
104
-------
Note: See SNO for estimate of AH°(SNO).
VNO = 9 ± 10
SNS -NS + S AH = 39 ± 10
AH°(SNS) = AH°(NS) + AH°(S) - 39 - 90 ± 20
Method II—The AH°(SNS) was estimated by adding 2X[AH°(.NS) -
AH°(NO)], i.e., 82 ± 20, to AH°(ONO).
AH°(NS) - AH°(NO) = 41 ± 10
AH°SNS = AH°(ONO) + 2(41) = 90 ± 20
Average of methods I and II:
AH°(SNS) = 90 ± 20
Note: These two methods are somewhat equivalent in that AH°(SNO)
was estimated from AH°(ONO) and AH°(NO) and AH°(NS).
NON
The AH°(NON) was estimated by removing four H-atoms from H2NONH2.
The AH°(H2NONH2) was estimated by replacing the OH group by an NH2
group on NH2OOH. AH°(H2NOOH) was estimated by inserting an 0-atom
into NH2OH. (21 ± 2, see NOO). The value for replacing an OH by NH2
was estimated from AH°(H2NOOH) - AH°(HOOOH).
AH°(HN2OOH) = AH°(H2NOH) + 21 (See NOO)
AH°(NH2OOH) = 12 ± 3
AH°(NH2OOH) - AH°(HOOH) = 25.5 ±4
AH°(HN2ONH2) - AH°(NH2OOH) + 25 = 37.5 ± 7
H2NONH2 NON + 4H« AH = 380 ± 20
AH°(NON) - 380 + AH°(H2NONH2) - 4[AH°(H-)]
105
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NNS
The AH°(NNS) was estimated by adding 41, the difference between
AH°(NS) and AH°(NO), to the AH°(NNO).
AH°(NS) - AH°(NO) = 41 ± 10
AH°(NNS) = AH°(NNO) + 41 •= 61 ± 10
NSN
The AH°(NSN) was estimated by adding 35, the value for replacement
of an 0-atom by an S-atom (See CSN), to the AH°(NON).
~~~~~ f
AH°(NSN) - AH°(NON) + 35 = 244 ± 27
NNN
The AH°(N3) was estimated by removing an H-atom from HN3.
AH°(HN_) - 70.3 ± 2
f 3
HN3 -H + N3 AH = 95 ± 5
AH°(N3) = 95 - AH°(H.) + AH°(HN3)
AH°(N3) = 111 ± 7
Note: JANAF gives value of 99 ±5 for AH°(N3).
The reaction
N + N2 N3
is spin forbidden, and a value of 60 ± 6 must be added to AH°(XYZ).
AH°(N3) - AH°(N3) + 60 - 171 ± 13
SOO
The AH°(SOO) was estimated by assuming that D(SO-O) - D(OO-O)
D(OO-O) was calculated from AH°(0-)
f 3
106
-------
o3 -oa + o
AH = D(OO-O) - AH°(02) + AH°(0) - AH°(03)
D(OO-0 = 25.5 ±0.4 = D(SO-O)
SOO -SO +0 AH = 25.5 A 0.4
AH°(SOO) -- AH°(SO) + AH°(0) - 25.5 = 35.3 ± 0.7
SOS
The AH°(SOS) was estimated by assuming that D(S-OS) = D(S-OO).
D(S-OO) was calculated from AH°(SOO) (see SOO).
SOO — S + O2
AH = Dg_oo = AH°(S) + AH°(S) + AH°(02) - AH°(SOO)
D(S-OO) -• D(S-OS) - 31.0 ±0.7
SOS ^SO + S AH = 31.0 ± 0.7
AH°(SOS) -- AH°(SO) + AH°(S) - 31 = 36.5 ±1.0
SSS
The AH°(S3) was estimated by assuming that the increase in AH° in
going from O2 to 03 would be the same as in going from S2 to S3.
