Kinetic study in a microwave-induced plasma afterglow of the Cu (2S) atom reaction with CH3Br at temperatures between 300 and 804 K and with CH3I between 300 and 696 K

Article abstract of DOI:10.1021/jp973386h

A kinetic study of the reactions Cu + CH₃Br → CuBr + CH₃ (k₁) and Cu + CH₃I → CuI + CH₃ (k₂) has been carried out in a fast-flow reactor. The gas-phase copper atoms were generated using the microwave-induced plasma (MIP) afterglow technique. Atomic absorption spectroscopy at 327.4 nm was used as the detection technique. The influence of experimental parameters such as the hydrogen content, sublimation temperature of the CuCl pellet, and reactor pressure on k₁ and k₂ has been verified. The rate constant k₁ was measured at temperatures between 300 and 804 K, which resulted in the Arrhenius expression k₁ = (1.7 ± 0.2) × 10^-11 exp[(-8.2 ± 0.5 kJ mol^-1)/RT] cm³ molecule^-1 s^-1. Since the Arrhenius plot shows a slight curvature, the values of k1 were also fitted to the modified Arrhenius equation k(T) = A Tⁿ exp(-E/RT). Meaningful kinetic parameters can only be derived when n is fixed. The measured values of k₁ can be best described as a function of temperature over the 300-804 K range by the expression log k₁(T) = +223.6669 - 264.2058(log T) + 97.7693(log T)² - 11.9244(log T)³. The Arrhenius expression for rate constant k² is k₂ = (7.9 ± 0.5) × 10^-11 exp[(-0.8 ± 0.2 kJ mol^-1)/RT] cm³ molecule^-1 s^-1 between 300 and 696 K. The obtained results will be discussed in terms of the electron-jump model, and some reactivity/structure relations will be presented.

Full text of DOI:10.1021/jp973386h

J. Phys. Chem. A 1998, 102, 1349-1355
1349
2
Kinetic Study in a Microwave-Induced Plasma Afterglow of the Cu ( S) Atom Reaction
with CH3Br at Temperatures between 300 and 804 K and with CH3I between 300 and
6
96 K
Chris Vinckier* and Inge Vanhees
Department of Chemistry, KU LeuVen, Celestijnenlaan 200F, B-3001 LeuVen, Belgium
ReceiVed: October 17, 1997; In Final Form: December 16, 1997
A kinetic study of the reactions Cu + CH
3
Br f CuBr + CH
3
(k
1
) and Cu + CH
3
I f CuI + CH
3
(k
2
) has
been carried out in a fast-flow reactor. The gas-phase copper atoms were generated using the microwave-
induced plasma (MIP) afterglow technique. Atomic absorption spectroscopy at 327.4 nm was used as the
detection technique. The influence of experimental parameters such as the hydrogen content, sublimation
temperature of the CuCl pellet, and reactor pressure on k
1
and k
2
has been verified. The rate constant k
1
was
measured at temperatures between 300 and 804 K, which resulted in the Arrhenius expression k
1
) (1.7 (
-
11
-1
3
-1 -1
0
.2) × 10 exp[(-8.2 ( 0.5 kJ mol )/RT] cm molecule s . Since the Arrhenius plot shows a slight
n
curvature, the values of k
1
were also fitted to the modified Arrhenius equation k(T) ) A T exp(-E/RT).
Meaningful kinetic parameters can only be derived when n is fixed. The measured values of k
described as a function of temperature over the 300-804 K range by the expression log k (T) ) +223.6669
264.2058(log T) + 97.7693(log T) - 11.9244(log T) . The Arrhenius expression for rate constant k is
between 300 and 696 K. The
1
can be best
1
2
3
-
2
-
11
-1
3
-1 -1
k
2
) (7.9 ( 0.5) × 10 exp[(-0.8 ( 0.2 kJ mol )/RT] cm molecule
s
obtained results will be discussed in terms of the electron-jump model, and some reactivity/structure relations
will be presented.
k1
Introduction
2
1
1
+
2
Cu (4 S) + CH Br ( A )
98 CuBr ( Σ ) + CH ( A′′ ) (2)
3 2
3
1
The reactions of halomethanes with alkali-metal atoms have
been investigated for more than 60 years. In the early 1930s
-1
∆
H ) -37.6 kJ mol
r
1
Polanyi and his collaborators studied reactions of alkali metals
with several halogenated molecules in a diffusion flame.
Numerous studies have been carried out using molecular beam
techniques to determine the reaction cross sections. For the
k2
2
1
1
+
2
Cu (4 S) + CH
I ( A
)
98 CuI ( Σ ) + CH
( A′′
)
(3)
3
1
3
2
2
-1
reactions with CH3I the following cross sections were obtained:
∆H ) +38.6 kJ mol
r
2
2
2
2
7 Å (Li), 5 Å (Na), and 35 Å (K). The reactions of Na and
2
K atoms with CH3Br resulted in values of 6 and 3 Å ,
For both reactions 2 and 3 the kinetic study has been carried
out in a fast-flow reactor. The microwave-induced plasma
(MIP) afterglow technique was used as a source of the copper
respectively.3 To explain the reactivity of Na atoms with
4
,5
halomethanes, the electron-jump model was introduced.
9
,10
According to this electron-jump or harpooning mechanism, a
metal atom throws out its valence electron, which is then
captured by the molecule. The distance rc where the covalent
potential-energy surface crosses the ionic potential-energy
surface is given by4
atoms in the gas phase.
Reaction 2 has been studied in the
temperature range from 300 to 804 K, while reaction 3 has been
followed between 300 and 696 K. An Arrhenius expression
for k and k will be derived. There are no other kinetic data
on these copper atom reactions available yet in the literature,
but the results will be compared with similar potassium atom
reactions. The Arrhenius parameters will be used as the basis
for a number of reactivity/structure relationships.
1
2
2
e
)
IE(Me) - EA(XY)
(1)
rc
Experimental Technique
where e is the electronic charge, IE(Me) the ionization energy
of the metal, and EA(XY) the electron affinity of the molecule
XY, which represents a halogen molecule X2 or an alkyl halide
RX.
