EPA-600/3-77-127
November 1977
Ecological Research Series
THERMOCHEMISTRY AND KINETICS OF SULFUR
CONTAINING MOLECULES AND RADICALS
Environmental Sciences Research Lat
Office of Research and Development
U.S. Environmental Protection Agency
Research Triangle Park, North Carolina 27711
-------
EPA-600/3-77-127
November 1977
THERMOCHEMISTRY AND KINETICS OF SULFUR
CONTAINING MOLECULES AND RADICALS
by
Sidney W. Benson
University of Southern California
Los Angeles, California 90007
Contract Number DA-6998290
Project Officer
Joseph J. Bufalini
Atmospheric Chemistry and Physics Division
Environmental Sciences Research Laboratory
Research Triangle Park, North Carolina 27711
ENVIRONMENTAL SCIENCES RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
RESEARCH TRIANGLE PARK, NORTH CAROLINA 27711
-------
DISCLAIMER
This report has been reviewed by the Environmental Sciences Research
Laboratory, U.S. Environmental Protection Agency, and approved for publication.
Approval does not signify that the contents necessarily reflect the views
and policies of the U.S. Environmental Protection Agency, nor does mention
of trade names or commercial products constitute endorsement or recommendation
for use.
11
-------
ABSTRACT
The relevant thermochemistry of sulfur oxides is discussed, and selected
"best" thermochemical values for use in kinetic systems are presented.
Although the kinetics of air pollution and combustion involve mostly homo-
geneous gas phase reactions, the data taken from condensed phases were also
considered. This was accomplished by using empirical rules that were used
to translate condensed phase values to equivalent gas phase values. All
available research through 1976 on the thermochemistry of organic and
relevant inorganic sulfur containing molecules and radicals is reviewed.
Some significant or controversial kinetic steps important in air pollution
chemistry and combustion are examined. The thermochemistry of divalent,
tetravalent, and hexavalent sulfur compounds, the relevant bond strengths
of radicals and the kinetics of oxidation processes are discussed. The
entropy and heat of formation measured experimentally or estimated are
presented for selected sulfur molecules and radicals.
111
-------
TABLES
Number
1 Some Revised and New Group Values for Use in Group
Additivity Estimates 3
2. AH o-qj, and S,, _ of Some Molecules and Radicals of
Divalent Sulfur 6
3. Effect of Polarity and Electronegativity on Differences in
Heats of Formation Between Hydrogen (HX) and Methyl Derivative
(CH3-X) 11
4. A Comparison of Double Bond Strengths In Some Divalent Sulfur
Compounds with Oxygen Analogues 13
5. Some S-H Bond Dissociation Energies for Divalent Sulfur 14
6. Some S-C Bond Dissociation Energies for Divalent Sulfur 16
7. Some S-S Bond Dissociation Energies for Divalent Sulfur 17
8. Heats of Formation and Entropdes of Some Molecules and
Radicals of Tetravalent Sulfur 23
9. S-S and S~0 Bond Dissociation Energies in Sulfoxide
Derivatives 24
10. Sum of Single Bond Dissociation Energies R-S + R'-S in
Sulfoxides RR'S = 0 and Thiosulfoxides and Estimates of
Dj 24
11. Heat of Formation and Entropies of Some Molecules and Radicals
of Hexavalent Sulfur 28
12. S-0 Bond Dissociation Energies in Hexavalent Sulfur Species.... 32
13. X-SO Single Bond Dissociation Energies in Sulfone; Derivatives. 33
VI
-------
CONTENTS
Abstract iii
Tables vi
1. Introduction 1
2. Thermochemistry of Dival.ent Sulfur Compounds 4
3. Thermochemistry of Tetravalent Sulfur Compounds 21
4. Thermochemistry of Hexavalent Sulfur Compounds 27
5. Oxidation of Sulfur-Containing Molecules '. 39
References 44
Appendix 48
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SECTION 1
INTRODUCTION
Sulfur is one of the abundant elements in the earth's crust. It is im-
portant in industry, in agriculture, in biology, and in air pollution. Be-
cause it occurs in crude oil to the extent of 0.2 to 5.0% and in coals in
the range of 0.2 to 10%, a great deal of research work has been directed to
develop processes for the desulfurization of coal, oil, and fuels generally.
An almost equal amount of work has been directed towards the removal of sulfur-
containing species from the exhaust stacks of power plants and factories (1).
The increasing stringency of air quality standards has required a more sophis-
ticated understanding of the chemistry and kinetics of sulfur-containing species,
particularly at low concentrations. This has accelerated efforts to model
the combustion and oxidation of sulfur compounds as a means to better control
both the production and the eventual removal of sulfur oxides (2). Comparable
efforts have been made to understand the detailed molecular steps whereby
sulfur oxides in the ambient atmosphere become converted to sulfuric acid
and visibility-reducing aerosol particles (3).
One of the basic requirements in such modeling efforts is detailed know-
ledge of the thermochemistry of the molecular and radical species involved
in these steps. Such information is of importance both in interpreting
some of the complex kinetic systems that have been studied and also in
simplifying the oppressively large sequence of possible kinetic steps that
may be significant in the molecular pathways for the overall reactions.
This report will present a review of the relevant thermochemistry and
select "best" values for use in analyzing the kinetic systems. Although the
kinetics of air pollution and combustion involve mostly homogeneous gas phase
reactions, the data taken from condensed phases will be included because of
their great utility. All of the available thermochemistry on organic and
relevant inorganic sulfur-containing molecules and radicals through 1976 will
-1-
-------
be reviewed, then more briefly the significant or controversial kinetic steps
of importance in air pollution and combustion.
The task in both these areas is enormously simplified by the availability
of a number of recent surveys. Authoritative compilations of the thermochemistry
of sulfur-containing molecules have been made by Cox and Pilcher (4) and by
Stull, Westrum, and Sinke (5). Perhaps the most detailed and critical evaluation
on selected compounds comes from the JANAF series (6). Extensive use will be
made of the NBS series of "Selected Values of Chemical Thermodynamic Properties",
Tech. Note 270-3 (7), a valuable supplement to the preceding surveys particularly
for inorganic compounds. Unfortunately, since it is neither documented nor
critical, the original literature sources have been reviewed where possible. A
critical survey of the thermochemical data on gas phase organic species con-
taining sulfur, published by the author and colleagues (8), will be used par-
ticularly for data on S and Cp and the methodology of group additivity.
Much less information exists on the heats of formation of sulfur-containing
radicals. Mackle (9) made the first extensive survey of bond strengths in
organic sulfur molecules, and some of these were included by Kerr (10) in his
review of bond energies obtained by kinetic studies. Many were omitted by
Kerr because of the "speculative" nature of the initial evidence. Much of this
work and subsequent data have been discussed and reevaluated by Benson and
O'Neal in their monograph on unimolecular reactions (11). Some of this work
has been in turn updated in a recent review (12). This report will also make
use of kinetic data obtained from studies in condensed phases. Empirical rules
can be employed to translate this data to equivalent gas phase species, albeit
with some uncertainty.
The format will present and discuss the thermochemistry of divalent, then
tetravalent, and finally hexavalent sulfur compounds. The relevant bond
strengths will be treated in each appropriate section together with the radicals
involved. The last section will treat the kinetics of oxidation processes. In
what follows all energies will be expressed in kcal/mole, while Cp and S will
be in cal/mole- K (e.u.). A large number, but not all of the sulfur-containing
compounds will be included in the tables. The omitted species may be found in
one or more of the sources quoted, or their thermochemical properties may be
-2-
-------
deduced by methods of group additivity from published tables (13). Table 1
lists all the revised group estimates and new groups obtained in the present
work.
TABLE 1. SOME REVISED AND NEW GROUP VALUES FOR USE IN GROUP ADDITIVITY
ESTIMATES
Group AH°£29g
S-(Cd)2 13.5
S-(C)(Cd) 13.0
S-(H)(Cd) 6.1
S-(S)2 3.2
S-(0)2 +9 +4
S0-(0)2 -51 +3
S02-(0)2 -101
S02-(F)(0) -142
S02-(C1)(0) - 97
Group
0-(H)(S02)
0-(H)(S)
0-(H)(SO)
o-(so2)2
0-(0)(S02)
Ring Corrections
Thiophene
Thiacyclopentene-2
cyclo-S,
cyclo-S.
cyclo-S,
cyclo-S0
o
AH°f298
-38.0
*
-38.0
*
-38.0
-4
3
AH° £298
-16.3
2.0
22.9
18.4
5.3
-1.1
These are assigned values in accord with usual conventions.
-3-
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SECTION 2
THERMOCHEMISTRY OF DIVALENT SULFUR COMPOUNDS
The thermochemistry of divalent sulfur compounds seems to be fairly well
established, very little new work having been done since the previous reviews
(4,5,8). Consequently, these values will be used in the discussions. The
thermochemistry of the organic divalent sulfur compounds seems not only
reliable but also self-consistent in that it seems to follow empirical rules
of group additivity (8) quite well. This is of considerable help since it
means that group additivity rules can be employed with confidence to deduce
the thermochemistry of species whose values have not been explicitly measured.
The one exception to this rule seems to be the derivatives of ethylene sulfide,
where the apparent strain energy seems to depend on the amount of ring sub-
stitution (8) . Consequently, these values may be considered uncertain to
about +_ 2 kcal despite the good calorimetric precision in measuring their
heats of combustion.
The group values used to estimate the thermochemistry of compounds not
given here have recently been republished (13), but some corrections based
on recent studies are in order. The changes are as follows:
For the S-(C)(C,) group, the value AH f2qs = 13.0 kcal instead of the
original 10.0 kcal will be used. For the related group S-(H)(C,), based
on various analogies, the value AH f;?q8 = 6.1 kcal has been derived. For the
S-(S)? group, AH f7qo ~ 3.2 kcal (instead of 3.0) will be used. For thiacyclo-
pentene-2 a strain energy of 2.0 kcal, has been assigned rather than the value
of 5.0 kcal, while for thiophene the value is not separable from the value of
the group S-(C,)_. If AH _ is assigned for the latter as AH f?q8 = 13.5 kcal,
rather than the -4.5 kcal originally assigned, to make for a more reasonable
behavior of open chain compounds, then it leads to a strain energy in thiophene
of -16.3 kcal/mole which is a much more reasonable reflection of the appreciable
resonance stabilization in this compound. Hence this -16.3 kcal/mole becomes
the value to use as a ring correction to thiophene derivatives rather than the
-4-
-------
previous value of + 1.7 kcal.
Table 2 lists values of AH° ~0 and S°__0 for key divalent molecules and
related radicals containing sulfur. The values of AH _ for S, S , and SO are
derived spectroscopically and are probably reliable to ^0.1 kcal. For the
radical SH, the value shown of 35 +_ 1 kcal has been adopted. This value derives
from a reassessment of the kinetic data on CH SH, CH SH, and C_H SH (11) and
for once is in good agreement with data on electron impact. Of these three
kinetic studies the first on CH SH is the most reliable, but the extraction of
a bond strength requires a scaling of the Arrhenius parameters to a reasonable
A-factor of about 10 sec and an assignment of the scaled activation energy
to the AE for the fission reaction. This latter is an important assumption
which seems in good agreement with the best current data on radical recom-
bination. It accounts for discrepancies of the order of about 1.5 kcal between
the AH ,. for a number of radicals listed (12) and the values listed in this
paper and in Ref. 13. It also accounts for the much larger discrepancies be-
tween the AH _ for CH S and fyS listed here and those in earlier reviews. The
values listed here are from recent studies using VLPP techniques (14) which
yield high pressure kinetic parameters in excellent agreement with values of
the absolute values of the rate constants from earlier studies (11) which
employed the toluene carrier technique. The assignment of the observed, "scaled"
activation energy to AET for the overall fission at reaction temperature, to-
gether with a correction of AhL to room temperature AH R based on an estimated
AC , lead to a change from earlier values of about 4 kcal. It would be difficult
o
to justify a change in the AH r^qn for these radicals by more than the indicated
uncertainties.
