Reaction rates of the reactions of OH(X 2Π ) with NH(a 1Δ ) and HN3(X)

Article abstract of DOI:10.1016/S0009-2614(99)00437-6

The rate constants of the radical-radical reaction OH(X ²Π)+NH(a ¹Δ)→products and the radical-molecule reaction OH(X ²Π)+HN₃→products were determined in a quasistatic laser photolysis cell at room temperature and a total pressure of 20 mbar. The radicals OH(X ²Π) and NH(a ¹Δ) were generated by exciplex laser photolysis of H₂O₂ and HN₃, respectively and detected by laser-induced fluorescence. The fluorescence time profiles of these radicals were monitored at variable delay times between photolysis and detection pulses and thus time resolution was obtained. The measurements yielded the rate constants k₁=(7.0±2)×10¹⁴ cm³ mol^-1 s^-1 and k₂=(7.7±1)×10¹¹ cm³ mol^-1 s^-1.

Full text of DOI:10.1016/S0009-2614(99)00437-6

11 June 1999
Ž
.
Chemical Physics Letters 306 1999 111–116
2
1
ž
/
ž
/
Reaction rates of the reactions of OH X P with NH a D and
˜
ž /
HN3 X
)
1
W. Hack , R. Jordan
Max-Planck-Institut fur Stromungsforschung, Bunsenstraße 10, D-37073 Gottingen, Germany
¨
¨
¨
Received 11 March 1999; in final form 19 April 1999
Abstract
The rate constants of the radical–radical reaction OH X P qNH a D ™products and the radical–molecule reaction
2
1
Ž
.
Ž
.
2
Ž
.
OH X P qHN3™products were determined in a quasistatic laser photolysis cell at room temperature and a total pressure
2
1
Ž
.
Ž
.
of 20 mbar. The radicals OH X P and NH a D were generated by exciplex laser photolysis of H2O2 and HN3,
respectively and detected by laser-induced fluorescence. The fluorescence time profiles of these radicals were monitored at
variable delay times between photolysis and detection pulses and thus time resolution was obtained. The measurements
yielded the rate constants k1s 7.0"2 =10 cm3 moly1 sy1 and k2s 7.7"1 =10 cm3 moly1 sy1. q 1999
Elsevier Science B.V. All rights reserved.
14
11
Ž
.
Ž
.
Ž
1. Introduction
two reaction pathways OqNH2 ™HNOqH ks
4.6=1013 cm3 moly1 sy1 and OqNH2 ™NH X
.
Ž .
There are few direct experimental data for the
H2 –N–O system. The dihydronitrosyl radical
12
Ž
qOH ks7=10
cm3 moly1 sy1 5 . The
. w x
atom–molecule reaction in the H2–N–O system N
qH2O™product has, to the best of our knowledge,
not yet been studied directly. A new approach to the
H2–N–O system is the radical–radical reaction
Ž 2
.
H2 NO B1 was observed via its microwave spec-
w x
trum 1 . The reaction between hydrogen atoms and
Ž
.
nitroxyl HNO : HqHNO™H2 qNO is known to
be the fast step in the nitric oxide catalysed recom-
bination of H atoms. The reverse reaction H2 qNO
™HNOqH proceeds with a large activation energy
NH a 1D qOH X 2 P ™products
1
Ž .
Ž
.
Ž
.
Ž
The reaction will due to the high excitation
energy of NH a not be important in thermal sys-
tems but it might be of interest in photochemical
reaction systems. Moreover, it is of fundamental
interest as one of the few singlet–doublet reactions
of EA s230 kJ moly1 2–4 . The atom–radical reac-
tion in the H2–N–O system
w
x
Ž ..
OqNH2 ™products
was found to be fast at room temperature with a rate
coefficient ks5.3=1013 cm3 moly1 sy1 5 . It has
1
w x
Ž
.
of NH a D .
The reaction of electronically excited imino radi-
1
Ž
Ž
..
cals NH a D with ground state molecules in sin-
)
Corresponding author. Fax: q49 551 5176 665; e-mail:
Ž
glet states like H2O or hydrocarbons e.g. CH4,
C2 H6, C3H8 proceeds via complex formation of an
whack@msfd12.gwdg.de
1
.
Present addres: Max-Planck-Institut fur biophysikalische
¨
intermediate in the singlet electronic ground state.