Only the essential characteristics of the technique will be
given here, since a detailed description of the experimental setup
1
1
has been published previously. The copper reactions were
studied in a fast-flow reactor, which consists of a quartz tube
with an internal diameter of 5.7 cm and a length of 100 cm. At
the upstream end, a sample holder carries a CuCl pellet. A
Kanthal resistance wire allows this solid pellet to heat up to a
temperature Ts of about 800 K, independently of the temperature
Tg in the reaction zone. The carrier gas argon transports the
Halomethanes are well-suited for a systematic study such as
6,7
testing the effect of electronegative substituents on reactivity.
The reaction of Cu atoms with CH3Cl has already been studied
8
at our laboratory. In the present work the reactions of copper
atoms with methyl bromide and methyl iodide have been
investigated.
S1089-5639(97)03386-0 CCC: $15.00 © 1998 American Chemical Society
Published on Web 02/03/1998

1350 J. Phys. Chem. A, Vol. 102, No. 8, 1998
Vinckier and Vanhees
evaporated copper chloride oligomers CuxClx,g downstream,
where they are mixed with the reaction products of a hydrogen/
argon microwave-induced plasma (MIP) afterglow. Hydrogen
atoms convert a fraction of the CuxClx,g molecules into Cu atoms
following a still unknown reaction sequence:
Cu Cl + H f ... f ... f Cu + products
(4)
x
x,g
g
Atomic absorption spectroscopy at 324.7 nm was used to detect
the copper atoms in the kinetic zone. Initial absorbances were
kept below 0.3, which corresponds to a copper atom concentra-
1
0
-3
tion of 4.3 × 10 atoms cm as an upper limit. However, the
CH3Br and CH3I concentrations were orders of magnitude
higher, which resulted in pseudo-first-order conditions for copper
atom decays.
Figure 1. Natural logarithm of the Cu absorbance as a function of the
In the kinetic zone, the temperature Tg of the gas phase can
be varied between 300 and 1000 K. The flow velocity V of the
reaction time. Experimental conditions: T
g
) 516 K, P
r
) 9 Torr, T
s
)
537 K, [H ] ) 9.9 mTorr, and the carrier gas is argon. The CH
2
3
Br
-
1
carrier gas argon was 324 ( 5 cm s at 298 K. While the
detection system remains at a fixed position, the fast-flow reactor
assembly is mounted on a carriage which allows a horizontal
displacement, so that copper absorbances can be measured along
the reactor axis.
concentrations are (+) 0, (0) 0.47, (]) 1.11, (4) 1.75, (O) 2.47, (*)
13
-3
3
.13, (-) 3.85 in units of 10 molecules cm .
value of η will not be repeated here, but in our experimental
conditions it is safe to set its value equal to 1.3 with an
associated systematic error of 10%.
First, ln ACu was followed as a function of the reaction time
t at various amounts of the reactant added, e.g. CH3Br, and a
linear regression of ln A versus t was carried out. Next, the
slopes of these lines were plotted versus [CH3Br]. A weighted
During the kinetic measurements several known amounts of
the reagent (CH3Br or CH3I) were added through the additive
inlet. For each amount the decay of the copper atoms was
followed as a function of the axial distance (z) and thus of the
reaction time (t) because t ) z/V.
Gas flows were regulated by using Brook’s precision needle
valves of the ELF type or Brook’s mass flow controllers, model
linear regression results in a straight line with an intercept of
2
7
.34DCu,Ar/2r and a slope equal to k1/η.
5850 E.
This procedure has been followed for many other reactions
The gases used were argon (5.0) from UCAR with a purity
better than 99.999%, mixtures of 1.02% and 5.3% CH3Br in
ultrahigh-purity argon (Praxair), and mixtures of 477.1 vpm and
studied at our laboratory. It takes into account the uncertainties
of several variables such as temperature, flow, reactor radius,
and total pressure. By combining these uncertainties according
0
.538% CH3I in UHP argon (BOC). Hydrogen was added as
1
9
to the method explained by Howard, the uncertainties σS and
σk for the calculated values of the slope S and the rate constant
k were calculated. Finally, the systematic error of 10% for the
correction factor 1.3 has been added, resulting in the total
standard deviation σk. The overall precision on the reported
values of the rate constants is in the range 15-25%.
a 0.998% mixture in UHP argon (L’Oxhydrique), a 4.95%
mixture in UHP helium (UCAR), or with a purity better than
99.9997% (L’Air Liquide).
Regression plots and statistical analyses were made by using
12
the SAS-6.08 statistical package available at our University
Computer Centre. We have quoted the 1 σ standard error.
The procedure is illustrated in Figure 1, where the natural
logarithm of the copper absorbance ln ACu is plotted against
the reaction time for various amounts of CH3Br added. The
experimental conditions were Tg ) 516 K, the reactor pressure
Pr ) 9 Torr, and the MIP afterglow parameters Ts and [H2]
were set respectively at 537 K and 9.9 mTorr. When the
absolute values S of the slopes of these lines are plotted versus
the CH3Br concentration, a straight line is obtained, as is shown
in Figure 2. A weighted linear regression yields a value for k1
Results
Cu + CH3Br Reaction. Kinetic Expression for the DeriVa-
tion of k1. The rate constant of reaction 2 can be determined
from the copper atom decays as a function of the reaction time
at various amounts of CH3Br added. The formalism used for
the derivation of k1 is the same as in our previous work on the
kinetics of copper,8
tions:
,10,11,13
sodium, and magnesium
14
15,16
reac-
-12
3
-1 -1
)
(2.5 ( 0.3) × 10
cm molecule
s
and an intercept I
-
1
of (23.1 ( 0.9) s at Tg ) 516 K.
k [CH Br]
7.34DCu,Ar
1
3
The points shown at the ordinate in Figure 2 are the observed
copper decays in the absence of the coreagent CH3Br. The
pseudo-first-order plots for the experiments at two other
temperatures are also shown. The values for k1 are (1.2 ( 0.2)
ln ACu ) -
+
t + B
(5)
{
2
}
η
2r
in which ACu is the copper absorbance, k1 the rate constant of
reaction 2, η a correction factor (depending on the flow
characteristics), DCu,Ar the binary diffusion coefficient of copper
atoms in the carrier gas argon, r the reactor radius, t the reaction
time ()z/V), and B an integration constant. A complete
discussion on the mathematics behind eq 5 is given by Howard
-
12
-12
3
-1 -1
× 10
and (5.4 ( 0.8) × 10
cm molecule
s
at 390
and 702 K, respectively. These results clearly indicate that the
rate constant k1 increases with Tg and will have an activation
energy.
