Rapid reduction of nitric oxide to dinitrogen by zirconium(II): Kinetic studies on a reaction controlled by gas-liquid transport

Article abstract of DOI:10.1021/ja983011p

Nitric oxide reacts with Cp₂Zr(PMe₃)₂ (1; Cp = η⁵-C₅H₅) in THF or toluene to yield dinitrogen and an oligomeric oxozirconocene species, [Cp_xZrO_y]_n. The reduction of NO occurs in two distinct steps: 1 reduces 2 equiv of NO to 1 equiv of N₂O, and then 1 reduces N₂O to N₂. In each step, 1 is converted to a monomeric oxozirconocene species [Cp₂ZrO], which may be trapped by the addition of Me₃SiCl or Cp₂ZrMe₂, to form Cp₂Zr(OSiMe₃)(Cl) and [Cp₂ZrMe]₂O, respectively. Kinetics for the reduction of NO by 1 were followed at low temperature (160 < T < 195 K) by monitoring the change in pressure of the system. Complete reaction was observed in less than 15 s, even at the lowest temperatures. The typical kinetic trace displayed two decay regimes, zero- and first-order, which were interpreted as the result of competing mass-transfer and chemical reaction processes. The kinetic results support a rate-limiting bimolecular reaction between NO and 1. The subsequent intermediates and mechanistic possibilities are discussed.

Full text of DOI:10.1021/ja983011p

8260
J. Am. Chem. Soc. 1999, 121, 8260-8269
Rapid Reduction of Nitric Oxide to Dinitrogen by Zirconium(II):
Kinetic Studies on a Reaction Controlled by Gas-Liquid Transport
,†
Kristopher McNeill* and Robert G. Bergman
Contribution from the Department of Chemistry, UniVersity of California, Berkeley, California 94720
ReceiVed August 21, 1998
5
Abstract: Nitric oxide reacts with Cp2Zr(PMe3)2 (1; Cp ) η -C5H5) in THF or toluene to yield dinitrogen and
an oligomeric oxozirconocene species, [CpxZrOy]n. The reduction of NO occurs in two distinct steps: 1 reduces
2
equiv of NO to 1 equiv of N2O, and then 1 reduces N2O to N2. In each step, 1 is converted to a monomeric
oxozirconocene species [Cp2ZrO], which may be trapped by the addition of Me3SiCl or Cp2ZrMe2, to form
Cp2Zr(OSiMe3)(Cl) and [Cp2ZrMe]2O, respectively. Kinetics for the reduction of NO by 1 were followed at
low temperature (160 < T < 195 K) by monitoring the change in pressure of the system. Complete reaction
was observed in less than 15 s, even at the lowest temperatures. The typical kinetic trace displayed two decay
regimes, zero- and first-order, which were interpreted as the result of competing mass-transfer and chemical
reaction processes. The kinetic results support a rate-limiting bimolecular reaction between NO and 1. The
subsequent intermediates and mechanistic possibilities are discussed.
Introduction
room temperature (or below), bleaching of the characteristic
black-red color is observed, and a colorless precipitate is
produced. The gaseous N-containing products are N2O and N2,
identified by FTIR (N2O) and GC (N2O and N2). The organo-
metallic products are less well-defined. The only product
The interconversion of nitrogen oxide species is important
1-4
5
in biological and environmental processes. Transition metals
play a prominent role in nitrogen reduction and oxidation in
6
biotic nitrogen cycling (by metalloenzymes ) and in conversion
1
15
observable by H NMR spectroscopy is the previously reported
of anthropogenic nitrogen oxide species to N2.7 The reaction
of nitrogen oxides with well-characterized organometallic
complexes might provide good models for these systems, but
little is known about the mechanisms of such reactions,
especially those that involve direct interactions with paramag-
,8
oxo trimer, [Cp2ZrO]3, which typically accounts for 21% of the
Zr-containing species. The remainder of the Zr-containing
material is presumed to be an insoluble oligomeric zirconium
oxo complex, [CpxZrOy]n, thought to arise (see evidence
summarized below) by oligomerization of monomeric
9
-14
netic NO.
We report here that the Zr(II) complex Cp2Zr-
15
Cp2ZrdO. The absence of nitrogen in the insoluble precipitate
is confirmed by combustion analysis. The insoluble material
may be a polymer (e.g., [Cp2ZrO]n), a cluster (e.g., Cp4Zr4O6,
by analogy to the material formed when (C5Me5)2M(C2H4) (M
(PMe3)2 reacts exceedingly rapidly with NO, even at -113 °C,
ultimately leading to N2 (eq 1) through the intermediacy of N2O,
and we give preliminary information on the mechanism of both
steps in this transformation.
1
6
)
Ti, V) are exposed to N2O ), or a mixture of the two.
When the reaction of 1 and NO is carried out with a strictly
(1)
stoichiometric amount (2 equiv) of nitric oxide, N2O is observed
as the reduced N-containing product. With a molar deficiency
of NO, N2 is observed as the predominant N-containing product.
This indicates that two sequential O-atom-transfer steps are
involved in the complete reduction of NO to N2. The first
involves reaction of 2 equiv of NO with 1 to produce
Cp2ZrdO and N2O (eq 2), and the second is the reaction of
N2O with 1 (eq 3), leading to N2 and a second equivalent of
Cp2ZrdO.
Results
Reactions of Cp2Zr(PMe3)2 with NO and N2O. When
solutions of Cp2Zr(PMe3)2 (1) are treated with gaseous NO at
†
Current address: Department of Chemistry, University of Minnesota,
2
07 Pleasant St. SE, Minneapolis, MN 55455.
1) Delwiche, C. C. Denitrification, Nitrification and Atmospheric Nitrous
Oxide; John Wiley and Sons: New York, 1981.
2) Smil, V. Carbon Nitrogen Sulfur: Human Interference in Grand
Biospheric Cycles; Plenum Press: New York, 1985.
(
(
(2)
(3) Butler, A. R.; Williams, D. L. H. Chem. Soc. ReV. 1993, 233.
(4) Payne, W. J. Denitrification; John Wiley and Sons: New York, 1981.
(5) Schwartz, S. E.; White, W. H. In Trace Atmospheric Constituents:
(3)
Properties, Transformation and Fates; Schwartz, S. E., Ed.; John Wiley
and Sons: New York, 1983; Vol. 12.
The second stage in this process can be observed directly.
When solutions of Cp2Zr(PMe3)2 (1) are exposed to N2O at -78
°C, fast reaction occurs with deposition of [CpxZrOy]n. As with
(6) Kroneck, P. M. H.; Beuerle, J.; Schumacher, W. In Degradation of
EnVironmental Pollutants by Microorganisms and their Metalloenzymes;
Sigel, H., Sigel, A., Eds.; Marcel Dekker: New York, 1992; Vol. 28.
(
7) Armor, J. N. EnVironmental Catalysis; American Chemical Society:
Washington, DC, 1994.
(11) MacNeil, J. H.; Gantzel, P. K.; Trogler, W. C. Inorg. Chim. Acta
1995, 240, 299.
(8) Armor, J. N. Appl. Catal. B 1992, 1, 221.
(
9) MacNeil, J. H.; Berseth, P. A.; Westwood, G.; Trogler, W. C. EnViron.
(12) Meyer, C. D.; Eisenberg, R. J. Am. Chem. Soc. 1976, 98, 1364.
(13) Hendriksen, D. E.; Meyer, C. D.; Eisenberg, R. Inorg. Chem. 1977,
16, 970.
Sci. Technol. 1998, 32, 876.
(10) MacNeil, J. H.; Berseth, P. A.; Bruner, E. L.; Perkins, T. L.; Wadia,
Y.; Westwood, G.; Trogler, W. C. J. Am. Chem. Soc. 1997, 119, 1668.
(14) Haymore, B. L.; Ibers, J. A. J. Am. Chem. Soc. 1974, 96, 3325.
1
0.1021/ja983011p CCC: $18.00 © 1999 American Chemical Society
Published on Web 08/31/1999

Rapid Reduction of NO to N2 by Zirconium(II)
J. Am. Chem. Soc., Vol. 121, No. 36, 1999 8261
Scheme 1
the reaction of 1 and NO, the only soluble Zr-containing product
seen by NMR spectroscopy is [Cp2ZrO]3, and this accounts for
2
6% of the Zr-containing species by integration vs an internal
standard. Analysis of the gas phase by GC shows consumption
of N2O and production of N2 in 86% conversion.
