Molecular, Thermodynamic, and Kinetic Parameters of the Free Radical C 2H5. in the Gas Phase

Article abstract of DOI:10.1023/A:1023430620009

The wave function, energy, equilibrium geometry, and normal vibration frequencies of the ground state of the free radical C₂H ₅^. were obtained by ab initio calculations with inclusion of electron correlation effects at the

Full text of DOI:10.1023/A:1023430620009

Russian Journal of General Chemistry, Vol. 73, No. 1, 2003, pp. 75 84. Translated from Zhurnal Obshchei Khimii, Vol. 73, No. 1, 2003,
pp. 79 89.
Original Russian Text Copyright
2003 by Skorobogatov, Dymov, Pogosyan, Khripun, Tschuikow-Roux.
Molecular, Thermodynamic, and Kinetic Parameters
of the Free Radical C H in the Gas Phase
2
5
G. A. Skorobogatov, B. P. Dymov, Yu. I. Pogosyan, V. K. Khripun, and E. P. Tschuikow-Roux
St. Petersburg State University, St. Petersburg, Russia
University of Calgary, Alberta, Canada
Received April 12, 2001
Abstract The wave function, energy, equilibrium geometry, and normal vibration frequencies of the
ground state of the free radical C H were obtained by ab initio calculations with inclusion of electron correla-
2
5
*
*
tion effects at the UB3LYP/6-311++G level. The resulting molecular parameters were used to estimate the
thermodynamic functions of an ideal gas of C H . From the thermodynamic functions of C H , I , C H I,
2
5
2
5
2 5
C H , and HI and the kinetic curves of isothermal pyrolysis of ethyl iodide, the absolute rate constants of
2
4
elementary reactions of free ethyl radical and the mentioned iodine compounds were estimated. The dissocia-
0
tion energy ED,0(C H I) and the standard formation enthalpy fH
(C H ) were found.
2
5
298
2 5
The formation enthalpy of the free radical C H
It is strange, however, that among products of ethyl
iodide pyrolysis (iodine, ethane, and ethylene) no
butane was found [3, 21 23]. To explain this fact,
Semenov [24] proposed a chain pyrolysis mechanism.
2
5
0
[ f
1
H
(Et )] has long been taken to equal 107
298
09 kJ/mol [1, 2]. Early thermochemical studies of
ethyl radical have been mainly based of the kinetic
data on C H I bond dissociation [3 5]. However,
2
5
beginning in late 1980s, C H H [6 8] or C H H [9]
I + EtI
Et + EtI
C H I
I2 + Et ,
C H + C H I ,
2
5
2
4
bond dissociations has come into study for this pur-
chain
2
6
2 4
0
298
propagation
pose. As a result, a much higher fH (Et ) value
C H + I .
2
4
2
4
[
120 121 kJ/mol] has immediately been obtained.
0
Such a high fH (Et ) value contradicts all previous
298
I + C H I
I + C H ,
2 2 4
I2,
2
4
thermochemical data [10, 11] but is consistent with a
0
298
2I
recent quantum-chemical estimate for fH (Et ) of
chain
termination
1
25 kJ/mol [12].
2Et
C H + C H ,
2
4
2 6
Recently we reinvestigated pyrolysis of gaseous
Et + I
EtI.
ethyl iodide by an improved procedure [13] where,
for more exact dissociation C H I dissociation
2
5
It is readily seen that the chain mechanism [24]
leads to the following brutto scheme of ethyl iodide
pyrolysis.
0
energies E , experimental kinetic data were treated
0
with use of a theoretical [14] preexponent of a mono-
molecular C H I bond dissociation reaction. Ho-
2
5
0
wever, the fH (Et ) value obtained in [13] is fairly
2C H I
C H + C H + I .
2 6 2 4 2
298
2
5
low (114 2 kJ/mol) and we no longer consider it
correct. The aim of the present work was to find out
why kinetic experiments with ethyl iodide give too
The same brutto scheme follows from the mole-
cular mechanism proposed by Benson and Bose [3].
0
low E (C H I) values and, as a result, too low
0
2
5
0
EtI
C H + HI,
formation enthalpies fH (Et ).
2
4
298
Mechanism of ethyl iodide pyrolysis. According to
published data (Table 1), ethyl radical has very high
gas-phase recombination and disproportionation rate
constants.
EtI + HI
C H + I .
2
6
2
Therewith, the referees [3] leave room for a reac-
tion involving the free radicals Et .
kr
I + EtI
Et + I2,
C2H5 + C H
C H ,
4 10
2
5
kd
C2H5 + C H
C H + C H .
Et + HI
C H + I .
2
5
2
6
2
4
2 6
1
070-3632/03/7301-0075$25.00 2003 MAIK Nauka/Interperiodica

76
SKOROBOGATOV et al.