Chemie, Am Faßberg 11, D-37077 Gottingen.
¨
0009-2614r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved.
Ž
.
PII: S0009-2614 99 00437-6

(
)
112
W. Hack, R. JordanrChemical Physics Letters 306 1999 111–116
w
x
The dynamics of these electronic chemically acti-
vated molecules was studied for a large number of
been investigated in Refs. 10–12 and leads exclu-
2
Ž
.
sively to OH-radicals in the state OH X P, Õs0 .
w
x
systems 6–8 . The reaction of the singlet imino
The reaction of OH with H2O2 ,
radical with a doublet species has been studied only
2
Ž
.
with NO X P . In these reactions, a doublet inter-
mediate is formed which gives rise to crossing over
to the triplet surface, i.e. quenching.
OHqH2O2 ™products,
3
Ž .
Ž
.
The aim of this study was to measure the rate of
has been taken into consideration see below . The
Ž .
Ž .
H2O2 s9.3=
the radical–radical Reaction 1 – a doublet species
absorption coefficient is
´
248 nm
with NH in the first electronically excited singlet
state. In this system also, the reaction of the OH
radicals with the HN precursor molecule HN3
10y20 cm2 moleculey1 13–16 , and the photolysis
w x
Ž
.
w
x
quantum yield F248 nm H2O2 s2.09"0.36 17,18 .
Ž .
The OH-concentration was observed by the Q1 1 -line
2
2
q
Ž
.
of the OH A S , Õs0§X P, Õs0 transition at
ls307.85 nm. The emitted fluorescence was ob-
served perpendicular to the laser beams. After pass-
ing a filter, to reduce scattered light, the photons
2
˜
OH X P qHN X ™products
2
Ž .
Ž
.
3Ž .
has to be considered quantitatively.
Ž
were detected by a photomultiplier tube R955,
.
2. Experimental
Hammatsu .
1
Ž
.
The NH a D radicals were produced in the
1
Ž
.
The experiments were performed in a quasistatic
HN3-photolysis which leads mainly to NH a D in
Ž
reaction cell i.e. the duration between two photoly-
the vibronic states Õs0 and Õs1 with high rota-
w x
tional energies 19 . Under the experimental condi-
sis pulses is large enough to yield a complete ex-
change of the gas volume; on the time scale between
pump and probe pulse the flow is negligible with a
photolysisrLIF system. The experimental arrange-
ment is described in detail elsewhere 7,9 . Briefly, it
consists of a photolysis and a detection laser system.
Ž
.
tions applied 20 mbar He , the rotational energies
are relaxed by collisions with the inert gas He to
room temperature in a time of 1 ms after the photoly-
.
1
X
1
w
x
w x
sis 20,21 . The transition NH c P, Õ s0,§a D,
Y
1
Ž
.
Ž
.
Õ s0 was used to follow the NH a D concentra-
tion time profile over the wavelength range 325(
lrnm(328.
Ž
The latter consists of a dye laser FL3002, Lambda
.
Physik that was optically pumped by an exiplex
Ž
.
laser LPX 205, Lambda Physik . The pump laser
All measurements were done with He as the
carrier gas at room temperature and a pressure of 20
mbar.
pulses had energies of 200–400 mJ and a duration of
Ž
. Ž
.
ts14 ns FMHW ls308 nm, XeCl . The probe
beam has a cross-section of about 9 mm2 and pulse
energy densities of 20(ErmJ cmy2 (220. Fre-
quency doubled light was obtained by a KPD crystal
Gases were supplied with the highest commer-
cially available purities He)99.9999%, Praxair .
HN3 was produced by melting a mixture of stearic
Ž
.
Ž
.
Ž .
NaN3, Merck . The gas was dried with CaCl2 and
FL30, Lambda Physik and led to energy densities
acid C17 H35COOH, Merck and sodium azide
between 2 and 3 mJrcm2. In all experiments, the
pulse energy was high enough to saturate the transi-
tion to the electronically excited states. For the pho-
Ž
.
Ž
.
Ž
stored in a bulb ps1 bar diluted in Ar )
.
99.9999%, Praxair . The maximum molefraction of
Ž
tolysis, an exiplex laser LPX 205, Lambda Physik,
HN3 was XHN (0.17.