Figure 1. Schematic representation of the experimental apparatus used
for measuring the kinetics of NO reduction by the change in pressure.
Evidence for Cp2ZrdO as a Product: Trapping Experi-
ments. Evidence for the initial formation of monomeric Cp2-
ZrdO as the first-formed product in this reaction was obtained
by chemical trapping studies. Carrying out the reaction of 1
with NO in the presence of 2 equiv of Me3SiCl eliminated the
Scheme 2
17
formation of precipitate and gave, instead, Cp2Zr(OSiMe3)(Cl)
1
(
2, 77% conversion based on H NMR integration vs an internal
standard, Scheme 1).
Similarly, treatment of 1 with N2O in the presence of Me3-
SiCl also gave complex 2 (100% conversion). Employing Cp2-
ZrMe2 as a trap, suggested earlier to be an efficient trap for
1
8,19
Cp2ZrdO,
gave [Cp2ZrMe]2O from the reaction of 1 and
N2O in 76% yield by NMR (Scheme 1).
We considered the possibility that the products from these
experiments did not arise from trapping of the intermediate but
instead from reaction of the added trap with the oligomeric
species. However, control experiments showed that allowing
the reaction of 1 with NO or N2O to proceed to give oligomeric
when NO is present in a limiting amount, the species that is
active in converting 2NO f N O f N is 1 and not PMe
3
2
2
(Scheme 2, path a).
Even though 1 reacts with NO much more quickly than does
[CpxZrOy]n, followed by addition of Me3SiCl, does not give 2
(eq 4). This reinforces the conclusion that a reactive precursor
PMe , the presence of the phosphine causes the N /N O ratios
3
2
2
produced in the reaction of 1 with NO to vary greatly, depending
on the conditions. It is simplest to consider two limiting cases.
When 1 equiv or less of NO is treated with complex 1, all of
the NO will be converted to N2O, and all of the N2O produced
will be consumed to give N2 (eq 5). In the other extreme, when
(
4)
to [CpxZrOy]n, presumably a monomeric oxo species,18 is being
trapped by Me3SiCl and that oligomerization of this species is
irreversible under these conditions.
Role of PMe3 in the Reduction of NO. One potential
complication in the analysis of this system is that free PMe3 is
also known to undergo rapid oxidation by NO, forming N2O
and Me3PdO.20 No Me3PdO was detected when the reaction
of 1 was carried out with a molar deficiency of NO, as indicated
(5)
complex 1 is exposed to a large excess of NO, such that all of
is consumed by NO in the first step and no amount of 1 is
1
left to react with N2O, it is expected that only N2O will be
produced. In this latter case, up to 6 equiv of NO will be
consumed, since the metal complex can react with 2 equiv and
the two phosphine ligands will each react with 2 equiv of NO
after 1 has been consumed (eq 6). These two extremes have
1
by H NMR spectroscopic analysis. However, Me3PdO could
be produced and then rapidly consumed by 1 (Scheme 2, path
b).
To rule out this possibility, 1 was treated with Me3PdO in
C6D6 at 20 °C. No reaction was observed under these conditions,
demonstrating that the reaction of PMe3 with NO is slower than
the reaction of 1 with NO (see also Kinetic Studies). Thus, if
Me3PdO were formed during the reaction of 1 with NO, it
would persist and be detected. Given these facts, it is clear that,
(6)
been approximated experimentally. With NO as the limiting
reagent, we have found by gas chromatographic analysis that
NO is converted to N2 in 86% yield. With excess NO, FTIR
analysis indicates that conversion to N2O is 69-87% based on
the stoichiometry of eq 6.
Kinetic Studies. It was possible to measure the rate of NO
consumption by the pressure change associated with the
conversion of 2NO to 1N2O. The reactions were performed in
a three-necked flask fitted with a known-volume bulb and a
pressure transducer (Figure 1). The reaction flask contained a
rapidly stirred solution of either PMe3 or 1 in THF and was
(
15) Fachinetti, G.; Floriani, C.; Chiesi-Villa, A.; Guastini, C. J. Am.
Chem. Soc. 1979, 101, 1767.
16) Smith, M. R., III; Matsunaga, P. T.; Andersen, R. A. J. Am. Chem.
Soc. 1993, 115, 7049.
(
(
(
(
17) Tilley, T. D. Organometallics 1985, 4, 1452.
18) Lee, S. Y.; Bergman, R. G. J. Am. Chem. Soc. 1996, 118, 6396.
19) Hanna, T. A.; Baranger, A. M.; Walsh, P. J.; Bergman, R. G. J.
Am. Chem. Soc. 1995, 117, 3292.
20) Halmann, M.; Kugel, L. J. Chem. Soc. 1962, 3272.
(

8262 J. Am. Chem. Soc., Vol. 121, No. 36, 1999
McNeill and Bergman
Figure 2. Typical kinetic trace for the reaction of PMe
3
and NO (entry
Figure 3. Typical kinetic trace for the reaction of 1 and NO (entry 6,
3
, Table 3). The solid line corresponds to a best-fit exponential function
Table 5). The best-fit line by least-squares regression for data for which
0 e t e 3 s has a slope of m ) -16.1 ( 0.03 µmol s and r )
-
1
2
-1
2
with a decay constant, kobs ) 0.0122 ( 0.0002 s , and r ) 0.9995.
0
.9983. This slope corresponds to a value for the NO flux JNO ) 1.71
-
2
-1
evacuated prior to introduction of nitric oxide. A kinetic run
was initiated by opening the stopcock separating the reaction
flask and the bulb, which was precharged with NO. The pressure
was observed to increase sharply and then decrease as the NO
was consumed. This technique proved to be very convenient
for the measurement of both slow rates (t1/2 ≈ 30 min) and
very fast rates (t1/2 ≈ 1 s). The temperature could be controlled
over a wide range, although lower temperatures, where the
solvent vapor pressure was low, provided the best signal-to-
noise ratios. Others have employed similar methods to measure
the NO consumption rates with P(OEt)321 and Rh salts.
In this study, the reaction rates for the reduction of NO by
both PMe3 and 1 were measured. The study of the kinetics of
the reaction of NO with PMe3 was useful both for confirming
its slower reaction rate (compared with that of 1) and for
providing a well-behaved system for comparison with the more
complicated kinetics for NO with 1.
( 0.04 µmol cm
s . The best-fit exponential decay for the data
-
1
collected after 4 s has a decay constant of kobs ) 0.617 ( 0.008 s
2
and r ) 0.9994.
role of the solvent, THF, was tested by performing the reactions
in the less-coordinating, sterically hindered analogue,23 2,5-
dimethyltetrahydrofuran (2,5-Me2THF). The rates for both
regimes were found to be the same within error for experiments
performed in THF and 2,5-Me2THF. The experimentally
determined rate laws for the two regimes are given in eqs 9
and 10.
22
(9)
(10)
The reaction of PMe3 with NO (eq 7) was followed at -78
The stirring rate affected the NO consumption rate differently
for the two systems studied, showing a pronounced effect on
the reaction of NO with 1 and a negligible one in the reaction
of NO with PMe3. The effects can be compared by plotting the
relative rate constants (krel) vs stirring rate, normalizing the
lowest stirring value to krel ) 1.0 (Figure 4).
°
C and was found to follow pseudo-first-order kinetics for the
consumption of NO (Figure 2). This system was assumed to
obey the second-order rate law established for the reaction of
P(OEt)3 and NO (eq 8).21 Employing the method of Kuhn et
(
7)
8)
Discussion
(
General Observations. Oxygen-atom-transfer reactions in-
volving Group 4 metallocene species have been of considerable
1
6,24-32
interest.
Nitrous oxide (N2O) has proven to be a relatively
al., a bimolecular rate constant for the consumption of NO by
1
6,25-28,33
29-31,34,35
-2
-1 -1 21
mild O-atom-transfer reagent for divalent Ti,
Zr,
PMe3 was calculated to be (1.3 ( 0.3) × 10
M
s . When
the rates of the reaction of 1 and NO were measured, the results
differed from those measured for the reaction of PMe3 with NO
in two important ways. The reaction with 1 was observed to be
much faster, and the kinetic traces were not simple first-order
decays. Instead, the traces were characterized as having an initial
zero-order (linear) decay, followed by a first-order (exponential)
decay (Figure 3).