Table 1. Rate constants of self-reaction of ethyl radical in
the gas phase in the limit of high concentrations
surprising, very much hexane was found. Thus, the
following arbitrary scheme of gas-phase ethyl iodide
pyrolysis arises.
K 10 11, cm molecules s 1
3
1
Refer-
ences
8
C H I
3C H + 2C H + C H + 4I2.
2 6 2 4 6 14
T, K
2
5
kr
kd
sum
That means that the pyrolysis involves more reac-
tions than those mentioned in [3, 21, 24]. We con-
cluded that under quasi-stationary isothermal pyro-
lysis conditions [13] reactions (1) (9) develop in
gaseous ethyl iodide.
323
373
423
298
295
298
298
298
2.5 1.5
3.3 0.8
7 2
0.3 0.2
2.8 1.7
[15]
[15]
[15]
[16]
[17]
[18]
[19]
[20]
3.8 0.5
2.5
1.8
2.0 0.5
0.7
M
k
k
1
EtI + (M)
EtI + I
Et + I + (M),
Et + I2,
(1)
(2)
(3)
(4)
(5)
(6)
M
1
0.2
0.23
1.8
2.03
k2
k 2
The same brutto scheme has been accepted by
Yang and Conway [21] but with an augmented me-
hanism involving, together with the molecular reac-
tions in [3], the following processes.
M
k
k
3
EtI + (M)
C H + HI + (M),
2
4
M
3
M
4
k
k
I2 + (M)
Et + I
2I + (M),
EtI
Et + I ,
I2 + M.
M
4
2
I + M
k5
C H + HI,
However, neither in the Semenov’s chain me-
chanism nor in the mechanisms in [3, 21] we re-
cognize factors preventing butane formation, as long
2 4
k 5
M
k
6
HI + (M)
H + I + (M),
C H + I,
as the recombination rate constant k is very high
M
r
k
6
(
Table 1). Therefore, we have put in doubt the very
experimental fact of formation of equimolar quantities
of ethane and ethylene by the brutto scheme accepted
in [3, 21, 24]. We examined the composition of final
products of gas-phase pyrolysis of ethyl iodide
k7
Et + HI
(7)
(8)
(9)
2
6
k8
Et
Et + C H4
C4H9
C H ,
6 14
2
(
Table 2). Actually, we never found butane among
k9
final pyrolysis products (less than 0.01 wt% per
ethane). But, contrary to the schemes in [3,
Et + H
C H .
2
6
2
1, 24], the yield of ethylene was always almost half
Isothermal pyrolysis as a kinetic method. The rate
constants k and equilibrium constants K in schemes
(1) (9) are related to each other by Eqs. (10) and (11).
that of ethane (except for the lowest pyrolysis tem-
peratures, i.e. lower 500 K). And, what is the most
i
c,i
Table 2. Relative yields of products of isothermal gas-phase pyrolysis of ethyl iodide (with initial concentration [EtI]0)
Pyrolysis
time,
Relative yield (by weight)
[
EtI]0a 10 19
,
T, K
3
molecule/cm
min
CH4
0.06
0.001
0.005
0.009
0.003
0.015
0.0003
C2H6
C2H4
butene
C6H14
EtI
495
520
545
545
578
578
634
1.81
2.5
1.5
1.88
0.62
2.3
240
150
30
45
30
1
1
1
1
1
1
1
3.1
0.5
7.5
6.0
1800
200
25
0.3
0.3
0.37
0.57
0.50
0.75
0.54
0.015
0.01
0.009
0.006
0.01
0.21
0.35
0.15
0.63
0.05
25
10.5
10.5
1.6
30
30
1.9
a
[
EtI] is the initial concentration of ethyl iodine.
0
RUSSIAN JOURNAL OF GENERAL CHEMISTRY Vol. 73 No. 1 2003

MOLECULAR, THERMODYNAMIC, AND KINETIC PARAMETERS
77
Kc,1 = k /k , K = k /k = Kc,1/Kc,4, Kc,3 = k /k , (10) we obtain simpler expressions (15) and (16).
1
1
c,2
2
2
3
3
Kc,4 = k /k , K = k /k = Kc,3/Kc,1, Kc,6 = k /k . (11)
d
4
4
c,5
5
5
6
6
(
[I] + [Et]) = 2k [EtI] 2k [I][Et]
1
1
dt
M
M
Here ki
k [M], k
k [M], and [M] is the
i
i
i
M
M
+
2k [C H ][HI]
2k [I][Et]
2k [C H ][Et]
5
2
4
5
8
2 4
concentration of any third species M. In isothermal
pyrolysis, reactions (1) (9) are quasi-stationary,
k9[H][Et],
(15)
specifically, in reactions (1) (6) there is a highly exact
d
dt
6
([HI] + [C H ]) = k [C H ][Et] k7[HI][Et]. (16)
2 4 8 2 4
(up to 10 %, see [25]) equilibrium between starting
and final components, and only reactions (7) (9)
involve irreversible binding of ethyl radicals to form
the final products C H and C H (this was checked
in a special experiment in which ethane and molecular
iodone were heated in a glass pyrolytic cell up to a
temperature and within a time specified in Table 2;
therewith, among final hydrocarbon products we
found nothing but the starting ethane).