3
.
Ž
ls248 nm, KrF was used. The photolysis beam
Commercially available H2O2 85%, Solvay In-
terox was enriched to 99% by trap-to-trap distilla-
tion at Ts78 K. The H2O2 concentration in the
liquid was measured via KMnO4 titration. The H2O2
concentration in the gas phase on the way to the
reaction cell was determined by freezing the gas
had a cross-section of about 1.4 cm2 with pulse
energy densities of 0.7(ErmJ cmy2 (23. A vari-
able delay between the pulse of the photolysis and
the probe laser in the range 0(tRrms(400 yielded
.
the time resolution.
2
Ž
.
Ž .
The OH X P radicals were produced by the
stream in a N2 l -trap and titrating the amount of
photolysis of H2O2. This photolysis process has
H2O2 frozen in a given time.

(
)
W. Hack, R. JordanrChemical Physics Letters 306 1999 111–116
113
3. Results
good agreement with the literature value k4 s7.5=
1013 cm3 moly1 sy1 24,25 . NH a is depleted by
HN3 in the reaction
w
x
Ž .
Ž .
was investigated by observing
Reaction
1
1
Ž
.
NH a D concentration time profiles under pseudo-
NH a qHN ™products
Ž .
5
Ž .
3
first-order conditions with
a
large excess of
2
OH X P over NH a in the range 2=102 (
with a rate coefficient k5 s6.4=1013 cm3 moly1
Ž
.
Ž .
2
1
OH X P ts0r NH a D ts0 (2=103. The OH
w x
sy1 8 .
The OH radicals are depleted by other reactions:
w
Ž
.x
w
Ž
.x
radicals were produced by the photolysis of H2O2.
The OH concentration was determined from the
H2O2 photolysis via:
Ž .
Reaction 3 ,
OH X 2 P qH O ™products
Ž
.
2
2
w
x
FPEL PlP´P H2O2 Pln 10
with k3 s1.2=1012 cm3 moly1 sy1 26 , and Reac-
w
x
OH s
I
Ž .
w
x
hPcPA
Ž .
tion 2 with the rate constant given in this Letter.
where: the quantum yield for OH was accepted to be
Ž .
Reaction 2 can be neglected due to the small HN3
w
x
Fs2.0 18 rather than the lower value given in
concentrations applied in the experiments to deter-
w
x Ž
.
Ref. 17 see Section 4 ; EL s30 mJ, ls248 nm,
y11
w
x
mine k1. For HN3 s2=10
mol cmy3, Reac-
y 20
´ 248 nm s 9.3 = 10
cm2 moleculey 1
Ž
.
Ž .
2
tion
contributes only a small amount to the
w
x w
x
16,22,23 H2O2 shydrogen peroxide concentra-
consumption of the initial OH concentration i.e.
tion as given in Table 1, A is the cross-section of the
w
xŽ
. w
x
OH ts20 ms r OH s0.9997. The OH con-
o Ž .
photolysis laser As1.4 cm2.
sumption via Reaction
3
has to be taken into
It has to be considered that the concentration of
consideration. This can be done by taking the initial
H2O2 in the reaction cell was about a factor of a
hundred higher than the OH X P concentration.
Ž
.
slope i.e. for reaction times smaller than 5 ms in the
2
Ž
.
w
Ž .x
ln NH a versus time plot to obtain the first-order
rate constant. However, no significant deviation from
linearity was observed in these plots.
Ž .
The NH a depletion in the reaction system is given
by:
w
x
d NH a
The variation of OH was performed in two
Ž .
o
w
x
syk NH a OH yk4 NH a
Ž . Ž .
Ž .
1
different ways: i the photolysis laser fluence was
dt
Ž .
varied at constant H2O2 concentration, and ii the
H2O2 concentration was varied at constant photoly-
w
x
w
x
= H2O2 yk NH a NH3
Ž .
.
5
sis laser fluence.
The rate constant for the reaction
1
Ž .
Ž
.
i To distinguish the NH a D depletion by Reac-
Ž .
NH a 1D qH O ™products
4
Ž .
Ž
.
2
2
Ž .
tion
1
from the depletion by Reaction
4 with
was measured under the experimental conditions and
H2O2 , the photolysis laser power was varied and
2
was found to be k4 s7.1=1013 cm3 moly1 sy1, in
thus the OH X P concentration as given in Fig. 1.