Kende et al (20) have measured the rates of fission of (CH_S-)_ in toluene
at 65 C using a radical scavenger to follow the first order reaction.
ecu c "\ _i o r'u • cc *
ILn O-J -»• £ L,H_oo
6 L i •*-. 6
They reported k f = 5 X 1017"36>6/'0sec~1 where f is the efficiency with
which the radicals are scavenged outside the initial cage and 0= 2.303RT(kcal/mole).
2
Their A-factor is too large by about 10 , and since their temperature range was
very limited (30 C), the Arrhenius parameters have been scaled to A = 5 X 10 sec
-5-
-------
TABLE 2. AH
AND S
OF SOME MOLECULES AND RADICALS OF DIVALENT SULFUR
Reference
(6)
(6)
(15)
(15)
(7,15)
(7)
(6)
(7)
*
(16,7)
4
(16)
(16)
(6)
t
*
(6)
(6)
*
(7)
t
(6)
(5)
(7)
Species
S
S2
cyclo-S
cyclo-S4
cyclo-S
6
cyclo-S8
SH
H2S
HS2
H2S2
HS3
H2S3
H2S4
SO
S-OH
S(OH)2
SF
SF2
SCI
SCI
SBr
FS-SF
s2ci2
S2Br2 (£)
" (g)
AH°£ono (E strain)"*"
TZJo
66.3
30.7
32.5 ± 1 (22.9)
31 ± 2 (18.4)
24.5 (5.3)
2.45 (-1.1)
35± 1
-4.9
[22.1 ± 1]
3.8
[25.3 ± 1]
7.4
10.6
1.2
[5 ± 4]
[-67 ± 4]
3 ± 2
-71 ± 3
[36.5 ± 2]
-4.7
[5 ± 4]
-80 ± 10
-4.7
-3
[+9]
S°298
40.1
54.5
63 ± 1.5
72 ± 2
84.9
103.0
46.7
49.2
[61.4]
62.3
[74.8]
[75.7]
[89.1]
53.0
[57 ± 1]
[70 ± 1]
53.8
61.6
57.3
67.2
70.3
76.4
-6-
(continued)
-------
TABLE 2. (continued)
Reference
(17)
(18)
(6)
(6)
(19)
(14)
(4)
(4)
(7)
(14)
(4)
(7)
(4)
(4)
4-
*
(7)
(4)
4=
4-
(4)
Species
SN
SC
cs2
cso
CH2=S
CH S
•J
CH3SH
CH =CHSH
CH SCH
C H SH
6 5
C6H5S
C,H SH
6 5
cyclo-CH9CH9S
C,HCCH0SH
DO L
(C6H5)2S
CH2(SH)2
CH3S2
CH3SSCH3
C,HCSSC,H..
ob ob
CH3SSS
CH.S,CH_
34 3
CH COSH
O
AH°f29g (E strain)1"
68 ± 5
64.8
28.0
-33.1
24.3
34.2 ± 1.5
-5.4
[21.0 ± 2]
-8.9
-11.0
56.8 ± 1.5
26.7
19.7 (19.5)
22.9
55.3
[ 8 ± 2]
[17.3 ± 1]
-5.8
58.4
[20.5 ± 1]
[0.4 ± 1]
-43 ± 1
(continued)
S° 298
53.1
50.3
56.8
55.3
[56 ± 1]
57.6
61.0
[67 ± 1]
68.3
70.8
76.5
80.5
61.0
[91.0]
80.5
74.9
-7-
-------
TABLE 2. (continued)
Reference
*
4
*
*
+
4-
(8)
(7)
(7)
(7)
(4)
(4)
Species AH°f298 ^E strain)f s°298
HCOSH [-30 ± 1]
(CH 0) S [-59 ± 5]
\j £
CH3SCL [-6.8 ± 1.5]
CH3SSC1 [-5.1 ± 1.5]
C6H5SC1 [25.3 ± 1.5]
C6H5S2C1 [ 27 ± 1.5]
(NH2)2C=S -6.0 72.4
HNC=S 30.0 59.2
CH NC=S - 31.3 69.3
CH SCN 38.3 [69 ± 1]
[(C HS) NS] -16.5 ± 1.5
(CNS)2 82.3
All species are ideal gas, standard states unless otherwise specified. AH ,.
are in kcal/mole, S in cal/mole °K.
t Values in parentheses are ring strain energies.
* Values in brackets have been estimated by the author; see text for details.
-8-
-------
(comparable to peroxide fissions) and E = 33.6 kcal/mole. This latter value is
in excellent agreement with values of 32.8 kcal for the S-S bond in liquid sulfur
deduced from measurements of radicals in liquid sulfur (21) . It will be assumed
that the gas phase value has the same value as has been frequently observed for
the fission of nitrites and peroxides. Then using group additivity (13) to deduce
a value for AH°£2g8 (MeS4Me) = 0.4 kcal/mole, the value of AH°f29g (CH^S') =
17.3 +_ 1 kcal/mole shown in Table 2 has been deduced. This value together with
group additivity yields the value AH° gg (HSS') = 22.1 +_ 1 kcal/mole (Table 2)
and the values also shown in Table 2 for HS ' and CH S'.
Similar values have been obtained from the same data by Friswell and Gowen-
lock (22). Note that a slightly different value has been used for the S_ ~
group than that listed in Ref. 13, namely AH° (S-S ) =3.2 kcal/mole. This
is based on the AH ,. data for the sulfanes (16,23), which indicate a very con-
sistent value for this group up to H0S . This value for the S-(S) group, to-
^6 ~ 2
gether with the observed value for cyclo-S (Table 2), leads to a value of
22.9 kcal for the strain energy in the S ring. This is comparable to values of
O
17.7 to 21 reported for the various ethylene sulfides (8). This new group value
has been used to find strain energies of 5.3 kcal in the c-S, ring and -1.1 kcal
in the c-S0 ring.
o
A very useful guide to thermochemistry comes from consideration of the
relative electronegativity of bonds. The SH group and Br atoms are expected to
have similar electronegativities and similar radii, and in fact the dipole mom-
ents of HBr and H2S are 0.82 and 0.97 Debye respectively (24), while the H-Br
and H-S bond lengths are 1.415 and 1.345 Ang, respectively (25). CH Br and
CH SH have similar dipole moments of 1.81 and 1.52 Debye, respectively (24);
the C-S and C-Br bond lengths in these compounds are 1.82 and 1.93 Ang, respec-
tively (25) . There are close similarities in the bond dissociation energies
in these compounds. A thermochemical datum which also parallels the electro-
negativities of atoms, X is the difference in the values of AH0,, for the com-
pounds HX and CH X.
It is observed that when X changes from a very electronegative element to
a very electropositive element, the difference AH° (HX) - AH° (CH X) changes
from a negative to a very positive quantity. This type of relation appears to
hold true whether or not X is a single atom or part of a more complex group.
-9-
-------
A typical range of values for this difference is illustrated by the data in
Table 3. Table 3 shows that neighboring groups can exert an important influence
on these differences. An excellent example is provided by CH, and CF_. Sim-
ilarly, while CH for H substitution in HOH makes AH°~ more positive by 9.8
kcal, a second CH,/H substitution increases AH - by only 4.0 kcal. The same
influence of substitution is seen in the nitrogen series and in the sulfur
family. This influence of nonbonded, next-nearest neighbors has been rationalized
as arising from a change in effective charge on the central atom (26-29), hence
its polarity.
As the polarity of the central atom goes from very negative to very
positive values, the CH /H substitution covers a range of from -10 to +14
kcal/mole. Such a relation permits us to estimate AH _ for compounds with un-
certainties of about +_ 2 kcal/mole. Thus we can estimate for the unknown H-NO_
isomer of nitrous acid (HOMO) a AH° = -6 +_ 2 kcal/mole based on the known AH°
(CH_NCL) = -17.9 kcal/mole. This accounts very well for the inability to pre-
pare this isomer, since it is about 12 kcal less stable than HONO for which
AH _ = -18.3 kcal/mole and in which the H atom is likely to be quite labile.
Such analogies permit us to estimate AH _ for CH? (SH)- from the value of
CH0Br0 as 6 + 2 kcal (Table 2). We shall make frequent use of these relations
£. £ —
and for convenience we shall refer to groups that show similar thermochemical
behavior as homothermal. The alkyl groups CH , ethyl, n-propyl, etcetera form
o
a homothermal family. Estimating from the relations in Table 3, R-SH compounds
(where R has about the polarity of carbon compounds) should differ in AH f from
R-Br compounds by 4.0 +_0.3 kcal. This is true for R=H, CH , and CJrt (Table 3)
and appears to be true for R-C_H_ for which the AH0- (C_H,SH) has been estimated
by other methods. It is therefore somewhat surprising that the phenyl compounds
AH0,, differ only by 1.7 kcal, since vinyl and phenyl have about the same kind of
carbon atoms (27). However, the uncertainty in AH°,.(C,H[.Br) is at lest 2.0 kcal
and may be the source of the apparent inconsistency. AH0,. (CH COBr) is 2.6 +_
1.5 kcal lower than AH0,. (CH,COSH), which is well within the expectations of our
Br/SH substitution rule.
Using the H/CH_ substitution value observed for HCOOH and CH COOH (Table 3),
«J *J
AH° (HCOSH) = -30 +_ 1 kcal can be deduced and is shown in Table 2.
-10-
-------
TABLE 3. EFFECT OF POLARITY AND ELECTRONEGATIVITY ON DIFFERENCES IN
HEATS OF FORMATION BETWEEN HYDROGEN (HX) AND METHYL
DERIVATIVE (CH -X)
X
p
OH
0(SO )CH
0(CO?CH 3
NH2
OCH3
ON02
Cl
NH(CH3)
°2H
NH(CH3)
Br
SH
N(CH3)2
CH3
I
SCH3
C0Hr
2 5
S2H
n"C3H7
C0H_
2 3
C,HC
6 5
NO
COCH3
CN
COOH
CF3
SiH3
SnH3
AH°(HX)*
- 64.8
- 57.8
-170.5
-103.8
- 11.0
- 48.0
- 32.1
- 22.0
- 5.5
- 32.6
- 5.5
- 8.7
- 4.8
- 4.5
- 17.9
6.3
- 5.4
- 20.2
3.8
- 24.8
12.5
19.8
23.8
- 39.7
32.3
- 90.5
-167
8
39
AH°(CH3X)
- 55 +_ 2
- 48.0
-164
- 98
- 5.5
- 44.0
- 28.6
- 19.6
- 4.5
- 31.3
- 4.5
- 9.5
- 5.4
- 5.9
- 20.2
3.3
- 8.9
- 24.8
- i.oa
- 30.2
4.9
12.0
16
- 51.7
[19 +_ 2]
-103.8
-178
- 4
[28 ± 3]
A(AH°)
-9.8^2
- 9.8
- 6.5
- 5.8
- 5.5
- 4.0
- 3.5
- 2.4
- 1.0
- 1.3
- 1.0
0.8
0.6
1.4
2.3
3.0
3.5
4.6
4.8
5.4
7.6
7.8
8
12.0
13 +_ 2
13.3
11
12
11^3
All values in kcal/mole. Data taken from sources listed in Table 2. Values
in brackets are estimated by author.