Influence of the MIP Afterglow Parameters. The possible
influence of a number of MIP afterglow parameters on the
magnitude of the derived rate constants has been verified.
Experimental conditions and results are summarized in Table
1. Changing the hydrogen content in the MIP afterglow makes
it possible to check the influence of excess H atoms on the
1
7
et al., and the influence of the various flow characteristics on
18
the magnitude of η is discussed by Fontijn et al. This factor
η takes into account the absence of plug flow conditons. In
argon the flow has neither a plug flow (η ) 1) nor a parabolic
(
η ) 1.6) character. The extensive arguing for selecting the

2
Cu ( S) Atom Reaction with CH3Br
J. Phys. Chem. A, Vol. 102, No. 8, 1998 1351
of the Cu + CH Br Reaction as a Function of
TABLE 2: ka
1
3
Temperature
2
] (mTorr)
P
r
(Torr)
1
k )
(cm molecule s-1
3
-1
T
g
(K)
T
s
(K) [H
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
4
4
4
4
00
00
00
01
01
01
01
01
02
02
02
02
02
04
04
27
44
59
90
04
07
08
17
514
514
525
513
513
513
513
513
513
513
513
513
514
513
532
522
512
512
522
514
514
514
514
520
520
514
537
556
537
538
537
530
529
514
536
555
549
554
554
553
3.3
32.7
3.3
3.3
3.3
3.3
3.3
3.3
3.3
32.5
3.3
3.3
3.3
3.3
3.3
4.9
4.7
4.7
8.1
4.7
4.9
4.7
4.9
5.2
6.5
4.9
9
9
9
(7.7 ( 1.1) × 10
(7.7 ( 1.0) × 10
(9.5 ( 1.7) × 10
(6.7 ( 1.1) × 10
(7.2 ( 1.1) × 10
(6.9 ( 1.0) × 10
(9.0 ( 1.3) × 10
(7.7 ( 1.1) × 10
(7.7 ( 1.3) × 10
(7.7 ( 1.1) × 10
(6.3 ( 1.1) × 10
(7.4 ( 1.0) × 10
(6.6 ( 1.0) × 10
(7.8 ( 1.3) × 10
(8.6 ( 1.4) × 10
(7.0 ( 1.1) × 10
(8.2 ( 1.2) × 10
(9.5 ( 1.5) × 10
(1.2 ( 0.2) × 10
(1.2 ( 0.2) × 10
(1.1 ( 0.1) × 10
(1.3 ( 0.2) × 10
(1.4 ( 0.3) × 10
(1.6 ( 0.2) × 10
(2.1 ( 0.3) × 10
(2.2 ( 0.3) × 10
(2.6 ( 0.4) × 10
(2.5 ( 0.4) × 10
(2.5 ( 0.3) × 10
(2.6 ( 0.4) × 10
(2.3 ( 0.4) × 10
(2.9 ( 0.5) × 10
(3.3 ( 0.6) × 10
(4.5 ( 2.0) × 10
(5.4 ( 0.8) × 10
(6.7 ( 1.3) × 10
(6.6 ( 1.3) × 10
(7.1 ( 1.2) × 10
(8.2 ( 1.1) × 10
(9.1 ( 1.5) × 10
7
10
10
10
11
9
9
9
9
9
8
9
9
9
9
9
9
1
9
7
9
9
9
9
9
9
9
9
9
9
8
9
9
9
9
9
Figure 2. Absolute value S of the slope of eq 5 as a function of CH
3
-
-13
-12
-12
Br concentration for three different temperatures: (9) 390 K, (0) 516
K, ([) 702 K.
-
12
-12
12
-12
TABLE 1: Influence of the MIP Afterglow Parameters on
the Value of k
1
for the Cu + CH
(K) [H ] (mTorr)
Hydrogen Content [H
3
Br Reactiona
-
(cm molecule s-1
3
-1
)
T
g
(K)
T
s
2
P
r
(Torr)
k
1
434
-
-
-
-
-
-
-
-
-
-
-
-
12
12
12
12
12
12
12
12
12
12
12
12
4
5
74
05
2
]
-
-
-
-
-
-
-
-
-
-
13
13
13
13
12
12
12
12
12
12
3
3
3
3
5
5
5
5
8
8
02
00
02
00
12
16
17
19
03
04
513
514
513
514
537
537
538
537
554
553
3.3
3.3
32.5
32.7
4.9
9
9
9
9
9
9
9
9
9
9
(7.7 ( 1.3) × 10
(7.7 ( 1.1) × 10
(7.7 ( 1.1) × 10
(7.7 ( 1.0) × 10
(2.6 ( 0.4) × 10
(2.5 ( 0.3) × 10
(2.6 ( 0.4) × 10
(2.3 ( 0.4) × 10
(8.2 ( 1.1) × 10
(9.1 ( 1.5) × 10
512
512
516
517
519
562
619
654
702
4.9
4.9
9.9
48.8
145.8
13.0
13.0
8.3
8.1
13.0
8.1
9.9
48.8
145.8
8.3
32.9
7
7
7
8
28
66
98
03
Temperature T
s
of the Solid
-12
-
-
-
-
-
-
-
13
13
13
13
12
12
12
302
302
300
304
505
512
512
513
513
525
532
514
537
556
3.3
3.3
3.3
3.3
4.9
4.9
4.9
9
9
9
9
9
9
9
(7.7 ( 1.3) × 10
-
-
-
12
12
12
8.3
8.3
32.9
(7.4 ( 1.0) × 10
(9.5 ( 1.7) × 10
(8.6 ( 1.4) × 10
(2.2 ( 0.3) × 10
(2.6 ( 0.4) × 10
(2.5 ( 0.4) × 10
804
9
a
Symbols are the same as in Table 1.
