The four isotopomer reactions of NH(a) and ND(a) with NH3(X) and ND3(X)

Article abstract of DOI:10.1524/zpch.218.4.439.29201

The reactions NH(a) + NH₃ (X) → products (1) ND(a) + NH₃ (X) → products (2) NH(a) + ND₃ (X) → products (3) ND(a) + ND₃ (X) → products (4) were studied in a quasi-static reaction cell at room temperature and pressures of 10 and 20 mbar with He as the main carrier gas. The electronically excited reactants NH(a) and ND(a) were generated by laser-flash photolysis of HN₃ and DN₃, respectively, at λ = 308 nm and detected by laser-induced fluorescence (LIF). Also the ground state species NH(X) and ND(X) as products were detected by LIF. From the measured concentration-time profiles of NH(a) and ND(a) under pseudo-first order conditions, the following rate constants were obtained: k₁, = (9.1 ± 0.9) × 10¹³ cm³ mol^-1 s^-1 k₂ = (9.6 ± 1.0) × 10¹³ cm³ mol^-1 s^-1 k₃ = (8.0 ± 1.0) × 10¹³ cm³ mol^-1 s^-1 k₄ = (7.2 ± 0.8) × 10¹³ cm³ mol^-1 s^-1. The major products are the corresponding NH_i-D_2-i(X) radicals (i = 0, 1, 2), whereas quenching processes such as NH(a) + ND₃ → NH(X) + ND₃ are of minor importance (1%). The isotope exchange NH(a) + ND₃ → ND(X) + NHD₂ is negligible, and the corresponding channel on the singlet surface NH(a) + ND₃(X) → ND(a) + NHD₂ (X) contributes with 1% to the overall NH(a) depletion in that reaction. The experimental findings are discussed in terms of a chemical activation mechanism by means of statistical rate theory.

Full text of DOI:10.1524/zpch.218.4.439.29201

Z. Phys. Chem. 218 (2004) 439–455
by Oldenbourg Wissenschaftsverlag, München
The Four Isotopomer Reactions of NH(a)
˜
˜
and ND(a) with NH3(X) and ND3(X)
By L. Adam1, W. Hack1, , and M. Olzmann
2
∗
1
Max-Planck-Institut für biophysikalische Chemie, D-37070 Göttingen, Germany
Institut für Physikalische Chemie, Universität Karlsruhe, Fritz-Haber-Weg 4,
2
D-76128 Karlsruhe, Germany
Dedicated to Prof. Dr. Klaus Scherzer on the occasion
of his 70th birthday
(Received February 2, 2004; accepted February 13, 2004)
Kinetics / Isotope Effect / Laser-Induced Fluorescence /
Complex-Forming Bimolecular Reaction
The reactions
˜
NH(a)+NH3(X) → products
(1)
(2)
(3)
(4)
˜
ND(a)+NH3(X) → products
˜
NH(a)+ND3(X) → products
˜
ND(a)+ND3(X) → products
were studied in a quasi-static reaction cell at room temperature and pressures of 10 and
20 mbar with He as the main carrier gas. The electronically excited reactants NH(a)
and ND(a) were generated by laser-flash photolysis of HN3 and DN3, respectively, at
λ = 308 nm and detected by laser-induced fluorescence (LIF). Also the ground state
species NH(X) and ND(X) as products were detected by LIF.
From the measured concentration-time profiles of NH(a) and ND(a) under pseudo-first
order conditions, the following rate constants were obtained:
k1 = (9.1 0.9)×1013 cm3 mol−1 s−1
k2 = (9.6 1.0)×1013 cm3 mol−1 s−1
k3 = (8.0 1.0)×1013 cm3 mol−1 s−1
k4 = (7.2 0.8)×1013 cm3 mol−1 s−1
.
˜
The major products are the corresponding NHi D2−i (X) radicals (i = 0, 1, 2),
whereas quenching processes such as NH(a) + ND3 → NH(X) + ND3 are of minor im-
portance (1%). The isotope exchange NH(a) + ND3 → ND(X) + NHD2 is negligible, and
*
Corresponding author. E-mail: whack@gwdg.de
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440
L. Adam et al.
˜
˜
the corresponding channel on the singlet surface NH(a) + ND3(X) → ND(a) + NHD2(X)
contributes with 1% to the overall NH(a) depletion in that reaction. The experimental
findings are discussed in terms of a chemical activation mechanism by means of statistical
rate theory.