-11-
-------
In the first long row of the periodic table, one of the rather startling
early observations on bond dissociation energies (30) was the weakness of the
single bonds between the iso-electronic groups. NH,, OH, and F. These are
among the weakest single bonds in the periodic table and decrease uniformly
in the sequence CH -CH , (88), NH -NH , (70), HO-OH, (50), F-F, (38). There
is a comparable decrease in bond strengths in the related sequence in the
second row SiH -SiH , PH -PH , HS-SH, C1-C1, but the bonds range from 0 to 20
o 3 2. 2.
kcal stronger than their first row group analogues. This tendency has been
rationalized on electrostatic grounds as arising from the repulsion of nonbonded
lone pairs. In molecular orbital terms the equivalent explanation comes from
the increasing destabilization of antibonding electrons. The increased bond
strengths in the symmetrical second row compounds is then explained on the basis
of a decreased repulsion of the long pair electrons arising from their greater
separation in the larger radius, second row elements. This larger radius of
the second row elements compared to first row elements should also lead to both
weaker sigma and pi bonds when the lone pair effects can be eliminated. As we
shall see, the data reflect this but the effects are much smaller than might have
been anticipated.
Table 4 lists the few compounds containing S atoms double bonded to some
other atom or group. The S bond dissociation energies in these compounds are
compared with those of their oxygen analogues. Notice that the S-S bond in S~
is some 17 kcal weaker than the 0-0 bond in 0 . As expected from considerations
of both electronegativity difference and lone pair repulsion, the bond dissociation
energy in SO is greater than in either homonuclear molecule.
Even larger differences exist in the CH 0 and CH S pair, where there is no
lone pair repulsion and in the CO, CS pairs which are really better described as
triple bonded compounds.
A measure of the relative abilities of S and 0 atoms to donate electrons
and act as Lewis bases is seen on comparing the C-0 bond strengths in CH^O with
C0_. The 45 kcal apparent greater bond strength in the former compound can be
associated with the extra pi bond formation in CO. The greater C-0 bond
strength in SCO compared to OCO is then a reflection of the weaker base pro-
perties of S in C=S. The same behavior is seen in the sulfur analogues. The
-12-
-------
TABLE 4. A COMPARISON OF DOUBLE BOND STRENGTHS IN SOME DIVALENT
SULFUR COMPOUNDS WITH OXYGEN ANALOGUES
Sulfur Compound
S2
SO
sc=s
CH2=S
OC=S
C=S
CH NC=S
O
- S Bond
Dissociation
Energy
102.5
124.7
103.4
129 +_ 5
73.3
173
71
Oxygen
Analogue
°2
OS
SC = 0
CH2 = 0
OC = 0
C = 0
- 0 Bond
Dissociation
Energy
119.2
124.7
157.5
172 +_ 3
127.2
257
CH =S is stronger than the SC=S bond, while the OC=S bond is one of the weakest
S bonds observed.
In the sequence CO , COS, CS?, there is a constant 61 kcal change in AH _
on replacing 0 by S. This difference is maintained in the related pair of very
polar compounds CO(NH_)~ and CS(NH?)9 for which data exist in aqueous solutions
£* £• £ £
(7), which suggests that it should be the same in the paired compounds CH-NCO/
o
CH3NCS and HNCO/HNCS. On this basis AH°f29g [HNCO(9)] = -30 kcal is assigned.
This would make it about 6+^2 kcal/mole more stable than the isomeric HOCN (7).
Table 5 lists some S-H bond dissociation energies derived from the data on
AH _ shown in Table 2 and the known AH _ of H and other free radicals (Ref. 13).
A number of features are noteworthy. In the saturated mono sulfur compounds
RS-H, the S-H bond is 92 kcal, independent of the nature of R. In the oxygen
homologues a similar behavior is seen except in the case of HOH where the 0-H
bond has a value of 119 kca.l in contrast to ROH compounds where it is 104 kcal.
This is a reflection of the polarity effects already discussed in connection
with Table 3.
-13-
-------
Phenyl exerts a bond-weakening effect on adjacent S-X bonds analogous to its
effect on CH_ and 0, reflecting a delocalization of the ring electrons and charge
donation to the radical center. The effect in
-------
compounds X?S is the observation that the first bond dissociation energy is about
8.5-11.0 kcal stronger than the second. This is opposite in behavior to the
oxygen analogues R 0 where the second bond in RO' is about 8 kcal stronger than
the first bond. This inverse behavior can again be seen as arising from polarity
effects on the AH°f of the two sets of compounds R_0 and R.S. We note from
Table 3 that the substitution of CH for H in H20 and CH_OH increases AH° while
the opposite is the case for CH,/H substitution in FLS.
Adjacent sulfur atoms again have a bond-weakening effect on S-C bonds. From
Table 6 we see the bond lowering is 20 kcal compared to 22 kcal for the S-H bonds.
In principle these two numbers should be the same, and within the experimental
uncertainty they can be represented by their average of 21 +_ 1 kcal. This is
a measure of the relative self-consistency of the AH ,. data for both the molecule
and radical species involved and the application of group additivity. A similar
consistency is found on comparing the S-C1 bond strengths in MeS-Cl and MeS2-Cl
(Table 7). The heats of formation of these mixed compounds have been estimated
by methods of bond additivity from AH ,. for SCI- and S_C1~. The differences in
these two bond strengths is estimated at 19 +_ 3 kcal, in good agreements with
the 21+1 kcal difference calculated for the S-H and S-C series. However, a
comparison of the similar S-S bonds in H S and H S (Table 7) reveals a
£. *• 2, O
difference of only 16 + 2.5 kcal with a similar value for the HS -S H/HS -SH
- 222
difference. These are real discrepancies, which reflect the fact that H S does
not follow the bond additivity rules followed by other sulfanes but is instead
more stable by almost 6 kcal.
Sulfur-sulfur bonds follow the same general trends noted for the S-H and
S-C bonds. They are, however, significantly stronger in the alkyl disulfides
than in the hydrogen disulfanes (Table 7). This effect disappears after R_S.
and thus is strictly a neighboring S-S effect.
Very few other S bond strengths are known, Table 7 listing the ones that
have been measured. A number of S-C1 bonds have been estimated by additivity
methods plus the observation that the first R-S bond dissociation energies
exceed the second in the R2S~ compounds by about 9.5 +_ 1 kcal.
This last observation, which appears to hold for R = H, alkyl, aryl, SH,
SCH_, and Cl, indicates the strength of the pi bond in S_ and related compounds.
-15-
-------
TABLE 6. SOME S-C BOND DISSOCIATION ENERGIES FOR DIVALENT SULFUR
RS-C
•S-CH3
'S-C2H5
'S-alkyl
'S-C6H5
HS-CH3
HS-C2H5
HS-iPr
HS-tBU
HS-C-H
£* J
HS-C,H-
D 5
HS-(CO)H
HS-COCH3
•S2-CH3
•YC2H5
'VC6H5
Bond
Dissociation
Energy
66 +_ 1 . 5
63 +_ 2
63 +_ 2
88.5 +_ 1.5
75 +_ 1.5
72 +_ 1,5
72 +_ 1.5
69 +_ 1 . 5
83 + 3
86.5 +_ 2
74 +_ 2
73 +_ 2
47.5 +_ 1.5
44.5 +_ 1.5
60 +_ 2
RS-C
CH S-CH
J J
alkyl S-CH3
C H S-CH
65 3
CH S-C_H
O £t j
n-alkyl S-C2H
n-alkyl S-iPr
n-alkyl S-tBu
CH.S-C,HC
J U D
CH3S-CN
HS2-CH3
alkyl S-CH
alkyl S2-C2H5
alkyl S^-C H
2 65
CH S-CN
Bond
Dissociation
Energy
77 +_ 1.5
77 +_ 1.5
67.4 +_ 1.5
74 +_ 1.5
74 +_ 2
73.5 +_ 1.5
71 +_ 1.5
89.2 +_ 2
97 +_ 1.5
57 +_ 1.5
57 +_ 1.5
54 +_ 1.5
69.5 +_ 1.5
97
The difference between the first and second bond dissociation energies in
symmetrically substituted alkanes RCH CH R can be equated to the pi bond
energy formed in the C_H. product (30). It has been shown to be a transferable
quantity independent of the groups R (32). In the case of unsymmetrical olefins
or heteronuclear olefins such as CH2=0 or HN=0 or CH2=NH, the bond strengths
in the two possible radicals, for example CH.O' and CH-OH must be known. For
-16-
-------
TABLE 7. SOME S-S AND OTHER BOND DISSOCIATION ENERGIES FOR
DIVALENT SULFUR
RS-SR1
HS-SH
CH S-SCH
«J O
alkyl S-S alkyl
HS2-SH
HS--SCH
z, o
HS2-S alkyl
HS0-SC,HC
i 65
HS2-S2H
alkyl S2-S2 alkyl
RS_ A -S, A R
2 + n 2 + m
HS-S'
CH3S-S'
C H S-S'
6 5
FS-SF
C,HCS-SH
6 5
C,HCS-SCH_
65 j
C,HCS-SC,HC
65 65
RS2-S'
Bond
Dissociation
Energy
66 1 2
74 1 2
74 1 2
50 +_ 2
54 +_ 2
54 +_ 2
44 +_ 2
33.6 i 2
33.6 +_ 2
33.6 +_ 2
79 +_ 1
83 +_ 1
74 +_ 1.5
61 +_ 4
61 i 1.5
65 + 1.5
55 +_ 1.5
63 i 1
RS-X
•S-F
FS-F
CH S-C1
CH3S2-C1
cis2-ci
's2-ci
C,ticS-Cl
o 5
C1S-C1
'S-C1
'S-Br
BrS2-Br
'S-OH
HOS-OH
<(>N=N-S
(Aryl)3CS-NO
CH S-NO
O
Bond
Dissociation
Energy
82 + 3
92 +_ 3
[70 +_
[51 +_
[51 +_
[42 +
[31 i
[70 +_
[60 +_
[52 +_
[42 +_
[70 +_
[81 +
[29 +_
[25 i
[25 i
3]
2.5]
2]
2]
2.5]
3]
2]
4]
4]
4]
4]
I]66
U67
1]
-17-
-------
symmetrical pi bonds there may be significant stabilization in the intermediate
radical as in the radicals RS~'. This leads to weakening of the first bond in
RS -R and strengthening in the second bond in R-S ', hence a smaller difference
DH j-DH0 by double the amount of stabilization in the radical.
If the stabilization energy in RS" is assumed to be 21 +_ 1 kcal the pi
bond strength in S9 can be estimated as the nearly universal DH -DH = 9.5
+• J. £»
kcal + 2X21 = 51.5^2 kcal. A similar calculation for perioxides yields a
value of 71 ^1.5 kcal for the pi bond strength in CL. This latter is very
reasonable compared to pi bond strengths observed in olefins (^60 kcal), acetylenes
(^72 kcal), and aldehydes O76 kcal).
The same reasoning can be applied to the relation between CH,SH and CH-=S.
