Reaction probabilities for N2O5 hydrolysis on sulfuric acid and ammonium sulfate aerosols at room temperature

Article abstract of DOI:10.1021/jp9627436

The uptake coefficients for N₂O₅ hydrolysis have been measured at room temperature on micron-sized aerosols composed of both sulfuric acid aqueous solutions and ammonium sulfate solutions. The measurements have been performed in a laminar flow tube which is coupled to a chemical ionization mass spectrometer for monitoring the concentration of N₂O₅ in the gas phase and an optical particle counter which sizes the aerosols and determines their number density. The aerosols are generated with an ultrasonic nebulizer from aqueous solutions of either sulfuric acid or ammonium sulfate, and their liquid-phase concentration is determined by the relative humidity (RH) set within the flow tube. For both the sulfuric acid and ammonium sulfate aerosols, the reaction probability (γ) is largest for the lowest relative humidities studied: for sulfuric acid aerosols, γ = 0.05-0.06 for RH = 9-20%, γ = 0.02 for RH = 90%; for ammonium sulfate aerosols, γ = 0.04-0.05 for RH = 50-69%, γ = 0.02 for RH = 83-94%. In the case of ammonium sulfate aerosols, significant reactivity with N₂O₅ is found at relative humidities below the deliquescence point of 80%, consistent with the observation that ammonium sulfate aerosols are readily formed in supersaturated, liquid states.

Full text of DOI:10.1021/jp9627436

J. Phys. Chem. A 1997, 101, 871-878
871
Reaction Probabilities for N2O5 Hydrolysis on Sulfuric Acid and Ammonium Sulfate
Aerosols at Room Temperature
J. H. Hu† and J. P. D. Abbatt*
Department of the Geophysical Sciences, The UniVersity of Chicago, 5734 S. Ellis AVe.,
Chicago, Illinois 60637
ReceiVed: September 10, 1996; In Final Form: NoVember 11, 1996X
The uptake coefficients for N2O5 hydrolysis have been measured at room temperature on micron-sized aerosols
composed of both sulfuric acid aqueous solutions and ammonium sulfate solutions. The measurements have
been performed in a laminar flow tube which is coupled to a chemical ionization mass spectrometer for
monitoring the concentration of N2O5 in the gas phase and an optical particle counter which sizes the aerosols
and determines their number density. The aerosols are generated with an ultrasonic nebulizer from aqueous
solutions of either sulfuric acid or ammonium sulfate, and their liquid-phase concentration is determined by
the relative humidity (RH) set within the flow tube. For both the sulfuric acid and ammonium sulfate aerosols,
the reaction probability (γ) is largest for the lowest relative humidities studied: for sulfuric acid aerosols, γ
) 0.05-0.06 for RH ) 9-20%, γ ) 0.02 for RH ) 90%; for ammonium sulfate aerosols, γ ) 0.04-0.05
for RH ) 50-69%, γ ) 0.02 for RH ) 83-94%. In the case of ammonium sulfate aerosols, significant
reactivity with N2O5 is found at relative humidities below the deliquescence point of 80%, consistent with
the observation that ammonium sulfate aerosols are readily formed in supersaturated, liquid states.
Introduction
It is now well recognized that the hydrolysis reaction of N2O5
this work measurements of the reaction probability of N2O5 on
both sulfuric acid and ammonium sulfate aerosols using the
aerosol flow tube technique. Motivations for this study are
twofold. First and foremost, although this reaction has now
been studied extensively under stratospheric conditions (i.e., low
temperatures and sulfuric acid compositions of 50-80 wt %),
notably fewer experiments have been performed on dilute
sulfuric acid surfaces and on surfaces other than sulfuric acid.
In particular, given the high relative humidities encountered
frequently in both the boundary layer and free troposphere, the
composition of tropospheric sulfate aerosols may be significantly
more dilute than those encountered in the stratosphere. In
addition, although stratospheric aerosols are believed to be
predominantly composed of sulfuric acid and water, in the
troposphere there is substantial evidence that ammonia plays a
significant role in neutralizing pure sulfuric acid aerosols.4 In
continental regions in the boundary layer, sulfate aerosols can
be fully neutralized in the form of ammonium sulfate, (NH4)2SO4,
whereas in the free troposphere remote from continental
influence, the aerosols are likely to be more acidic.5-7
N2O5 + H2O f 2HNO3
(1)
is extremely important in determining the photochemical steady
state of the stratosphere, converting reactive nitrogen oxide
(NOx) species over to a longer-lived reservoir species, HNO3.