1. Introduction
The reactions of electronically excited singlet radicals like NH(a 1∆) with
molecules in their electronic ground state can be used to produce chemically
activated complexes of well-known stable species in their electronic ground
ꢀ
ꢁ
ꢀ
ꢁ
1
1
1
*
˜
˜
state, e.g. CH (a A ) + H O X A → CH3OH X A1 [1, 2]. Since in add-
˜
2
1
2
1
ition to the chemical energy from the newly formed bond, the electronic energy
contributes to the internal excitation of the molecule, the method should be
termed “electronic chemical activation”. An interesting aspect of this method is
that molecules with various amounts of vibrational energy can be generated by
properly choosing the chemical nature and the electronic states of the reactants.
The reactions of NH(a 1∆) with species containing hydrogen-element
bonds generally proceed via insertion mechanisms [3]. Therefore, the reaction
of NH(a 1∆) with NH3 can be used to produce vibrationally excited hydrazine,
*
N2H4 , in the electronic ground state. Its subsequent decomposition can be
compared with that induced by other chemical activation processes such as
*
H + N2H3 → N2H4 → NH2 + NH2 [4]. For the overall reaction
ꢀ ꢁ
1
˜
NH(a ∆)+NH3 X → products
(1)
rate constants of 8.8×1013 cm3 mol−1 s−1 [5] and 6.6×1013 cm3 mol−1 s−1 [6]
were determined at room temperature.
In contrast to NH(a 1∆), the reaction of ground state NH(X 3Σ−) with am-
monia is very slow with a rate constant < 4.8×107 cm3 mol−1 s−1 at 298 K [7].
No indication for an insertion mechanism NH(X) + NH3 → N2H4 was found.
Many pyrolysis or photodissociation experiments with N2H4 have been
performed [7–14]. In early studies by Wagner et al., the decomposition of
hydrazine behind reflected shock waves was investigated at temperatures
between 1000 and 1600 K [12–14]. Besides the main dissociation chan-
nel N2H4 → 2NH2, also a possible contribution from the reaction N2H4 →
NH3 + NH was discussed [14]. Therefore, it is interesting to look for NH(X) as
a possible reaction product in our electronic chemical activation experiment.
The kinetics of reaction (1) can be compared with the kinetics of the re-
actions of ammonia with O( 1D) and CH (a 1A ), which are isoelectronic to
˜
2
1
NH(a 1∆).
For O( 1D) + NH3 rate constants of 3.8×1014 cm3 mol−1 s−1 [15] and 1.5×
1014 cm3 mol−1 s−1 [16] are reported with no obvious temperature dependence
in the range 204 ≤ T/K ≤ 354 [16]. As reaction products, OH(X 2Π) and
NH(a) were detected, where the NH(a) concentration relative to that of OH(X)
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˜
˜
The Four Isotopomer Reactions of NH(a) and ND(a) with NH3(X) and ND3(X)
441
is in the range 3%–15% [17]. A bimodal rotational distribution in OH(X,
v = 0) found by Rettner et al. [18] is interpreted as being due to the simultan-
eous occurrence of an abstraction and an insertion channel.
The reaction of CH (a) with NH proceeds in the temperature range 210 ≤
˜
2
3
T/K ≤ 475 with a rate constant of 1.7×1014 (T/295 K)−1.2 cm3 mol−1 s−1. Be-
cause NH2 radicals were detected as major products [19], an insertion mechan-
ism was suggested [20].
In the present work, the four isotopomer reactions
ꢀ ꢁ
1
˜
NH(a ∆)+NH3 X → products
(1)
(2)
(3)
(4)
ꢀ ꢁ
1
˜
ND(a ∆)+NH3 X → products
ꢀ ꢁ
1
˜
NH(a ∆)+ND3 X → products
ꢀ ꢁ
1
˜
ND(a ∆)+ND3 X → products
are studied. Overall rate constants are determined and special emphasis is put
on the possible isotope exchange pathways in reaction (2) and (3) on the singlet
surface, viz.
ꢀ ꢁ
ꢀ ꢁ
1
1
˜
˜
ND(a ∆)+NH3 X → NH(a ∆)+NDH2 X
(2b)
(3b)
ꢀ ꢁ
ꢀ ꢁ
1
1
˜
˜
NH(a ∆)+ND3 X → ND(a ∆)+NHD2 X .
ꢀ ꢁ
ꢀ ꢁ
˜
˜
All active species, NH(a), NH(X), ND(a), ND(X), NH2 X , NHD X , and
ND2 X , can be directly observed by laser-induced fluorescence.