O 4*
From Table 2 the sum of the C-H and S-H bonds that are broken in the process
can be estimated to be 133.5 +_, 3 kcal. The S-H bond is known to be 92 kcal
(Table 5), while the C-H bond is not known. In fact, it can be anticipated that
the C-H bond will be weakened by the adjacent S atom relative to the C-H bond in
ethane. If a value of 98 kcal for a hypothetically unperturbed C-H bond strength
in CH_X is adopted, then 190 kcal can be estimated to be the sum of the C-H +
•J
S-H bonds in CH,SH in the absence of interactions. The difference between this
value and the experimental 133.5 +_ 3 can then be taken at the pi bond strength
in CH S, namely, 56.5 +_ 3 kcal. This is very close to the value of the pi bond
strength in olefins and is consistent with the observation that AH f(CH = S)
is very closs to the average of AH _ for S_ and C?H.. The average is 21.6 kcal/
mole compared to the 24 +_ 3 reported (Table 2).
The above value of the C=S pi bond strength is only 3 +_ 3 kcal lower than
the values observed in olefins and can be used to rationalize the fact noted
earlier that C,H,.S' has a stabilization energy about 3.5 kcal lower than found
in C,CrCH0, which is in turn about 3.5 kcal weaker than the value found in 4>0'.
DO /.
On this basis it can be predicted that the S-H bond strength in CH-=CHSH will
be about 84 kcal reflecting an estimated 8 kcal "allylic" stabilization energy
in the CH^CHS' radical.
The pyrolysis of divalent sulfur compounds has proven fairly difficult to
interpret. Part of this difficulty has come from the occurrence of parallel
radical and molecular path (11) as well as appreciable sensitivity to vessel
wall condition and traces of oxygen. Compounds containing pi bonds to sulfur
-18-
-------
are extremely susceptible to polymerization (19,33), and this is generally a
heterogeneous process, probably acid and/or base catalyzed. One known but
unappreciated difficulty arises from reactions producing elementary sulfur as
a product (34), such as in the pyrolysis of episulfides which produce olefins
plus sulfur.
The stable form of sulfur in the gas phase is S_ if it is below its vapor
pressure. But the equilibrium
c-Sg J 4S2
is readily attained and leads to a small but significant and almost constant
concentration of the very reactive S2 species:
1/4fS 1 1/4
-------
where after a very brief induction period during which S? and Sft build up,
1/4
the first term becomes negligible and (SQ) varies only slightly. A value
o
of E, in the range 11-14 kcal would then account quite well for the observed
3
apparent first order rate constants. Reaction 3 is close to being thermo-
•
neutral for most R and presumably goes through a biradical R-CH-CH^S,*
intermediate. It is also therefore reversible and might show a resultant
inhibiting effect on the overall reaction as product olefin is produced,
which might then obscure the small auto-catalytic effect due to increasing SR.
A final observation is in order regarding the strain energies in small
ring compounds containing sulfur. Compared to first row ring compounds con-
taining C, 0, N where strains seem to be dependent only on ring size, rings
with a single S atom have about 8 kcal less strain than the carbon analogue.
What is surprising then is that this seems to hold true for rings with 3 or 4
sulfur atoms as well.
-20-
-------
SECTION 3
THERMOCHEMISTRY OF TETRAVALENT SULFUR COMPOUNDS
The higher valence states of sulfur are conspicuous by the fact that they
are known only in the form of oxygen or fluorine, derivatives. These can be
classified as derivatives of ^SQ orx'SF- in the tetravalent states or >SO»,
SOF2, and>SF derivatives in the hexavalent states. As such they are strongly
reminiscent of the noble gas compounds and the higher valence states of the halo-
gens. Relatively little is known about the thermochemistry of the tetravalent
sulfur compounds, and most of this is of lower quality than that for divalent
suflur. Most of the data available is shown in Tab.le 8. One of the important
compounds in this table is sulfurous acid for which AH ,, (aq.) is well known,
although some uncertainty still exists as to how much H»SO, in aqueous solution
is better considered the isomer H?0' S0». Based on data for differences in AH _
between gas phase and aqueous solutions for comparable species, a difference of
18.5 +_ 3 kcal for the two phases has been estimated. This gives a value for
the gas phase species that appears to be consistent with other related values.
An interesting example of the effect of electronegative species on the
relative stability of the two and four valence states of sulfur is seen in
the isomeric compounds FSSF and SSF^. Both of these compounds can be prepared,
presumably pure (35). However, if the liquid FSSF is allowed to warm up above
0°C, it spontaneously changes over to the more stable SSF~. In contrast dialkyl
i ^
disulfides RSSR appear to be stable and known only in the indicated bonding
state. However, substantial evidence indicates that the thiosulfoxide form
i
SS(R)R is .probably not more than 10 kcal less stable.
Hoffle and Baldwin (36) have convincingly demonstrated that allyl disulfides
can undergo a Cope-type rearrangement with a thiosulfoxide intermediate
1 P
CH =CH-CHSS-R' ~" S=Sr—CH-CH=CH
2 D "~ ^R* 2
R _ K
-21-
-------
This intermediate can be trapped by P<|>_ to give SPA and R'SCHRCH=CH .
•53 L
At high enough concentrations of the trapping agent P_, the reaction is
4 i
observed to be first order with AHr = 20 +_ 1 kcal and AS = -9 +_ 1 eu. If the
PSCL) as shown in Table 8 can be made.
The bond strengths deduced in this fashion are reasonably consistent with those
deduced by other methods as will be seen in the following.
The best solution under these conditions is to list the sum of the two
bonds dissociation energies and perhaps speculate on how they may differ. This
is shown in Table 10. They show the same decrease in binding energy with
electronegativity that we have already seen in the S=0 and S=S bond strengths.
The general tendency in the sulfur bond strengths that we have considered
so far is for the first of a pair of identical ligands to be more strongly
bound than the second. The one set of data that exists in the tetravalent
-22-
-------
TABLE 8. HEATS OF FORMATION AND ENTROPIES OF SOME MOLECULES AND RADICALS
OF TETRAVALENT SULFUR
(Reference)
(6)
(7)
(2,6)
(6)
(7)
(7)
(6)
(7)
(4)
(4)
37
37, 38
(4)
(4)
(6)
(6)
(4)
(4)
(4)
Species
so2
S02(aq)
s2o
SOF2
soci2
SOBr2
SF4
SO(HO)2(aq)
SO (HO) 2
SO(OMe)2
SO(OEt)2
-------
TABLE 9. S=S AND S=0 BOND DISSOCIATION ENERGIES IN SULFOXIDE DERIVATIVES
Bond Bond
Dissociation Dissociation
Species Energy Species Energy
s=o
os^o
ss=o
F2S=0
(HO)2S=0
(MeO)2S=0
d2s=o
Br2S=0
C.H.^0
6 5
*sso*
4>SOSO<|>
124.7
132
100
118 + 6
[118 +_ 6]
[116 +_ 6]
105
[86 +_ 4]
[103 +_ 2]
[83 +_ 4]
[83 +_ 4]
H2S=0 [71
ME2S=0 86
Et2S=0 88
(C HS) S=0 89
OS=S 77
F2S=S [>57
Me2S=S [53
H2S=S [51
+ 4]
.6
.7
.3
+ 8]
±4]
±7]
TABLE 10. SUM OF SINGLE BOND DISSOCIATION ENERGIES R-S + R'-S IN
SULFOXIDES RR'S = 0 AND THIOSULFOXIDES AND ESTIMATES OF D,
Species
F2SO
ci2so
Br2S°
[F2SF2]
(HO) SO
(MeO) 2SO
(EtO)2SO
(Et2N)2SO
S-SCXl>
Dl + D2
169
no .
75
105 +_ 6]
146 ^ 6
125
125
122
-
Estimated
1 Species
(87) H2SO
(58) Me2SO
(40) Et SO
(83 +5) 4 SO
2
(76)
(65) F2SS
(65) Me2SS
ff.?} U CO
(.v5) H2bb
36 <()SO
Sum of Bond
Dissociation
Energies
121 +_ 4
105
102
133
[>129 +_ 6]
95 +_ 3
125 +_ 7
-
Estimated
Dl
(63)
(55 +_
(54)
66 +_ 2
(47 +_
(64 +_
67 +_
2)
3)
7)
2
Values in parentheses indicate estimated value of DI based on DI-D- =5+^2,
See text.
-24-
-------
sulfur group is for successive S-F bonds in SF . The data in Table 8 can be
used to estimate the first bond dissociation energy as 83 +_5 while the second
becomes 67 +_ 5, the difference being 16 kcal in favor of the first. On the
other hand, for the thiosulfoxides of CH and H, the first bond dissociation
energies can be estimated from the data in Table 10; they suggest within the
large uncertainties shown that D.,% D^, although a difference DI -D^ 8^3 would
also be compatible with the data.
Data on the pyrolysis of Me_SO, which is a radical chain process (39), can
be employed to yield a value of DH°(CH -SO(CH3)) >53 kcal but <56 kcal. If we
take the mean as 55 +_ 2 kcal, then DH_ (Me-SO) = 50 +_ 2 kcal, which is in
reasonable accord with the preceding observations on Me SS and SF.. It would
suggest D - D ^ 5+^1 kcal in Me SO, which in turn suggests that this might
be applicable to the other sulfoxides as well.
Additional information comes from the pyrolysis of ethylene sulfoxide (40),
which decomposes to ethylene + SO + S in chlorobenzene solution at 100 c- The
activation energy was estimated at 36 kcal/mole. However, the overall reaction
to eliminate SO is only endothermic by about 25 kcal,
CH2 -CH2-SO + C2H4 + SO
if the strain energy is assumed to be like that in the episulfide, namely 18 kcal/
mole. If it is assumed that in R_SO, D -D_ = 5 +_ 1, then in Et2SO the C-S bond
strength is 53 kcal. Thus the activation energy for ring opening to the biradical
is only 34 kcal/mole 1
CH2-CH2-SO t CH2-CH2-SO + C2H4 + S0
The second step in this process is exothermic by 11 kcal and probably has very
little activation energy, thus making step 1 rate determining. If ring closing
has only a few kcal of activation energy, the data would be compatible with the
observations. A concerted process cannot be ruled out. It would be spin
forbidden and would involve a crossing of the singlet-triplet surface at an
appreciably higher activation energy than the overall endothermicity.
Qualitative rate data on the pyrolysis of trimethylene sulfoxide (41) to
give CH = SO + C H is also in agreement with the biradical mechanism, reaction
starting with C-S bond fission to give the unstable '(CH?) SO biradical.
-25-
-------
From these estimates of R-SOR1 bond strengths, an estimate can be obtained
of the pi bond strength in CH SO. Starting with CH SOCH_, the sum of the CH_-
SOCH3 (55 +_ 2) and the C-H in the "unperturbed" methyl (98 kcal) as 153 +_ 2
Real can be estimated. But the overall reaction
CH3SOCH3 + CH2=SO + H + CH3
is endothermic by 110 +_ 5 kcal. Hence the C-S pi bond strength in CH-=SO
is 43 +_ 5 kcal, appreciably less than the pi bond strength of 56.5 we have
calculated for CH =Sf
It is interesting to nqte that the <(>SO radical has an estimated stabilization
energy of only 3 kcal, considerably less than the 9.6 kcal observed in S and
also less than the 13 found in 4*50 This would be in accord with the weak pi
bond formation in CH =SO just commented on.
-26-
-------
SECTION 4
THERMOCHEMISTRY OF HEXAVALENT SULFUR COMPOUNDS
Hexavalent sulfur compounds can all be represented as derivatives of the
^SF. or^SO.. groups, and they are presented in this fashion in Table 11. The
data are again very meager compared to that for divalent sulfur compounds, and
their accuracy, with few exceptions, is not better than +_ 2 kcal (8). To
interpret oxidation kinetics, thermochemical data for the oxy and peroxy mole-
cules and radicals in this series should be known, but the data are particularly
sparse. However, a number of empirical rules will be of assistance. The first
is that F and OH turn out to be a homothermal pair. The replacement of OH by
F in compounds where the attachment is to an electronegative element X (RXOH-*
RXF) results in an increase in AH f of about 7 kcal. For X=H or CH, this re-
verses to -7 kcal. When X is more positive as in vinyl, phenyl, or carboxyl
compounds, substitution of F for OH makes AH0,, more negative by about -2 kcal.