Under quasi-stationary conditions, the time deri-
vatives of concentrations are near zero and, moreover,
relations (12) (14) are valid. As a result, from the
differential equations (15) and (16) we obtain
algebraic expressions.
2
6
6
14
k [EtI] + k [HI][C H ] = (k + k )[I][Et]
1
5
2
4
1
5
+
k [C H ][Et] + 1/2k [H][Et]
8 2 4 9
The quasi-stationary conditions imply a highly
exact fulfillment of relations (12) (14).
k [HI][Et] = k [C H ][Et].
7
8
2 4
2
[I]st = (Kc,4[I2])1/2,
k [I ] = k [I] ,
(12)
4
2
4
st
From the above formulas we can obtain a simple
relation (17) between the concentrations [HI] and
[C H ], which we do not observe in our experiments,
Kc,6[HI]st
Kc,4[I2])1/2
,
k [HI] = k [H][I], [H] =
6
6
st
2
4
(
and a measured concentration [EtI].
2
[
C H ]
2 4
(
13)
k8
k7
Kc,3
=
,
k8
k7
(Kc,3[EtI])1/2
.
[
HI] =
[C H ] =
[
EtI] [C H ]
st
2
4 st
(17)
2
4
i.e.
The measured total rate of accumulation of mole-
cular iodine [W in Eq. (18)] is determined by the ir-
reversible consumption of ethyl radicals in reac-
tions (7) (9).
1
/2
1
2
1
4
[
C H ] =
Kc,3
+
(Kc,3)2 + Kc,3[EtI]
2
4 st
Kc,3[EtI])1/2
(14)
(
.
d[I2]
dt
d
3
2
1
2
Let us write kinetic equations for the free radical
W(t)
=
[C H ] +
[C H ]
2 6
6
14
dt
species I and Et and the intermediate components
HI and C H .
2
4
3
2
1
2
1
2
=
k [C H ][Et] +
k2[HI][Et] +
k9[H][Et]. (18)
8
2 4
d[I]/dt = k [EtI]
k [Et][I] + k [Et][I ]
1 2 2
1
Using Eqs. (13) and (17) we can remove from the
right part of Eq. (18) the unmeasured concentrations
[H] and [HI].
2
k [I][EtI] + 2K [I ]
2K [I] + k [C H ][HI]
4 5 2 4
2
4
2
k [I][Et] + k [HI]
k [H][I] + k [HI][Et],
6 7
5
6
d[Et]/dt = k [EtI]
k [Et][I] + k [I][EtI]
1
1
2
W(t)= 2k (1 + 0.5a )[C H ] [Et] .
8
j
2
4 st
st
k [Et][I ] + k [C H ][HI]
k5[I][Et]
2
2
5
2 4
Here and hereinafter we used the notation a =
j
k7[HI][Et]
k [Et][C H ]
k9[H][Et],
1/2
8
2 4
k K (T )/2k (K (T )[I ] ) .
9
c,6
j
7
c,4
j
2 j
d[C H ]/dt = k [EtI]
k [HI][C H ]
2
4
3
3
2 4
Using the resulting equation for W(t) and formula
k [C H ][HI] + k [I][Et]
k [Et][C H ],
(14) we can express an unmeasured quasi-stationary
concentration of ethyl radicals through measured
values [Eq. (19)].
5
2
4
5
8
2 4
d[HI]/dt = k [EtI]
k [HI][C H ]
k [C H ][HI]
5 2 4
3
3
2
4
+
k5[I][Et]
k [HI] + k [H][I]
k7[HI][Et].
6
6
W(t)
M
M
Here K = k , K
=
k .
[Et]st =
.
4
4
4
4
(19)
2
k [C H ] {1 + k K /4k (K [I]2)1/2}
8 2 4 st 9 c,6 7 c,4
From these equations, using Eqs. (12) and (13),
RUSSIAN JOURNAL OF GENERAL CHEMISTRY Vol. 73 No. 1 2003

78
SKOROBOGATOV et al.
Here [C H ] is the notation for expression (14).
of dissociation (1) at any other mean temperature <T>
by Eq. (23).
2
4 st
Using the above expressions we can obtain the fol-
lowing interrelationship between the rate constants,
equilibrium constants, and experimentally measured
W(t), [I ], and [EtI] values (at temperature T ).