(23) Wax, M. J.; Bergman, R. G. J. Am. Chem. Soc. 1981, 103, 7028.
24) Vaughan, G. A.; Rupert, P. B.; Hillhouse, G. L. J. Am. Chem. Soc.
987, 109, 5538.
25) Polse, J. L.; Andersen, R. A.; Bergman, R. G. J. Am. Chem. Soc.
(
1
1
1
1
(
995, 117, 5393.
(26) Bottomley, F.; Lin, I. J. B.; Mukaida, M. J. Am. Chem. Soc. 1980,
02, 5238.
27) Bottomley, F.; Brintzinger, H. H. J. Chem. Soc., Chem. Commun.
(
978, 234.
Both the zero-order and the first-order decreases in PNO were
found to be independent of [PMe3]. While the zero-order rates
varied directly with [1], the first-order rates did not. Instead,
the first-order decay constants appear to scale with the square
root of the metal concentration (see Discussion section). The
(28) Vaughan, G. A.; Sofield, C. D.; Hillhouse, G. L.; Rheingold, A. L.
J. Am. Chem. Soc. 1989, 111, 5491.
29) Howard, W. A.; Trnka, T. M.; Waters, M.; Parkin, G. J. Organomet.
(
Chem. 1997, 528, 95.
(30) Howard, W. A.; Parkin, G. J. Am. Chem. Soc. 1994, 116, 606.
(31) Howard, W. A.; Waters, M.; Parkin, G. J. Am. Chem. Soc. 1993,
1
15, 4917.
(
21) Kuhn, L. P.; Doali, J. O.; Wellman, C. J. Am. Chem. Soc. 1960,
2, 4792.
22) Reed, J.; Eisenberg, R. Science 1974, 184, 658.
(32) Howard, W. A.; Parkin, G. J. Organomet. Chem. 1994, 472, C1.
(33) For a rare example in which N2O reacts with a transition metal
species without loss of N2, see ref 28.
8
(

Rapid Reduction of NO to N2 by Zirconium(II)
J. Am. Chem. Soc., Vol. 121, No. 36, 1999 8263
Scheme 3
pyridines, phosphine oxides, amines, ethers) have been found
that efficiently trap Cp2ZrdO and prevent oligomerization, either
1
8,19
earlier
or in this study. The successful traps employed in
this study were of the latter class. Cp2ZrMe2 and Me3SiCl
proved to be efficient traps, providing the bridging oxo species
(
Cp2ZrMe)2O and Cp2Zr(OSiMe3)(Cl), respectively.41 Other
known traps for Cp2ZrdO were found to react either with 1 or
with the nitrogen oxide reagent.
Figure 4. Effect of stirring rate on the observed reaction rate for PMe
3
+
+
NO (9) and 1 + NO. (0) Pseudo-first-order rate constants for PMe
3
Kinetic Studies. Two-regime kinetic traces, like those
obtained for the reaction of 1 with NO, are characteristic of
systems exhibiting saturation behavior. A general mechanistic
scheme that would predict such behavior is one involving a
reversible first step, followed by an irreversible second step.
Sensible mechanisms can be written that employ either only
chemical transformations or both chemical and mass-transfer
steps. Two mechanistic hypotheses involving only chemical
reactions which seem particularly reasonable are those involving
either initial reversible phosphine dissociation (Scheme 3A) or
NO normalized to krel ) 1 for the lowest stirring rate. Initial zero-
order fluxes (JNO) for 1 + NO normalized to krel ) 1 for the lowest
2
stirring rate. The lines are parabolic fits to the data (y ) a + bx ).
and Hf 32,36,37 metallocene complexes. Terminal and bridging
oxo species as well as oxygen-insertion products are known to
be formed in these reactions. In contrast, the interaction of nitric
oxide (NO) with Group 4 metallocenes is poorly understood.
Well-defined Group 4 nitrosyl complexes appear to be extremely
rare.38 Bottomley and co-workers have examined reactions of
5
initial reversible Cp slippage (change in binding mode from η
Cp2Ti(CO)2 with NO and have found that oxidized Ti-containing
3
2
7,39
to η ) (Scheme 3B). Both of these hypothetical mechanisms
species and reduced N-containing species are formed.
involve opening a coordination site at the metal center for NO
binding and represent dissociative and associative ligand
substitution schemes consistent with saturation kinetics. In
addition to these, a mechanism which involves reversible attack
of the solvent on the complex, followed by irreversible reaction
with NO, would also predict saturation kinetics (Scheme 3C).
Several pieces of data argue against these three possible
mechanisms. The very small effect of temperature on the rate
is inconsistent with the enthalpy of activation expected for an
initial bond cleavage (either Zr-PMe3 or Zr-Cp). The lack of
any effect on the kinetic traces due to added PMe3 (0-1 M)
rules out a reversible phosphine dissociation mechanism. The
fact that no change in rate is observed when the solvent is
changed from THF to 2,5-Me2THF argues against the participa-
tion of a solvent molecule. Most importantly, none of these
mechanisms can account for the pronounced effect of stirring
speed on the rate of NO consumption.
However, these transformations are relatively complicated.
Depending on stoichiometry, temperature, solvent, and other
factors, the products may include N2O, N2, isocyanate com-
2
7,39
plexes, hyponitrite complexes, and titanium oxo species.
By comparison, the overall reaction of Cp2Zr(PMe3)2 with
NO is apparently uncomplicated. Nitric oxide is completely
reduced by 1 to dinitrogen, and the experimental results indicate
that this transformation occurs in two distinct steps: the
reduction of 2NO to N2O, followed by reduction of N2O to N2.
Both of these steps are very fast, even at reduced temperatures.
The reaction of NO and 1 is complete within 15 s at -113 °C
(from kinetic studies), and the reaction of N2O and 1 is complete
within minutes at -80 °C (low-temperature NMR studies) and
may be considerably faster.40
Despite the rapidity of these transformations, a fair amount
of mechanistic information regarding them has been obtained.
In both the reduction of NO and N2O, a transient oxozirconium
species is formed which may be trapped. The trapping of
monomeric Group 4 oxo species has been developed only in
the past decade, and the set of efficient oxo traps fit broadly
into two classes: those that keep the MdO bond intact and
those that react with it. No traps of the former class (e.g.,
The effect of stirring speed indicates that the reaction of 1
with NO is controlled, to a large degree, by the rate of mass
transfer of NO into solution. Comparing the observed NO
absorption rates vs stirring speed for the reaction of 1 with NO
and PMe3 with NO gives the clearest picture of how stirring
affects the rate (Figure 4). For the reaction of 1 with NO, the
rate dramatically changes with different stirring speeds, a clear
indication that the mass-transfer rate is important to the observed
rate of reaction. Indeed, an empirical correlation of the NO
absorption rate and the square of the stirring rate is observed.
By comparison, the rate change for the reaction of PMe3 with
NO is negligible for different stirring rates, demonstrating that
mass transfer is a much less important part of the overall rate
of NO consumption for this inherently slower reaction.
There are many studies of the uptake of a gas by a solution
(
34) Vaughan, G. A.; Hillhouse, G. L.; Rheingold, A. L. J. Am. Chem.
Soc. 1990, 112, 7994.
35) Vaughan, G. A.; Hillhouse, G. L.; Lum, R. T.; Buchwald, S. L.;
Rheingold, A. L. J. Am. Chem. Soc. 1988, 110, 7215.
36) The reaction of Cp*2Hf(Ph)(H) with N2O (ref 24) is proposed to
proceed through the benzyne complex (refs 34 and 35).
37) In contrast to the reaction of Cp*2Zr(CO)2 with N2O (refs 29-31),
Cp*2Hf(CO)2 and N2O are reported not react to give well-defined products
ref 32).
38) Richter-Addo, G. B.; Legzdins, P. Metal Nitrosyls; Oxford Univer-
sity Press: New York, 1992.
(
(
(
(
(
4
2-44
(
39) Bottomley, F.; Lin, I. J. B. J. Chem. Soc., Dalton Trans. 1981, 271.
containing a chemically reactive species.