S0? can be fitted into this sequence by observing that S0? (OH)~ is 4 kcal less
stable than SO^F-, while FS07(OH) is almost precisely the arithmetic mean.
Thus the SO group seems to follow bond additivity rules to about +_ 1 kcal
with respect to elements of similar electronegativities such as Cl, F, and OH.
On this basis we have estimated AH° for C1(SO )OH(g) as -133 +_ 1 kcal (Table 11);
This appears to be compatible with the known AH ,. for the liquid and AH
extrapolated from F(SO_)OH (Table 11).
Data on the peroxy sulfuric acids exist only in aqueous solution. If the
40 kcal difference betweenn AH°.p(aq.) and AH°o(g) for H_SO. is used as a starting
point for extrapolation and consider that H^Og is a very strong acid like
H-SO., then a difference of 47 +_ 3 kcal for H_S_0R can be estimated, then a
value of AH°f (gas) = 273 +_ 3 kcal can be assigned to H-S-O as shown in Table 11.
This value together with group additivity gives a value of -153 +_ 2 kcal for ^ti°f
(HO(SO-)OOH) . Further assuming that H SO has a difference in AH°f between
gas and aqueous states similar to H_SO. leads to AH°f(H_S05) = -193 +_ 3 kcal.
-27-
-------
TABLE 11. HEAT OF FORMATION AND ENTROPIES OF SOME MOLECULES AND RADICALS
OF HEXAVALENT SULFUR
(Reference)
(6)
(6)
(6)
(6)
(6)
(6)
(6)
(7)
(4)
(7,6)
(6)
(7)
(4)
(4)
(4)
(4)
(4)
Species
SO'F
so2a2
SO C1F
SF6
SF4C1
SF5
SF5C1
S02H2
S02(OH)2
(A)
(aq)
(g)
SF5OH
FS02(OH)
(A)
(g)
C1S02(OH)
(A)
(g)
F(S02)0'
HO(S02)0'
SF4C12
•S03H
S02(Me)2
S02 (OMe) 2
S02*2
S02(OEt)2
S02(Et)2
AHf298
-94.6
-181 +_ 2
-84.8 ^0.5
[-133 +_ S]
-291.7
[-177]
[-218 +_ 3]
-233 +_ 5
-250.5
[-64 +_ 4]
-194.5
-217.3
-177.0 +_ 2
[-290 +_ 2]
-190.5
-180
-143.7
[-133 +_ 1]
[127 +_ 1.5]
[-125 +_ 2.0]
[-205 ± 3]
[-98 ± 3]
-88.7
-164
-28.3
-180.7
-102.5
S°
298
61.3
67.8
74.3
72.3
69.7
77 +_ 2
76.3
37.5
4.8
69.1
71.0
[68.5 +_ 1]
[72 +_ 1]
[78 +_ 1.5]
[67 ± 1]
74.2
(continued)
-28-
-------
TABLE 11. (continued)
(Reference) Species ^-fiaa S
f298 298
(4) S02-SO(J) -115
cyclo(SO.-O) -314
(aq) [-192 +_ 2]
(g) [-152+2] [81.5+1]
(7) [HO(S02)0]2
(aq) -320 59.3
(g) [-272 + 2] [104 + .:
(7) HO(S02)2OH
(aq) -286.4
(g) [-246 ± 5]
[F(S02)0]2
(g) [-276 +_3] [101 +_2]
[HO(S02)]20 [-282 +_ 3]
HO(SO)02H [-105 +_ 5]
cyclo 02S-0-$ [-76 +_ 3]
biradical SO. [-73 +_ 5]
HOS0202' [-114 +_ 4]
S02(02H)2 [-127+_ 3]
(37,42) C6H5S°2 ["3? - 1]
(37) C H (SO )SOC H [-52 + 2]
6 •> 2 65
C6HS(S02)SC6H5 [-22.4]
SF50' [-236 +_ 4]
(43) SF40 [-226 +_ 4]
(SFC0). -509 + 5
O £ —
Values in brackets have been estimated by the author.
-29-
-------
Monger and Redlich have measured the equilibria in aqueous solution (44) :
and found an apparent equilibrium constant of about 0.1 at 25 C which increased
to about 0.2 at 75°C. This latter would suggest AH % + 2.8 kcal and require
AS = 5 e.u. to account for AG^ 1.4 kcal. This would lead to AH0- (H SO ) = .
188 kcal, in only fair agreement with our previous estimate. However, the best
a priori estimates of AS°for this equilibrium yield a value of ^+ 13 e.u. and
r\,
hence a AH^ -2.8 e.u. The increase in Keq with T would then have to be ascribed
to an anomalously high value for AC . This latter choice would give AH -
(H7SO')aq = -193 kcal, in excellent agreement with an earlier estimate. A
resonable reconciliation would be to use -191 +_ 2 kcal which leads then to
AH __00(H0SO_) , , = -151 + 3 kcal, thence via group additivity to AH f~no
r/yo . z 6 (.gasj — rzyo
(H2S2Og) , , = -270 +_ 6 kcal. As a reasonable compromise among these values,
AH° no(H.S,,00) , , = -272 + 2 kcal will be used. This then leads to
r^yo i & o tgasj —
AH° _.0(H-SO_) , , = -152 + 2 and the other related values shown in Table 11.
±298 2 5 (gas) —
Let us note in passing that a similar equilibrium study of formic acid (44)
H202 + HCOOH £ H20 -i- HC03H
leads to a value for AH° (HCO H) gas in excellent agreement (+_ 1 kcal) with
independent estimates from group additivity and kinetic data on diacyl peroxides
(450.
Now making use of the observation that F and OH .form a homothermal pair
relative to SO with a A(AH° ) of 2 kcal, AH° [F(SOJOO(SO JF] = -276 •*• 3 kcal
2 i t 2 2 gas —
can be estimated.
A number of studies have been made of the reversible dissociation of F S_0*
226
2FSO (4(i) , AH and AS are known with reasonable accuracy. From these measurements
and the data already discussed, estimates of AH _(FSO') and S (FSO') shown
I
-------
is not affected by removing the first, then AH ,.(50.) = -73 +_ 4 can be calculated
for the SO. biradical. This has some very interesting consequences which will
be pursued later in the discussion of the kinetics of S0? oxidation. For the
moment simply note that SO. is a stable biradical with an 0 S-0 bond dissociation
r\
energy =28+4. At 25 C SO would be expected to be a long-lived species. It
4 __„
has a more stable cyclic analogue 0_S-0-0 whose AH _ gg can be estimated from
known groups and an assigned strain energy of 18 +_ 2 kcal as -77 +_ 2. Whereas
SO biradical can be triplet or singlet, the cyclic three -membered ring isomer
can only be singlet.
Using an assumption that has been very successful in treating organic
hydroperoxides ROOH, namely that the 0-H bond dissociation energy is the same
as in H000, namely 90+1 kcal, then it can be estimated that AH° OQ[HO(S00)
f. i — rzyo i
00'] = -114 +_ 4 kcal and that this radical is stable relative to dissociation
into HOSO' radical + 0- by only 16 +_ 5 kcal. This implies that this radical is
probably a very important intermediate in photochemical smog involving sulfur-
containing species.
Bond dissociation energies for the double bonded 0 atoms in sulfone
derivatives are tabulated in Table 12. They seem surprisingly insensitive to
the substituents on the central group with the exceptions of C1?SO? and S0_.
All of the other values can be approximated as 111 +_ 2 kcal. The exceptional
stability of SF. is indicated by the high value of 146 + 5 for removing two
6 —
F atoms.
Comparing these R S0=0 bond dissociation energies with the values for
R~S=0 (Table 9) reveals that they are uniformly less by about 8 kcal for
electronegative R. Even for the SO C1-/SOC1? pair, this relation holds. This
is not the case for the alkyl sulfones where the DH (R?S=0) values are uniformly
less by about 23 kcal than DH (R?SO=0) . One consequence of these relations
is that the four valence states of sulfur will be unstable with respect to dis-
porportionation when the ligands to S are alkyl or aryl groups, while the opposite
will be true for electronegative groups. As examples of this tendency
2 <}>SO j <|>S + «(»SO
-------
2F SO
2C12SO
SF2 + S02F -7 kcal
SC1
- 10 kcal
Kice (37) has noted the "bond-weakening effect'1 of SO on adjacent bonds
ascribing the effect to the stability of the SO radicals. From the above as
well as from data to be presented on bond strengths, it can be concluded that
the instability actually arises from the AH ,. of the parent molecule; for the
sulfones and sulfoxides the principle of alternating polarity (26, 29), which
is so important in determining thermochemical stability is illustrated again.
It has already been noted that the <|>SO radical has less stabilization energy
than (fiS'or <$>SQ .
Very few direct measurements of single bond dissociation energies for
hexavalent sulfur compounds have been made. Mackle and colleagues (47) used
toluene carrier techniques to measure the rates of pyrolysis of alkyl and
aryl sulfones. However, their assignments of Arrhenius parameters were in-
consistent and usually too low. Reinterpretation and scaling of their Arrhenius
parameters using presently available thermochemical data lead to the bond
dissociation energies shown in Table 12.
TABLE 12. S=0 BOND DISSOCIATION ENERGIES IN HEXAVALENT SULFUR SPECIES
Species
Bond
Dissociation
Energy
Species
Bond
Dissociation
Energy
°2S = °
F2SO = 0
ci2so = o
(HO)2SO = 0
(MeO)2SO = 0
(EtO)2SO = 0
[F4S = F2
SF = 0
4
83.3
110 +_ 5
95
110 +_ 3
108
109
146 +_ 5]
102 +_ 6
Me2SO = 0
Et2SO = 0
SO=0
Gt>S02)SO=0
(SO)SO=0
(<}>S)SO=0
112
112
113
109
122
122
115
+ 3
1 4
-32-
-------
The data on the alkyl sulfones are self-consistent within +_ 2 kcal, which
is about the reliability of the AH°f data. From complex kinetic studies of
the radiolysis of CH,SO Cl in cyclohexane, Horowitz (4.8) has evaluated Keq
•^ 2
for
MeSO.
Me + SO
2 «- -" "2
o 0 0
in the range 60 -122 C,' from its temperature coefficient the values AH =
15.6 kcal/mole and AS° = 23 e.u. were derived. In the gas phase AS0 = 35 e.u.,
so an estimated AH = 17.2 kcal/mole would be the appropriate value for the gas
phase dissociation, in excellent agreement with the data in Table 13.
Further corroborating evidence for both of these bond dissociation energies
comes from the work of Good and Thynne (4g) who measured the direct gas phase
equilibrium between CH_ + S0_. They found AH.. = 20 +_ 2, while values for the
equilibrium C_H5 + S0_ + C-HgSCL gave AHw. = -17 +_ 1 kcal/mole, in excellent
agreement with our estimate of 16 +_ 2 (Table 13). Interestingly, they claimed
TABLE 13. X-S02 SINGLE BOND DISSOCIATION ENERGIES IN SULFONE DERIVATIVES
Species
Bond
Dissociation
Energy
C,HCS00-S00C.,H_ 41 + 1
D o Z i o b —
C,HCSO_-SOC,HC 28 + 1
O O 2. D D —
Species
Bond
Dissociation
Energy
CH3(S02)-CH3
Et(S02)-C2H5
CH3(S02)-allyl
CH3(S02) -benzyl
C6H5(S02)C6H5
wii— (oVJ— ) \-i s ri—
3 2 o S
CLJ rcr\ ~\ r*\ i
jf n.- i ovj ,_ i ^n _
68
68
55
56
70
83
54
86
84
73
74
114
101
101
S°2F2
so2ci2
cr^ r c\\ \"\
o \j i v/n i
S02(F)(OH)
S02 (HO) (02H)
F(SF4)F
[100]
[63]
[88] .