As the sublimation of CuCl occurs through the formation of
Reactor Pressure P
r
20
CuxClx oligomers, a change of the sublimation temperature
-
-
-
-
-
-
-
-
-
-
13
13
13
13
13
13
12
12
12
12
3
3
3
3
3
3
4
4
4
4
01
04
02
01
01
01
17
04
08
07
513
513
513
513
513
513
514
514
514
514
3.3
3.3
3.3
3.3
3.3
3.3
4.9
4.7
4.7
4.9
7
8
9
10
10
11
7
9
9
11
(6.7 ( 1.1) × 10
(7.8 ( 1.3) × 10
(7.7 ( 1.3) × 10
(9.0 ( 1.3) × 10
(7.2 ( 1.1) × 10
(7.7 ( 1.1) × 10
(1.4 ( 0.3) × 10
(1.2 ( 0.2) × 10
(1.3 ( 0.2) × 10
(1.1 ( 0.1) × 10
Ts from 513 to 532 K raises the gas-phase concentration of the
CuxClx oligomers by a factor of 3.2 at Tg ) 302 K.9 Around a
gas temperature of 510 K the oligomer concentration increases
by a factor of 11.7 in the Ts range 514-556 K. The results in
Table 1 show that a variation of the temperature Ts of the CuCl
pellet does not have any systematic effect on the value of k1.
Another MIP afterglow parameter is the reactor pressure Pr,
which was varied between 7 and 11 Torr. The results in Table
1 indicate that Pr has no systematic effect on the value of k1.
This confirms a second-order character for reaction 2. More-
over, a lower reactor pressure enhances the diffusion of the
reagents toward the reactor wall, so the absence of a pressure
effect on k1 leads to the conclusion that hydrodynamic flow
characteristics do not have any influence on the value of k1.
Temperature Dependence of k1. A summary of the experi-
mental conditions and derived values for k1 is given in Table 2
in the temperature range from 300 to 804 K. A weighted
nonlinear regression on these data yields the Arrhenius expres-
sion
a
T
g
, reaction temperature in gas phase; T
solid; [H ], hydrogen content of the MIP; P
microwave power P ) 40 W.
s
, temperature of the CuCl
2
r
, reaction pressure;
W
measured rate constant. These H atoms, which are left after
the production of Cu atoms, might react with a fraction of the
added CH3Br or with CuBr to regenerate Cu atoms. The results
in Table 1 show that there is no systematic effect of the
hydrogen content on the derived value of k1 at temperatures
around 300, 516, and 803 K. Therefore, the interference of H
atom reactions seems to be negligible under these experimental
conditions.
The microwave power was kept constant at 40 W.
A
k1 ) (1.7 ( 0.2) ×
variation of this parameter is equivalent to changing the H atom
concentration in the MIP afterglow, which as said above had
no effect.
-
1
0-11
-8.2 ( 0.5 kJ mol
cm molecule s-1 (6)
3
-1
1
exp(
)
RT

1352 J. Phys. Chem. A, Vol. 102, No. 8, 1998
Vinckier and Vanhees
n
TABLE 3: Two-Parameter Fit of the Expression k(T) ) AT
exp(-E/RT)a
n
A
E
residual sum
of squares
fixed) (×10 cm molecule s-1
-
14
3
-1
)
(kJ mol-1)
(
0.5
1
1.5
2
2.5
49.8 ( 6.4
1.5 ( 0.2
0.042 ( 0.004
0.0012 ( 0.0001
0.000035 ( 0.000003
6.5 ( 0.4
4.7 ( 0.4
60
50
41
34
28
3.0 ( 0.3
1.2 ( 0.3
-0.56 ( 0.25
a
The value of n is fixed for the calculation of A and E. The sum of
the squares of the residuals is also given.
The very large standard deviation for the parameter A indicates
that a three-parameter fitting procedure is rather unrealistic.
21
Heberger et al. stated that three-parameter expressions derived
in this way are to be considered as merely a representation of
experimental points, which should be used only for interpolation
or extrapolation of the rate coefficient values.
In another approach one parameter can be fixed, which
reduces the fitting to a two-parameter problem. In analogy with
8
the reaction between Cu and CH3Cl, n is fixed in the range
between 0.5 and 2.5, and values for the two remaining
parameters A and E are calculated with increments for n of 0.5.
The results, summarized in Table 3, show that the sum of
squares of the residuals decreases with an increasing value for
n. Moreover, the standard deviations on the parameter A are
much smaller than in the three-parameter fit of eq 9. It should
Figure 3. Arrhenius plot of ln k
regression of k versus 1/T described by eq 6; dotted line (‚‚‚), linear
regression of ln k versus 1/T described by eq 7; dash-dot line (-‚-
), nonlinear regression of k versus T according to the three-parameter
expression 8 with the value of n fixed at 2 (see Table 3); dashed line
- - -), polynomial expression described by eq 10.
1
versus 1/T: Full line (s), nonlinear
-18
be noticed that the preexponential factor A ) (5 ( 105) × 10
1
3
-1 -1
cm molecule
s
and the activation energy E ) 2.4 ( 0.6 kJ
1
-
1
mol given in eq 9 fall within the range of values mentioned
in Table 3 when the error of (1.0 for n ) 2.2 in eq 9 is taken
into account. As an example, an Arrhenius plot using the
parameter set for n ) 2 is shown in Figure 3. The figure
illustrates that the three-parameter expression considerably
improves the fit of the experimental points.
‚
1
(
A weighted linear regression of ln k1 versus 1/T results in the
expression
8
As was shown for the Cu + CH3Cl reaction, rigorous
+
0.3
-0.2
k1 ) 2.0
×
transition state theory calculations allowed us to refine the exact
value of n. Ab initio molecular orbital calculations at the
Hartree-Fock level were used to obtain vibrational frequencies
and moments of inertia of CH3Cl and the transition state Cu-
Cl-CH3. Analogous calculations of the transition state Cu-
Br-CH3 have not yet been carried out at that level. In view of
the uncertainty on the value of n between 0.5 and 2.5 an energy
-
1
0- exp
11
-8.5 ( 0.4 kJ mol
cm molecule s-1 (7)
3
-1
1
(
)
RT
In Figure 3 the experimentally measured rate constants together
with eqs 6 and 7 are plotted as a conventional Arrhenius graph.