Astarita has
(40) Notable is the extreme difference in the reaction conditions required
to initiate reaction between N2O and 1 (-78 °C, <10 m) and N2O and
Cp2Zr(CO)2 (+80 °C, 12 h, ref 29).
(41) Me3SiCl is known to react with Cp*2ZrdO to form Cp*2Zr-
(OSiMe3)(Cl), or Cp*2ZrCl2 and (Me3Si)2O (ref 29).

8264 J. Am. Chem. Soc., Vol. 121, No. 36, 1999
McNeill and Bergman
µ
µ
Figure 6. Schematic representations of the concentration gradients of
4
4
NO and 1 near the gas-liquid interface (adapted from Astarita ). (A)
In the instantaneous reaction regime, the reaction rate is limited by the
diffusional transport of 1 from below. (B) In the fast reaction regime,
the transport of 1 is no longer limiting. Instead, the rate of NO
absorption is related to both the diffusivity of NO and the rate of
chemical reaction. These figures are not drawn to scale.
Figure 5. Zero-order flux (µmol cm-2 s-1) at 195 K vs [1] (mM),
showing a linear dependence. The best-fit line by least-squares
-
1
regression has slope m ) 0.044 ( 0.003 cm s , intercept b ) 0.01 (
-
2
-1
2
0
.07 µmol cm
s
, and r ) 0.9724.
significant, penetration depth into the solution. The surface-
film concentration gradients are shown schematically in Figure
summarized the results of these studies and identified four
6
A. The reaction plane, where NO and 1 meet, is at the depth
important regimes: slow reaction-diffusional, slow reaction-
determined by the relative diffusivities and concentrations of
the two species. This can be shown by considering the fluxes
of the two species. According to Fick’s law, the flux of NO
into solution is given by eq 13, where l1 is the distance from
the interface to the reaction plane. Similarly, the flux of 1 toward
the surface is given by eq 14, where l2 is the distance from the
bottom of the surface film to the reaction plane. Since the two
fluxes must be equal, one can combine these expressions to
give eq 15. The result is that the ratio of the diffusion lengths
can be determined from the diffusivities and the bulk and
interface concentrations of the reacting species. The ratio of
44
kinetic, fast reaction, and instantaneous reaction regimes. The
flux of the gas into solution for each of these scenarios is well
understood, and the four regimes can be distinguished by a
4
4
number of tests. Using the criteria outlined by Astarita, we
suggest that the uptake of NO by a solution of 1 is a process at
the boundary of the fast reaction and instantaneous reaction
regimes. At low NO pressures, the uptake is in the fast reaction
regime, and at higher NO pressures it is in the instantaneous
reaction regime.
The zero-order consumption of NO by solutions of 1 at high
NO pressures (PNO > 1 Torr) is a clear indication that the
absorption process is in the instantaneous reaction regime. For
all other chemical absorption regimes, there is some dependence
2
concentrations in this regime is typically on the order of 10 ,
which results in a ratio of l2/l1 ≈ 15.
44
of the flux on the interfacial gas concentration. To be in this
regime, the rate of chemical reaction does not need to be
(
13)
14)
“instantaneous”, but rather it must be fast enough so that a small
volume near the liquid surface becomes completely depleted
in 1. The result is that the uptake is controlled by the rate at
which 1 can diffuse toward the surface to meet the incoming
(
NO. The flux of NO, JNO, entering the solution is given by eq
(
15)
o
1
1, where kL is the physical mass-transfer velocity of NO into
2
solution (in cm/s) and D is the diffusivity of NO and 1 (in cm /
s). Because [NO]interface , [1]bulk, the flux can be approximated
by eq 12. A linear relationship between the zero-order flux and
In the fast reaction regime, the diffusion of the reactive
solution species is no longer limiting. By contrast to the
instantaneous reaction regime, the fast reaction regime is
characterized by having a flux of a gas into solution which is
related to the interfacial concentration of the gas. The flux of a
compound, X, is proportional to the interfacial concentration
raised to the (n + 1)/2 power (eq 16), where n is the reaction
44
(11)
4
4
order. Consequently, the reaction order of the absorbing
(12)
(16)
[1] can clearly be seen (Figure 5). From this plot, using a
diffusivity ratio of D1/DNO ) 0.15 (see Appendix), a transfer
species can be determined experimentally. For first- and second-
o
velocity, kL , of 0.16 ( 0.01 cm/s is obtained.
order reaction orders in X, the absorption rates are proportional
Because [1] near the surface is completely depleted in the
instantaneous reaction regime, the NO can have a small, but
1
3/2
to [X] and [X] , respectively.
The absorption of NO by solutions of 1 is observed to be
first-order at low NO pressures, indicating that the reaction order
in NO is 1. An expression for JNO in the fast reaction regime,
assuming a first-order reaction in [NO]interface, is given in eq
(
42) Sherwood, T. K.; Pigford, R. L.; Wilke, C. R. Mass Transfer;
McGraw-Hill: New York, 1975.
43) Atkins, P. W. Physical Chemistry, 4th ed.; W. H. Freeman and
Co.: New York, 1990.
44) Astarita, G. Mass Transfer with Chemical Reaction; Elsevier:
Amsterdam, 1967.
(
4
4
1
7, where m is the reaction order in [1]. One can see that the
(
uptake rate is controlled by both the diffusivity of NO and the

Rapid Reduction of NO to N2 by Zirconium(II)
J. Am. Chem. Soc., Vol. 121, No. 36, 1999 8265
(17)
reaction rate constant. The flux can be related to the first-order
rate (expressed as the change in the number of moles of NO
with respect to time, d(nNO)/dt) by recognizing that flux is equal
to the rate divided by the interfacial area A (eq 18). Setting the
(18)
two flux expressions (eqs 17 and 18) equal, one obtains an
expression that predicts a square-root dependence of the
m
observed rate constant, kobs, on [1] (eq 19). The constants Vg
(19)
Figure 7. Pseudo-first-order rates (s-1) at 195 K vs [1]0.5. The solid
and H in eq 19 are the gas-phase volume and the dimensionless
Henry’s law constant for NO in THF, respectively. They arise
from the sequential conversions of [NO]interface first into a gas-
phase concentration, [NO]g, and then into the number of moles
-
0.5
line corresponds to the least-squares best-fit line (m ) 7.0 ( 1.6 M
-
1
-1
2
s
, b ) 0.22 ( 0.22 s , r ) 0.7653).
Scheme 4
0.5
2
of NO, nNO. A plot of kobs vs [1] is reasonably linear (r )
.765 for the linear regression), indicating that the reaction is
0
first-order in [1] and yields a bimolecular rate constant of (1.5
8
-1 -1
(
0.3) × 10 M
s
(Figure 7). The expressed uncertainty is
the propagated uncertainty of the line fit and, therefore, only
takes into account the scatter in the data. Because the constants
in eq 19 can also contribute to the uncertainty, with the two
largest contributors being the values for H and A (see Ap-
pendix), the true uncertainty is much higher. It can be said that
the derived value for krxn is an upper limit since the value of A
2
used is a lower limit and krxn is proportional to 1/A .
The transition between the instantaneous and fast reaction
4
4
regimes occurs when the equality given in eq 20 is satisfied.
Empirically, the changeover is observed when the ratio [1]bulk/
3
8
-1
[
s
NO]interface is on the order of 10 . Given krxn ) 1.5 × 10 M
-1
-2
and a typical concentration of [1] ) 10 M, a time constant
-
7
for reaction, τrxn, of 6.7 × 10 s is calculated. The value of
the time constant for diffusion, τD, from eq 20 is, therefore,
approximately 0.67 s. This quantity is useful in determining
limiting. Instead, the rate of NO consumption is proportional
to the pressure in the gas phase, giving rise to first-order
absorption kinetics.
(
20)
the thickness of the surface film using the Einstein-Smolu-
Mechanism of Reduction of NO by 1. On the basis of the
above analysis, we conclude that nitric oxide is reduced to
nitrous oxide by Cp2Zr(PMe3)2 in a sequence of steps that are
very fast and that occur near or at the gas-solvent interface.
Our proposed mechanism is outlined in Scheme 4. The kinetics
indicate a bimolecular reaction as the initial, rate-controlling
process. This is possibly a bimolecular ligand substitution
process similar to that observed by Basolo, Rausch, and co-
workers in the PR3-for-CO ligand substitution at Cp2Zr(CO)2.