Indeed, inclusion of reaction 1 in stratospheric models has led
to markedly better agreement between predicted ozone depletion
rates and those being observed1 and to a reordering of the
catalytic cycles most important in destroying odd oxygen in
the lower stratosphere.2 Given the role of NOx species in
photochemical production of ozone in the lower atmosphere,
inclusion of reaction 1 in global tropospheric photochemical
models also leads to pronounced changes in the predicted levels
of key species such as NOx, O3, and OH. For example, with
reaction 1 included in a three-dimensional photochemical model,
Dentener and Crutzen predict for the free troposphere in the
summertime mid-latitudes (45° N, 500 hPa, mid-June) that NOx
and O3 levels will be only 55 and 90%, respectively, of their
values when modeled with gas-phase chemistry alone.3 Even
larger relative changes are predicted for higher latitudes and in
the planetary boundary layer. In addition to the importance of
reaction 1 on a global scale, it is also well recognized that the
reaction plays an important role in the reduction of NOx levels
in polluted urban air.
A second motivation for this study is that reaction 1 on
concentrated sulfuric acid surfaces is by far the most frequently
studied heterogeneous reaction,8 making it the best chemical
system to use to evaluate the performance of an aerosol flow
tube experimental technique we have been developing in our
laboratory. For a number of reasons, aerosol flow tubes are
being increasingly employed for heterogeneous studies of this
type.9-12 In particular, for reaction probabilities of roughly 0.1
and smaller measured on micron-sized aerosols, there is the need
for only a relatively small correction to observed uptake
coefficients for the effects of gas-phase diffusion. On the other
hand, the coated-wall flow tube technique is largely inoperable
if a few Torr of water vapor is present in the flow tube because
gas-phase diffusion becomes rate limiting for all but the smallest
uptake coefficients. A second advantage, illustrated by Hanson
and Lovejoy, is the ability of experiments performed on aerosols
A major uncertainty in model estimates such as those of
Dentener and Crutzen are the appropriate heterogeneous reaction
rates, which are determined by a variety of factors including
total aerosol surface areas, the chemical composition of
tropospheric aerosols, and the corresponding reactivity of N2O5
on these surfaces. To address this latter point, we report in
* To whom correspondence should be sent.
† School of Earth and Atmospheric Sciences, Georgia Institute of
Technology, Atlanta, GA 30332.
X Abstract published in AdVance ACS Abstracts, January 1, 1997.
S1089-5639(96)02743-0 CCC: $14.00 © 1997 American Chemical Society

872 J. Phys. Chem. A, Vol. 101, No. 5, 1997
Hu and Abbatt
piezocrystal. A small flow of N2 gas (10-50 sccm) carries the
aerosols into a 47 cm long, 3 cm i.d. conditioning region where
they have a residence time of typically 10 s. We can vary the
aerosol number density in the conditioner either by varying the
voltage applied to the crystal or by changing the flow of the N2
carrier gas through the nebulizer.
The aerosols adjust their composition in the conditioner to
the ambient relative humidity, which is set by adding both a
dry flow of N2 and a water-saturated flow of N2 coming from
a bubbler kept at constant temperature. The small amount of
water vapor from the moist flow of N2 coming from the
nebulizer is also taken into consideration. The total N2 flow
from these three sources is about 2000 sccm. From the error
estimates in the flows and temperatures of the bubbler, we
estimate the errors in the relative humidity in the conditioner
to be (1% and no larger than (2%. Indeed, during the
ammonium sulfate experiments, we compared the relative
humidity calculated in this manner to that monitored by a dew
point hygrometer (Fisher Scientific) and found that the two were
in agreement to this degree. Assuming that the aerosols are in
equilibrium with the ambient flow conditions, this potential error
in the relative humidity corresponds to an inaccuracy of no more
than (2 wt % in the composition of the aerosols, where the
relationship between the relative humidity and the composition
of the aerosols is taken from refs 14 and 15.
Figure 1. Schematic of experimental apparatus.