93 +_ 3
79 (Ref.
50)
148
75
125
136
95
147]
147 + 3
(Ref. 50)
-33-
-------
to observe activation energies of about 3 kcal/mole for both of these addition
reactions and found them very much slower than the same radical reactions with
0-. This would tend to support the analogy betueen CO (or CO-) and SO-. CO
has an appreciable reorganization energy of about 75 kcal and shows a small
activation energy for radical or atom addition which varies with the electro-
negativity of the radical.
Cornell and Tsang (51) have conducted toluene carrier studies of the
pyrolysis of trimethylene sulfone and 2-methyl sulfolane. Very interestingly,
for the former they find only cyclopropane and only traces of propylene,
suggesting that trimethylene is not an intermediate. The high A-factor of
10 ' sec and E =56+1 kcal suggest an open ring, very loose transition
act —
state. Assuming 19 kcal strain energy for the ring, an estimated 49 kcal
would be required for the AH of ring opening to form the biradical:
SO 1 .2
_t CH2-CH2-CH2S°2 -T A + S°2
If reaction 2, which is 38 kcal exothermic, has a loose transition state for the
S - displacement of SO- from C by the free radical end and an activation energy
of 7 kcal, this would be compatible with the observations. The competing
reaction 2" to form trimethylene + SO- with a 16 kcal activation energy and a
higher A-factor would still be about tenfold slower than reaction 2, which is
in agreement with the very small amount of propylene found. Their study of 3-
methyl sulfolane
,SO. * S02 * C2H4 * C^
yields again a high A-factor suggestive of a loose transition state and an
activation energy of 66.4 kcal. This would suggest an estimated value for
AH ~ 63 +_ 2 kcal, which suggests that step 1 is rate determining with sub-
sequent steps having an activation energy not exceeding 8-11 kcal and a high
A-factor on the assumption that E ~ 3 kcal with an expectedly low A-factor of
12 -1
about 10 sec . Since the energy to detach SO- from the biradical requires
approximately 15 kcal, this is a barely possible intermediate step. It is not
-34-
-------
unlikely that the biradical cleaves into the three final species with an
activation energy appreciably lower than this. Alternatively, a displacement
reaction similar to that observed for the trimethylene sulfone might be expected.
Its parameters are in the range of interest and would lead to methyl cyclobutane
as a metastable intermediate which decomposes about threefold faster than the
sulfone. The authors actually found a CL product, which they could not identify
and which amounted to about 10% of the decomposition, could well be the cyclo-
butane derivative.
On this basis are derived the values for D for the sulfones shown in
Table 13. If D.-D is considered for the symmetrical sulfones, it has the
value 50 +_ 2 kcal, which can be considered a reorganization energy of the
SO group. While there is no reason to expect this to be a constant independent
of R in R^SO.., note that it is consistent with one of the few directly measured
values of F-SO_F from shock tube studies (5z)• The authors fitted their data
using RRK theory to bond strengths of 81 and 95 kcal/mole. They chose the former
as giving a better fit to their data. However, the number of degrees of freedom
and their A-factor were unjustifiably small. More acceptable values for the
latter yield higher values for E closer to 100 kcal when extrapolated back to
room temperature.
This latter value gives D.-D.- = 52 +_ 2 kcal, which is in good agreement with
the other sulfones. Assuming that this difference applies to C12SO_, it can be
estimated that DH°(C1S02-C1) = 63 as shown in Table 13. In similar fashion
reanalysis of the shock tube data on SFfi leads to a F,-S-F bond dissociation energy
at room temperature of 93 kcal (53"), which is also compatible with electron impact
and electron affinity data on SF- and SF (54). This differs appreciably from
the values selected by Hildenbrand (50), so the subject deserves further study.
Note, however, that it yields D-D = 39 for the SF series.
Assignment of the constant difference for SO R_, D -D = 50 +_ 2 yields the
bond strengths DH°(HOSO -OH) = 88 kcal shown in Table 2 and AH°f(S02OH) = -98
kcal.
The AH ,. deduced for the substituted SO, radicals permit us to draw some
conclusions concerning SO . From the data in Table 11 it can be estimated
that DH°(F-S020") = 51 +_ 1.5 kcal and DH°(HO-S020') = 39 +_ 2 kcal. From AH°f
-35-
-------
(HOSCL) = -98 + 3 can be calculated an H-0 bond dissociation energy of 81 kcal
^ """"" •
for the first bond in H.SO, and a value of 55 kcal for DH°[H-OSo ]. This
gives 26 kcal as the reorganization energy of the isomeric SO biradical
0-SO-O to SO . This permits a calculation of the R-0 bond dissociation energies
3
in the sulfites (RO)2SO. The data in Table 13 reveals 89 kcal for D + D for
CH_-OS09CH ; using D.-D9 = 26 kcal to estimate, D1 = 57.5 kcal and D_ = 31.5
•J Z O ( J. Z J. £•
kcal. DH (HO-SO )= 36 kcal, which is only slightly weaker than the attachment
of the OH bond to S03<
In H-SOj. the 0-0 bond strength can be estimated to be 36 kcal, appreciably
stronger than the 22 kcal estimated for the 0-0 bond in hLS?0,, but typical of
the differences in 0-0 bond strengths between peroxides and hydroperoxides.
While AH°~[HO(SO)0_H] is not known, upper and lower limits can be estimated
for it from AH° of the sulfur analogue HOCSO^O-H and the >S=0 bond dissociation
values listed in Table 12. For polar species OH, OR, and F, or even alkyl and
aryl substituents, this bond is 111 +_ 2 kcal. For 0 substituent it is 15 kcal
lower. With one OH and one OOH substituent, an estimate would be that 107 +_ 4
may well bracket all likely values and thus give AH° (HO(SO)02H) = 105 +_ 5
kcal. This would make the 0-0 bond dissociation energy in this compound only
16 +_ 6 kcal, from which it can be concluded that the acid is unstable at tem-
peratures above 200*K. This is the weakest of 0-0 bonds in the entire sequence.
An interesting bond strength is the central 0-S bond in pyrosulfuric acid
HOS02-0-S02OH. For this bond an estimate would be that DH°(HOS02-OS03H) = 59 +_
5 kcal, which explains why the various polymeric forms of S0_ are quite stable
in the absence of an acid or base catalyst.
The observation (37,42) that the SO -SO <}> bond fission has an activation
energy of 41 kcal in inert solvents permits us to estimate AH°- (SO') (Table
13) and a stabilization energy in S' is some 4.5 kcal less than that in SO_, and this is probably to be expected
since the source of the stability is the donation of charge from$ to the SO- group,
and the latter is much more electrophilic than S.
For dithionic acid H^S^O, where AH0,- is known only approximately, it can
be estimated that DH°(HOS02-S02OH) = 50 +_ 10 kcal. It would be anticipated from
the analogy with (QSO^j that a more negative AH0,, and a stronger bond closer to
-36-
-------
60 kcal would be more likely.
One of the more interesting compounds of sulfur is the SO. discussed
earier. The cyclic form is stable relative to the decomposition into SO^ + 0_
by about 5 +_ 3 kcal but might have a high activation energy for such a de-
composition because of spin forbiddeness. It is marginally more stable than
the biradical SO by about 3+5 kcal. The SO birdadical is stable realtive
4 — 4
to decomposition into SO + 0 by 38 kcal and also stable relative to decom-
o
position into SO + 0 by 2 +_ 5 kcal. If SO is a stable or metastable species,
however, this latter mode of decomposition is probably restrained by dynamic
considerations rather than energetic ones.
There is good experimental evidence for believing that SO. biradical is
a stable species in the gas phase. Westenberg and deHass (55) have shown that
at room temperature 0 atoms and SO, added together in a very rapid thermolecular
reaction with rate constants that can be rationalized only by assuming a
reasonably deep well for the reaction with no activation barrier. A 38 kcal
0_-S-0 bond would fulfill this requirement. The fate of SO. is somewhat
mysterious in this system as it does not lead to S0? + 0_. In fact, at much
higher temperatures 0 + S0_ •> S0? + 0^ appears to be a slow reaction (56,57)
with appreciable activation energy. One would expect from its manner of
formation from 0 + SO, that the stable form of biradical SO. would be the triplet
state and that this could account for its dynamic stability relative to cyclic
peroxy-SO..
One fate that could be anticipated for radical SO is self polymerization to
(SO.) , either linear or cyclic, or polymerization with S0_ to form linear or
cyclic (SO ) SO with a peroxide linkage. The polymer (SO ) could be looked
3 n 4 4 JJ
upon as a copolymer of S0« and 0 , and an estimate of its AH extrapolated
from known groups is -95 kcal/mole SO.. Thus it would be stable by about 24
kcal/mole against decomposition into SO,., + 07, and it would be thermoneutral
with respect to the depolymerization into SO, + 1/2 02. The 0-0 bond in such
a polymer is estimated to be 22 kcal/mole, like that in J-LS.O- so it could unzip
i L O
at about room temperature.
The copolymer with SO is expected to be more stable with an 11 kcal bond
energy for the process
-37-
-------
SO + SO + 0(SO )0(SO )0
tO £• £*
o
While this is not enough to render the gas phase dimer stable at 300 K, it could
readily stabilize by sorbing on glass surfaces, or by forming there in a
heterogeneous reaction.
It has been reported (58) that when an electric discharge is passed through
a S0_/0_ mixture at 0.5 torr (09 >> S09) a white solid can be condensed with
£ £• £ .. £
formula SO. and a melting point of +3 C. On melting it evolves 0 and leaves
a liquid residue with the composition S 0 . These substances could well be the
polymers discussed above which would be more stable in condensed states.
-38-
-------
SECTION 5
OXIDATION OF SULFUR-CONTAINING MOLECULES
"v
The kinetics of oxidation of sulfur compounds may be divided into two
categories; the oxidation at low temperatures (~25 C), which is of interest in
photochemical smog formation and stratospheric chemistry, and the high temperature
oxidation, which is of interest in fossil fuel burning plants and smelters.
There has been at least one very recent review in each of these two regimes which
summarizes current thinking and evidence on reaction steps, so there is no need
to repeat the discussions to be found there (2,59). There is in addition a
recent critical update of some of the elementary gas phase reaction rate constants
involving simple S-containing radicals with 0, H, and other simple molecules
and radicals in flames (60). An additional article of interest in examining
low temperature oxidation processes and their relation to aerosol formation has
also appeared recently (61). The discussion here will be confined to considering
some of the critical elementary steps in these oxidation schemes, starting
with the low temperature photochemical system.
Photochemical smog formation refers to the oxidation of hydrocarbons pre-
sent in ambient atmosphere at low concentration (1-10 ppm) triggered by photo-
chemical (sunlight) decomposition of NO also present in low concentrations
(0.1-2.0 ppm). The process is accompanied by a catalytic production of 0
O
(0.1 to 0.5 ppm maximum) and other oxidized species and usually aerosols.