2
chowskii equation, τD ≈ l /D, where l is the length scale of
4
3,45
-5
molecular diffusion.
Using a value of DNO ) 1.1 × 10
2
-1
cm s , l ≈ 30 µm.
From the parameters derived from the instantaneous, fast, and
changeover regimes, a physical picture of the rate-controlling
processes and length scales involved develops. The reaction
between NO and 1 occurs in a surface film with an approximate
thickness of 30 µm. The rate of reaction is extremely fast, krxn
8
-1 -1
)
(
1.5 × 10 M s , approaching the diffusion-controlled limit
3
3
5
For this process, an η -Cp intermediate, (η -Cp)(η -Cp)Zr(CO)2-
(
9
-1 -1
5.8 × 10 M s , see Appendix). When the NO pressure is
46
PR3), was proposed. An analogous ligand substitution process
high enough, the incoming gas rapidly depletes the concentration
of 1 in the volume near to the surface. The major consequence
of this is that the consumption of NO in this regime is controlled
by the diffusion of 1 from the bulk solution through the surface
film, and the rate is “saturated”. From eq 15, the NO is
calculated to have a penetration depth into solution of ap-
proximately 2 µm. As the NO pressure decreases, it eventually
reaches a point at which the mass transfer of 1 is no longer
leading to Cp2Zr(PMe3)(NO) (4) would have the intermediate
3
5
structure (η -Cp)(η -Cp)Zr(PMe3)2(NO) (3). However, the rate
constant for the bimolecular reaction observed in this study is
8
-1 -1
approximately 10 M s , which is 11 orders of magnitude
faster than those observed by Basolo and Rausch. Alternatively,
the rate-limiting bimolecular step may be an outer-sphere
47
electron-transfer process, leading to ion pair 5. Ligand
(46) Palmer, G. T.; Basolo, F.; Kool, L. B.; Rausch, M. D. J. Am. Chem.
(
45) Barrow, G. M. Physical Chemistry, 5th ed.; McGraw-Hill: New
Soc. 1986, 108, 4417.
(47) We thank a reviewer for this suggestion.
York, 1988.

8266 J. Am. Chem. Soc., Vol. 121, No. 36, 1999
McNeill and Bergman
substitution at the cationic Zr(III) center in 5 would be much
faster than that at Zr(II) in 1. While this would provide an
explanation for the very fast bimolecular rate observed, further
studies are required in order to rigorously establish the presence
or absence of an electron-transfer pathway.
Cp
2
Zr(PMe
3
)
2
(1). The following synthesis is based on that
4
9
published for other bis-phosphine complexes by Gell and Schwartz.
It was found to provide the product in higher purity than the published
procedure.5 PMe
containing Cp Zr(H)(CH
cooled to -196 °C. The reaction flask was warmed to 0 °C, and the
contents were stirred for 2 h (until all of the Cp Zr(H)(CH Cy)
0,51
(25 mL) was condensed into an evacuated flask
3
Cy)52 (Cy ) cyclohexyl) (911 mg, 2.9 mmol),
2
2
The subsequent steps in the transformation of NO to N2O
are even faster than the initial bimolecular process, and their
exact nature is unclear. One reasonable product-forming inter-
mediate is a zirconium dinitrosyl complex (6), since it is known
that dinitrosylmetal complexes often decompose to give oxo
species and N2O.38 The dinitrosyl complex 6 could arise from
a second ligand substitution (NO for PMe3). Alternatively, the
second NO may attack the nitrosyl ligand directly, as has been
proposed by Trogler and co-workers for the reduction of NO
2
2
dissolved). The volatile materials were removed in vacuo, and the black-
red residue was extracted with pentane (3 × 8 mL). The combined
extracts were filtered through a column of Celite (2 cm × 1 cm), and
the filtrate was evaporated to dryness in vacuo to yield a brown solid
1
(690 mg, 1.9 mmol, 64%). H NMR (400 MHz, C D , 20 °C): δ 4.81
s, br), 0.99 (s, br). P{ H} NMR (162 MHz, C
6
6
31
1
(
6 6
D , 20 °C): δ 18.9 (s,
50 1
br). Lit. H NMR (90 MHz, toluene-d
Hz, 10 H), 0.96 (vt, J ) 4.9 Hz, 18 H). P{ H} NMR (toluene-d
20 °C): δ 24.0.
Reaction of 1 with NO. Method A. NO (5.0 µmol) was transferred
under vacuum into an NMR tube containing 1 (1.2 mg, 3.2 µmol) and
p-(MeO) (an internal standard, 1.4 mg, 10 µmol) in C (0.5
8
, -20 °C): δ 4.75 (t, J ) 2.0
31
1
8
,
-
2+
10
to N2O by Pd salts. Such a process would produce an N-N-
bonded species, Cp2Zr(PMe3)(N2O2) (7). Each of these inter-
mediates could lead to Cp2Zr(N2O2) (8), either through coupling
of the nitrosyl ligands in complex 6 or through loss of a
phosphine ligand from complex 7. Complex 8 could then
decompose to Cp2ZrdO and N2O.
2
C
6
H
4
6 6
D
mL) at -196 °C. The tube was flame-sealed. Upon thawing of the
solution, fast bleaching of the dark red color was observed along with
precipitation of a colorless material. A yield of 21 ( 2% [Cp
.21) was calculated by integration of the product peak vs the internal
standard.
Method B. A degassed solution of Cp
mmol) in THF (10 mL) was cooled to -78 °C and exposed to NO
mmol) with stirring for 20 min. The gaseous materials were removed
in vacuo, and the solution and precipitate were transferred to a centrifuge
tube by cannula. Following centrifugation, the supernatant was removed,
and the precipitate of [Cp
mL).
2 3
ZrO] (δ
6
We favor a chelating hyponitrite structure for complex 8, as
shown in Scheme 4, based upon the chemistry of zirconium
tetrazene complexes, the all-nitrogen analogues of a chelating
hyponitrite complex (eq 21). The tetrazene complexes have been
shown to cleave reversibly to give organic azides and imido
complexes, the isoelectronic nitrogen analogues of Cp2ZrdO
and nitrous oxide.48
2
3 2
Zr(PMe ) (181 mg, 0.485
(
x
ZrO
y
]
n
was washed with hexanes (3 × 10
Reaction of 1 with NO in the Presence of Me
3
SiCl. NO (0.26
mmol) was transferred under vacuum into a glass bomb containing 1
96 mg, 0.26 mmol) and Me SiCl (0.48 mmol) in C (15 mL) at
196 °C. Upon thawing of the solution, fast bleaching of the dark red
(21)
(
-
3
6 6
H
color was observed. The volatile materials were removed in vacuo,
leaving a pale yellow residue. The residue was extracted with toluene
Conclusion
(
3 × 8 mL), and the combined extracts were filtered through a short
column of Celite (1 cm × 2 cm). The pale yellow filtrate was cooled
Cp2Zr(PMe3)2 (1) reacts quickly with nitric oxide to produce
nitrous oxide and Cp2ZrdO. This reaction is so rapid that this
chemical process is kinetically competitive with transport of
NO into THF solution. The kinetic data were interpreted using
the chemical absorption formalism outlined by Astarita, in
which penetration of the liquid surface by gaseous NO is
important in the reaction kinetics. The data indicate that a
bimolecular reaction between NO and 1 is the chemically rate-
limiting step. The nitrous oxide produced is further reduced to
dinitrogen by addition of an additional equivalent of 1. In both
of these reductions, the Cp2ZrdO produced may be trapped by
either Cp2ZrMe2 or Me3SiCl, prior to its oligomerization.
to -35 °C overnight. Colorless crystals were recovered (20 mg, 22%
1
yield). H NMR (400 MHz, C
6
D
6
): δ 5.93 (s, 10 H), 0.11 (s, 9 H).
13
1
16 1
C{ H} NMR (100 MHz, C
6
D
6
): δ 114.2, 1.9. Lit. H NMR: δ 6.00
13
1
(
s, 10 H), 0.12 (s, 9 H). C{ H} NMR: δ 114.0, 1.8. The identity of
4
4
the isolated material was further confirmed by comparison with an
1
7
authentic sample of 2 prepared from Cp
In a separate experiment, NO (7.1 mmol) was transferred under
vacuum into an NMR tube containing 1 (2.3 mg, 6.2 mmol), Me SiCl
11 mmol), and p-(MeO) (an internal standard, 1.1 mg, 8.0 mmol)
in C (0.5 mL) at -196 °C. Fast reaction was apparent upon thawing
of the solution. A yield of 77 ( 2% Cp Zr(OSiMe )(Cl) was calculated
by integration of the product peaks vs the internal standard.
