MECHANISM OF GAS-PHASE OXIDATION OF HYDROGEN SULFIDE AT

H I G H TEMPERATURES

A. V. Chernysheva, V. Ya. Basevich, V. I. Vedeneev, and V. S. Arutyunov

UDC 541.124:541.126:542.943:546.22 I. I

A kinetic model of oxidation of hydrogen sulfide is proposed. The model contains 201 elementary

stages, 23 particles, and satisfactorily describes the experimental data in a wide range of temperatures and pressures.

Hydrogen sulfide is contained in natural gas as an impurity, is obtained as a by-produc t in many processes,

and on oxidation and combustion as a function of the conditions yields sulfur, a useful product, and sulfur dioxide, in

most cases undesirable from both a technological and an ecological point of view. Unfortunately, it is currently

difficult to say that the mechanism of the reaction of H2S with O z is adequately understood in all of its aspects. For

this reason, further studies of this process are required for both practice and for the theory of gas-phase kinetics.

Important experimental data and theoretical hypotheses which make a large contribution to the study of the

mechanism of oxidation of hydrogen sulfide are given in [1-6]. A large number of basic findings and measurements

are reported and theoretical generalizations on the kinetics of the reaction of hydrogen sulfide with oxygen are made

in many articles reviewed in [7], in later studies, for example [8], and research up to the present [9-I 1 et al.]. The most

complete kinetic scheme of combustion of hydrogen sulfide is contained in [10]. The mechanism of oxidation of H2S

is given there, which includes 57 elementary reactions with the participation of 17 particles.

By analyzing the existing schemes and conducting quantitative estimations, it will apparently be possible to

conclude that there is still no sufficiently completely detailed kinetic mechanism which would permit equally

satisfactorily quantitatively describing the experimental data in a wide range of conditions with respect to the

composition of the mixture, temperature, and pressure with one set of reactions and rate constants.

An attempt was made in the present study to construct such a mechanism. Due to the complexity of the

reaction and primarily due to the lack of reliable kinetic data, the proposed scheme should be considered a first

approximation subject to fur ther development and definition. It should be noted that a relatively large number of

probable elementary reactions is included in the mechanism of oxidation of hydrogen sulfide based on kinetic

considerations, but there are no direct confirmations nor data on the rate of their occurrence. The only way to judge

the satisfactoriness and noncontradictory nature of the mechanism obtained in this situation is to compare the

parameters calculated with it with the experimental data. The correspondence obtained should only be considered a

necessary, but not a sufficient condition.

Detailed Kinetic Mechanism. The experimental material in the literature permits hypothetically naming the

basic particles which participate in the reaction of oxidation and combustion of hydrogen sulfide at high temperatures.

These are the starting molecules of H2S and O2, sulfur-containing intermediate and final products S, S z, SH, HS z,

H2S 2, SO, $20, HSO, HOS, HSO 2, HOSO2, (HSO) 2, SO2, SO3, and all radicals and molecules involved in oxidation of

hydrogen, H2, OH, H, O, HO 2, H202, and H20 (which is justified by the appearance of hydrogen as an intermediate

product in the reaction of oxidation of H2S): a total of 23 particles. After preliminary estimations, 164 reactions involving sulfur-containing particles were written out (Table 1 ), of which only a small number was studied previously,

and whose rate constants had been determined, if only once. Most (although not all) Of the remaining reactions were mentioned in some way or other and discussed in the literature, but the rate constants were apparently not determined

or they were determined for one temperature. For this reason, semiempirical estimations of the activation energy were

N. N. Semenov Institute of Chemical Physics, Academy of Sciences of the USSR, Moscow. Translated from

Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 9, pp. 1956-1966, September, 1990. Original article submitted July 13, 1989.

0568- 5230/90/3909-1775 $12.50 �9 1991 Plenum Publishing Corporation 1775

T A B L E 1. Detailed Kinet ic Mechanism of Oxidat ion and Combust ion of Hydrogen Sulfide

Reaction

1. 0 1 1 + l l : = H + H 2 0 .." H+II20=t I~ .+OtI 3. O I I + O = H + O z 4. H- -O==OH+O 5. OH+it =O+H~. 5. O + t l = = O H + H 7. O t I + O H = O + H z O 8. O + t l z O = O H + O H 9. H + H + M = H z + M