ꢀ ꢁ
˜
2. Experimental
The experiments were performed at room temperature in a quasistatic laser-
flash photolysis/laser-induced fluorescence (LIF) system, where “quasistatic”
means that the flow through the reaction cell is negligible between the pump
and the probe pulse but sufficient to exchange the gas volume between two
subsequent pump pulses. The carrier gas was He at total pressures of 10 and
20 mbar.
The experimental set up is described in detail elsewhere [21], and only the
essentials are repeated here. For the photolysis, a XeCl-exciplex laser (Lambda
Physik LPX 205) with pulse energies in the range 200 ≤ E/mJ ≤ 400 and
a beam area of about 1.1 cm2 was used. The probe laser was a dye laser
(Lambda Physik FL 3002) with a fluence in the range 20 ≤ E/mJ cm−2 ≤ 220
and a beam area of 7 mm2. It was pumped by an exciplex laser (Lambda Physik
LPX205, XeCl; 230 ≤ E/mJ ≤ 290). The fluence of the dye laser was shown to
be sufficient to saturate the excited transition, and the frequency doubled laser
beam with a fluence of 2 ≤ E/mJ cm−2 ≤ 3 was also sufficient to saturate the
observed transition in OH (see below).
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442
L. Adam et al.
The NH(a) (ND(a)) radicals were produced by HN3 (DN3) photolysis in
˜
˜
the A − X band at λ = 308 nm with a rotational excitation significantly above
room temperature. The rotationally hot population, however, relaxes to a ther-
mal distribution mainly by collisions with He on a µs time scale.
NH(a, v = 0) was detected by exciting the P3 line at λ = 326.22 nm of the
1
transition c Π, vꢀ = 0 ← a 1∆vꢀꢀ = 0, in the wavelength range 325 ≤ λ/nm
≤ 328. The undispersed fluorescence from the excited state was observed per-
1
pendicular to the laser beam. ND(a, v = 0) was excited via the transition c Π,
vꢀ = 0 ← a 1∆vꢀꢀ = 0 in the wavelength range 324 ≤ λ/nm ≤ 326. For the ki-
netic measurements, the transition excited at λ = 324.94 nm (P4-line) was used.
We detected the undispersed fluorescence, using filters to suppress scattered
radiation from the excitation beam.
For the detection of NH(X), the transition A 3Πvꢀ = 0 ← X 3Σ, vꢀꢀ = 0 was
excited in the wavelength range 335.5 ≤ λ/nm ≤ 338.5, and the fluorescence
signal from the A 3Πvꢀ = 0 state was recorded.
ꢀ
ꢁ
2
˜
The NH2 X B1 radicals were detected by the fluorescence induced by the
2
2
˜
˜
transition A A1(090) ← X B1(000) at a wavelength of 597.65 nm.
Gases with the highest commercially available purity were used: He,
99.9999%, Praxair; NH3, 99.998%, UCAR; D2O, 99.8%, Merck and N2,
99.995%, UCAR. HN3 was synthesized by melting stearic acid, CH3(CH2)16
COOH, with NaN3. It was dried with CaCl2 and stored in a bulb at partial
pressures ≤ 200 mbar diluted with He (overall pressure ca. 1 bar). For safety
reasons, the HN3 containing devices were covered with a wooden box since
HN3 is highly explosive even at low pressures.
The isotopomer DN3 was obtained via the exchange reaction
HN3 +D2O → DN3 +HDO
(5)
by adding D2O to the storage bulb. Furthermore, it is to be noted that the reac-
tion sequence
ND3 +HN3 ⇔ HD3N4 ⇔ NHD2 +DN3
(6)
can also lead to isotope exchange.
3. Results and discussion
3.1 Reaction rates
The reactions (1)–(4) were studied under pseudo-first order conditions with
ammonia in large excess over the imino radicals. The NH(a) radicals also react
with the precursor molecules,
NH(a)+HN3 → products
(7)
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˜
˜
The Four Isotopomer Reactions of NH(a) and ND(a) with NH3(X) and ND3(X)
443
and, hence, the depletion of NH(a) has to be described by:
−d[NH(a)]/dt = ki [NH(a)][R]+k7[NH(a)][HN3]+kq[NH(a)][He] (I)
with i = 1 and 3 and [R] = [NH3] and [ND3], respectively.
Because DN3 is produced by reaction (5), the reactions of ND(a) with the
different species occurring in this isotope exchange process have to be included
into the rate law for the depletion of ND(a), viz.