Although photolysis produces 0 atoms from both NO- and 0_, these are
rapidly scavenged by 0_ molecules in a process that achieves a very low photo-
stationary concentration dominated by:
N02 + hv (x* 4100R) i NO + 0
0 + 02 + M + 03 + M
3
NO + 0 -> N0 + 0
-39-
-------
(0) . VVNV (N(V
ss
k2(02)(M)
,o
where I is the flux of radiation and £N00 is the weighted extinction coefficient
o *~ 2
of NO,,. Because of the low concentrations achieved, reactions of 0 atoms with
ambient molecules will not be of interest unless their bimolecular rate constants
Q .
exceed 10 ^./mole-sec. Instead it appears that other radicals such as OH, H0?,
and R00, which react only very slowly or not at all with 00, will dominate the
L o L
reaction chemistry. Saturated hydrocarbons, for example, appear only to be
attacked at significant rates by OH radicals.
The most important sulfur-containing species in ambient atmosphere is SO^,
and secondarily, SO . Both of these react with 0 atoms at rates whose apparent
8
bimolecular rate constants of about 10 £/mole-sec (55,60) are close to the
minimum rate considered significant. In very bright sunlight at higher NO
concentrations, these reactions may be important, but not otherwise.
The reaction of OH with both SO and SO is expected to be extremely rapid
11 If 2 2
with rate constants approaching 10 and 10 a /mole -sec:
OH + S02 + M -»• HOS02 + M
OH + SO + M -»• HOSO + M
J O
The resulting radicals have DH°(HO-SO ) =36+3 kcal and DH°(HO-SO ) =39+2
£• ^"" O "*™
kcal and thus are expected to be quite stable with respect to dissociation. The
addition reactions are expected to have negative temperature coefficients.
The HSO. radical can form a very strong OH bond (104 kcal) and is expected
to be more active than RO radicals in either adding to double bonds of olefins
or in abstracting H atoms from hydrocarbons. It can also react with NO to form
mononitrosyl sulfuric acid HO(SO_)ONO with DH°(HOS000-NO) =22+2 kcal and DH°
£. L —
(HOSO--ONO) = 35 +_ 2 kcal. This addition reaction is expected to have very
little or zero activation energy. The nitrosyl sulfuric acid has a very large
heat of condensation and will be readily sorbed on surfaces and exothermically
hydrolyzed to sulfuric plus nitrous acids. It should also form metastable
-40-
-------
complexes with H,,0 in the gas phase if the humidity is high enough.
HSO. will also react rapidly with NO- at almost every collision (lo 10 I/
mole-sec) to form nitryl sulfuric acid HO(SO )ONO . This species has an
estimated AH°ror.0 = -139 + 3 kcal and about the same bond energy for redissociation
—
as the nitrosyl ester, namely 22 +_ 2 kcal. It will also form complexes with
H 0 in the gas phase and hydrolyze readily on surfaces to H?SO + HNO,.
Nitryl and nitrosyl sulfuric acid have relatively week 0-N bonds as
estimated and at STP will have half-lives of about 1-10 seconds. At lower
temperatures typical of the stratosphere (220 K) , thermal dissociation is
negligible, while on hot, smoggy days, redissociation is very fast.
It has been suggested that HSO. can react with 0_ to form the peroxy
radical HO(S07)0 ', which can then go on to react with NO to form NO, and
HS05 (62). Starting with the estimated AH° [HO(S02)0,H] = -152 +_ 2, it can be
estimated using group additivity rules for polyoxy compounds that AH f[HO(SO-)
03H] = -133 +_ 3 kcal and H £[HO(S02)04H] = -114 +_ 3 kcal. In such polyoxides
the RO-H« bond strength appears to be 90 +_ 1 kcal as in H_0_, so that the
estimate AH° [HO(S02)0 '] = -95 +_ 3 kcal can be made. Thus the addition of
0^ to HSO. is endothermic by 20 ^3.5 kcal, and HSO,' is not expected to exist.
In contrast, the radical HOSO? can form a bond with 0~ with a dissociation
energy of about 16 +_ 5 kcal, hence the radical HSO,. is expected to be a
significant species in smoggy atmospheres containing SO-. DH (HOSO.-O) is
estimated to be 48 +_ 5 kcal, so that this radical should be capable of oxidizing
NO to NO . Note that the adduct with NO or NO will not be stable. The
reaction HSO + NO ->• NO + HSO is estimated to have AH°= 0 + 4 kcal.
'•52*34
If we employ our rule that the reorganization of SO is 51 kcal, then
AH°f (HO--SO ) = -73 +_ 4 kcal can be calculated. This suggests that the radicals
HO and RO may react with SO to form SO + HO and RO, respectively, with
little or no activation energy. Thus S02 can, like NO, act as a catalyst for
the conversion of realtively inert peroxy radicals into more active oxy
radicals:
SO + RO -> SO + RO
The intermediate adduct, R02S02 has a relatively weak RO-OS02 bond, 4^4
kcal, and will not be stable.
-41-
-------
The HSO_ radical has a fairly strong HSO -0 bond, estimated at about 97 +_ 4
kcal, hence it will not oxidize NO-, NO, or SCL. According to calculations,
it will not have an affinity for NO. However, it should react readily with
NO to form the fairly stable nitrosyl sulfuric acid:
NO + HSO ->• HO (-SO -)ONO + 37 +_ 5 kcal
AS we have noted this will have a relatively short half-life at 300 K to dissociate
into HSO + NO or to hydrolyze.
The oxidation of sulfur compounds in flames and at high temperatures
involves all possible valence states. Hence, isomeric forms of these species,
particularly as radicals, become of interest. A very important reaction
involves the interactions of H atoms with SO and SO . DH°(SO -H) = 55 +_ 3 kcal
so that one expects H atoms to add very rapidly to S0_. In high temperature
regimes the adduct is expected to have a very short life time for redissociation
into SO + OH for which DH°= 36, so that the reaction
H -i- S03 + HOS02* -> HO + S02
is expected to proceed very rapidly with little or no activation energy. The
reactions of H atoms with S0_ are probably more interesting in most flame
L*
systems. These reactions are complicated by the existence of isomeric forms
of radicals and molecules. The compound H SO has three isomeric forms: (HO) •*
S, HSO(OH), and H SO . For these forms we have estimated AH°£ of -67 +_ 5, -72
+_ 5, and -64 +_ 4, respectively. The radical HSO has two isomeric forms, H-SO
o
and H0-S=0, for which by our various rules we can deduce AH of -42 +4 and -60
f
+_ 3 kcal, respectively. Thus the latter will be significantly more stable with
an H-OSO bond dissociation energy of 41 kcal. Efforts to measure the rate of
addition of H atoms to SO™ in flow systems have been made difficult by the very
rapid wall recombination (63). However, flame studies which have been recently
reviewed (60) indicate a fairly rapid three-body reversible recombination above
1600 K. This would be compatible with the 41 kcal bond energy.
Sulfur compounds in the divalent state will be expected to react very
rapidly with 0 atoms to form sulfoxides:
RS + 0 + RSO
-42-
-------
This reaction is very exothermic (Table 9) and in the gas phase can be
followed by dissociation of the weaker R-S bond. Slagle and co-workers (64)
have shown that these reactions at room temperatures proceed with zero activation
energy for RSH and R-S and have suggested that with H-S the excited adduct
* *• * *•
H-SO can rearrange to give the isomeric HOSH , which is estimated to be about
20 ^ 5 kcal more stable. With the internal energies available in these adducts,
this seems entirely reasonable.
One of the other high temperature reactions which has excited some interest
is the bimolecular reaction between NO- and SO-:
N02 + S02 -» NO -S03 +11 kcal
Despite its exothermicity this reaction appears to have a surprisingly high
activation energy of the order of 26 kcal (65). Rate studies on this system
have proven difficult because the bimolecular reaction of 2NO_ ->• 2ND + 0_ is
faster than the competing reactions. In examining this reaction note that the
transition state must be close in structure to the radical species:
0 - N - 0 - S02
We can estimate the AH0,- for this species by observing that AH°f (ONOSO,H)
= -125 +_ 3 kcal. If the S-OH bond dissociation energy in this anhydride is
the same as its value in H SO (Table 9), then AH° (ONO-SO-) = -46 ^4 kcal can
be calculated. Thus the radical lies above SO- + NO- by 17 +_ 4 kcal, and this
would be a minimum activation energy for the reaction. On this basis the
transition state for the reaction lies between the free molecules and the
above radical with an intrinsic energy only 9 kcal above the radical. This
9 kcal would be a reasonable intrinsic activation energy for an atom transfer
reaction. A similar situation occurs in the reaction of NO- with CO, which is
exothermic to form NO + CO- by 54 kcal, but has an activation energy of 27
kcal. By similar methods AH - (ONOCO) = 1^3 kcal can be estimated, so that
the radical lies 19.5 +_ 3 kcal above NO + CO in AH°_, and the transfer reaction
has an intrinsic activation energy of only 8 kcal.
-43-
-------
REFERENCES
1. Air Quality and Stationary Source Emission Control. National Research
Council Report. Serial No. 94-4, U.S. Government Printing Office,
Washington, D.C. (1975).
2. C.F. Cullis and M.F.R. Mulcahy. Combustion and Flame, 18: 225, (1975).
3. S.P. Sander and J.H. Seinfeld. Environ. Sci. and Tech., 10: 1114, (1976).
4. J.D. Cox and G. Pilcher. Thermochemistry of Organic and Organometallic
Compounds. Academic Press, London, 1970.
5. D.R. Stull, E.F. Westrum, Jr. and G.C. Sinke. The Chemical Thermodynamics
of Organic Compounds, John Wiley and Co., New York, 1969.
6. JANAF Thermochemical Tables. Dow Chemical Co. Thermal Lab., Midland,
Michigan. 1966 plus later supplements to 1976.
7. Selected Values of Chemical Thermodynamic Properties. Tech. Note-270-3,
U.S. Government Printing Office, Washington, D.C. 1968.
8. S.W. Benson, F.R. Cruickshank, D.M. Golden, G.R. Haugen, H.E. O'Neal,
A.S. Rodgers, R. Shaw, R. Walsh. Chem. Rev., 69: 279, 1969.
9. H. Mackle. Tetrahedron, 19: 1159, 1963.
10. J.A. Kerr. Chem. Rev. 66: 465, 1966.
11. S.W. Benson and H.E. O'Neal. Kinetic Data on Gas Phase Unimolecular
Reactions. NSRDS-NBS 21, U.S. Government Printing Office, Washington,
D.C., 1970.
12. H.E. O'Neal and S.W. Benson. Thermochemistry of Free Radicals.
Chapter 17 in Free Radicals. Vol. II. Edited by J.K. Kochi, John Wiley
and Sons, New York, 1973.
13. S.W. Benson. Thrmochemical Kinetics. 2nd Ed., John Wiley § Sons,
New York, 1976.
14. A. Colussi and S.W. Benson. Int. J. Chem. Kin., 9, 1977.
15. D. Detry. J. Drowart, P. Goldfinger, H. Keller, and H. Rickert. Advances
in Mass Spec., 4: 499, 1968; Zeit. Phys. Chem., 55: 314, 1967.
-44-
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16. F. Feher and G. Winkhaus. Zeit. F. Anorg. Chem., 292: 210, 1957.
17. P.A.G. O'Hare. J. Chem. Phys., 52: 2992, 1970.
18. H. Okabe. J. Chem. Phys., 56: 4381, 1972.
19. A. Jones and P.P. Lossing. J. Phys. Chem., 71: 4111, 1967.
20. I. Kende, T.L. Pickering and A.V. Tobolsky. J. Am. Chem. Soc., 87:
5582, 1965.