i0. ti,,.+ M = H + H + M 11. O - , O + M - - 0 z + M 12. 0 2 + M = O + O + M 13. O t t + H + M = H 2 0 + M l-i. } I ~ O + M = H + O H + M 15. O + I I + M - - O H + M 15. 01-t+M = O + } I + M 17. 0 t I + O H = H . - + 0 2 "18, 1tu+O-.=OH+OIl 19. 11 + 1tO,_,= H_~+O,_, 20. I I2+O.~=H+HO: 21. I I+Oz+M=itO.~+M 22. 11()._,+ M = H + O z + M ""' l i+ l tO OH+Oil 2~. (ill + O H = H O 2 + I t 25. (.)+}IO,a=O2+OH 26. O._,+OH=O+HOz 27. OtI+HO,.=O~.+}I=O 28. (_)=+II=O=OH+HO= 29. tI+HO_~=II=O+O 30. }I_~O=H+H02 31. OH+H202=HOz+HaO 32. ll~ L~+H_oO=OH+H2(L, 33. H+HzO. ,=H20+OH 2A. OH+H.~O=H+H20z 35. Ot I+OI t+M =HzO2+M 35. I I : 0 2 + M = O H + O H + M 37. O+HzO~_=O2+H20 38. O : + H z O = O + H 2 0 z 39. } t + t t 2 0 ~ _ = H ~ _ + H O 2 40. I IO.~+H:=H+H20: 41. 1t()2+ It0.2= HzO-.+O-. 42. ll,_O2+O2=t-lOz+H02 43. O+lizO.~=HOa+OH 44. HO_o+OH=O+H=O: 45. S H + O 2 = H S O + O 46. H 2 S + M = S H + H + M 47. H + S H + M = H 2 S + M 48. S i t + S H = t I 2 S + S 49. S + H 2 S = S H + S H 50. t4+Slt = H a + S 51. } I+ I t2S=H2+SH 52. II_,S2+M = H ~ S + S + M 53. S+H~S+M=HzS, ,+M 54. H+I t2S :=H2S+HS2 55. H+H2S2=I i2S+SH 56. t I+H:S2=H2S+HS2 57. SIi+Hs-_=H~S+S2 58. 11S2+M=SH+S+M 59. SH+S+M=HS~.+M G0. I I S z + M = H + S e + M 131. I I + S + + M = H S z + M 62. S+SII=S~_+tI 63. S l l + S H + M = H 2 S e + M 54. H S ~ + S = S H + S :

A* k c a l / mole

- 15 2 , 4 . 1 0 ' " - - 1 5 1 .14. lO It - t7 4 , 1 6 - 1 0 ~ - 17 7 . 8 - 1 0 'n

" 6.9' 10" - '2 1 , 5 . 1 0 '~

- ! 7 t , 4 4 - I0 '+

-17 t .51 . t0" - l i t ' , 3,6. t tP - It I:; 1 ,74 .10' : ; - I IS 1 , 8 - I 0 ~'

! I~ - ' l iP:: - - l + q "

- I f ' , 3.6-10'" -- 1 l~ 8 ,3- I<H ~ - I I I I 1.4/, . 10'" - I t l l 3 . 1 . 1 0 t3

-- !!t 6 -107 - t!~ 2.5'1 t'~ --.,i; 6" 10 9 -.',,, 2.1" 10"' - - ' J 4.14.10 :+ - -G7 5,7.10"-' -37 2.10 '~' . 27 1,62.10" - 5 't 6.10 '0 "-,i 9.43-t0 t~ - 7 1 6 . 1 0 9 -71 9,9"10 '0

"' 6- t 0 ~ -7, i 5,28.10 s - 3 t 7,8"t09 +31 8,45.109 -t;i; 7,05.109 4-. ~i+; 6,4.108 - .5 t ) 1.6.10 s +5t~ 4,07.1013 --t- , , 2,8"10 '+ +42,5 4.77.10 '~ - l t~ 7 , 1 0 9 + If; t.6.10 o -40 2.5. l0 s +G0 3 . 8 . 1 0 " -14 2.8.10 '~ +14 2,9.10' - 3 0 6.10 '0 +91,5 4,6.t01' -91,5 3,6-10 ~

-8 ,6 1,2'1@ o +8,6 6.10 o

-20.3 1.5.10 '~ - 11,7 t , 0 8 ' 10 '~ +57,6 6-10" -7,7.6 3.6-109 -21.6 5.2.t0 '*

"3" .3 - _ ; ) , o 6 .10" -33,3 6' 109 -31.3 1"t0 'c +79.2 6. t0 ~

-( ,) - , J,_ 3.6.10 '~ +(30,2 6.10" -60,2 3.6.10 9

19 '~ 7 10 '~ -~i5,2 -22,7

L ' .

kca i / mole

5,2 2V.4 -7 ,8 15.9 7,0 G 8.9 O,O

17,0 0.~

)5.~ 0+0

20.~

20.U 0,0 OILG 20. G 39,t~

56,0 0,0

28,8 o.0

3%6 0,o

3,2.10 'o [ 0,0 6.10 ,~ 5,8

Litera- ture

See text

[17]

[18]

[10] [17]

[2o1

[21] [201

Variant No.

I i 3 -', 5

' 776

T A B L E I ( con t inued)

Reaction

65. H S.~ + I-t52 = I 128._,+ S: (~(i. tl+HS,_,+ M = It-S,_+M (;7. I i a S e + M = H + H S : + M (i8. II+HS~_= t ieS+S (i9. 11+HS2=t t e+S: 70. I t + S + M = S H + M 7l. S H + M = H + S + M 72. S + H z S ~ = S I I + H S : 73. S,.+O+M = S:O+.M 74. S+O. .= SO+O 7.5. S()+O._,=SO2+O 7(i..q+(l..+.M = SO_~+M 77. ,SO=,+M = S • 78. S+O+/H = SO+.'q 79. SO+M =S+O+.M 80..'4 + SeO= Sa+S(-) 8 I. SO+ SO:,= SO.2+SO: 82. SO+O..,+.M = SO:,+M 83. SO.~+~ =S()+( ) , .+M 8~. SO+SO---- SO._,+S 85, SO,_,+S = S()+S() 8(L S ( ) + O + M = S ( ) e + M 87. S()..+M = S O + O + M 88. S O : , + S = S O + S O . 89. SO+S_~O=SOo+S2 ill). O+SO.o+M =SO: ,+M 91. SOa+M =SO._,+O+M ( ' ) ,)_. O + S : O = S O + S O q" O+SoO=O~+So �9 q l O+SOa=SO_o+O: 95. S~.+O=SO+S 9(i. S~O+M-:--SO+S+M 97, S O + S + M = S , O + M 98. S + S + M = 5 . ~ + M 99, S ~ + M ~ S + S + M