Aerosol Surface Area Determination. After the conditioner,
the flow containing the aerosols passes through a 6 mm o.d.,
12 cm long Pyrex tube which is inserted into the detection region
of a commercially built optical particle counter (Particle
Measuring Systems, Inc., No. SSIP-S2). The optical particle
counter uses a 780 nm polarized light source which sits at right
angles to the scattered-light collection optics and detection
photodiodes; i.e., the laser beam is perpendicular to the page in
Figure 1. The intersection of the laser beam and collection
optics defines a detection volume that was designed to be
particularly small so as to keep coincidence errors negligible
for aerosol number densities below 105/cm3. Using a calibration
performed by Particle Measuring Systems with latex and glass
spheres of known size, aerosols are sized based on the intensity
of the scattered signals from individual aerosols which enter
the detection volume. The lower detection limit for aerosol size
is 0.2 µm diameter, the upper limit is 20 µm, and aerosols are
classified into one of 31 channels between these two limits.
Using latex and glass spheres of 0.50, 1.0, 2.0, and 9.6 µm
diameter (Duke Scientific), we routinely check that the calibra-
tion of the instrument is good to at least one size channel, or
roughly 10-15% sizing accuracy.
Scattered light signals per unit time are converted into aerosol
number densities via knowledge of the detection volume
sampled per unit time, which is defined by both the optical
configuration and by the flow velocity in the detection volume.
Assuming fully developed laminar flow in the 6 cm o.d. intake
tube, we take this velocity to be twice the bulk velocity in the
tube. Using a Pitot-static probe with a small sampling inlet
(1.0 mm) which is coupled to a differential capacitance
manometer (MKS-220CD, 1 Torr full scale), velocities measured
in the aerosol detection region agree with the velocities
calculated from the bulk flow to within 4%. In general, the
instrument has been calibrated to have better than 10% counting
accuracy (J. Knollenberg, Particle Measuring Systems, personal
communication).
Figure 2. Schematic of chemical ionization mass spectrometer.
to study the dependence of observed uptake coefficients upon
aerosol size.13
Although the general approachsthe measurement of the loss
of a gas-phase species upon aerosol distributions of varying total
surface areasis similar to other aerosol flow tube experiments,
the instrumental techniques we are using are somewhat different
from those used previously. In particular, the aerosol flow tube
configuration used in this work employs a laminar flow tube,
coupled to a chemical ionization mass spectrometer for monitor-
ing the gas-phase composition, to an optical particle counter
for the determination of aerosol size and number density, and
to an ultrasonic nebulizer aerosol source. Results that agree
well with previous measurements are reported for the room
temperature uptake coefficients of N2O5 on relatively concen-
trated sulfuric acid aerosols, i.e., 59-66 wt %. In order to better
model tropospheric sulfate aerosol compositions, we also report
measurements for both more dilute sulfuric acid compositions
(17 and 40 wt %) and a variety of ammonium sulfate aerosol
compositions. Because these measurements have been per-
formed over a wide range of aerosol compositions using the
same experimental technique, this data set allows us to ac-
curately assess the dependence of the overall reaction probability
upon the water content of sulfate aerosols.
Experimental Section
Aerosol Generation. The overall experimental configuration
is shown in Figures 1 and 2. Aerosols are generated from
sulfuric acid and ammonium sulfate solutions by an in-lab-built
ultrasonic nebulizer driven by a 2.5 cm diameter piezocrystal.
A 5 cm long coupling region, filled with water and sealed with
Teflon-coated Viton O-rings and a thin Teflon sheet, isolates
the solution being nebulized from the metallic coating of the
Typical aerosol number density and surface area density
distributions for ≈60 wt % H2SO4 aerosols are shown in Figure
3. Two polydisperse aerosol distributions are clearly being

N2O5 Hydrolysis on Aerosols
J. Phys. Chem. A, Vol. 101, No. 5, 1997 873
tubing between the two to the minimum (≈5-10 cm long), and
consequently we believe the losses to be minor.
The number of moles of either sulfuric acid or ammonium
sulfate which flowed through the optical particle counter during
the collection period is then calculated according to
moles solute from electrical conductivity ) (CVt)/Λo (2)
where C is the measured electrical conductivity (in µmho/cm),
Vt is the volume of the aqueous trap (in cm3), and Λo is the
molar conductivity for the solute of interest (in (µmho cm2)/
mol).16 Typical conductivities measured were on the order of
hundreds of µmho/cm for a collection time of 5 min, whereas
the background conductivity of the distilled/deionized water in
our laboratory is about 1 µmho/cm.