ND(a)+HN3 → products
ND(a)+DN3 → products
ND(a)+D2O → products
ND(a)+HDO → products
ND(a)+H2O → products .
(8)
(9)
(10)
(11)
(12)
It follows
−d[ND(a)]/dt = ki [ND(a)][R]+k8[ND(a)][HN3]+k9[ND(a)][DN3]
+k10[ND(a)][D2O]+k11[ND(a)][HDO]+k12[ND(a)][H2O]
+kq[ND(a)][He]
(II)
with i = 2 and 4 and [R] = [NH3] and [ND3], respectively.
Since all terms in Eqn. (I) and (II) are first-order with respect to the imino
radical, they can be combined to give
−d[NH(a)]/dt = keIff[NH(a)]
and
II
eff
−d[ND(a)]/dt = k [ND(a)] .
In general, the physical quenching by He can be neglected, because kq <
6×108 cm3 mol−1 s−1 [22]. The relevant concentrations of the other species,
HN3, DN3, D2O, HDO and H2O, are given in the headings of Tables 1–4. In
the case of reaction (2) (Table 2), it was assumed that [DN3] is nearly equal
to [HN3] in presence of an excess of D2O due to the isotope exchange reac-
tion (5). This assumption, which is not essential for the determination of the
rate constants, is supported by the observation of nearly equal NH(a)/ND(a)
fluorescence signal intensities. In Table 4, the sum of the concentrations of D2O
and HDO is given. The formation of H2O due to the secondary reaction
HDO+HN3 → H2O+DN3
(13)
was neglected since it does not influence the resulting rate constants signifi-
cantly. The consumption of NH(a) and ND(a), respectively, in the absence of
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L. Adam et al.
Table 1. Experimental results for reaction (1), NH(a) + NH3 → products, [HN3] = 3.4×
10−11 mol cm−3
.
T
P
time range
[NH3]
10−9 mol cm−3
keIff
105 s−1
k1I
105 s−1
K
mbar
µs
293
293
293
293
293
293
293
10.1
10.0
9.9
10.0
10.0
9.9
0–200
0–80
0–34
0–18
0–11
0–8
0
0.027
0.35
0.69
1.29
1.87
2.68
3.23
0
0.3
0.7
1.4
2.1
2.8
3.6
0.32
0.66
1.26
1.84
2.65
3.20
9.9
0–7
Fig. 1. Semilogarithmic plot of [ND(a)] as a function of reaction time (tR) for reaction (2);
NH3 concentration (in 10−9 mol cm−3): = 0.0, = 0.3, =0.7, = 2.1, = 3.6.
NH3 and ND3 was measured in independent experimental runs, and the results
are also included in Tables 1–4. We note that the upper limit of the NH3 con-
centration is determined by the equilibrium HN3 + NH3 ⇔ NH4N3(s) since the
formation of solid NH4N3 is to be avoided.
Reaction (1) was studied at a pressure of 10 mbar under pseudo first-order
conditions in the range 1.6 ≤ [NH3]0/([NH(a)]0 ×104) ≤ 20, and the results
are given in Table 1. The depletion of NH(a) solely by the precursor molecule
HN3 was measured in independent experiments ([NH3]0 = 0). They lead to
a pseudo-first order rate constant k7[HN3] = 2.7×103 s−1, which corresponds
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˜
˜
The Four Isotopomer Reactions of NH(a) and ND(a) with NH3(X) and ND3(X)
445
Table 2. Experimental results for reaction (2), ND(a) + NH3 → products, [DN3] ≈
[HN3] ≈ 1×10−11 mol cm−3, [D2O] + [HDO]≈ 4×10−11 mol cm−3
.
II
T
K
P
mbar
time range
[NH3]
10−9 mol cm−3
k
k2II
105 s−1
eff
µs
105 s−1
293
293
293
293
293
293
293
10.0
10.0
10.1
10.1
10.1
9.9
0–200
0–80
0–34
0–18
0–11
0–8
0
0.026
0.38
0.72
1.45
2.02
2.73
3.46
0
0.3
0.7
1.4
2.1
2.8
3.6
0.35
0.69
1.42
1.99
2.70
3.43
10.0
0–7
to k7 = 7.9×1013 cm3 mol−1 s−1 in good agreement with the value of 7.3×
1013 cm3 mol−1 s−1 reported in Ref. [23]. Consequently, k7[HN3] is subtracted
from all values for keIff in order to obtain k1[NH3]. A plot of k1I = keIff −k7[HN3]
versus [NH3] leads to a straight line through the origin, and the slope provides
the second-order rate constant:
k1 = (9.1 0.9)×1013 cm3 mol−1 s−1
,
which is in good agreement with a value of 8.8×1013 cm3 mol−1 s−1 deter-
mined earlier in our laboratory [5]. The determination of the rate constant k1
was repeated in the present work in order to allow for a direct comparison with
the other isotopomer reactions.