E<T> = E0 + nR<T>.
(23)
2
j
Here n is the exponent in the exponential expression
(25) of the temperature dependence (24) of the pre-
exponent A1.
2
k k [C H ]
2 4 st
5
8
k K
[EtI] +
1
c,1
k k K
1 7 c,3
0
(
T)
c
1
RT
e
=
[Et]st (k 1 + k )(K [I2])1/2
A1(T) = exp
=
exp
,
(24)
(25)
5
c,4
R
R
k k K
9 c,6
k7(Kc,4[I2])1/2
8
A (T) = constTn = A T .
0
n
+
k8 +
[C H ] .
2
4 st
1 1
In particular, for <T> 298 K, from Eq. (23) follows
a practically important formula (26).
In particular, from here we can obtain for the equi-
librium constant Kc,1 of interest an explicit expression
through other constants and measured values
E<298> = E 0 + 298Rn.
(26)
0
[
Eq. (20)].
Knowing E<T>, we can calculate the formation
1
/2
k 1 + k5
kc,4(Tj)[I2]j
enthalpy of free ethyl radical by formula (27), since
W (t) 1 + a +
j
j
0
0
T
k8
Kc,3(T )[EtI]j
experimental
H (EtI) and
H (I ) values are
j
f
T
f
known [27, 28].
Kc,1(T ) =
.
j
aj
2
k ([EtI]
2[I ] ) 1 +
(1 + bj)
1
0
2 j
0
0
0
2
H (Et ) = H (EtI)
H (I ) + E<T>.
(27)
f
T
f
T
f
T
(
20)
The use of formula (20) suggests knowledge of the
equlibrium constants K , K , and K and the rate
c,3
c,4
c,6
Here b = k k /k k .
j
5 8
1 7
constants k , k , k , k , k , and k . If this is the case,
1
2
5
7
8
9
In the Arrhenius representation, the equilibrium
constants Kc,1 has form (21).
then, by formulas (10), (11), and (20) (22), one can
find previously unknown rate constants k , k , and k .
1
2
5
Calculation of molecular parameters and thermo-
dynamic functions. As follows from Eq. (24), the
c(T) values in Eq. (21) can be found by Eq. (28).
c(T)
H(0)
Kc,1(T) = exp
exp
R
RT
0
0
E0
RT
(T) =
(T)
e
Rln (RT).
(28)
=
A1(T)exp
.
c
(21)
Here Eq. (29) is valid.
Here R is the gas constant, H(0) is the enthalpy of
reaction (1) at 0 K, c(T) is the reduced Gibbs
0
0
0
0
(T) =
(Et ) +
(I )
(EtI).
(29)
e
e
e
e
energy of reaction (1) at constant concentration and at
For the right-hand part of Eq. (29), reliable pu-
blished data are available for I [27, 28] and EtI [29].
Abundant literature is also available for the radical Et
temperature T, and E is the activation energy of
0
thermal dissociation (1) at 0 K. From Eq. (21) follows
Eq. (22).
[27, 30, 31], but it is unsuitable. The case in point is
RTj
that the lowest vibration frequencies of Et have never
been observed experimentally and have been cal-
E0 =
[log A (T ) log Kc,1(T )].
(22)
1
j
j
log e
Here e is the base of natural logarithms.
culated:
21.7 cm 1 [32] have been reported (Table 3). It is
readily seen that monotonically decrease as the
accuracy of the calculations increase. Based on the
results in [35] we expect that the true value of is
values of 230 [27], 149 [30], and
1
5
1
As seen from Eq. (22), we can find the E value for
0
dissociation (1), having the preexponent value at
15
temperature T , calculated by Eq. (21) from the experi-
j
1
5
mental K (T ) value found by formula (20) for the
1
c,1
j
7
0 80 cm . As to higher vibration frequencies, then
same temperature Tj.