1(~). SH+O-_=OH+SO I()1. S H + O 2 = H + S 0 2 102. S H + O = S O + H t03. S H + O = O H + S 104. S H + O + M = H S O + M 105. SH+OH =II.~O+S 101i. S H + S O = S . , O + H 107. S,.O+H----SH+SO I08. S H + S 2 0 = H S : + S O 109. H S , , + S O = S H + S 2 0 110. SH+OH=H.~S+O I l l . H~S+O----SH+OH t12. S H + H O ~ = H S O + O H

13. S H + H S O = H 2 S + S O 114. S H + H O 2 = H 2 S + 0 2 t15. H~S+O_.=SH+HO: t16. SH+HO- .=H202+S

17. S + H 2 0 2 = S H + H 0 2 t 18. SH+H2Oe=H2S+HO., 119. HO,~+H2S = SH+H~.02 120. SH+HSO~--H~S+SO: I21. S + H S O 2 = S H + S 0 2

9 9 ' I.,. SH+SO~=HSO+SO.~ 123. H S O + S O : : S H + S O a t24. SH+HSO., = H~.S+SO,. 125. SH+HOS=HS.~+OH 126. H ~ S + O H = H , O + S H 127. S O + O H = S O , . + H

All .

k c a l / mole

-9 ,7 - (19,,q -(;9,9 - 12.3 - 4 3 -~2 ,9 +82,9 - 1 3

-113 -6 .1

- 13.2 -137 +137 -121.1 -124,1

-21.5 -48,7, -95 ,9 + 95,9

-7,1 =7,1

- 131,2 + 131,2 -41,4 -28,(; -82,7 +82.7 -43 .7 -15,4 -35 ,3 - 2 2 , 2 -~80,4 -80,4

-101,9 +101,9

-24 ,5 -54,4 -41 ,2 - 18.4 -81,1 -35,1

+8.1 - 8 . 1

+1t ,8 - 1 t , 8

+9.8 -9 ,8

-18 ,8 -51 ,6 -45 ,9 +45,9

~ ; 3 , t

+5,7 - 2 . 9 +2,9

-28,5 -19 .9

+I .6 -1 ,6

-41 ,9 -18 .8 -26 ,5 -29 ,9

A ~"

6. I(P 3,1J-7~I ~'

6. I(I" 6. lit" 6. I0 ~'

6.1(I ~ (;. 10" 6.10 ~*

1.4-ll~" 1,4- 10.' 3,(;-I0"

6. l(J"

6.10" (;. 10"

1.2-tO" 1. i ~)"' 6. I0" 5. l i p 6 t 0 "

3,2- ~q)'" 8. l fP: 6.1()" 6. I(P

3,9. lq)"' 6.1W' 6. l(i" 6- IO"

1.3.10." 6. t 0" 6 . I 0 ~'

3.6.10 ~-' 1. l 0 :~ 6- 1() '~

1,1.10 ~ 2. I0 ~

9,(i 10 > 9,6. t0 '" 3.6.109

6.10" 6.10 ~' 6.1():' 6. I0 "~ 8. I0 "~ 6,10 ~ 6' 109 6' 109 6.~09 6.t09 6.10'o 6- t 0" 6. t0 ~ 6.10 ~ 6.1()" 6. t()" 6-1()~ 6. I() ~ 6. t0 .~ 6. t0 ~

E,

kcal/ mole

Litera- 1 ture

['2'e. 23 ] I" 2. 23 ]

I2/,} I1()]

I2r,]

12~;. 27 } ' ) '~ ' ) ( } l

[3o1

131]

[ 3 2 ]

I22] [33]

[22]

Variarlt No.

6 . 1 0 9 3.109 4. I0,.~

[34] [22, 23]

r ' . 2 _

"-7"

§ -7"

+

i "m

"-F

..2._

-2-

-7"

1777

1778

T A B L E 1 (continued)