Reaction (2) was studied under pseudo-first order conditions in the range
1.6 ≤ [NH3]0/([ND(a)]0 ×103) ≤ 20. The rate constant keIIff follows from a plot
of log ([ND]/[ND]0) vs. time as displayed in Fig. 1. The nearly horizontal line
for [NH3] = 0 corresponding to a rate constant of keIIff = 2.6×103 s−1 demon-
strates that reactions with molecules other than NH3 contribute with less than
10% to the overall rate of depletion of ND(a) (cf. Table 2). The plot of
II
k2II = k −2.6×103 s−1 versus [NH3] leads to a straight line through the origin,
eff
the slope of which provides the second-order rate constant:
k2 = (9.6 1)×1013 cm3 mol−1 s−1
.
The results for reaction (3) are summarized in Table 3. A rate constant
keIff = 3.2×103 s−1 is obtained in absence of ND3, which can be again essen-
tially attributed to the reaction of NH(a) with HN3. The rate constant keIff is
determined in a completely analogous manner to that for reaction (1). From
the slope of a plot of k3I = keIff −3.2×103 s−1 vs. [ND3], a second order rate
constant
k3 = (8.0 1.0)×1013 cm3 mol−1 s−1
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L. Adam et al.
Table 3. Experimental results for reaction (3), NH(a) + ND3 → products, [HN3] = 4.4×
10−11 mol cm−3
.
T
P
time range
[NH3]
10−9 mol cm−3
keIff
105 s−1
k3I
105 s−1
K
mbar
µs
293
293
293
293
293
293
293
293
293
10.0
10.0
10.0
10.1
10.1
10.0
10.1
10.1
10.1
0–200
0–80
0–34
0–18
0–11
0–8
0–8
0–7
0–7
0
0.032
0.32
0.70
1.18
1.64
2.30
2.96
3.31
6.47
0
0.3
0.7
1.4
2.1
2.8
3.6
4.1
8.1
0.29
0.67
1.15
1.61
2.27
2.93
3.28
6.44
Table 4. Experimental results for reaction (4), ND(a) + ND3 → products, [DN3] ≈[HN3]
≈ 1×10−11 mol cm−3, [D2O] + [HDO] ≈ 4×10−11 mol cm−3
.
II
T
K
P
mbar
time range
[NH3]
10−9 mol cm−3
k
k4II
105 s−1
eff
µs
105 s−1
293
293
293
293
293
293
293
293
293
293
293
10.0
10.0
10.0
10.1
10.1
10.0
10.1
10.1
10.2
10.1
10.1
0–200
0–80
0–34
0–18
0–11
0–10
0–10
0–10
0–8
0
0.03
0.31
0.63
1.07
1.66
2.39
2.56
2.93
4.33
5.80
8.70
0
0.3
0.7
1.4
2.1
2.8
3.6
4.1
6.0
8.1
12.2
0.28
0.60
1.04
1.63
2.36
2.53
2.90
4.30
5.77
8.67
0–8
0–7
was obtained, i.e. the reaction of NH(a) with ND3 is somewhat slower than the
reaction with NH3.
The results for reaction (4) are contained in Table 4. The pseudo-first order
plots are shown in Fig. 2, and the rate constant k4 follows from a plot of k4II =
II
eff
k
−3.0×103 s−1 vs. [ND3] as described above. We obtained
k4 = (7.2 0.8)×1013 cm3 mol−1 s−1
which is the lowest value of all isotopomer reactions. Obviously, ND3 reacts
slower than NH3 whereas ND(a) and NH(a) react with similar rates.
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˜
˜
The Four Isotopomer Reactions of NH(a) and ND(a) with NH3(X) and ND3(X)
447
Fig. 2. Semilogarithmic plot of [ND(a)] as a function of reaction time (tR) for reaction (4);
ND3 concentrations (in 10−9 mol cm−3): = 0.3 ; = 0.7 ; = 1.4; = 2.1, = 4.1.