here, too, calculated values [30 32] appreciably differ
from experimental [34]. Thus, by refining normal
Knowing E we can find [26] the activation energy
0
RUSSIAN JOURNAL OF GENERAL CHEMISTRY Vol. 73 No. 1 2003

MOLECULAR, THERMODYNAMIC, AND KINETIC PARAMETERS
Table 3. Equilibrium molecular parameters of the radical Et
79
Molecular
parameter
Data of
Data of
[30]
Data of
[31]
Data of
[32]f
Present
work
a
[33]b and [34]
c
d
e
g
r(C C )
r(H C )
r(H C)
r(H C)
1.487
1.077(2)
1.094
1.088(2)
120.5(2)
111.8
111.4(2)
117.3
1.498
1.075(2)
1.091
1.086(2)
120.4
111.7
111.3(2)
117.3
81.9
37.9
3071
2983
2937
2906
2845
1471
1467
1448
1397
1178
1002
1.489
1.080
1.098
1.499
1.086(2)
1.103
1.096(2)
120.5(2)
111.6
111.3(2)
117.6
1.4881
1.0831(2)
1.1023
1.0942(2)
120.965(2)
111.760
111.830(2)
119.221
93.90
1.091
(HC C)
(C CH)
(C CH)
(HC H)
(HC CH)
(HC CH)
120.80
111.63
111.57
85
3124
3026
2987
2946
2871
1442
1440
1426
1362
1161
1030
958
89
1(A )
2(A )
3(A )
4(A )
5(A )
6(A )
7(A )
8(A )
9(A )
3112
3033
2987
2920
2842
1440
1440
3272.1
3168.9
3119.6
3075.5
2996.5
1507.6
1505.2
1491.6
1421.9
1207.8
1076.0
995.2
3239.0
3138.6
3078.9
3035.5
2946.9
1480.2
1481.2
1463.6
1398.2
1190.0
1060.5
978.1
1366
1175
1138
10(
11(
12(
13(
14(
15(
A )
A )
A )
A )
A )
A )
975
784
413
149
780
435
145
815.7
473.0
121.7
812.1
489.5
95.9
540
Ia
0.8005
3.7134
3.9931
0.1846
0.817
3.736
4.019
0.186
0.8091
3.6935
3.9852
0.185
Ib
Ic
Ir
0.186
a
1
39
2
b
Interatomic distances (r, ), angles (deg), vibration frequencies ( , cm ), and inertia moments (I 10 , g cm ). The geometry
c
d
*
e
is optimized in the MP2/6-31G(d,p) basis [33]. Measured frequencies. Calculated in the UHF/3-31G basis. Calcualted in the
f
QCISD/6-311G(d,p) basis with the fitting parameter of 0.956 for frequencies. The geometry was optimized in the QCISD/6-
11G basis, and the frequencies were obtained from the QCISD/6-311G + [MP2/6-311+G(2df,p)
*
*
**
**
3
MP2/6-311G ] fre-
g
**
quencies.
Calcualted in the UB3LYP/6-311++G basis.
vibration frequencies we can much impove the thermo- ground electronic state of the free radical Et using the
dynamic functions of the radical Et , calculated in
program package [37]. The resulting data are given in
Table 3. The table also lists the principal inertia and
internal rotation moments, calculated from the equi-
librium geometry of Et .
[
27, 30, 36]. The improvements will arise because the
frequency is so low that the corresponding degree
1
5
of freedom should be considered as free rotation at
T > 600 K, where Et should be given the symmetry
number of 6. This has not been made in [27], and the
authors used 1 for calculations in the range 100
As seen from Table 3, more accurate quantum-
chemical calculations do not appreciably change the
theoretical equilibrium geometry, and, therefore, our
inertia moments coicide within 1% with those re-
ported in [27, 30, 32]. Our normal vibration fre-
quencies are much closer to experimental,
T
6000 K. On the other hand, one should not use
in the range 600 6000 K, as it has been
done in [30, 32].
6
T
We calculated the energy, equilibrium molecular
structure, and normal vibration frequencies of the
especially low frequencies. Our
much differ from those in [27, 30 32]. As a result,
and
values
1
4
15
RUSSIAN JOURNAL OF GENERAL CHEMISTRY Vol. 73 No. 1 2003

80
SKOROBOGATOV et al.