Reaction

128. } I : & + O H = H 2 0 + H S 2 129. I t 25 :+OH=HOS+H=S 130. H>:+OH =H..O+S_. 131. S + O H + M = H O S + M t32, 50 , ,+OH+M=HOSOa+M 133. HOSO2+M=OH+SO2+M 134. H S O : + O H = H 2 0 + S 0 2 135. S + O H = S O + I t t36. H S O + O H = I I : O + S O 137. SO: ;+OH=HOS03 138. I I : S + O = t t S O + t I 139. HSO+H--O+H2S t40. H > ~ + O = S H + S O 141. HS2+O=OH+S2 142. H S O + O = O I t + S O t43. H S ( ) + O = S H + O : 14t I I : , ' ; . ,+(}=OtI+HS: 145. II :S,_,+O=tI:S+SO 145. HSO2+O----01t+SO- 147. H S O 2 + O = H + S 0 3 148. IIOSO2+O=HO._+SO: 14{). It.%+O._,=SH+SO: t50. ll,<: + t102 = It202+S.., 151. H ~ : + H O : = I t 2 S 2 + O : 152. t tS :+HSO=H2S2+SO t53. HSa+HSO:=H2S:+SOz 154. SO+H+M-=HSO+M 155. t tSO+M = S O + H + M t56. S{)+ HO..= ttOS+O.. t57. H O S + O : = S O + H O ~ t58. SO+H2S.-=S20+HzS 159. SO+t lOS=S~O+OH t6(}. 5()-,-HO802= ttOS+SO~ 161. H S O B + H = l t : + S 0 2 162. II~-SO2+M = H S O : + M 163. HSO, .+M=H+SO2+M 16s S : O + H = O H + S 2 165. S : + O H = H + S 2 0 161i. I]OSO~.+H = t t :+SOa 167. t I S O + I t = t I : + S O t68. SO : ,+ I t =OI i + SO: 169. I I :S . ,+HO:=HaOz+HS: 170. S + I I O : = O H + S O 17 I. S . :+HO:=OH+S~O 172. SO:+HO~_=SO~+OH 173. SO:+HO2+M=HO~SO2+M 17& HSO+I tO,~=H,O:+SO t75. HSO2+ItO2=H~O~+SO: 176. HO:+ttOSO2=H~O~.+SO: I77. I t 8 0 + O 2 = 0 H + S O 2 t78. H O S + S = S : O + H 179. H S O + S = S H + S O 18(I. I-ISO+S_.=S~O+SI{ 181. t t O S + ~ = S 2 + O H 1822 HSO+SO-=HSO~+SO 183. S+HSO2=SH+SO~. 185. I-tS:+O._, = OH+S20 /$5. S2+O~_=SO+SO 18(i. I-I:S+O=tt.~+SO 187. S+HO2=SH+Oz t88. . ' ;2+HSO_,=HS2+SO: 189. 1 I S ( ) + t-t = S H + O I t lq0. S t l + S O : = S 2 0 + O H

A l l .

k c a l / mole

-48,1 9 I

-57,8 -60,.'~ -31 +31 - - ~ ; )

_ . ) 9

-7 .8 -31 + 10,'i - lO,'l -_% - ~ l , t - 6 1 . 4

-36,9 -31,4 -66.5 -38,3 - 1 9 , 3

9{ - . 3 ,3 -58,1 - 9 8 - % 3 -3()

-6 ,9 -4{) +40

+8 - 8

-33,4 -30,6 +12 -40,2 - 6 3 +63

+t .3 - 1.3

-56,3 -65,6 -18.8 -18.8 ,61 ,8 -51 -20,4 -31 -48,7 -25,6

-3 ,9 - 74,6 -53,1 - 4 3 -3'1.3 - 4 1 , 5 -25,~ - 19.9 -36.3 -28,3 -52,9 -37.3

+2,5 _ 9 0 9

+21,8

5. I0" 6-10 ~' 5. I0" 5.10 !)

2,4.107 6. t0 '~

4,6-10 "~ 6-10 ,~ 6. tW'

2,4.1(_) 7 6- 11}" 6. lip 6.10 ('' 6- 10 :) 6.10 :~ 6 .11) 9 ti. t0 v 5. IW' 5 . 1 0 9 6.10 ~ 6- ]0 !' 5.1(}" 6- I[} 9 6" 11) !' 6. I(P 6-10 '{' �91 109 6" 10:' 6" ~0" 6' 10." 6-10." 6. t0 9 8- I(P

2.3. t09 5,1-t0 s

6" 1(} 8 6-10 '~ 6.10" 6. t0." 6. t09 6.10 9 6- I{P 6. t0." 6- ](}'~

2,6.10 .~ 6.10: 6.10." 6- t09 6.109 t.106 6.10" 6 ' 1 0 9

6. t0" {i. 10 -~ 6.1(} v 6 .10 9 6- t0 ~' 0.0 (i. t0 f' 1 . 1 ( } 9

6-10 .~ 6 - 1 0 "~ 6.1 (I '(~

k c a l / mole

0,0 21.6

0,0 0,0

-3.8 34,8

U,0 -3 .8 t9,3 8,9 0.5 1.2 0,0 2,3 3,6 0,0 1,9 6,6 42 {},0 .5,4 5,.'i 4.0 5,9 3,0

41.5 17.5 9,5 3,2 3.8

19,5 1,5 0,0

58,8 20,4

8,5 0,0 0,0 6,8 6.8 0,0 0,0 6,4 0.0 0,0 5,1 1,7 0,0 0,0 0.7 2,9 1, I 5,1 6,5 2,4 0,0

i0,0 0.0

t3,4 6,4

27.8

Litera- ture

[35]

[361

[371 [381

[39. 401 [4tl

[42]

[1o1 [to]

Variant No.

1 2 3 i 5

-r-

.22

-2-'

- . .

-7

.2.-'

"-7-

-7-

s

- -2

-7- ..2-'

--i-,

+ +

-7-

+

_2.

2

I (;

"T- ....