Both expressions yield consistent Arrhenius parameters, but in
view of the symmetric error on the preexponential factor for
the nonlinear regression method, expression 6 will be used
further in the discussion. However, a slight deviation from
linearity can be observed, which indicates non-Arrhenius
behavior for reaction 2, as will be discussed in the next section.
Non-Arrhenius BehaVior of the Cu + CH3Br Reaction. The
Arrhenius plot of the experimental points in Figure 3 apparently
shows a slight curvature, which was also found for the reaction
between Cu and CH3Cl.8 To describe this non-Arrhenius
behavior, three-parameter expressions of the type
-
1
barrier for reaction 2 in the range 3 ( 3.5 kJ mol may be
adopted.
The experimentally measured values of k1 can even be fit
better as a function of temperature by means of the polynomial
expression 10, as is also illustrated in Figure 3:
log k (T) )
1
2
+
223.6669 - 264.2058(log T) + 97.7693(log T)
3
-11.9244(log T)
(10)
n
-E
RT
cm molecule s-1
3
-1
k(T) ) AT exp
(8)
Non-Arrhenius behavior is also observed when different reaction
channels, leading to the formation of reaction products in various
electronic states, are accessible. In reaction 2, however, CuBr
(
)
are frequently used.
1
+
is formed in its electronic ground state X ∑ because the
A weighted nonlinear regression for the values of k1 in Table
leads to the modified Arrhenius equation
-
1
reaction exothermicity of 37.6 kJ mol does not allow the
formation of the lowest electronically excited state lying at 245
2
-
1
22
kJ mol above the ground state.
k1 ) (5 ( 105) × 10 18T (2.2(1.0)
-
×
Cu + CH3I Reaction. The same experimental procedure
as described for the Cu + CH3Br reaction was followed to study
the reaction between Cu and CH3I.
-1
-
2.4 ( 0.6 kJ mol
cm molecule s-1 (9)
3
-1
exp(
)
RT

2
Cu ( S) Atom Reaction with CH3Br
J. Phys. Chem. A, Vol. 102, No. 8, 1998 1353
of the Cu + CH I Reaction as a Function of
TABLE 4: Influence of the MIP Afterglow Parameters on
the Value of k
TABLE 5: ka
2
3
for the Cu + CH
(K) [H ] (mTorr) (Torr)
Hydrogen Content [H
I Reactiona
3
Temperature
2
3
-1
2
k )
(cm molecule s-1
3
-1
T
g
(K)
T
s
2
P
r
k
2
(cm molecule s-1
)
T
g
(K) (K) [H
T
s
2
] (mTorr)
P
r
(Torr)
-
11
2
]
300
300
300
300
300
300
300
300
508
514
515
526
531
534
535
536
537
537
537
513
527
527
516
516
516
516
516
513
527
538
525
525
525
518
525
511
513
538
527
527
514
526
5.0
5.0
4.7
5.0
5.0
12.9
12.9
50.4
5.0
12.9
12.9
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
15.2
50.4
5.0
30.0
5.0
5.0
5.0
10
5.0
5.0
5.0
9
9
9
9
9
7
8
9
9
9
11
9
9
9
11
10
8
9
7
9
9
9
9
9
9
9
9
9
9
9
9
9
9
10
(5.2 ( 0.7) × 10
(5.9 ( 0.8) × 10
(5.1 ( 0.7) × 10
(5.8 ( 0.8) × 10
(5.8 ( 0.8) × 10
(5.8 ( 1.0) × 10
(5.8 ( 0.8) × 10
(6.0 ( 0.8) × 10
(5.7 ( 0.8) × 10
(6.2 ( 0.8) × 10
(5.4 ( 0.8) × 10
(5.6 ( 0.8) × 10
(5.6 ( 1.0) × 10
(5.3 ( 0.9) × 10
(6.3 ( 0.8) × 10
(6.3 ( 0.8) × 10
(6.0 ( 0.8) × 10
(6.8 ( 0.9) × 10
(7.6 ( 1.2) × 10
-
-
-
-
-
-
-
11
11
11
11
11
11
11
-11
-11
-11
-11
-11
-11
-11
3
3
3
5
5
5
5
00
00
00
22
22
24
22
537
537
536
525
525
525
525
5.0
12.9
50.4
5.0
15.2
30.0
50.4
9
9
9
9
9
9
9
(5.7(0.8) × 10
(6.2(0.8) × 10
(6.0(0.8) × 10
(7.5(1.1) × 10
(7.3(1.1) × 10
(6.4(1.0) × 10
(6.4(1.0) × 10
-
-
-
-
-
-
-
-
-
-
-
11
11
11
11
11
11
11
11
11
11
11
3
00
s
Temperature T of the Solid
-
-
-
-
-
-
-
-
-
11
11
11
11
11
11
11
11
11
300
300
339
360
393
406
412
415
417
3
3
3
3
3
5
5
5
5
00
00
00
00
00
27
24
22
16
508
514
526
531
537
511
518
525
538
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
9
9
9
9
9
9
9
9
9
(5.2(0.7) × 10
(5.9(0.8) × 10
(5.8(0.8) × 10
(5.8(0.8) × 10
(5.7(0.8) × 10
(6.9(1.3) × 10
(6.4(1.3) × 10
(7.5(1.1) × 10
(6.0(1.1) × 10
4
18
Reactor Pressure P
r
433
472
516
522
522
522
524
524
527
550
(5.6 ( 0.9) × 10-11
-
-
-
-
-
-
-
-
-
11
-11
3
3
3
3
4
4
4
4
4
00
00
00
00
18
15
17
12
06
534
535
537
537
516
516
516
516
516
12.9
7
8
9
11
7
(5.8 ( 1.0) × 10
(5.8 ( 0.8) × 10
(6.2 ( 0.8) × 10
(5.4 ( 0.8) × 10
(7.6 ( 1.2) × 10
(6.0 ( 0.8) × 10
(6.8 ( 0.9) × 10
(6.3 ( 0.8) × 10
(6.3 ( 0.8) × 10
(5.6 ( 0.9) × 10
11
11
11
11
11
11
11
11
-11
12.9
12.9
12.9
5.0
(6.0 ( 1.1) × 10
-11
(7.5 ( 1.1) × 10
-11
(7.3 ( 1.1) × 10
-11
(6.4 ( 1.0) × 10
5.0
5.0
8
9
(6.4 ( 1.3) × 10
-11
-11
(6.4 ( 1.0) × 10
5.0
5.0
10
11
(6.9 ( 1.3) × 10
-11
-11
(5.5 ( 1.1) × 10
-
-
-
-
11
11
11
11
5
5
6
6
6
62
99
05
61
96
(5.3 ( 1.1) × 10
(6.9 ( 1.6) × 10
(8.2 ( 1.2) × 10
(7.4 ( 1.0) × 10
(6.2 ( 1.3) × 10
a
Symbols are the same as in Table 1.