Reaction of 1 with N O. A degassed, frozen solution (-78 °C) of
Cp Zr(PMe (3.2 mg, 8.6 µmol) and p-(MeO) (internal standard,
.5 mg, 11 µmol) in C (0.5 mL) was exposed to N O (ca. 0.5 atm).
2 2 3
ZrCl and KOSiMe .
3
(
2 6 4
C H
6 6
D
2
3
2
2
)
3 2
2 6 4
C H
Experimental Section
1
6
D
6
2
The tube was flame-sealed and warmed to room temperature. Upon
General Methods. Unless otherwise indicated, all reactions were
thawing of the solution, bleaching of the dark red color and deposition
2
performed under an inert atmosphere (N , Ar, or He). A description of
1
instrumentation and general procedures has been published.48 Unless
otherwise specified, all reagents were purchased from commercial
of a precipitate was observed. H NMR spectroscopic analysis showed
2
6 ( 2% [Cp
internal standard.
Reaction of 1 with N
solution (-78 °C) of 1 (120 mg, 0.32 mmol) and Me
.59 mmol) in C was exposed to N O (1 atm) for 10 min. The
2 3
ZrO] by integration of the product peak against the
suppliers and used without further purification. PMe
was dried over Na prior to use. 2,5-Dimethyltetrahydrofuran (Aldrich,
mixture of cis and trans) was dried first over CaH and then over
sodium/benzophenone ketyl. NO (Matheson) was purified by passage
O (Airco) was purified by passage
3
(Strem or Aldrich)
2
O in the Presence of Me
3
SiCl. A stirred
SiCl (75 µL,
3
2
0
6
H
6
2
solution was brought to room temperature over 30 min. The volatile
materials were removed in vacuo, and the pink residue was extracted
with toluene (6 × 8 mL). The extracts were combined and the volatile
through two -130 °C traps. N
2
through a -78 °C trap. In the trapping studies, control experiments
were performed which verified that the traps did not react with the
nitrogen oxide substrates under the relevant reaction conditionssCp
ZrMe does not react with N O, and Me SiCl does not react with either
O or NO at room temperature in benzene or THF.
2
-
(
49) Gell, K. I.; Schwartz, J. J. Chem. Soc., Chem. Commun. 1979, 244.
2
2
3
(50) Kool, L. B.; Rausch, M. D.; Alt, H. G.; Herberhold, M.; Honold,
N
2
B.; Thewalt, U. J. Organomet. Chem. 1987, 320, 37.
51) Kool, L. B.; Rausch, M. D.; Alt, H. G.; Herberhold, M.; Thewalt,
(
(
48) Meyer, K. E.; Walsh, P. J.; Bergman, R. G. J. Am. Chem. Soc. 1995,
U.; Honold, B. J. Organomet. Chem. 1986, 310, 27.
(52) KaleidaGraph, version 3.06; Synergy Software, 1996.
1
17, 974.

Rapid Reduction of NO to N2 by Zirconium(II)
J. Am. Chem. Soc., Vol. 121, No. 36, 1999 8267
materials removed. The faint pink residue was washed with cold toluene
Table 1. Gas Chromatographic Data for the Conversion of N
by Cp Zr(PMe
2
O to
(
2 × 5 mL). The washed material (now colorless) was dissolved in
N
2
2
3 2
)
toluene (ca. 15 mL), filtered through Celite (1 cm × 2 cm column),
entry
N
2
O injected (mL)
N
2
produced (mL)
yield (%)
and concentrated to ca. 5 mL. The toluene solution was cooled to -35
1
2
3
4
0.50
1.00
1.50
2.00
0.33
0.94
1.32
1.64
66
94
88
82
°
(
0
C for 12 h. Colorless crystals of Cp
2
ZrCl(OSiMe
3
) were recovered
1
43 mg, 39% yield). H NMR (400 MHz, C ): δ 5.93 (s, 10 H),
6 6
D
1
3
1
15 1
.11 (s, 9 H). C{ H} NMR (100 MHz, C
6
D
6
): δ 114.2, 1.9. Lit.
H
1
3
1
NMR: δ 6.00 (s, 10 H), 0.12 (s, 9 H). C{ H} NMR: δ 114.0, 1.8.
The identity of the isolated material was further confirmed by
Table 2. FTIR Data for the Conversion of NO to N
2
O by
2 2
comparison with an authentic sample of 2 prepared from Cp ZrCl and
1
7
2
Cp Zr(PMe
3 2
)
KOSiMe
In a separate experiment, N
NMR tube containing a degassed, frozen solution of 1 (3.0 mg, 8.0
µmol), Me SiCl (18 µmol), and p-(MeO) (as an internal standard,
.0 mg, 36 µmol) in toluene-d . Fast reaction was observed upon
thawing of the solution. H NMR spectroscopic analysis showed 102
2% Cp Zr(OSiMe )(Cl) by integration of the product peak against
the internal standard.
Reaction of 1 with N
µmol) was condensed into an NMR tube containing a degassed, frozen
solution (-78 °C) of Cp Zr(PMe (3.0 mg, 8.0 µmol), Cp ZrMe (3.0
mg, 12 µmol), and p-(MeO) (an internal standard, 3.0 mg, 22
µmol) in C (0.5 mL). The tube was sealed and warmed to room
3
.
O (18 µmol) was condensed into an
NO (µmol)
remaining
2
N O (µmol)
2
2 3 2
Cp Zr(PMe ) (1)
produced
(yield, %)
3
2 6 4
C H
entry
mg
µmol
initial
(yield, %)
5
8
a
1
2
3
4
11.6
14.2
6.1
31.0
38.1
16
60.4
72.9
151
b
b
29.5 (98)
33.8 (93)
33.5 (69)
49.3 (87)
1
a
(
2
3
75.3 (79)c
c
c
20.1 (98)c
7.1
19
132
2
2 2 2
O in the Presence of Cp ZrMe . N O (31
a
Based upon stoichiometry of eq 2. b None detected. c Based upon
stoichiometry of eq 6.
2
)
3 2
2
2
2
6 4
C H
2
Gas Chromatography: Reaction of 1 with N O. A 50-mL Schlenk
6 6
D
flask equipped with a stir bar was charged with a solution of 1 (63
mg, 170 µmol) in toluene (5.0 mL). The contents were degassed by
three freeze-pump-thaw cycles, and 1 atm of He was placed over
the solution. N O was added by syringe in four batches (0.50 mL, 22
2
µmol each). After each addition, the reaction mixture was allowed to
temperature. Upon thawing of the solution, bleaching of the dark red
1
color was observed. H NMR spectroscopic analysis showed 76 ( 2%
2 2
[Cp ZrMe] O by integration of the product peaks against the internal
standard.
Gas Chromatography: General Procedures. Headspace gas
analysis was performed using either a Varian Aerograph 90-P or 920
gas chromatograph. A CTR-I column (Alltech) comprised of two
coaxial columns with different packings (hydrophobic polymer mixture/
molecular sieves) was employed and was found to provide good
stir for 10 min, and then the headspace gas was analyzed by GC. The
results of these analyses are listed in Table 1. N
9% yield based on N O added.
Infrared Spectroscopy. A cylindrical cell (20 cm × 2 cm) with
CaF
windows and a sidearm (4 cm × 1 cm) was employed in these
experiments. In a typical procedure, the cell was evacuated, and NO
60.4 µmol) was transferred into the liquid nitrogen-cooled sidearm.
2
was produced in 86
(
2
2
separation of the gaseous analytes important to this study (N
2 2
, O , NO,
N
2
O) at room temperature. Calibration experiments with known
(
volumes showed that the GC response for each of these gases varied
linearly with molar amount. The GC response was calibrated prior to
use by injection of standard samples. To account for the different
partitioning between the solvent and headspace for the various gases,
standard curves relating the headspace concentration and the total
amount of a given analyte were prepared for each solvent and
temperature used.