AH°(03) - AH°(02) = 34.1 ± 0.4
.'. Let AH°(S3) - AH°(S2) = 34.1 ± 0.4
AH°(S3) = 34.1 + AH°(S2) = 65 ±1
107
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REFERENCES TO APPENDIX B
1. JANAF Thermochemical Tables. Dow Chemical Company, Midland, Michigan,
1975.
2. Cox, J.D., and G. Pilcher. Thermochemistry of Organic and Organo-
metallic Compounds. New York, Academic Press, 1970.
3. Benson, S. W., Thermochemical Kinetics. New York, John Wiley and
Sons, Inc., 1968.
4. Stull, D. R., E. F. Westrum, Jr., and G. C. Sinke. The Chemical
Thermodynamics of Organic Compounds. New York, John Wiley and
Sons, Inc., 1969.
5. Fine, D. H., and J. B. Westmore. Can. J. Chem. £8:495, 1970.
6. Wagman, D. O., W. H. Evans, V. B. Parker, I. Halow, S. M. Bailey,
and R. H. Schumm. National Bureau of Standards (U.S.) Technical
Note 270-3. January 1968.
7. Shaw, R., Estimation of the Thermochemistry of Imidic Acid
Derivatives in Chemistry of Imidic Acid Derivatives. S. Patai,
Ed. New York, John Wiley and Sons, Inc., 1975.
8. Barroeta, N., Acta Cient. Venezolana 22:129, 1971.
108
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA-600/2-75-019
3. RECIPIENT'S ACCESSION-NO.
4. TITLE AND SUBTIT.!. R
Estimating the Kinetics of Combustion--
Including Reactions Involving Oxides of Nitrogen
and Sulfur
5. REPORT DATE
August 1975
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S),
S.W. Benson, D. M. Golden, R. W. Lawrence,
Robert Shaw, and R. W. Woolfolk
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Stanford Research Institute
333 Ravenswood Avenue
Menlo Park, CA 94025
10. PROGRAM ELEMENT NO.
1AB014; ROAP 21BCC-019
1. CONTRACT/GRANT NO.
Grant R-800798
12. SPONSORING AGENCY NAME AND ADDRESS
EPA, Office of Research .and Development
Industrial Environmental Research Laboratory
Research Triangle Park, NC 27711
13. TYPE OF REPORT AND PERIOD COVERED
Final: 8/72 - 4/75
14. SPONSORING AGENCY CODE
15. SUPPLEMENTARY NOTES
. ABSTRACT The report describes the rate estimation of some elementary chemical
reactions that are important in combustion systems, including those involving the
production and destruction of oxides of both nitrogen and sulfur. The estimates were
made as part of a systematic effort to investigate the rate constants of reactions of
species containing carbon, hydrogen, nitrogen, oxygen, and sulfur. The effort was
concentrated on the atom transfer reactions between atoms and diatomic molecules
containing these elements. All previously measured rate constants for these reactions
were found to have the same value (plus or minus a factor of 3) in the exothermic
direction at 2000 K. Rate constants in the endothermic direction are readily available
from the equilibrium constants, all of which can be calculated. A FORTRAN computer
program enables a user with no previous kinetics experience to estimate the rate
constants at any temperature between 200 and 3000 K for any of the 75 pairs of atom
transfer reactions involving the five elements.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS
c. COSATI Field/Group
Air Pollution
Reaction Kinetics
Combustion
Atoms
Mathematical Models
Nitrogen Oxides
Sulfur Oxides
Air Pollution Control
Stationary Sources
Rate Constants
Transition State Theory
Atom Transfer Reaction
13B
07D
2 IB
20H
12A
07B
13. DISTRI3UTIC
Unlimited
19. SECURITY CLASS (This Report)
Unclassified
21. NO. OF PAGES
116
!0. SECURITY CLASS (Thispage)
Unclassified
22. PRICE
EPA Form 2220-1 (9-73)
TTO
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