Ž
.
Table 1
1
2
Ž
.
Ž
.
Experimental conditions for the reaction NH a D, Õs0 qOH X P
kX1
Ž
2
w
x
w
x
w
Ž
.x
T
p
HN3
H2yO92
OH X P
.
mbar
mol cmy3
10 mol cmy3
mol cmy3
10 sy1
y11
y11
4
Ž
K
.
Ž
.
Ž
10
.
Ž
.
Ž
10
.
295
295
295
295
295
295
295
295
20
20
20
20
20
20
20
20
2.2
2.2
2.2
2.2
2.2
2.2
2.2
2.2
0.727
1.45
2.09
2.82
3.64
4.36
5.09
5.82
0.8
1.6
2.3
3.1
4.0
4.8
5.6
6.4
0.6
1.2
1.7
2.4
3.0
3.5
4.2
4.8

(
)
114
W. Hack, R. JordanrChemical Physics Letters 306 1999 111–116
Fig. 1. First-order rate constant as a function of photolysis laser
Fig. 3. Semilogarithmic plot of the concentration profiles of
Ž .
fluence. v, First-order rate constant for Reaction 1 .
2
Ž
.
OH X P versus reaction time in the presence of various HN3
y9
w
x
concentrations: HN3 in =10
4.1; I, 6.1; ^, 8.9.
mol cmy3; v, 0.2; B, 2.7; `,
It was observed that with decreasing laser power, kX1
also decreases. This can be explained by a lower
1
Ž .
Ž
.
contribution of the fast Reaction 1 to the NH a D
By varying the H2O2 concentration at fixed pho-
depletion.
tolysis laser power, the rate constant k1 was deter-
Ž .
2
mined from a plot of kX1 versus the OH X P
ii A second method to obtain different OH
concentrations was applied by varying the H2O2
concentration. The data are given in Table 1. The
pseudo-first-order rate constant kX1 for a given H2O2
concentration was obtained by subtracting kX4 at
Ž
.
concentration under first-order conditions as shown
in Fig. 2. The results look much better than expected
from the unfavourable kinetic situation. The slope of
the plot in Fig. 2 resulted in the second-order rate
constant:
Ž .
measurement conditions. Reaction
1 contributed
1
Ž
.
approximately 10% to the total NH a D depletion,
Ž .
k s 7.0"2 =1014 cm3 moly1 sy1
.
Ž
.
the main contribution is NH a qH2O2.
1
The large error takes into account that the contri-
Ž .
bution of Reaction 1 is smaller than that of Reac-
Ž .
tion 4 .
2
Ž .
Ž
.
Reaction 2 was followed by the OH X P de-
pletion under pseudo-first-order conditions in the
presence of a large excess of HN3 over OH-
Table 2
Experimental conditions for the determination of the rate constant
k2
w
x
w
x
T
p
OH
Ž
HN3
Ž
kX2
Ž
0
y12
y9
3
mbar 10
mol cmy3 10 mol cmy3 10 sy1
Ž
K
.
Ž
.
.
.
.
294 20
294 20
294 20
294 20
294 20
294 20
294 20
294 20
7
7
7
7
7
7
7
7
0.0
0.2
0.8
2.7
4.1
6.1
7.9
8.9
1.29
1.31
1.40
3.42
4.21
5.57
7.72
7.69
2
Ž
Ž
.
.
Fig. 2. First-order rate constant as a function of the OH X P
1
2
Ž
.
concentration for the reaction of NH a D, Õs0 with OH X P .

(
)
W. Hack, R. JordanrChemical Physics Letters 306 1999 111–116
115
though obtained under unfavourable kinetic condi-
tions. The rate constant k1 was determined by fol-
1
Ž
.
lowing the NH a D depletion in the presence of
2
Ž
.
excess OH X P and H2O2. The room temperature
rate constant is k1 298 K s7.0=10 cm3 moly1
sy1 which is extremely fast compared to other radi-
cal–radical reactions. It is by far the fastest reaction
14
Ž
.
Ž .
of NH a which has been observed. A lower photoly-
sis quantum yield for the H2O2 laser photolysis
would lead to an even higher value of k1. Also
taking into account OH consuming reactions would
change k1 in the same direction. From the large
value of k1 it can be stated that it is unlikely that
Ž .