First, the possible influence of a number of MIP afterglow
parameters on the derived value of k2 was checked. Experi-
mental conditions and results are given in Table 4. The results
indicate again that neither the concentration of molecular
hydrogen, nor the temperature Ts of the solid, nor the reactor
pressure Pr have any systematic effect on the value of k2.
Next, the rate constant k2 was measured between 300 and
-11
a
Symbols are the same as in Table 1.
6
96 K. Table 5 summarizes the experimental conditions and
derived values for k2.
A weighted nonlinear regression gives the Arrhenius expres-
sion
k2 ) (7.9 ( 0.5) ×
-
1
1
0- exp
11
-0.8 ( 0.2 kJ mol
cm molecule s-1 (11)
3
-1
(
)
RT
Because of the symmetric error, eq 11 is preferred to a linear
regression. The expression and the experimentally derived rate
constants are illustrated on an Arrhenius plot in Figure 4. The
error ranges for the experimental points may seem large, but
this is only due to the scale chosen for ln k2. As a matter of
fact, the standard deviations for k2 in Table 5 vary between 13
and 23%, which is comparable to the values for the Cu + CH3-
Br reaction. Although a slight deviation from linearity was
observed for the Cu + CH3Cl and CH3Br reactions, non-
Arrhenius behavior does not seem to occur in the case of the
reaction between Cu and CH3I.
Figure 4. Arrhenius plot of ln k
2
versus 1/T: Full line (s), nonlinear
regression of k versus 1/T described by eq 11.
2
-1
endothermic by 17.6 kJ mol , and one would have an activation
energy of at least the same magnitude. The activation energy
-1
of 0.8 ( 0.2 kJ mol derived in our work cannot be reconciled
with the available thermochemical data for the reaction between
Cu and CH3I. However, the situation could become quite
different if the value of 3 eV is taken for the CuI dissociation
In addition the value of k2 is high taking into account that
25
-
1
energy. In this case reaction 3 becomes exothermic for -53.4
the enthalpy of reaction 3 ∆Hr ) +38.6 ( 21.5 kJ mol . The
-
1
kJ mol , and a small activation energy for the reaction is
entirely plausible.
reaction enthalpy ∆Hr is calculated using values given in the
JANAF tables23 and dissociation energies in ref 24. This large
uncertainty is mainly due to the value of the dissociation energy
Discussion
-
1 24
of CuI, which is quoted as 197 ( 21 kJ mol . But even
-
1
when the highest value of 218 kJ mol is taken for the
Since the kinetics of the reaction between Cu atoms and CH3-
Cl has already been investigated, this publication adds the
8
dissociation energy of CuI, the reaction Cu + CH3I stays

1354 J. Phys. Chem. A, Vol. 102, No. 8, 1998
Vinckier and Vanhees
TABLE 6: Arrhenius Parameters A and E for the Reactions Me + RX f MeX + R with the Temperature Range, the Vertical
of RX,2
9,31,32
and the Dissociation Energy D(C-X) for the C-X Bond in RX. The Values of E with (*)
24
Electron Affinity EA
v
Are Obtained Using the Three-Parameter Expression 8
Cu + CH
3
X
3
K + CH X
EA
(eV)
v
D(C-X)
A
E
A
E
-
1
(cm molecule s-1
3
-1
(kJ mol-1)
(cm molecule s-1
3
-1
(kJ mol-1)
RX
(kJ mol
)
T (K)
)
T (K)
)
ref
+
1.1
0.7
-10
-10
CH
3
F
-6.2
-3.45
452
351
822-922
831-917
1.9- × 10
59 ( 3.3
32 ( 3.6
27
28
-
-
-
11
+2.0
CH
CH
CH
3
Cl
Br
I
389-853
300-804
300-696
(1.7 ( 0.4) × 10
(1.7 ( 0.2) × 10
(7.9 ( 0.5) × 10
34.4 ( 1.1
3.2- × 10
1.2
2
4.8*
8.2 ( 0.5
( 3.5*
0.8 ( 0.2
11
11
+0.3
-10
3
3
-0.5
293
236
798-903
1.7- × 10
15.9 ( 1.2
27
33
0.2
3
0.3
0
TABLE 7: Calculated r
c
Values for the Reactions Cu + RX f CuX + R. The Values Are Obtained Using the Expression A )
2
29,31
26
Q
r
W
r
) π(r
c
) W
r
, the Vertical Electron Affinity EA
v
of RX,
and the Adiabatic Electron Affinity EAad of RX
A (cm molecule s-1
3
-1
)
V
( m s-1
)
Q
r
(Å2)
r
( Å)
EA
r
(Å)
EAad(RX) (eV)
Cu + RX
r
c
v
(RX) (eV)
c
c
r (Å)
-
-
-
11
11
11
Cu + CH
Cu + CH
Cu + CH
3
Cl
3
Br
3
I
(1.7 ( 0.4) × 10
(1.7 ( 0.2) × 10
(7.9 ( 0.5) × 10
475
408
380
3.58
4.16
20.77
1.07
1.15
2.57
-3.45
-0.5
0.3
1.29
1.75
1.94
0.1
0.4
0.6
1.89
1.97
2.02
results for the reaction of Cu with CH3Br and CH3I. Conse-
quently, it is possible to check the effect of electronegative
substituents on the reactivity of methyl halides for a number of
metal atom reactions. The Arrhenius parameters, i.e. the
preexponential factor A and the activation energy E, are given
in Table 6.