Figure 4 is a typical aerosol volume calibration plot where
moles of solute determined from the conductivity measurements
is plotted against moles of solute determined from the optical
particle counter during the aerosol trapping period:
moles solute from optical particle counter )
(VdætF wt %)/MW (3)
where Vd is the average aerosol volume measured by the counter
(in cm3/cm3), æ is the carrier gas rate (in cm3/min), t is the
trapping time (in minutes), F is the density of the aerosol (in
g/cm3), wt % is the percentage weight composition of the
aerosol, and MW is the molecular weight of the solute of
interest.
For all the calibrations which we have performed, plots such
as these are highly linear which is indicative that the counter is
responding linearly to typical total aerosol volumes used in this
work. For aerosols of 66 wt % sulfuric acid, the slope of this
plot is relatively close to unity, whereas for more dilute
solutions, such as 17 wt % sulfuric acid shown in Figure 4, the
slopes are somewhat smaller than unity. The change in the
counter response as a function of aerosol composition is a well-
known observation, due to the smaller refractive index of the
more dilute aerosols.17 That is, the smaller refractive index leads
to a reduction in the ability of the more dilute aerosols to scatter
light when compared to more concentrated aerosols of higher
refractive index. Because the counter is undersizing the dilute
aerosols, we use plots such as Figure 4 to calibrate the counter
response by correcting the observed aerosol size by a factor
equal to the reciprocal of the slope of these plots to the one-
third power.
During the course of running a full kinetics experiment, we
monitor a small buildup of aerosol material on the walls of the
flow tube immediately opposite the inlet from the optical particle
counter. This is most likely due some of the aerosols failing
to follow the flow around the 90° bend. We performed an
extensive set of experiments with the electrical conductivity
technique to determine, for constant flow and aerosol composi-
tions, the aerosol volumes determined at the outlet of the kinetics
flow tube relative to the volumes determined by trapping at the
outlet of the optical particle counter. Aerosol volumes were
consistently lower at the flow tube outlet by an average of 15
( 5%. Consequently, for the kinetics experiments described
below, we have corrected our total aerosol surface areas by this
factor to account for the loss of aerosols at the top of the flow
tube. No kinetics measurements were made in the region of
the flow tube where aerosol was seen to be accumulating on
the wall.
Figure 3. Typical aerosol number density (a, top) and surface area
(b, bottom) distributions observed by the optical particle counter for
sulfuric acid aerosols at a relative humidity of 20%.
generated by the nebulizer: a distribution with large aerosols
(≈1-6 µm in diameter) characteristic of mechanical formation
mechanisms and a distribution of much smaller aerosols in the
submicron range. Although a number of quite small aerosol
particles (<0.3 µm diameter) are generated by the nebulizer
source, they do not contribute significantly to the overall aerosol
surface area in the flow tube. For example, aerosols smaller
than 0.3 µm typically contribute less than 1% of the measured
aerosol surface area in the flow. Typical number densities of
the large particles present in the flow tube for kinetics studies
were 3 × 103-2 × 104 aerosols/cm3, and corresponding aerosol
surface areas were 3 × 104-7 × 105 cm2/cm3. The peak of
the surface area distribution was typically between 2 and 4 µm
diameter.
In light of the importance of accurately determining aerosol
sizes and number densities (and thus, total aerosol surfaces areas
and volumes) in kinetics experiments of this type, we have
determined the sensitivity of the instrument to total aerosol
volumes using a calibration approach which is independent of
the optical particle counter. In particular, the approach we have
taken is to establish a flow of either sulfuric acid or ammonium
sulfate aerosols of known composition through the counter under
flow conditions used in the kinetics experiments. All the
aerosols passing through the counter within a measured time
period are collected in an aqueous trap located immediately
downstream of the counter. After the collection period, the
electrical conductivity of the aqueous trap is then measured.