Table 4. Ideal gas Thermodynamic functions of Et
0
C ,
0
0
H )/T, H0
0
0
0
H ,
f
J/mol
0
G ,
f
J/mol
T,
K
p
S ,
(G
J mol 1
H ,
0
0
logKf
J mol K 1
1
J mol 1 K 1
K
1
J/mol
0
0.00
42.75
53.76
68.45
68.75
0.00
205.15
235.28
257.01
257.38
276.62
293.73
309.21
323.26
338.54
352.74
366.01
378.40
390.04
400.97
411.31
421.02
0.00
166.59
192.16
207.98
208.27
220.81
231.47
240.88
249.37
259.58
269.13
278.17
286.71
294.83
302.62
309.99
317.07
0.00
3.85
8.62
133.0
128.8
126.6
124.30
124.26
122.5
121.3
120.7
120.5
120.7
121.3
122.1
123.2
124.3
125.6
127.0
128.4
133.0
134.0
140.5
148.6
148.7
158.1
168.4
179.3
190.9
200.9
210.8
220.7
230.5
240.2
249.8
259.3
268.7
0.00
69.91
36.65
25.99
25.86
20.62
17.57
15.59
14.22
13.10
12.22
11.51
10.93
10.45
10.02
9.664
9.347
1
2
2
3
4
5
6
7
8
9
00
00
98.15
00
00
00
00
00
00
00
000
100
200
300
400
500
14.61
14.74
22.32
31.15
40.99
51.71
63.18
75.24
87.84
100.86
114.22
127.91
141.81
155.96
82.35
93.66
103.16
111.16
117.90
123.47
128.16
132.01
135.28
138.00
140.30
142.23
1
1
1
1
1
1
1
0
Table 5. Calculation of the preexponential term A(T) = (RT) exp(
/R) in the equilibrium constants Kc,1 and Kc,3 and
e
of the dissociation degree
= [C H ] /[EtI] for [EtI]0 = 760 mm at 20 C
2
4 st
0
0
J mol 1 K 1
3
,
log (A /molecule cm )
i
e
T, K
, %
I [27]
Eta
EtI [29]
HI [27]
C H [28]
i = 1
i = 3
2
4
1
2
2
00
00
98.15
137.183
151.590
159.890
160.018
165.998
170.636
174.426
177.630
180.406
182.854
185.044
187.025
188.834
190.499
166.65
192.50
208.63
209.00
221.00
231.50
241.20
250.50
259.57
269.14
278.17
286.71
294.86
302.58
205.94
231.95
249.28
249.57
263.86
276.46
287.94
298.60
308.60
318.03
326.97
335.50
343.62
351.40
145.814
165.862
177.445
177.624
185.983
192.481
197.811
202.343
206.299
209.819
212.996
215.898
218.572
221.054
147.30
170.42
184.09
184.32
194.90
203.91
212.00
219.46
226.45
233.05
239.33
245.26
250.99
256.50
24.979
25.422
25.622
25.626
25.696
25.731
25.757
25.786
25.825
25.909
25.982
26.045
26.103
26.152
24.419
25.014
25.255
25.258
25.376
25.431
25.453
25.456
25.447
25.432
25.413
25.388
25.365
25.342
300
400
500
600
700
800
900
0.005
0.34
4.29
19.63
44.7
66.1
79.3
1
1
1
1
000
100
200
300
86.7
a
From the data in Table 4.
the thermodynamic functions of Et , reported in [27,
0, 36], should change considerably. The best results
for the low-frequency range is the manifestation of the
advantage of the UB3LYP/6-311++G level over the
UHF/3-31G* level used in [30]. This advantage
consists in that the B-LYP/6-31G(d) approximation,
by contrast to the Hartree Fock one, accounts for
electron correlation in calculations of vibration fre-
quencies of rather large molecules [38].
3
*
*
From the resulting molecular parameters of the
radical Et we calculated its thermodynamic functions
in the range 0 1500 K. Therewith, two sets of thermo-
dynamic functions, for 1 and 6, were obtained, and
RUSSIAN JOURNAL OF GENERAL CHEMISTRY Vol. 73 No. 1 2003

MOLECULAR, THERMODYNAMIC, AND KINETIC PARAMETERS
81
for the final result (see the first five columns of
Table 4) we took the result of combining data for
of 1 at T 100 K, for of 6 at T 700 K, and their
tude higher that the quasi-equilibrium concentration
of ethyl radicals [Eq. (19)], the latter are consumed
not by the recombination yielding butane but by re-
actions (7) (9) yielding ethane and hexane (Table 2).
linear interpolation in the range 200
resulting thermodynamic functions of Et (Table 4,
rd and 4th columns) we used to calculate reduced
Gibbs energies (Table 5, 3rd column) by formula (30).
T
600 K. The
Table 6 lists the results of treatment, using for-
mulas (18) (20) and the data in Table 5, of the expe-
rimental kinetic data represented in Fig. 1 in [13]. We
approximate [13] the equilibrium constant Kc,4 [42] in
the range 300 700 K by function (34).
3
0(
T) = S (T)
0
[H (T)
0
H (0)]/T.
0
(30)
for
0
p
Formula (30) was also used for calculating
300 1/2
T/K
1791 10
Kc,4 = 1024.25 0.05
exp
,
EtI and C H from the data in [29] and [28], respec-
2
4
T/K
tively. Then, by formulas (21), (28), and (29), the
preexponent A (T) in the equilibrium constant K (T)
1
c,1
was calcualted. The preexponent A (T) in the Ar-
molecule/cm3.
(34)
3
rhenius representation (31) of the equilibrium con-
stant (3) was calculated in a similar way.
The activation energy of the dissociation reac-
tion (1) was calculated by formula (22) under the
0
Kc,3(T) = A (T)exp( H /RT).
(31)
consumption that the activation energy of recombina-
3
0
0
0
tion (1) is equal to zero. The resulting E values are
The A (T) and A (T) values for the range 100
500 K are listed in Table 5.
listed in the last column of Table 6; from these data
1
3
0
1
we obtain the mean value <E > [expression (35)].
0
Kinetic experiment. As shown above, pyrolysis
0
<
E > = ED,0(Et I) = 235 3 kJ/mol.