3.2 Reaction products
The main product channel for reaction (1) is:
ꢀ ꢁ
ꢀ ꢁ
˜
˜
NH(a)+NH3 X → 2NH2 X
(1a)
with k1a/k1 = 0.93 [5], and the analogous reaction pathways were found to be
dominant for all four isotopomer reactions.
Additionally, there are exchange-reaction pathways on the singlet surface
conceivable, which are detectable for reaction (2) and (3), viz.
ND(a)+NH3 → NH(a)+NH2D
NH(a)+ND3 → ND(a)+NHD2 .
(2b)
(3b)
In the present work, we restrict our investigations on reaction (3b), since
NH(a) can be directly generated from HN3 whereas ND(a) is obtained from
DN3, which has to be produced in the preceding isotope exchange reaction (5).
The measured concentration-time profile for ND(a) as a product of reac-
tion (3) is shown in Fig. 3. The finite concentration of ND(a) at tR = 0 is caused
by the isotope exchange reaction
ND3 +HN3 ⇔ HD3N4 ⇔ NHD2 +DN3
(6)
which already occurs in the mixing region of our experimental setup. The pho-
tolysis of DN3 then leads to the observed [ND(a)]0 = 0. The shortest mixing
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448
L. Adam et al.
Fig. 3. The ND(a) fluorescence intensity vs. reaction time for reaction (3) with [ND3] =
4.1 × 10−10 mol cm−3
,
[HN3] = 5 × 10−10 mol cm−3
,
[ND(a)]0 = 2 × 10−15 mol cm−3
,
[NH(a)]0 = 5 × 10−13 mol cm−3, [ND3] = 4.1 × 10−10 mol cm−3, mixing time t ≈ 1 ms,
experimental results; simulations of the reaction system with: - - - - k3b = 1.6 ×
1012 cm3 mol−1 s−1, — k3b = 8×1011 cm3 mol−1 s−1 and · · · k3b = 4×1011 cm3 mol−1 s−1
.
time led to a ratio of the initial concentrations [ND(a)]0/[NH(a)]0 ≈ 0.01. It
can be seen from Fig. 3 that there is an increase of [ND(a)] for small reac-
tion times, which is interpreted as a formation of ND(a) in a chemical reaction.
From the concentration-time profile in Fig. 3, a rate constant for reaction (3b)
was estimated by a simulation of a complex reaction mechanism consisting of
reactions (1), (2), (3), (3b), and (4), where only the rate constant k3b was treated
as a parameter (cf. Fig. 3).
The initial concentration [ND(a)]0 was estimated to be 2×10−15 mol cm−3,
and it was found in the simulation that the [ND(a)] profile is not very sensitive
to this initial concentration. The interpretation of the ND(a) concentration-
time profiles is not simple due to the small ND(a) concentrations and the low
signal to noise ratio. The measured concentration profiles can be interpreted
with a rate constant k3b ≈ 8×1011 cm3 mol−1 s−1, and, thus, it can be esti-
mated that about 1% or less of the reaction proceeds via the exchange channel
(3b).
This reaction pathway is endoergic with ∆Ezp = 2.6 kJ/mol (zero-point en-
ergies from HF/6-31G* frequencies scaled by 0.89, see below), and from an
energetic point of view, it would be more favourable to study the reaction (2b).
However, there was no way to get DN3 sufficiently pure. For reaction (2), in
which the isotope exchange reaction pathway is exoergic by −2.3 kJ/mol, one
could expect a contribution of about 3% to the overall depletion of NH(a) via
reaction (2b). From these results it can be concluded that the NH(a) forma-
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The Four Isotopomer Reactions of NH(a) and ND(a) with NH3(X) and ND3(X)
449
tion is of minor importance in the N2H4 decomposition even at high excitation
energies.
The quenching channel
NH(a)+NH3 → NH(X)+NH3
(1c)
has been investigated by comparing [NH(X)] from reaction (1) with [NH(X)]N ,
2
the NH(X) concentration in the reaction
NH(a)+N2 → NH(X)+N2 .