= l - r - I

_T_ - -

4l=-

; I ' t

-7-

T

- 7

..2_'

.2_

-7 -F"

-i- +

.2_ §

- I - : -

T A B L E 1 (cont inued)

Reaction

191. SO2+1t=SO+Oti 192. S+HO.~=SH+O2 193. H S O + 0 2 = S O + t t O z 19t. HSOe+O.-=SO2+HO2 195. SO+tl~.S= S~O+Ii~. 196. S :O+I t2S=SO+H2S2 197. SOz+H_.S=HSO2+SIt 198. S H + O z + M = H S O z + M 199. HOSO~+O_. =HO2+SO:, 2~ . 2HSOe+M= (HSO)..+O~+M 201. (HSO) ~+M = t t S O + I t S O + M

A/q, k c a l / m o l e

--29.9 - - O / , t

-?,.T +7.4

-19,8 -~33,4 -'28,5

- I I 7 +.4

+ 5 t l

A :v

1;. l i p 5. f l )~' tl. 1(t +' 6- | l I~' 5 ,1( l lo 6. l ( i~ 6, 10 9

,'7,7, ItF" tl. | 0 9

3,6.109 4" 10 I::

mole

' i t ( ,) ,)

17 92

36.6 28,4

3,3 1,5

42

Litera- ture

m

[43]

Variant No.

1 2 3 i 5

-f-

b +

i = -7

i

§ ' -2- i §

-% .4--

*Concentra t ion, mole / l i t e r ; time, sec.

Note: The values of the constants for the corresponding reactions

available in the literature are reported below: 47) k47+s 0 = 101~

liters-mole-lsec -1 [18]; 74) k = 6.3.107T ~ liters.mole-lsec -1 at 250-

2200 K [44]; k = 1.26.109 liters.mole-lsec -1 at 250-450 K [45]; 79) A =

1.6.10111iters.mole-lsec -1, E-- 110 kcal /mole at 3300-6000 K [46], A =

4.10 n liters.mole-lsec -1, E = 107.2 kcal /mole at 3000-5000 K [47]; 82)

kTs/ksz = 0.51-2.1 for 300 K and P = 760 torr [48]; 91) k = 105 liters.mole-lsec -1 at 1740 K [49], A = 1.4.1012 liters.mole-lsec -1, E =

63.3 kca l /mole at 6000 K [50]; 92) k = 8.9.10 s liters-mole-lsec -1 (298

K) [51]; 95) k =6.72.109 liters.mole-lsec -1 (409 K) [52]; 100) at 298 K:

k < 6-103 liters-mole-lsec -1 [53], k < 8.9.106 liters-mole-lsec -1 [54],

and k < 2.4.102 liters.mole-lsec -1 [55]; 103) for n -- 0.67 [33]; I11) k =

2.2.107 liters.mole-lsec -1 at 293 K [56]; 126) A = 3.5.109 liters.mole-

Xsec-1, E = 0.13 kcal /mole [22]; A = 3.5.109 liters-mole-lsec "1, E =

0.114 kcal /mole , and k = 102T 2"43 liters.mole-lsec -1, E = --1.46

kcal /mole for 2 .5-450 K [57]; A = 109 liters.mole-lsec -1, E = 0.78

kcal /mole [58, 59]; 132) k = 1.6.1019T -3"3 liters-mole-2sec "1 [22]; 135)

k -- 4.101~ liters.mole-lsec -1 (298 K) [22]; 138) E > 3.34 kcal /mole [60,

61]; 162) k -- 5.1.109 at 1660-2120 K [38]; 177) for HSO + 02 = HSO 2 +

O, k = 1.2.104 liters.mole-lsec -1 (298K) [62]; 185) k = 1.4.103

liters,mole-~see -1 (409 K) [51]; 194) k = 1.8.108 liters-mole-lsec -1

(296 K) [62]; 199) k = 2-108 liters.mole-lsec -1 (298 K) [63, 64], k =

2.6.10 s liters-mole-lsec -1 (298 K) [65].

made for these reactions based on its correlat ion with the heat of the reaction, pr imari ly with the Semenov equations

[4] for radical reactions. For most of the reactions which take place without per turbat ion o f the rules o f multiplicity,

with an unknown preexponent ia l , it was statistically derived with the average for bimolecular reactions, 6.100

liters.mole-lsec -1 for bimolecular reactions, and 3.6.108 liters2mole-Zsec -1 for t r imolecular reactions. The rate

constants of the forward and reverse reactions were correlated with the equi l ibr ium constant (the reactions which take

place with heat release were considered the forward reactions). Only the reverse reactions whose activation energies

were _<20 kcal /mole , except for some nucleation reactions, were considered reverse reactions. Af ter prel iminary

calculations, some of the rate constants were corrected (adjusted) to obtain a better fit between the calculated and

experimental data, but were subsequent ly not changed. The first 22 pairs o f fo rward and reverse processes relate to

oxidation of hydrogen and were taken with their rate constants almost unchanged f rom [12].

1779

T A B L E 2. M a x i m u m C o n c e n t r a t i o n s o f the S ta r t ing Subs tances and

P r o d u c t s ( m o l e / l i t e r )

T.]: (p, t o r r ) Variant No.