Ž2
.
quenching of NH a by OH P is a significant
w
x
Fig. 4. First-order rate constants versus HN3 for Reaction 2.
Ž .
Ž .
NH a – depletion channel of Reaction 1 .
Ž .
Reaction 1 has besides the quenching channel
2
2
Ž
.
w
x w
Ž
.x
X P ts0, i.e. 29( HN3 r OH X P ts0 (1270.
NH a 1D qOH X 2 P ™NH X qOH X
DR Hsy150.3 kJ moly1
2
Ž
.
Ž
.
Ž .
Ž .
Ž
.
The OH X P concentration as a function of time is
shown at various HN3 concentrations in Fig. 3. The
experimental conditions for this reaction are summa-
rized in Table 2.
1q
Ž
.
several exothermic reaction pathways:
Ž .
Reaction 1 also causes depletion of OH radicals.
X
˜
NH a qOH™NHOH 2A X
Ž .
Ž .
Ž .
The initial NH a concentrations are in the range
y12
0.2( NH a or10
mol cmy3 (9. But the fast
w
Ž .x
DR Hsy499.7 kJ moly1
1a
1b
1c
1d
Ž
Ž
Ž
Ž
.
.
.
.
Ž .
reaction of NH a with the HN3, present in large
Ž .
NH a qOH™NO X 2 P qH
X
concentration, reduces the NH a concentration
Ž .
Ž
.
2 Ž .
w
Ž .xŽ . w Ž .x
within the first 20 ms to NH a t r NH a o (1=
10y5; a value which is insignificant for the OH
concentration profiles.
The pseudo-first-order rate constants as a function
of the HN3 concentration is shown in Fig. 4. The
DR Hsy474.5 kJ moly1
4
˜
NH a qOH™N S qH O X
DR Hsy334.8 kJ moly1
NH a qOH™NH X B qO 3P
DR Hsy127.7 kJ moly1
Ž .
Ž
.
Ž .
2
Ž .
intercept is determined by Reaction 3
2
˜
The rate constant calculated from the intercept
Ž .
Ž
.
2 Ž
.
1
12
cm3
Ž
.
given in Fig. 3 is k3 s 2.0"0.3 =10
moly1 sy1. This value can be compared with the
value of k3 s1.0=1012 cm3 moly1 sy1 given in
Ž
.
Ž .
Reactions 1b and 1c can be regarded as the
decompositions of the initially formed HN–OH radi-
cal.
w
x
the literature 22,26 .
From the slope in Fig. 4, the rate constant k2 s
7.7"0.3 =10 cm3 moly1 sy1 was obtained for
11
Ž
.
Ž .
For Reaction 2 , the probable pathway is H atom
Ž .
Reaction 2 at room temperature.
abstraction via
OHqHN3 ™H2OqN3
which is exothermic with DR Hsy160 kJ mol-1.
Also the formation of HO–NH via
4. Discussion
Ž .
The rate constant of Reaction 1 has not yet been
determined directly. It may be of importance in
several H–N–O photolytic systems. Therefore it is
necessary give this value of the rate constant al-
2
2 X
˜
˜
OH X P qHN X ™HONH X A qN X
3Ž .
2 Ž .
Ž
.
Ž
.
DR Hsy266.9 kJ moly1

(
)
116
W. Hack, R. JordanrChemical Physics Letters 306 1999 111–116
2
w x
6
W. Hack, K. Rathmann, Ber. Bunsenges. Phys. Chem. 94
Ž
.
and the formation of NO X P via
Ž
.
1990 1304.
2
2
˜
OH X P qHN X ™NO X P qH qN
3Ž .
Ž
.
Ž
.
w x
Ž .
7
W. Hack, K. Rathmann, Z. Phys. Chem. 176 1992 151.
2
2
w x
Ž
.
8
W. Hack, in: Z.B. Alfassi Ed. , NH Radical Reactions in
DR Hsy241.7 kJ moly1
N-centered Radicals, John Wiley, 1998, p. 413.
w x
Ž . Ž .
W. Hack, A. Wilms, Z. Phys. Chem. NF 161 1989 107.
10 S. Klee, K.-H. Gericke, F.J. Comes, J. Chem. Phys. 85
are possible from the thermodynamic point of view.