(14)
In the absence of NH3 and in a large excess of N2 over HN3, all
NH(a) initially present is converted to NH(X) at long reaction times, i.e.,
[NH(a)]0 = [NH(X)]N . The consumption of NH(X) under these experimen-
∞
2
tal conditions can be neglected as seen from the NH(X) profiles. In the absence
of N2, the NH(X) radicals are formed in reaction (1c) since quenching by other
species in the system (HN3, He) is unimportant. The NH(X) consumption can
again be neglected. Thus, the fraction k1c/k1 can be determined directly from
the ratio
k1c
k1
[NH(X)]∞
[NH(a)]0
[NH(X)]∞
[NH(X)]N
=
=
∞
2
where [NH(X)] and [NH(X)]N are the NH(X) concentrations at long reac-
∞
∞
2
tion times due to reaction (1c) and (14), respectively. The reaction
NH(a)+HN3 → NH(X)+HN3
(7c)
leads to a small correction which could be neglected.
It turns out that reaction (1c) is of minor importance, and
k1c/k1 = 0.006 0.003 .
From an analogous analysis of [ND(X)], it follows that this is true for the
isotopomer reactions
ND(a)+NH3 → ND(X)+NH3
(2c)
and
ND(a)+ND3 → ND(X)+ND3 .
(4c)
The contributions of the quenching channel were too small to detect an
exchange reaction pathway as e.g.,
NH(a)+ND3 → ND(X)+NHD2
(15)
due to the ND(a) being present in the system (see above).
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450
L. Adam et al.
Fig. 4. Schematic energy diagram of the lowest singlet surface of N2H4 and steady-state
population f(E) of HN–NH3.
3.3 Modeling by statistical rate theory
There are several theoretical studies dealing with the structure and energetics
of the intermediates occurring in the NH(a) + NH3 reaction [24–27]. How-
ever, there is only one work, where also kinetic quantities are estimated [28].
Hence, in order to characterize the reaction mechanism and to verify the rate
constants and the isotope effect, we perform in the following an analysis using
RRKM [29–32] and SACM [31–35] calculations.
The basic mechanism was proposed by Pople et al. [24] and essentially
confirmed by two more recent studies [25, 26]. It is assumed that NH(a) and
NH3 at first form an adduct, HN–NH3, which subsequently isomerizes to
H2N–NH2. Then, H2N–NH2 can dissociate into NH2 + NH2:
NH(a)+NH3 ⇔ HN–NH3
HN–NH3 ⇔ H2N–NH2
(A)
(B)
(C)
H2N–NH2 → H2N+NH2 .
Because the following considerations are independent of the specific iso-
topic substitution, these unimolecular steps are denoted here in a general way
as (A), (B) and (C).
A schematic energy diagram for this reaction sequence is shown in Fig. 4,
and the relative energies used in this work are compiled in Table 5. They
are based on the following heats of formation (in kJ mol−1) [36]: NH(a), 502
(term energy from Ref. [37]); NH3, −45.9; H2N–NH2, 95.4; NH2, 185. For the
adduct HN–NH3 and TSB, the transition state of reaction step (B), we adopted
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The Four Isotopomer Reactions of NH(a) and ND(a) with NH3(X) and ND3(X)
451
Table 5. Energies relative to H2N–NH2; in parentheses values for the deuterated species
relative to D2N–ND2; ꢂEꢃf represents the average energy of the intermediate population
for T = 300 K.
Erel/kJ mol−1
NH(a) + NH3
HN–NH3
TSB
NH2 + NH2
H2N–NH2
ꢂEꢃf
361 (367)
182 (182)
281 (285)
274 (282)
0 (0)
366 (373)
the ab initio results from Skurski et al. [27] (MP2/aug-cc-p VDZ + diffuse
s, p, d, ( f ) functions).
It becomes evident that, due to the exoergicity of reaction steps (A) and (B),
HN–NH3 as well as H2N–NH2 are ro-vibrationally excited, and the kinetics of
the system has to be described by the rate constants for electronic chemical
activation conditions. Because of the low pressures in our experiments, the uni-
molecular reactions of the excited intermediates turn out to be much faster than
the collisional deactivation (see below). Therefore, the steady-state populations
of the intermediates can be approximated by the distribution function [30–32]
W(E) exp(E −/kBT )
f(E) =
dε
(III)
∞
ꢂ
W(ε) exp(−ε/kBT)
0
where W is the sum of states of HN–NH3, kB is Boltzmann’s constant, and
T denotes the temperature. The rate constants for the unimolecular steps
i = (−a), (B), (−B) and (C) follow by averaging:
∞
ꢃ
ki = ki(E) f(E)dE
(IV)
0
where the specific rate constants ki (E) are calculated by statistical models [30–
32] according to:
Wi(E − E0i)
ki(E) =
.