Sub -

stance

11,.>S (I.,

S I I S t IP-;:~

I I ~,,_, ~ t l ~,1 I:, ,~<,( }

5{ t:: list) IIOS 11~4{),, l l( }.,4 O: {11~40): (HI II {} I [ ( ; z I1: I I...() Ilzt}:~

tINII i ; ~ i l

: l . I . l l ~ - i B,7. I l l - i

6- I l l 7 5 : t - I I } - s 8,7- I l l - " 2,Y: I l l ~ 3,2-10-."

t,}. I l l i; 3 5 . l i ) - '~ fl, l - 1 0 -,~ {i,t;. li i - 4,8. l i t - { } 1,2.10 - s

3.9. l F t - ; I .~-1{ t -~'~

2. t t l - r 7,3- I0- r, 9,B. l l l - r ' 5,, i- I l l :,

3 10 -~

2,7. IO :, 6,2-Ill ;

lilNI25

2,G, l { i - ; 3,9. I(} '

1,6. l i p ~ 1 ,1 .10 - ' [ {1.1.1{1-- ~ I t.2.10 :' 9 , 4 . t 0 " '; 3.4. l l ) " 1,5. l l i ~,t}" 1{~ :r

I J l . l i l '; 7,7.1l} ':: 3)4. I0 '~ 1,2.1(I ;

2.1(I i ,

3,5. 111 t~ 7.3. l{I ~'' 9,.~. Ill il 3.1.1{I I<' 1,7. 111- 8,5.1{t :' 1.9.10

GI8{13.5,

1.1" tip ; 2,1. Ill- ' 3,3- Ill- : 3.7-11) ''~ 1,2-t{}-" 1,3- |l1-5 1,1-10 "

3,3. l l i '; <'4{. I( i ' 3,7- lit :' 1,3. I{} ;

9.1{I " J.~- lip ~'

I. I l l : 9 . 1 . | 0 ~' 7,3" UI v_' :I.I. |0 -' 2./I , 1(} ;

2.10-" 2,2.1(I -~ 5,2. ll}- ~' ~J.2. I/i-:' 1,3. l(t "

"qt~ (2.5;

l,I.Ui ' 3,:~. l I I- :' 3.2. lU " 2,2.11)- '~ 1,7,: 1it- ;I

l. l{} '~ 2.1. Ill i-.. �9 "l,5. Ill l , l . I l l r, 2.3. It) " 4. { ; - I I } ~ 3 , 1 - I l l l:~ 1,2" l f l la I . t i . l i i t'' 2 ,7- l i i ,:'. 9,9- I l l 17

I. l i t 7 .~,?I- l i i ~ 1.5. l f ) - `~ 9,!t. 1 ( ) t

Ii. 111 6 l . t . l l } - ~ 2 , T - l i l ~l

111~;13~17m

7.5" 10 2 8,4.10--' 3,6. lit " 2.3.10 1.2. t0-~ 4, t . I O- :~

5 .10 ; 1,7.1(} :: :-},3- Ill : 1,8- 10 :

I - 1{} : 1,8-:11t'

3, I0- 3 , 3 . 1 0 :: tU}- lip :' 1,1.10 4,7.1~) : 1,8.10 ~ 7.4-Ill . 1,5- I l l 4,5.1(I ~ 6.5. t0 -' 2.2-Ill ;

1 212:1 ~ l '_ql!l ~

3,3.10 :: 1,7. I(t- :: 2,4. li) -'~ 7,9. UI- s 2,3.10- 3,8. l l i - 1,2. I(t :' '~,3.1() s 7,9. I(} ; 9.2- It)- 2.5. I() :' 1 ,.-,. 10 1.7.10 ~o IA. I l l - ',

1. 9. t{} ~'' 7,6. tO " ~ 2,ti-111 8 1.t;. l ip ~ 7,2. 111- !' 2,1. UI 7 1.{) �9 Ill ,~ 1,2. lli a 2,7. lql

R e s u l t s o f t h e C a l c u l a t i o n s . As no t ed p r e v i o u s l y w i t h r e spec t to the a p p r o x i m a t e c h a r a c t e r o f the k i n e t i c

mode l , i t is no t poss ib le to c o u n t on the r i go rous c o r r e s p o n d e n c e o f the c a l c u l a t e d and e x p e r i m e n t a l data. T h e

c o r r e s p o n d e n c e b e t w e e n t h e m shou ld be c o n s i d e r e d s a t i s f ac to ry w i t h a p r e c i s i o n o f less than o n e o r d e r o f m a g n i t u d e .

The c o n d i t i o n s f o r c o m p a r i n g the c a l c u l a t e d and e x p e r i m e n t a l da ta w e r e s e l ec t ed in a w i d e r ange o f t e m p e r a t u r e s T,

p ressures P, and c o m p o s i t i o n s o f the m i x t u r e to ob t a in a s u f f i c i e n t l y gene ra l p i c t u r e ( T a b l e 2). T h e ca l cu l a t i ons w e r e

c o n d u c t e d w i t h a k i n e t i c p r o g r a m w i t h o u t c o n s i d e r a t i o n o f d i f f u s i o n in the n o n i s o t h e r m a l v a r i a n t (w i th c o n s i d e r a t i o n

o f hea t re lease a c c o r d i n g to the da t a in I13, 14] and hea t t r a n s f e r ) and the i s o t h e r m a l va r i an t .

1. T o = 618 K , "average" t e m p e r a t u r e o f the s e l f - i g n i t i o n p e n i n s u l a , n o n i s o t h e r m a l v a r i a n t s ( 1 - 3 , T a b l e 2).