Upon thawing of the solution, an initial spectrum of the NO was
acquired. The NO in the cell was then condensed into an evacuated
flask containing 1 (14.2 mg, 38.1 µmol) in toluene (15 mL). After the
solution was stirred for 20 min at 20 °C, the volatile materials were
transferred into the sidearm of the IR cell. Upon thawing of the solution,
an infrared spectrum of the gas-phase materials was acquired. Com-
parison of the integrated infrared band intensities against standard curves
gave quantitative values for the NO consumed (>58 µmol, >96%) and
Gas Chromatography: Reaction of 1 with NO. The gaseous
products from the reaction of 1 with both a stoichiometric amount and
a molar deficiency of NO were examined. The reaction apparatus and
procedures were effectively identical in both cases. A vial (12.2 mL)
equipped with a small stir bar was charged with 5.0 mL of a toluene
solution of 1 (0.013 M, 65 µmol). The vial was sealed with a three-
holed screw cap over a GC septum. The solution was degassed by
bubbling He gas through it for ca. 2 min. The reaction vial was then
fitted with two syringes: a 5.0-mL gastight syringe equipped with a
stopcock charged with 3.0 mL of NO (130 µmol), and a 5-mL glass
syringe filled with 1.3 mL of He. The second syringe provided a means
of measuring the system volume. The barrel of this syringe was
lubricated with mineral oil to allow smooth movement and to prevent
leaking of gas in to or out of the reaction vial. The NO was added all
at once. The system volume was observed to increase by ca. 3 mL (a
reading of 4.3 mL on the volume-monitoring syringe) and then to
decrease over 1 min to a net 1.4 mL increase (a reading of 2.7 mL).
N O produced (29.5 ( 0.5 µmol, 98% yield). Data from these
2
experiments are given in Table 2.
Kinetic Measurements: General Procedure. A schematic repre-
sentation of the apparatus is shown in Figure 1. In a typical procedure,
a three-necked flask was loaded with a solution of the reactants in the
glovebox. The flask was also fitted with a known-volume bulb (6.6
mL). Outside the glovebox, one of the stoppers on the flask was replaced
with an adapter, connecting the flask to a pressure transducer (Baratron)
under flow of inert gas (Ar or N ). The system was degassed by two
2
freeze-pump-thaw cycles. The known-volume bulb was charged with
NO (typically 100 Torr). After temperature equilibration, a pulse of
NO was introduced by opening the stopcock separating the NO-
containing bulb and the reaction flask. The pressure was recorded by
charting the dc output from the pressure gauge using a chart recorder.
Commercial software was used to fit data and calculate endpoints.52
The stirring rates for the stirring plate used (IKA, RCT basic) were
determined in an experiment performed with Mr. Jake Yeston. A
Teflon-coated stir bar, modified previously to have a hole halfway
through the bar along the stirring axis, was mounted with epoxy to the
Teflon tip of a syringe plunger, normally used with a gastight syringe.
The tip of the syringe plunger, and thus the stir bar, could spin freely
on the body of the plunger. The beam chopper of a flash photolysis
apparatus, described elsewhere,53 was removed and replaced with the
modified stir bar suspended above the stir plate. The stir bar was placed
such that it blocked the IR laser beam when the stir bar’s long axis
Analysis of the headspace gas by GC showed a N
and NO was not detected. Conversion of the headspace concentrations
to total quantities of N O and N gave 44 (68%) and 8.1 (12%) µmol,
2 2
O/N ratio of 5:1,
2
2
respectively. Based on the total volume of change observed, 107 (
1
0% of the NO was consumed.
In the case where a deficiency of NO was employed, 1 (17.4 mg,
7 µmol) was treated with 0.52 mL of NO (23 µmol). Headspace gas
4
analysis showed a N
quantities of N O and N
were 0.8 ( 0.3 (7%) and 10 ( 0.3 (86%) µmol, respectively.
Control experiments in which no Cp Zr(PMe was added showed
no consumption of NO and no N from leaks.
2 2
O/N ratio of 1:20, and no NO was detected. Total
2
2
determined from the headspace concentrations
(53) Schultz, R. H.; Bengali, A. A.; Tauber, M. J.; Weiller, B. H.;
2
3 2
)
Wasserman, E. P.; Kyle, K. R.; Moore, C. B.; Bergman, R. G. J. Am. Chem.
Soc. 1994, 116, 7369.
2

8268 J. Am. Chem. Soc., Vol. 121, No. 36, 1999
McNeill and Bergman
Table 3. Kinetic Data for the Reaction of NO with PMe
195 K) at 19.6 Hz Stir Rate
3
in THF
Table 5. Kinetic Data for the Reaction of NO and Cp
in THF at 19.6 Hz Stir Rate
2
Zr(PMe
)
3 2
(
2
2
a
b
[
PMe
(M)
3
]
P
NO (init)
(Torr)
n
NO (init)
k
obs × 10
k × 10
P
NO (init) nNO (init) temp [1] [PMe
3
] JNO (µmol
k
obs
-
1
-1 -1
-2 -1
(s-1)
entry
(µmol)
(s
)
(M
s
)
entry (Torr) (µmol) (K) (mM) (M)
cm
s )
1
2
3
4
1.07
1.05
1.03
1.03
18.7
12.8
2.4
110
75
14
1.45(6)
1.56(4)
1.22(2)
1.20(2)
1.36(7)
1.48(5)
1.16(3)
1.17(3)
1
2
3
4
5
6
7
8
9
8.23
6.30
6.30
6.30
6.12
6.78
1.21
1.82
2.06
2.54
6.66
5.15
3.57
3.57
3.57
3.39
3.39
1.15
0.97
4.66
5.81
5.81
48.3
36.9
36.9
36.9
35.9
39.8
7.1
10.7
12.1
14.9
39.1
30.2
21.0
21.0
21.0
19.9
19.9
6.7
160 102
0.88
1.72
1.56
1.44
1.57
1.02
1.71
0.69
1.87
1.67
2.71
2.72
1.44
1.45
1.16
1.19
0.55
0.39
0.26
0.17
1.73
1.71
1.52
0.78
1.06
0.89
1.17
0.48
0.57
0.74
1.50
1.52
1.30
1.05
0.61
0.80
0.79
0.59
0.63
0.40
0.42
0.25
0.61
0.51
0.48
160
160
160
160
160
178
178
178
178
178
195
195
195
195
195
195
195
195
195
195
195
91
87
84
79
70
28
85
84
82
66
29
32
30
27
11
9
0.88
0.88
0.88
0.00
0.00
1.00
0.24
0.48
0.96
0.00
1.00
0.00
0.00
0.01
0.00
0.01
0.00
0.00
0.00
0.00
0.00
2.0
12
Table 4. Kinetic Data for the Reaction of NO with PMe
195 K)
3
in THF
(
2
2
[
PMe
3
]
P
NO (init)
(Torr)
n
NO (init) stir rate
k
obs × 10
k × 10
-
1
-1 -1
entry (M)
(µmol)
(Hz)
(s
)
(M
s
)
10
1
1
1
1
1
1
1
1
1
1
2
3
4
5
6
7
8
1
2
3
4
5
0.84
5.2
5.2
5.2
5.2
5.2
31
31
31
31
31
21.7
19.6
15.7
11.8
9.35
1.35(3)
1.28(2)
1.19(2)
1.14(2)
1.06(2)
1.61(4)
1.54(3)
1.43(3)
1.39(2)
1.29(2)
0.83
0.83
0.82
0.82
6
4
46
43
40
was perpendicular to the beam but allowed the beam to pass to the
detector when its long axis was parallel to the beam. In this way, the
stir bar acted as a beam chopper, blocking the beam twice per
revolution. The stirring rate was measured for stirring speeds important
to this study (ca. 10-25 Hz) by reading the chop period from the
oscilloscope.
9
5.7
c
2
2
2
0
27.3
34.1
34.1
c
c
1
2
a
Apparent zero-order flux from the beginning of each kinetic run.
b
c
Pseudo-first-order rate constant from the end of each kinetic run.
Reaction performed in 2,5-dimethyltetrahydrofuran.