(V)
hρ(E)
Here, ρ(E) is the density of states of the respective reactant, HN–NH3
or H2N–NH2, and h denotes Planck’s constant. The number of open reaction
channels Wi is calculated for reactions steps i = (−A) and (C) by the sim-
plified Statistical Adiabatic Channel Model [35] and is identified for reaction
steps (B) and (−B) with the sum of states of the transition state according to
the RRKM model [29]; E0i is the corresponding threshold energy.
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452
L. Adam et al.
Table 6. Rate constants for the unimolecular steps (s−1) from Eqn. (IV) and bimolecular
rate constants (cm3 mol−1 s−1) from canonical SACM.
Reaction step
H
D
*
*
(A)
(−A)
(B)
9.1×1013
1.8×109
6.0×1011
9.4×109
1.2×1012
4.8×1013
8.4×1013
7.0×108
3.0×1011
3.7×109
6.1×1011
4.5×1013
(−B)
(C)
(−C)
*
adjust, see text.
All sums and densities of states were exactly counted [35, 38] for a total
angular momentum quantum number J = 20, which is essentially governed
by the orbital momentum caused by the capture process NH(a) + NH3 [39].
The molecular properties required were taken from the following sources:
NH(a) [37]; ND(a), calculated from the NH data by exchanging H for D; NH3
and ND3 [40]; NH2 and ND2 [41]; HN–NH3, TSB and H2N–NH2 as well as
their deuterated isotopomers, calculated ab initio on HF/6-31G*-level [42]
(frequencies scaled by 0.89 [43]).
The high-pressure limiting value of the bimolecular rate constant for
NH(a) + NH3 was computed by the canonical version of the simplified
SACM [34], where the anisotropy parameter α/β [44] was adjusted so as
to reproduce our measured rate constant of k1 = 9.1 × 1013 cm3 mol−1 s−1
(α/β = 0.493). As isotopic substitution does not alter the anisotropy of the in-
terfragment potential, the same value for α/β has been used in the calculation
for ND(a) + ND3, and a rate constant of k4 = 8.4×1013 cm3 mol−1 s−1 was ob-
tained. It is to be noted that the predicted ratio of k(NH(a) + NH3)/k(ND(a) +
ND3) = 1.1 is somewhat below the experimental value of 1.3; neverthe-
less, the isotope effect is reproduced in the correct order of magnitude.
The above value of α/β was also employed in the calculations of the spe-
cific rate constants for the reaction step (−A) by the microcanonical version
of SACM.
In an analogous approach, the specific rate constants for the reaction step
(C) were calculated. Here, a value of α/β = 0.65 was used; it was obtained
from an adjustment of the recombination rate constant for NH2 + NH2 to
an average experimental value of ∼ 5×1013 cm3 mol−1 s−1 [45]. Because the
available experimental data exhibit a considerable scatter [45], the results for
kC(E) are rather uncertain. As, however, they exceed k−B(E) by at least two
orders of magnitude, this has no influence on the overall kinetics. The resulting
rate constants for the steps (A)–(C) and their reverse reactions are summarized
in Table 6.
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The Four Isotopomer Reactions of NH(a) and ND(a) with NH3(X) and ND3(X)
453
4. Conclusions
From the analysis of our experimental results on the isotopomer reactions of
˜
˜
NH(a) and ND(a) with NH3(X) and ND3(X) in terms of statistical rate theory,
the following conclusions can be drawn:
1. the measured bimolecular rate coefficients represent high-pressure limiting
(or capture) values, because back dissociation (−A) is at least two orders of
magnitude slower than isomerization (B) to hydrazine,
2. hydrazine, once formed, essentially dissociates into NH2 + NH2 via reac-
tion step (C); back isomerization (−B) is again two orders of magnitude
slower,
3. the vanishing contribution of the isotope-exchange channels for the par-
tially deuterated species becomes evident in this way,
4. the lifetimes of HN–NH3 and H2N–NH2 formed from NH(a) + NH3 are in
the picosecond range; collision numbers > 1012 s−1 are required for a stabi-
lization of the intermediates,
5. the overall kinetics is not influenced by isotopic substitution; the isotope ef-
fect observed is due to the isotope dependence of the capture rate, it can be
reproduced by canonical SACM calculations,
6. our experimental results are compatible with the reaction route (A)–(C).
Acknowledgement
Thanks are due to the Deutsche Forschungsgemeinschaft (Sonderforschungs-
bereich 357 “Molekulare Mechanismen unimolekularer Prozesse”) and the
Fonds der Chemischen Industrie for financial support.
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