electron affinity EAv has to be used, while for small rc values
the adiabatic electron affinity EAad is more appropriate. In Table
7 the results for both electron affinities are shown. The values
of EAad are derived from a figure in ref 26 which represents
the potential-energy curve as a function of the C-X bond
-
distance for both the CH3X molecule and the CH3X molecular
Regarding the three copper atom reactions studied, no other
kinetic data are presently available in the literature for com-
parison. In contrast, reactions of alkyl halides RX with alkali-
metal atoms have been investigated in more detail for more than
ion. These curves were calculated using the Morse potential
for the molecule and Wentworth’s empirical potential-energy
function for the negative ion.
The preexponential factor A for the reaction between Cu and
CH3Cl corresponds to a distance rc of 1.07 Å. Inserting IE(Cu)
6
0 years. The electron-jump model was introduced to explain
4,5
24
29
the reactivity of Na atoms with halomethanes. The reaction
between the metal Me and CH3X is initiated by a sudden
electron jump from Me to CH3X in the vicinity of the crossing
between the covalent and ionic potentials. As an approximation,
it is reasonable to assume that the CH3X molecule is unaware
of the presence of the Me atom just before the electron jump
) 7.7 eV and EAv(CH3Cl) ) -3.45 eV in eq 1, one arrives
at an rc value of 1.29 Å, while with EAad(CH3Cl) ) 0.1 eV26
rc becomes equal to 1.89 Å. Since the experimentally derived
rc is smaller than the theoretically calculated values and all these
rc values are smaller than the equilibrium distance re in the
2
3
molecule CuCl (re(Cu-Cl) ) 2.05 Å), it is obvious that the
reaction Cu + CH3Cl does not occur according to the electron-
jump mechanism.
-
and that the CH3X molecular ion represents the initial state of
the product immediately after the electron jump. Under such
conditions, the multidimensional potential surfaces can be
replaced by a potential-energy curve as a function of the C-X
For a metal atom reaction with CH Br the activation energy
3
E is smaller compared to the CH Cl reactions, as can be seen
3
-
bond distance for both the CH3X molecule and the CH3X
in Table 6. However, the preexponential factor for Cu + CH3-
molecular ion. K. T. Wu26 has estimated potential-energy
barriers for the reactions of alkali atoms with various methyl
halides, based on this model.
Br is as small as for Cu + CH Cl, which results again in an rc
3
smaller than the values calculated using EAv and EAad.
Therefore, the electron-jump mechanism can be excluded here
too.
The discussion will be limited to the reactions of Cu and K
with the methyl halides since both atoms have an electronic
configuration with one 4s electron in the outer shell. Arrhenius
As is shown in Table 6, the reaction between Cu + CH I
3
-
1
has a low activation energy E of 0.8 ( 0.2 kJ mol . The
27,28
-11
3
-1
expressions for K
have only been derived in rather limited
preexponential factor A is (7.9 ( 0.5) × 10 cm molecule
-
1
temperature ranges from 798 to 922 K, and the parameters are
s , which results in an r of 2.57 Å. In this case, the
c
also shown in Table 6. Previous studies of metal atom reactions
experimentally derived r is larger than 1.94 Å and 2.02 Å,
c
with Cl21
3,16
have indicated that the electron-jump mechanism
calculated with EA and EA respectively. These data might
v
ad
is characterized by a large preexponential factor A and a low
activation energy E. Since the reaction of Cu with CH3Cl has
indicate an electron-jump mechanism. However, it is clear that
the A factor is lower than for other metal atom-halogen
-
11
3
13
2
a preexponential factor of only (1.7 ( 0.4) × 10
cm
reactions. For instance, the reaction between Cu and Cl has
a preexponential factor A ) 3.3 × 10
-
1
-1
-10
3
-1 -1
molecule and the activation energy E is 34.4 ( 1.1 kJ
s
cm molecule s .
This can simply be explained by the values of the vertical
-
1
8
mol , the electron-jump mechanism could be ruled out. This
is confirmed by considering the distance rc at which the electron
transfer should occur. A value for rc can be calculated in two
ways. On the one hand, the experimentally derived preexpo-
nential factor A can be used to calculate reaction cross sections
Qr and thus also rc values using the expression A ) QrVr )
electron affinity of 0.3 eV for CH I compared to the much larger
3
value of 1 eV for Cl . Considering this and the fact that the rc
2
values are smaller than 3 Å, a close-range electron-transfer
mechanism is proposed for the Cu + CH I reaction.
3
For the reaction between K and CH Cl the activation energy
3
2
π(rc) Vr. The values obtained are given in Table 7.
is comparable to the value for Cu, but the preexponential factor
On the other hand, rc can be calculated using expression 1.
is a factor of 10 higher. With the vertical electron affinity of
CH3Cl (-3.45 eV) and the ionization energy for K (4.3 eV)
It has been mentioned16 that for large values of rc the vertical
26
24

2
Cu ( S) Atom Reaction with CH3Br
J. Phys. Chem. A, Vol. 102, No. 8, 1998 1355
activation energy of the reactions and the bond strength of the
methyl halides.
It may be reasonable to conclude that the harpooning
mechanism, which successfully describes alkali metal-methyl
halide reactions, cannot provide a quantitative approach for the
copper atom reactions with methyl chloride and bromide. For
these reactions the electron-jump mechanism can be excluded.
On the other hand, it can be stated that the reaction between
Cu and CH3I occurs according to a close-range electron-transfer
mechanism. The good correlation between the activation energy
and the dissociation energy of the C-X bond in RX is rather
an indication for an atom-transfer mechanism.
Acknowledgment. The authors are grateful to the Joint Fund
for Basic Research (FKFO) for a research grant. I.V. was a
Research Assistant of the Fund for Scientific Research (FWO),
Flanders. C.V. is a Research Director of the FWO.