Kinetic Measurements: Reaction of PMe
reactions were run at -78 °C with an 11.0-mL solution of PMe
3
with NO. These
(1.1
3
M) in THF. The procedure followed is described in the general section
above. In each experiment, first-order decay of the pressure was
observed (Figure 2). The total volume of the system was determined
to be 120 ( 4 mL. These values were used for calculation of the
bimolecular rate constant according to the method of Kuhn et al. (eq
2 3 2
Table 6. Kinetic Data for the Reaction of NO and Cp Zr(PMe )
in THF (195 K)
a
P
NO (init)
(Torr)
n
NO (init) stir rate [1]
J
NO (µmol
L
k °
-2 -1
(cm s-1)
entry
(µmol)
(Hz) (mM) cm
s )
1
2
3
4
5
6
7
8
1.88
5.52
1.88
4.85
1.88
1.88
5.14
1.88
11.0
32.3
11.0
28.4
11.0
11.0
30.1
11.0
21.7
21.7
19.6
19.6
15.7
11.8
11.8
9.4
14
32
12
35
9.6
7.4
29
5.2
1.43
0.31
0.26
0.20
0.23
2
2), assuming a dimensionless Henry’s constant, H, of 0.5 (V
g
) volume
2.73
0.78
2.69
0.43
0.19
0.92
0.099
of the gas, V ) volume of the liquid).
l
0.14
(22)
0.079
0.097
0.058
The bimolecular rate constant for the reaction of PMe
3
and NO (kPMe3)
at this temperature was found to be (1.3 ( 0.1) × 10 M-1
-2
s
-1
. Specific
a
Apparent zero-order flux from the beginning of each kinetic run.
data for these reactions are given in Tables 3 and 4.
Kinetic Measurements: Reaction of 1 with NO. The apparatus
and procedure were effectively identical to those used in the kinetic
study of the reaction of PMe with NO, except that the total solution
3
volume was 10.0 mL. The conditions of each experiment are recorded
in Tables 5 and 6. The zero-order and first-order regimes of each decay
were easily deconvoluted by inspection of the pressure (P) vs time (t)
Table 7. Calculated Values for the Viscosity of THF, the
Diffusivities of NO and 1, and the Diffusion-Controlled Rate
Constant at Various Temperatures
D × 10 (cm s-1)
6
2
diff × 10-9 (M-1 s-1
T (K) η(THF) (cP)
NO
1
k
)
and ln(P - P) vs t plots.
f
1
1
1
2
60
78
95
98
6.2
3.5
2.3
0.47
3.3
6.5
11
0.50
0.99
1.7
1.7
3.4
5.8
43
Some of the reactions were run at 160 K, which is below the freezing
point of pure THF (164.8 K). The presence of solutes lowers the
freezing point, and others have reported freezing points below 150 K
83
13
5
4
for THF solutions in cryoscopy experiments. The concentrations
employed in this work give expected freezing point depressions between
3
f
and 6 K (depending on the value of the cryoscopy constant, K ,
chromatograph. This work was supported by NSF Grant No.
CHE-9416833.
5
4,55
used).
At 160 K, these solutions were fluid and nonviscous.
Acknowledgment. We thank Prof. Richard A. Andersen
Department of Chemistry, University of California, Berkeley)
Appendix
(
and Prof. Philip M. Gschwend (Department of Civil and
Environmental Engineering, Massachusetts Institute of Technol-
ogy) for helpful discussions and Prof. David L. Sedlak and Ms.
Abra Bentley (Department of Civil and Environmental Engi-
neering, University of California, Berkeley) for use of their gas
A.1. Viscosity. The viscosity of THF was calculated using
eq 23, which gives values in units of Pa/s. To convert to cP
3
(
mPa/s), one must multiply by 10 . The equation and constants
5
6
were obtained from Daubert et al. For temperatures where a
comparison is available, the calculated viscosities (Table 7)
(
54) Gerold, A.; Jastrzebski, J. T. B. H.; Kronenburg, C. M. P.; Krause,
N.; van Koten, G. Angew. Chem., Int. Ed. Engl. 1997, 36, 755.
55) Cooper, A. R. Determination of Molecular Weight; John Wiley and
Sons: New York, 1989; Vol. 103.
(56) Daubert, T. E.; Danner, R. P.; Sibul, H. M.; Stebbins, C. C. Physical
and Thermodynamic Properties of Pure Chemicals: Data Compilation;
Taylor & Francis: Washington, DC, 1997.
(

Rapid Reduction of NO to N2 by Zirconium(II)
J. Am. Chem. Soc., Vol. 121, No. 36, 1999 8269
agree very well with published values determined by experi-
ment.57
(23)
A.2. Diffusivity. The diffusivity of NO in THF was calculated
using the method of Wilke and Chang58 (eq 24), where Φ is
the solvent association factor, Msolv is the molecular weight of
Figure 8. Cross section of the model interfacial surface.
-
1
the solvent in g mol , T is the temperature in K, η is the
viscosity of the solvent in cP, and Vsolute is the molecular volume
in the experiments makes it difficult to know the surface area
accurately. Our estimate is based on the mathematical descrip-
3
-1
of NO in cm mol . An association factor of Φ ) 1 was used,
6
1
tion of the stirred solution vortex by Nagata. It assumes a
smooth, well-defined surface and does not take into account
irregularities such as ripples and momentary splashes. Accord-
ingly, this estimate should be Viewed as a lower limit. The vortex
shape can be described by a parabola within a certain radius
and by a hyperbola outside of it. The cross section of our model
(24)
3
and the molecular volume of NO was taken to be 13.9 cm
-
1 56
mol . The diffusivity of 1 was calculated similarly using a
3
-1
molecular volume of 324 cm mol . This molecular volume
was arrived at by calculating the volume of the Cp and
phosphine ligands by the group contribution method of Fuller
interfacial surface is shown in Figure 8. The interior portion
2
(
radius < 1 cm) of the cross section is described by z ) kx -
k, and the exterior portion (1 cm < radius < 2 cm) is described
5
9
et al. and adding the spherical volume of the Zr atom (r )
-2
by z ) k - kx , where k is half the depth of the vortex. For
1
.06 Å).60 The calculated diffusivities are given in Table 7. At
our calculations, k ) 1 cm. The surface of revolution generated
all temperatures, the ratio DNO/D1 is 6.6.
by rotation of this cross section about the bisecting axis has a
Using the diffusivities, the diffusion-controlled rate constant
can be estimated according to eq 25.43,45 In this expression, r is
the spherical radius, and NA is Avogadro’s number. Calculated
values of kdiff using rNO ) 1 Å and r1 ) 5 Å are presented in
Table 7.
2
surface area of 9.4 cm .
A.4. Henry’s Law Constant. Since no data were available
for the solubility of NO in THF (dielectric constant, ꢀ ) 18.5),
this value for H was estimated to be 0.5 from the Henry’s
constants for EtOAc (ꢀ ) 6.02, H195 ) 0.84) and CH3CN (ꢀ )
62,63
35.0, H195 ) 0.34).
While this method of estimation is crude,
(25)
it is supported by the fact that the solubility of NO is similar
(0.35 < H195 < 1.1) for the range of organic solvents reported
(e.g., hexanes, toluene, Et O, CCl ), and it is relatively insensi-
A.3. Interfacial Surface Area. The interfacial surface area
A) is a crucial component in the calculation of the flux of nitric
oxide into solution. Unfortunately, the rapid stirring employed
(
2
4
6
2,63
tive to temperature.
(
57) Carvajal, C.; Toelle, K. J.; Smid, J.; Szwarc, M. J. Am. Chem. Soc.
965, 87, 5548.
58) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases
and Liquids, 4th ed.; McGraw-Hill: New York, 1987.
59) Fuller, E. N.; Schettler, P. D.; Giddings, J. C. Ind. Eng. Chem. 1966,
8, 19.
60) CRC Handbook of Chemistry and Physics, 72nd ed.; Lide, D. R.,
Ed.; CRC Press: Boca Raton, FL, 1991.
JA983011P
1
(
(61) Nagata, S. Mixing: Principles and Applications; Kodansha Ltd.:
Tokyo, 1975.
(62) Fogg, P. G. T.; Gerrard, W. Solubility of Gases In Liquids; John
Wiley and Sons Ltd.: Chichester, UK, 1991.
(63) Oxides of Nitrogen; Young, C. L., Ed.; Pergamon Press: Oxford,
1981; Vol. 8, pp 160-349.
(
5
(