9
x
w
w
w
˜
Ž .
The formation of NH2 X is endothermic:
Ž
.
1986 40.
OH X qHN X ™NH X qN X qO 3P
˜
˜
Ž .
3Ž .
2 Ž .
2 Ž .
Ž
.
x
11 M.P. Docker, A. Hodgson, J.P. Simons, Chem. Phys. Lett.
Ž
.
128 1986 264.
DR Hsq105.1 kJ moly1
x
12 G. Ondrey, N. van Veen, R. Bersohn, J. Chem. Phys. 78
Ž
.
By comparison of the rate constant with those
other H atom abstraction reactions, e.g. for CH4,
NH3 and HCN, it can be assumed that the H atom
abstraction is the main reaction pathway.
1983 3732.
w
w
x
Ž
.
13 L.T. Molina, M.J. Molina, J. Photochem. 15 1981 97.
x
14 C.L. Lin, N.K. Rohatgi, W.B. De More, Geophys. Res. Lett.
Ž
.
5 1978 113.
w
w
w
w
w
x
15 L.T. Molina, S.D. Schinke, M.J. Molina, Geophys. Res. Lett.
Ž
.
4 1977 580.
x
16 G.L. Vaghjiani, A.R. Ravishankara, J. Geophys. Res. 94
Acknowledgements
Ž
.
1989 3487.
x
17 A. Schiffman, D.D. Nelson, D.J. Nesbitt, J. Chem. Phys. 98
The continued interest of Prof. H.Gg. Wagner
is gratefully acknowledged. Thanks are due to
Ž
.
1993 6935.
x
Ž
.
18 G.L. Vaghjiani, A.R. Ravishankara, J. Chem. Phys. 92 1990
996.
Ž
the Deutsche Forschungsgemeinschaft Sonder-
x
19 T. Mill, Dissertation, MPI fur Stromungsforschung, Gottin-
¨
¨
¨
forschungsbereich 357 ‘Molekulare Mechanismen
gen, Report 14, 1990.
.
unimolekularer Prozesse’ and the Fonds der
w
w
x
Ž
.
20 F. Rohrer, F. Stuhl, J. Chem. Phys. 88 1988 4788.
Chemischen Industrie for financial support.
x
Ž
.
21 R. Freitag, F. Rohrer, F. Stuhl, J. Phys. Chem. 93 1989
3170.
w
x
22 W.B. DeMore, M.J. Molina, S.P. Sander, D.M. Golden, R.F.
Hampson, M.J. Kurylo, C.J. Howard, A.R. Ravishankara, J.
References
Ž
.
Phys. Lett. 87 1987 41.
w x
1
H. Mikami, S. Saito, S. Yamamoto, J. Chem. Phys. 94
w
x
23 W.B. DeMore, M.J. Molina, S.P. Sander, D.M. Golden, R.F.
Hampson, M.J. Kurylo, C.J. Howard, A.R. Ravishankara,
Chemical Kinetics and Photochemical Data for use in Strato-
spheric Modeling Evaluation No. 8, JPL Publ. No. 87-41, Jet
Propulsion Laboratory, Pasadena, CA, 1987.
Ž
.
1991 3415.
w x
2
D.L. Baulch, D.D. Drysdale, D.G. Horne, A.C. Lloyd, Evalu-
ated Kinetic Data for High Temperature Reactions, Butter-
worth, 1973.
w x
3
D.J. Nesbitt, Report University of Colorado, Boulder, CO,
AFOSR-TR-90-0514.
L.T. Molina, S.D. Schinke, M.J. Molina, Geophys. Res. Lett.
w
w
w
x
24 R. Jordan, Dipl. thesis, Max-Planck-Institut fur Stromungs-
¨
¨
forschung, Report 19, University Gottingen, 1996.
¨
w x
4
x
25 W. Hack, R. Jordan, Ber. Bunsenges. Phys. Chem. 101
Ž
.
4 1977 580.
Ž
.
1997 545.
w x
5
P. Dransfeld, W. Hack, H. Kurzke, F. Temps, H.Gg. Wag-
x
Ž
.
26 G.L. Vaghjiani, A.R. Ravishankara, J. Phys. Chem. 93 1989
7833.
Ž
.
ner, 20th Symposium Int. on Combustion, 1984, pp. 655.