21. W.J. McKnight and A.V. Tobolsky. Elemental Sulfur, Chemistry and Physics.
Interscience Publ. Co., New York, 1965. Chapter 1.
22. N.J. Friswell and B.C. Gowenlock. Inorganic Hydrogen and Alky1-Containing
Free Radicals - Part II, Groups V and VI. From Advances in Free Radical
Chemistry. G.H. William, Editor, Vol. 2, Logos Press, London, 1967.
23. F. Feher and G. Hitzemann. Zeit. F. Anorg. Chem., 294: 50, 1958.
24. R.D. Nelson, Jr., D.R. Lude, Jr. and A.A. Margott. Selected Values of
Electric Dipole Moments for Molecules in the Gas Phase. NSRDS-NBSID.
U.S. Government Printing Office, Washington, D.C., 1967.
25. Tables of Interatomic Distances and Configurations in Molecules and
Ions. Spec. Publ. 11, The Chem. Soc. (London), 1958. No. 18
(Supplement), 1965.
26. S.W. Benson and M. Luria. J. Am. Chem. Soc., 97: 704, 1975.
27. Idem, Ibid. 97^, 3337 (1975).
28. Idem, Ibid., 97_, 3342 (1975).
29. S.W. Benson, unpublished work.
30. S.W. Benson. J. Chem. Ed., 42: 502, 1965.
31. A. Colussi and S.W. Benson. Int. J. Chem. Kin., 9_, 295, 1977.
32 A.S. Rodgers and J.M. Pickard. J. Am. Chem. Soc., 98, 6115, 1976.'
33. D.R. Johnson, F.Y. Powell and W.H. Kirchoff. J. Molec. Spect., 39: 136, 1970.
34. O.P. Strausz, H.E. Gunning and J.W. Lown. Chemical Kinetics, 5, Chapter
6, Elsevier Publ. Co., Amsterdam, 1972.
35. R.D. Brown, G.P. Pez andM.F. O'Dwyer. Austr. J. Chem., 18: 627, 1965.
36. G. Hoffle and J.E. Baldwin. J. Am. Chem. Soc., 93: 6307, 1971.
37. John L. Kice. Sulfur Centered Radicals, Free Radicals Vol. II:
Chapter 24. Edited by J.K. Kochi, John Wiley § Sons, New York, 1973.
-45-
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38. E.G. Miller and K. Mislow, J. am. Chem. Soc. 9£, 4861 (1968). I have
assigned an A-factor of 10 ' to his rate constant and estimated
E = 36 kcal.
39. F.C. Thyrion and G. Debecker. Int. J. Chem. Kin., 5: 583, 1973.
40. G.E. Hartzell and J.N. Paige. J. Am. Chem. Soc., 88: 2616, 1966.
41. E. Block. R.E. Penn, R.J. Olsen and P.E. Sherwin. J. Am. Chem. Soc.,
98: 1264, 1976.
42. J.L. Kice and N.A. Favrostritsky. J. Org. Chem., 35: 114, 1970.
43. J. Czarnowski and H.J. Schumacher, Int. J. Chem. Kin. 9_, (1977).
44. J.M. Monger and 0. Redlick. J. Phys. Chem., 60: 797, 1956.
45. S.W. Benson and R. Shaw. Adv. Chem. Series, 75: 288, 1968. Am. Chem.
Soc., Washington, DC.
46. P.M. Nutkowitz and G. Vincow. J. Am. Chem. Soc., 91: 5956, 1969.
Earlier studies are referenced here.
47. H. Mackle, work interpreted by S.W. Benson and H. E. O'Neal.
48. A. Horowitz. Int. J. Chem. Kin., 8: 709, 1976.
49. A. Good and J.C.J. Thynne. Trans. Far. Soc., 63: 2708, 1967; 63:
2720, 1967.
50. D.L. Hildenbrand. J. Phys. Chem., 77: 897, 1973.
51. D. Cornell and W. Tsang. Int. J. Chem. Kin., 7: 799, 1975.
52. K.L. Wray and E.V. Feldman, J. Chem. Phys., 54: 3445, 1971.
53. J.F. Bott and T.A. Jacobs. J. Bott., 50: 3850, 1969; J. Chem. Phys.,
54: 181, 1971.
54. P. Harland and J.C.J. Thynne. J. Phys. Chem., 73: 4031, 1969; 75:
. 3517, 1971.
55. A.A. Westenberg and N. de Haas. J. Chem. Phys., 62: 725, 1975.
56. A. Jacob and C.A. Winkler. J. Chem. Soc. Far. I., 68:2077, 1972.
57. See discussion in Ref. (,Q, page 573.
58. J.P. Durant and B. Durant. Intro, to Advanced Inorg. Chem. John Wiley
$ Sons, New York, 1962, p. 821.
-46-
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59. Stanley P. Sander and J.H. Seinfeld. Environ. Sci. and Tech., 10:
1114, 1976.
60. D.L. Baulch, D.D. Drysdale, J. Dixburg and S.J. Grant. Evaluated
Kinetic Data for High Temperature Reactions, Vol. 3. Buttersworth
(London), 1976.
61. P.T. Roberts and S.K. Friedlander. Environ. Sci. and Tech., 10:573,
1976.
62. D.D. Davis, G. Smith, and G. Klauber. Science, 186: 733, 1974;
D.D. Davis and G. Klauber. Int. J. Chem. Kin., Symp. 1: 543, 1975.
63. R.W. pair and B.A. Thrush. Trans. Far. Soc., 65: 1550, 1969.
64. I.R. Slagle, R.E. Graham and D. Gutman. Int. J. Chem. Kin., 8: 451, 1976.
65. J.W. Armitage and C.F. Cullis. Combustion and Flame, 16: 125, 1971.
66. H. van Zwet, E.G. Kooyman. Rec. Trav. Chim., 86:1143, 1967. The
value shown is estimate made from author's absolute rate constant.
67. Idem., Ibid. 87:45, 1968.
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APPENDIX
METHOD OF ESTIMATION OF AH°f OF ACID ANHYDRIDES
To estimate the AH ,. of the various sulfur and nitrogen oxy-acid anhydrides,
analogies have been used which represent a correction to the rules of bond
additivity. Data exist for a number of acid anhydrides and for the corresponding
acids. These are summarized in Table A-l where we list in addition data on the
heats of hydrolysis of these anhydrides in the ideal gas state. The listings
are roughly in order of exothermicity and range from AH = -14 to +6.0 kcal.
The range is not random but appears to be correlated with the acidity (pKa)
of the two acids involved. Thus anhydrides of acids whose pKa ^ 5 seem to
hydrolyze with AH, ,^ -10 +_ 2 kcal. As the pKa of one or more of the acids
decreases, this changes to positive. Anhydrides of MeOH, for example, seem
to have AH^ %5 +_ 2 kcal.
On the basis of the above correlations, it would be expected that anhydrides
of nitric, sulfuric, and acetic in any combination would have AH, , = -12 +_ 2
kcal. And on this basis it could be estimated:
AH°f [HO(S02)0 COCH3] = - 212 +_ 2
AH°f [HO(S02) ON02] = - 139 +_ 2
AH°£ [CH3(CO)ON02] = -65 +_ 2
On the same basis it could be estimated:
AH° [0 N-NH2] = 15 +_ 2
AH°f [HO(SO )NH ] = -124 +_ 2
For HONO the anhydride AH _ can be bracheted between that of stable N 0
(+19.8 kcal) and separated NO + NO (+29.4 kcal). A reasonable choice would be
0
A-H f [(ON)20) = 24 +_ 2 kcal. Bond additivity would then yield AH°f (ONONO ) =
-48-
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13.5 +_ 1 kcal which can be compared to 2.5 kcal for the stable forms of N-0..
AH°h d [(ON(20] is then -2.5 kcal, while A HK d [ONONCy = -6 kcal, both of
which seem quite reasonable. On this basis, guided by the pKa considerations,
it can be estimated.
AH°f [HO(S02)ONO] = -129 +_ 2 kcal
AH°_[CH_(CO)ONO] = -56 + 2 kcal
to —
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TABLE A-l. AH° FOR SOME ACID ANHYDRIDES AND THEIR HEATS OF
HYDROLYSIS IN THE IDEAL GAS STATE
Ref.
4
6
(Table 11)
7
(Table 11)
(Table 11)
(4)
(4)
(4)
(4)
(Table 11)
(Table 11)
Table 2
4
4
4
22
4
46
Table 11
Anhydride
(CH3CO)20
(N02)20
(HOS02)20
C12°
HOS02F
HOS02C1
CH3COF
CH3COC1
CH3COBr
CH3COI
S°2F2
so2ci2
HCOSH
HCONH
2
02NOMe
ONOMe
CH3COOMe
Me20
HOOOH
HOS02 (OMe)
AH°f
-137.1
2.7
-282 +_ 3
21.0
-180
-133
-104
-58.9
-45.6
-30.3
-181 + 2
-84.8
-30
-44.5
-28.6
-15.6
-98.0
-44.0
-13
.-170.5 +_ 2
AH°, ,
hyd
-11.7
- 9.1
-14 +_ 3
- 7 1 5
-4
-8
-6
-8.5
-8.6
-8.9
-5.7 ^2
-12.4
-7.5 + 1
1 1 2
6.4
7.1
4.5
6.0
7.0
4.0
-50-
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA-600/3-77-127
3. RECIPIENT'S ACCESSION'NO.
4. TITLE ANDSU8TITLE
5. RE
1977
THERMOCHEMISTRY AND KINETICS OF SULFUR CONTAINING
MOLECULES AND RADICALS
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
Sidney W. Benson
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
University of Southern California
Los Angeles, California 90007
10. PROGRAM ELEMENT NO.
1AA603
11. CONTRACT/GRANT NO.
DA-6998290
12. SPONSORING AGENCY NAME AND ADDRESS
Environmental Sciences Research Laboratory - RTF, NC
Office of Research and Development
U.S. Environmental Protection Agency
Research Triangle Park, North Carolina 27711
13. TYPE OF REPORT AND PERIOD COVERED
Final
14. SPONSORING AGENCY CODE
EPA/600/09
15. SUPPLEMENTARY NOTES
16. ABSTRACT
The relevant thermochemistry of sulfur oxides is discussed, and selected
"best" thermochemical values for use in kinetic systems are presented. Although
the kinetics of air pollution and combustion involve mostly homogeneous gas
phase reactions, the data taken from condensed phases were also considered.
This was accomplished by using empirical rules that were used to translate con-
densed phase values to equivalent gas phase values. All available research
through 1976 on the thermochemistry of organic and relevant inorganic sulfur
containing molecules and radicals is reviewed. Some significant or controversial
kinetic steps important in air pollution chemistry and combustion are examined.
The thermochemistry of divalent, tetravalent, and hexavalent sulfur compounds,
the relevant bond strengths of radicals, and the kinetics of oxidation processes
are discussed. The entropy and heat of formation measured experimentally or
estimated are presented for selected sulfur molecules and radicals.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS C. COSATI Field/Group
Air pollution
Sulfur inorganic compounds
Sulfur organic compounds
Thermochemistry
Reaction kinetics
13B
07B
07C
07D
18. DISTRIBUTION STATEMENT
RELEASE TO PUBLIC
19. SECURITY CLASS (ThisReportj
UNCLASSIFIED
21. NO. OF PAGES
57
20. SECURITY CLASS (This page)
UNCLASSIFIED
22. PRICE
EPA Form 2220-1 (9-73)
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