(35)
0
of ethyl iodide occurs by the mechanism (1) (9)
which differs from that accepted in [13]. We have also
corrected thermodynamic functions of the free radical
Et (cf. Table 4 in the present work and Table 2 in
This value is much different from that reported in
22].
[
0
[
13]). Thus, it is makes sense to treat the kinetic ex-
To pass from the resulting <E > value [expression
0
perimetal data reported in [13] by the new formulas
(35)] to the activation energy at 298 K, we should find
n in formula (26). It can be shown [13] that from
functions (21) and (25) follows expression (36).
(18) (22) with new thermodynamic functions.
0
0
According to [1, 39], for the enthalpy H of reac-
tion (3) we obtain an estimate of 83.32 kJ/mol. From
here and the data in the 8th column of Table 5 we
obtain the analytical expression (32) for Kc,3 in the
range 400 900 K.
n = [log A (300 K)
1
log A (298.15 K)]/(log 300
log 298.15). (36)
1
Substitution into expression (36) of the data in
Table 5 gives n 1.48, and from here, using fourmulas
(26) and (35), we obtain the E 0< 298> value [expres-
sion (37)].
Kc,3(T) = 1025.44 0.02exp[ (10014 K)/T],
molecule/cm3.
(32)
From this expression by formula (14) we can find
the fraction of ethylene in equilibrium with the start-
ing ethyl iodide (Table 5, last column). As seen, under
0
E
= ED,298(Et I) = 238 3 kJ/mol.
298>
(37)
<
the experimental conditions in [13], i.e. at 500
T
This result appreciably differs from those in [1, 23].
6
50 K, about one tenth of the starting ethyl iodide is
Using known fH0 values for ethyl iodide [40]
and atomic iodine [27], we obtain, by formulas (37)
and (27), the formation enthalpy of free ethyl radical
298
dissociated [reaction (33)].
C H I
C H + HI
C H + 0.5H + 0.5I . (33)
2
5
2
4
2
4
2
2
[
expression (38)].
0
But this is not pyrolysis yet, since equilibrium (33)
fH (Et ) = 124 3 kJ/mol.
(38)
298
is shifted to the left and the starting ethyl iodide is
completely regenerated if heating is discontinued.
Pyrolysis occurs when ethyl radicals are irreversibly
consumed by reactions (7) (9). And since the fraction
of ethylene in equilibrium (33) is 3 orders of magni-
0
0
The thermodynamic functions H and G in
f
f
Table 4 were calculated on the basis of the above
experimental fH (Et ) value. Irrespective of the
0
298
accepted symmetry number
of ethyl radical, the
RUSSIAN JOURNAL OF GENERAL CHEMISTRY Vol. 73 No. 1 2003

82
SKOROBOGATOV et al.
0
Table 6. Calculation of the equilibrium constant Kc,1 and the dissociation energy E for the reaction EtI
Et + I
0
from the experimental total rate W of ethyl iodide pyrolysis
3
1
log(k /cm s )
Kc,3
,
Kc,1
,
logA1
(from
Table 5) kJ/mol
0
E ,
0
Tj,
Wj,
1 cm 3 s 1a
[I2],
1/cm3 a
3
3
Kc,4 [I ]b
2
cm ,
Eq.
(32)
cm ,
d
= 5
40]
= 7
[40]
= 8
[40]
Eq.
K
c
[
(20)
15
25.152
17.46
3.825
5
5
6
45 4.0 1012
1.6 10
5.0 10
11.4
11.4
11.4
12.10
12.07
12.04
15.33
15.16
14.89
10
10
10
10
10
10
10
25.74
25.75
25.76
229
237
238
1
3
15
17
26.448
17.92
4.332
78 1.1 10
10
34 6.3 1014
1.15 10
10
26.98
18.58
6.133
a
19
3
b
c
Experimental data from Fig. 1 in [13] for [RI] 2.5 10 cm
.
K
was calculated by Eq. (34).
The k value of
1
0
c,4
1
0.93
3
1
1
d
1
0
cm molecule
s
was used [41].
Calculated by Eq. (22).
0
0
calculations in Table 4 gave the following H (Et )
value.
Finally, from functions (32) and (40) and formula
(11) follows the exponential representation (45) for
the constant of equilibrium (5).
f
0
H (Et ) = 133 3 kJ/mol.
(39)
f
0
Kc,5(T) = 10 0.29 0.12exp[(18236 350 K)/T].
(45)
Using Eqs. (21) and (35) and the data in Table 5
we obtain the analytical expression (40) for the equi-
librium constant Kc,1 in the range 300 800 K.
According to [40], we have
k5
10 11.41
0.29
cm molecule s . From here by for-
3
1
1
mulas (45) and (11) we find the absolute rate constant
of a reverse reaction (5).