A c c o r d i n g to [15], in the 5 9 0 - 6 3 0 K t e m p e r a t u r e and l - 1 0 0 to r r p re s su re r a n g e , a s e l f - i g n i t i o n p e n i n s u l a w i t h th ree

bounda r i e s is o b s e r v e d f o r s t o i c h i o m e t r i c m i x t u r e s o f HzS wi th 02 , and the r eg ions o f c o m b u s t i o n w i t h r e spec t to the

p ressu re are b r o a d e r the l a rge r the d i a m e t e r o f the vessel . O n l y the s e c o n d and th i rd b o u n d a r i e s in a vessel o f the

larges t size w e r e e x a m i n e d in o r d e r to no t take in to c o n s i d e r a t i o n the h e t e r o g e n e o u s r e a c t i o n s on the wal l . T h e

ca lcu la t ed d e p e n d e n c e o f the m a x i m u m t e m p e r a t u r e g r a d i e n t ( A T / A r ) m ~ x on the p r e s su re is s h o w n in Fig . I . T h e

r eg ion o f the smal les t c a l cu l a t ed r e a c t i o n ra te a p p r o x i m a t e l y c o r r e s p o n d s to e x p e r i m e n t a l r e g i o n I I - I I I o f the s low

reac t ion , a l t h o u g h it is s h i f t e d s l igh t ly to the l e f t to l o w e r p re s su res r e l a t i v e to it. We no te tha t t he t i m e scale o f the

r eac t ion c h a r a c t e r i z e d by an i n d u c t i o n p e r i o d nea r the b o u n d a r i e s has an o r d e r to tens o f s econds in t he ca l cu la t ions ,

w h i c h m o r e or less c o r r e s p o n d s to the e x p e r i m e n t a l da t a [15].

2. T o = T -- 898 K , s t a t i ona ry r a r e f i e d f l a m e [6], i s o t h e r m a l v a r i a n t (4, T a b l e 2). S t r i c t l y s p e a k i n g ,

c o n s i d e r a t i o n o f d i f f u s i o n is r e q u i r e d in the analys is o f a s t a t i ona ry f l a m e . I t is poss ib le to h y p o t h e s i z e tha t c a l cu l a t i on

o f i gn i t i on w i t h o u t c o n s i d e r a t i o n o f d i f f u s i o n wil l resul t in d i s t o r t i o n o f the t e m p o r a l c o u r s e o f the reac t ion :

p r o l o n g a t i o n o f the in i t i a l phase , i n d u c t i o n phase (no i n p u t o f hea t and a c t i v e si tes f r o m the r e a c t i o n zone to the f resh

m i x t u r e ) and a c c e l e r a t i o n o f its d e v e l o p e d phase ( the re are no hea t losses and a c t i v e si tes f r o m the r e a c t i o n zone) . T h e

above c o n c e r n s a o n e - s t a g e r eac t ion . In a m u l t i s t a g e process , because o f d i f f u s i o n in the f l a m e , a d d i t i o n a l a c c e l e r a t i o n

( s lowing) o f the r e a c t i o n is poss ib le due to m i x i n g o f c o m p o n e n t s s e p a r a t e d in space . F o r this r eason , the c o m p a r i s o n

o f the ca l cu l a t i on w i t h the e x p e r i m e n t a l da ta can on ly be q u a l i t a t i v e in the p r e s e n t case. T h e c a l c u l a t i o n was

p e r f o r m e d in the i s o t h e r m a l v a r i a n t w i t h the e x p e r i m e n t a l l y o b t a i n e d va lue o f the t e m p e r a t u r e .

1780

~,"[kiZS~ O, re l . units J

[A T/A ~]m~=, K/sea

l ' lg ~ I g

' i

/0 20

,/ JO

m

I L

+0 50 P, torr

1oo

r 7s

a, SO

0,25

g O/S

•

J

<2 !i 0.el o, z3 o, zs

t sec

Fig. 1 Fig. 2

Fig. 1. Dependence of the maximum temperature gradient during the reaction on the pressure for T o =

618 K for the stoichiometric mixture [H2S]o = 40%, [02] o = 60%, I, II, III: first, second, and third

ignition limits [15], line: calculation.

Fig. 2. Dependence of the calculated relative concentrations of the initial, intermediate, and final

products on the time for the mixture [H2S]o = 25%, [02] -- 75% (T o -- T = 898 K, Po -- 2.5 mm Hg): l)

H2S/(H2S)o; 2) H2/(H2S)o; 3) SO2/(H2S)o; 4) [SO/(H2S)o ]. 109; 5)[OH/(H2S)o ].102; 6) H20/(H2S) o.

The calculated dependence of the concentrations of the basic components of the reaction on time is shown in

Fig. 2. The calculated values of the maximum relative concentrations Y/(H2S)o, where Y = SO 2, H 2, OH, SO, are equal

to 1, 0.55, 0.93.10 "z, and 4.1-10 -2. The corresponding experimental values are: I, 0.67, 0.5.10 -z, and 2.5.10 -3. In

both the calculation and the experiment, a "two-stage character" of the reaction is observed: the hydrogen sulfide

reacts first, hydrogen accumulates, then the reaction of burning o f f of the hydrogen takes place. In the experiment,

the reaction time is one order of magnitude less, apparently due to not considering diffusion in the calculation, as indicated.