Figure 5. Activation energy E for the reactions Me + RX f MeX +
R (given in Table 6) as a function of the vertical electron affinity EA
v
of RX (0 Cu; 4 K; b Cu with E obtained using the three-parameter
expression).
References and Notes
(
1) Polanyi, M.; Atomic Reactions; Williams and Norgate Ltd.: London,
1
932.
(
(
2) Parrish, D. D.; Herm, R. R. J. Chem. Phys. 1971, 54, 2518.
3) Weiss, P. S.; Mestdagh, J. M.; Schmidt, H.; Covinsky, M. H.; Lee,
Y. T. J. Phys. Chem. 1991, 95, 3005.
(
(
(
(
4) Herschbach, D. R. AdV. Chem. Phys. 1966, 10, 319.
5) Ogg, R. A.; Polanyi, M. Trans. Faraday Soc. 1935, 31, 1375.
6) Warhurst, E. Q. ReV. Chem. Soc. 1951, 5, 44.
7) Haresnape, J. N.; Stevels, J. M.; Warhurst, E. Trans. Faraday Soc.
1
940, 36, 465.
8) Vinckier, C.; Vanhees, I.; Sengupta D.; Nguyen M. T. J. Phys.
Chem. 1996, 100, 8302.
9) Vinckier, C.; Dumoulin, A.; Corthouts, J.; De Jaegere, S. J. Chem.
Soc., Faraday Trans. 2 1988, 84, 1725.
10) Vinckier, C.; Corthouts, J.; De Jaegere, S. J. Chem. Soc., Faraday
Trans. 2, 1988, 84, 1951.
11) Vinckier, C.; Verhaeghe, T.; Vanhees, I. J. Chem. Soc. Faraday
Trans.1994, 90, 2003.
(
(
(
(
(12) SAS statistical package; SAS Institute Inc.: Cary, NC, 1992.
(13) Vinckier, C.; Verhaeghe, T.; Vanhees, I. J. Chem. Soc., Faraday
Figure 6. Activation energy E for the reactions Me + RX f MeX +
R (given in Table 6) as a function of the dissociation energy of the
C-X bond in RX (0 Cu; 4 K; b Cu with E obtained using the three-
parameter expression).
Trans. 1996, 92, 1455.
(14) Vinckier, C.; Dumoulin, A.; De Jaegere, S. J. Chem. Soc., Faraday
Trans. 2 1991, 87, 1075.
(15) Vinckier, C.; Christiaens, P. J. Phys. Chem. 1992, 96, 2146.
(16) Vinckier, C.; Christiaens, P. J. Phys. Chem. 1992, 96, 8423.
(17) Talcott, C. L.; Ager, J. W., III; Howard, C. J. J. Chem. Phys. 1986,
an rc value of 1.85 Å is obtained. In case the adiabatic electron
affinity of CH3Cl ()0.1 eV)26 is used, rc is 3.42 Å. The results
indicate that the electron jump might take place over a rather
short distance. For the reactions of K with CH3Br and CH3I,
84, 6161.
(
18) Fontijn, A.; Felder, W. In ReactiVe Intermediates in the Gas Phase,
Generation and Monitoring; Setser, D.W., Ed.; Academic Press: New York,
1979; Chapter 2.
(19) Howard, C. J. J. Phys. Chem. 1979, 83, 3.
the electron jump occurs over longer distances.
K. T. Wu26 has estimated potential-energy barriers for the
(20) Guido, M.; Balducci, G.; Gigli, G.; Spoliti, M. J. Chem. Phys. 1971,
5, 4566.
5
reactions of alkali atoms with various methyl halides, on the
basis of the electron-jump model. The values obtained are 183,
(
21) Heberger, K.; Kem e´ ny, S.; Vid o´ czy, T. Int. J. Chem. Kinet. 1987,
19, 171.
(22) Herzberg, G. Molecular Spectra and Molecular Structure I: Spectra
of Diatomic Molecules; Van Nostrand Reinhold Co., Inc.: New York, 1950.
23) JANAF Thermochemical Tables; J. Phys. Chem. Ref. Data 1985,
-
1
5
2, 24, and 2.5 kJ mol for Me + CH3F, CH3Cl, CH3Br, and
CH3I, respectively, so the barrier decreases as the halogen
changes from F to I. A comparison of these theoretically
calculated values with the experimentally measured activation
energies in Table 6 reveals a remarkable difference. However,
the experimentally determined values do decrease from CH3F
to CH3I.
(
1
4, Suppl. 1.
(24) Weast, R. C.; Astle M. J. CRC Handbook of Chemistry and Physics;
CRC Press: Boca Raton, FL, 1996-1997.
25) Radzig, A. A.; Smirnov, B. M. Reference Data on Atoms, Molecules
and Ions; Springer: Berlin, 1985.
26) Wu, K. T. J. Phys. Chem. 1979, 83, 1043.
(
(
For several types of reactions correlations have been observed
between the reactivity and the ability of reagents to accept
(27) Husain, D.; Lee, Y. H. Int. J. Chem. Kinet. 1988, 20, 223.
(28) Husain, D.; Lee, Y. H. J. Photochem. Photobiol. A: Chem. 1988,
3
0
42, 13.
29) Burrow, P. D.; Modelli, A.; Chiu, N. S.; Jordan, K. D. J. Chem.
Phys. 1982, 77, 2699.
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electrons described by their electron affinity EA. Table 6
shows a strong negative correlation between the activation
energy E of the reaction and the vertical electron affinity EAv
of RX, as is also illustrated in Figure 5. The activation energy
E of the Me + RX reactions can also be related to the
dissociation energy D(C-X) of the C-X bond in the molecule
RX. As can be seen in Table 6 and as is illustrated in Figure
(
(
(
(
31) Moutinho, A. M. C.; Aten, J. A.; Los, J. Chem. Phys. 1974, 5, 84.
32) Giordan, J. C.; Moore, J. H.; Tossell, J. A. Accounts Chem. Res.
1
986, 19, 281.
33) Kerr, J. A.; Lissi, E. A.; Trotman-Dickenson, A. F. J. Chem. Soc.
1964, 2, 1673.
(
6
, a good correlation is observed between the magnitude of the