Kc,1(T) = 1025.73 0.10exp[ (28250 350 K)/T],
molecule/cm3.
(40)
k 5 = k /K
= 10 11.1 0.4exp[ (18236 350 K)/T],
5
c,5
cm molecule 1 s .
3
1
(46)
From here and the k 1 value [41] we obtain, by
formula (10), the rate constant k (T) of thermal dis-
sociation (1) in the limit of high concentrations.
1
Thus, in the range 300 800 K in the limit of high
concentrations we could obtain a complete kinetic
information for all the six elementary reactions (1),
k (T) = 101
4.8
0.3
exp[ (28250 350 K)/T], s . (41)
1
1
(
2), and (5), involving ethyl radical.
This result much differs from those reported in
21, 22, 43].
[
Discussion. The resulting formation enthalpies of
ethyl radical [expressions (38) and (39)] are nicely
consistent with up-to-date experimental and theore-
tical results [6 9, 12]. This means that the true value
From functions (40) and (34) by formula (10) we
find the analytical equation (42) for the constant of
equilibrium (2).
0
of H (Et ) can be obtained from experimental ki-
f
T
netic data for ethyl iodode, but only in terms of the
correct pyrolysis mechanism represented by reactions
(1) (9).
Kc,2(T) = 101.38 0.3[T/(300 K)]1/2
exp[ (10340 360 K)/T).
(42)
It is known that the formation enthalpies of normal
hydrocarbons and their derivatives are linearly related
to the number of carbon atoms in the molecule (n) and,
what is more, with the same increment (see figure).
But with all types of derivatives the linear dependence
is established for n 2 only. Therefore, in our pre-
vious work (see Fig. 2 in [13]) the recommended
value [expression (47)] contradicted neither the
recently reported formation enthalpy [expression (48)]
of methyl radical [8] nor commonly accepted [1,
According to [4, 41], the rate constant k 2 can be
represented by the analytical expression (43).
k (T) = 10 1 exp[ (100 K)/T], cm molecule s . (43)
1.28
3
1
1
2
From functions (42) and (43) by formula (10) we
find the absolute rate constant k (T) for a direct reac-
2
tion (2).
k (T) = 10 9 0.3[T/(300 K)]1/2exp[ (10440 360 K)/T],
.9
2
1
0, 11] formation enthalpies of alkyl radicals C H
n 2n+1
3
1
1
cm molecule s .
(44)
(n
3).
RUSSIAN JOURNAL OF GENERAL CHEMISTRY Vol. 73 No. 1 2003

MOLECULAR, THERMODYNAMIC, AND KINETIC PARAMETERS
83
REFERENCES
5
1, 6 2 4
1
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10
3
4
0
0
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1
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C H
{(solid line) our recommendation and (dotted
n
2n+1
line) published data [1, 44]}, (2) bromides C H
Br
n
2n+1
[
45, 46], (3) alkanes C H
[45, 46], (4) chlorides
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C H
Cl [45, 46], (5) alcohols C H
OH [45, 46],
n
2n+1
n
2n+1
and (6) iodides C H
I [39, 46].
n
2n+1
1
1. Ponomarev, D. and Takhistov, V., J. Mol. Struct.,
997, vol. 435, no. 2, p. 259.
0
fH (Et ) = 115 2 kJ/mol,
(47)
(48)
298
1
0
fH
298
(Me ) = 146.5 0.5 kJ/mol.
12. Curtiss, L.A., Radhavachan, K., Redfem, P.C., and
Pople, J.A., J. Chem. Phys., 1997, vol. 106, no. 3,
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0
298
However, the new fH (Et ) value [expres-
sion (38)] instead of the old value [expression (47)]
gives, together with the fH (Me ) value [expres-
sion (48)], a strictly linear dependence for n
Therefore, in accordance with the straight line 1 in
the figure, we recommend the following corrected
formation enthalpies of free radicals.
0
298
13. Skorobogatov, G.A., Dymov, B.P., Pogosyan, Yu.I.,
and Chuikov-Ru, E.P., Zh. Org. Khim., 1998, vol. 34,
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1
4. Skorobogatov, G.A., Dymov, B.P., Shcherba, R., and
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0
fH (Pr ) = 104 3, fH (Bu ) = 82 3,
15. Shepp, A. and Kutschke, K.O., J. Chem. Phys., 1957,
298
298
vol. 26, no. 5, p. 1020.
0
0
fH (Pent ) = 61 3, fH (Hex ) = 0 3 kJ/mol.
298
298
1
1
6. Munk, J., Pagsberg, P., Ratajczak, E., and Sillesen, A.,
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fH (C H2n+1) values obtained in [47]. However,
298
n
our values for Bu , Pent , and Hex coicide within
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