3. T O -- 1146 K, ignition in a shock tube, nonisothermal variant (5, Table 2). The delays in ignition of hydrogen

sulfide--oxygen mixtures at high temperatures and very high pressures are reported in [I0]. The high value of the

pressure makes it very probable that trimolecular processes of recombination with the participation of particles containing three and more atoms and occurring in the kinetic mechanism will take place in the bimolecular or

transitional region. This holds for reverse processes of decomposition. The rate constants of these reactions were not

precisely defined in the calculations, but a test was conducted which showed that the concrete rate constants of

recombination and decomposition do not exceed their limiting values. For trimolecular processes with null or low

activation energies, they are not higher than the number of binary collisions, etc. A comparison of the calculations and experimental data is shown in Fig. 3 (r:. ignition lag).

4. T O = T = 1323 K, combustion of rich mixtures of hydrogen sulfide and air, nonisothermal variant (6, Table 2). The degree of conversion of hydrogen sulfide into sulfur in the thermal stage of the Claus process was investigated

in experiments [16] on a semi-industrial setup. Gas containing -50% hydrogen sulfide (the remainder was impurities,

primarily CO2) is burned in air on a diffusion burner. Modeling which'hypothesizes combustion of a homogeneous

mixture can only claim qualitative agreement with the experiment. The kinetic curves for characteristic experimental

1781

. . O, JT, L~(~/LHz~3 o )

J20 1100 l

z~y8

470 -

3 , $ -

3j Z -

2T~

1000 T~g

I 0 ~ "" :/

[ �9 t [ I I 0,|5 0,• O, ffff 1,0 IO;~/T(K "1 )

2[S2]/([~#] ~- E"2S])

0,5 t 0,~ [ +

0,3 ~ +

t ,, ,

0,2

01~r L l ] I

0,8 0,8 7,0

Fig. 3 Fig. 4

H-

~ SeC

Fig. 3. Comparison of the parameter log (r[H2S]o ~ (#sec, mole/cm3). Points: experimental [10], line:

calculation.

Fig. 4. Relative yield of sulfur for different contact times, [H2S]o = 22.9%, [09.]o = 11.9%; T o -- T ---

1323 K, Po = 1.6 atm. Points: experimental [16], line: calculated.

conditions are shown in Fig. 4. The relative yield of S 2 is equal to 20%. It is 30-50% in the experiments. The

agreement can be considered satisfactory if we consider the fact that neither polymerization and heterogeneous

processes which accompany the formation of sulfur particles, nor their growth, coalescence, decomposition, etc., were

considered in the calculations. The results of the calculations of interest are reported in Table 2.

RESULTS AND DISCUSSION

It was noted above that the lack of quantitative information on the elementary reactions and the

approximateness of the estimations of the probable channels of the reactions and their rate constants will permit

considering the convergence of the calculated and experimental values only with respect to the order of magnitude.

Such precision was apparently obtained here. Based on such an approximate kinetic mechanism, it is hardly useful to

attempt to of:rain better convergence by variation of the individual rate constants.

All of the calculations were conducted based on the scheme of reactions reported in Table 1. The determining

reactions were selected with the following procedure at the same time as the calculation. The decreasing (with respect

to the modulus) order of the rates of the reactions which affect their concentration were determined at each time for

previously isolated "control" substances. The reaction was not selected if the modulus of the reaction rate was a times

less than the algebraic sum of the rates of all preceding reactions.

Almost all of the reactions were selected at least once during the calculations for a value of a = 0.2 and

isolation of the following 16 substances as "control" substances: OH, H, O, HO 2, H 2, H20, H2S, SH, S, H2S 2, O 2, HS~,

S 2, SO, SO 2, $20. The reactions selected for the rougher selection for a value of a = 0.4 and based on one "control"

substance H2S are indicated in Table 1 by the symbol %" for all calculated variants. Note that first, both the same and

different groups of reactions are selected for the different conditions and second, the number o f processes selected in

this way is relatively large, from 45 to 167. This number of reactions can naturally be reduced if necessary with an acceptable loss of precision with respect to the calculation based on the complete detailed mechanism. The most

important reactions are those indicated by the symbol "+" in all experiments in Table 1.

I782

The total contribution of the individual reactions was also determined with the value of the integrals of the

rate (/i = f Widt , where W i is the reaction rate and t is the time) which were calculated at the end of each reading. T

Using the values of the integrals li, it is possible to separate the reactions with a relatively large contribution which

determine the direction of the reaction. For example, in the conditions of a self-ignition peninsula, these are the reactions

It,,S + 0., = SH --' H(),, (t15) SIt +O._, = O H + SO (100) SIt + O. = SO,., + II (101)

Stl _ 02 + M = HSO~ +.M (198)

S() _L ~)., = SO., --' O (75) II.,S -1., () . - SH -r" OH (t11) If.,S + ()It = SfI + H..,O (t2(~)

The mechanism discussed should undoubtedly be considered a first approximation which is probably

sufficiently satisfactory for high temperatures. Attempts to apply the proposed mechanism to relatively low temperatures and to the data in [3] without any changes have been unsuccessful so far.

We would like to thank M. G. Neigauz, the author of the kinetic program, for providing the program and constant assistance in performing the calculations.

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6. 7.

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18.

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1783

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1784