We believe that the trap is 100% efficient at aerosol collection
because we placed on one occasion a second trap in series with
the first and recorded no conductivity increase in the second
trap. Although there is the possibility that there were aerosol
losses between the counter and the trap, we kept the length of
The calibrations performed with the electrical conductivity
technique show very high precision and are quite reproducible
(to at least 10%) over extended time periods of months. Because

874 J. Phys. Chem. A, Vol. 101, No. 5, 1997
Hu and Abbatt
occurs across a pinhole in a Teflon sheet mounted between the
two flow tubes. In the CIMS reactor, 3.5 SLM of N2 pass
through a radioactive (Po-210) ion source (NRD Inc.) mounted
at the end of a 6 mm o.d. stainless steel tube. An additional 7
SLM passes around the outside of the ion source. I- ions,
generated by passing trace amounts of CH3I (Aldrich) over the
Po-210 source, react with N2O5 during a 10 ms time period
defined by the overall flow and the distance between the end
of the ion source and the sampling pinhole to the mass
spectrometer. Ions generated at high pressure pass through three
stages of differential pumping en route to an Extrel quadrupole
mass spectrometer. The pinholes that separate the different
pumping stages are biased with voltages of -200, -40, and
-15 V for the high-, middle-, and low-pressure stages,
respectively. The first stage, at 1 Torr pressure and pumped
with a rotary pump, was found to be a very efficient declustering
region for ion-water clusters which readily form in the
expansion of high-pressure flows containing high partial pres-
sures of water vapor.20 With this declustering region in
operation, we observe no water clusters in the final mass
spectrum, whereas without this region, the mass spectrum was
very much more complicated. The second stage of the
differential pumping, evacuated with a diffusion pump, is at 1
× 10-3 Torr, and the final stage, containing the quadrupole mass
spectrometer and pumped with a turbomolecular pump, is at 1
× 10-5 Torr.
Figure 4. Optical particle counter calibration plot using electrical
conductivity analysis of collected aerosols (see text).
this approach is directly measuring total aerosol volumes which
are flowing through the flow tube, we estimate that systematic
errors in total aerosol volumes are no larger than (25%. The
systematic errors in total aerosol surface areas will be equal to
or smaller than this estimate.
Delivery of N2O5 and Aerosols to the Kinetics Flow Tube.
The aerosol flow passes from the optical particle counter to the
3.0 cm i.d. reaction flow tube which is oriented vertically, at
right angles to the conditioner and the flow path through the
optical particle counter. For the majority of the studies reported
here the reaction flow tube was 90 cm long whereas for some
of the initial studies, a shorter flow tube of 48 cm length was
used. The total pressure in the flow tube was 750 ( 10 Torr,
and the bulk flow velocity was roughly 5 cm/s. The terminal
fall velocity of the largest aerosols used in this work was less
than 2% of the carrier gas bulk velocity.
For some of the original studies on 40 and 59 wt % sulfuric
acid aerosols, the overall sensitivity of the CIMS system was
relatively low, requiring the use of high concentrations of N2O5
(≈1 × 1014 molecules/cm3) in the aerosol flow tube. However,
for all the other studies reported here, the geometry of the CIMS
source was altered slightly, and the sensitivity was considerably
higher. For these studies, a concentration of 7 × 1012 molecules/
cm3 of N2O5 in the aerosol flow tube was used. This
corresponds to a concentration of 1.7 × 1011 molecules/cm3 in
the CIMS flow tube, and it gives rise to a signal of roughly
200 counts/s. Although the reaction between I- and HNO3 is
endothermic and not expected to proceed, we nevertheless
observed a weak signal arising from HNO3 in the presence of
I- under certain conditions. Similar behavior has been observed
by other workers.21 We believe that the HNO3 arises principally
as a product of reaction 1 because in separate experiments with
an electron-impact mass spectrometer we have quantified the
HNO3 partial pressure impurity arising from our N2O5 samples
to be no more than 50% of the N2O5 signal. Thus, the HNO3
background of ≈5-10 counts/s was determined by decaying
away all the N2O5 in the flow tube by operating under conditions
of high surface area and long reaction times; i.e., the injector
was pulled fully out. Simple first-order kinetics analysis predicts
that this background will be essentially constant compared to
the relative changes in the N2O5 signal for the reaction times
and first-order rate constants characteristic of our experiment.
For these conditions, the detection limit (S/N ) 1) for N2O5
was roughly 3 × 109 molecules/cm3 in the CIMS flow tube,
corresponding to 1 × 1011 molecules/cm3 in the aerosol flow
tube. These are likely to be upper limits to the detection limit
because we are assuming that there is no decay of N2O5 along
the Teflon lines connecting the N2O5 trap and the flow tube.
For all the kinetics studies, the I- signal was on the order of
200 000 counts/s, and it was stable as the N2O5 concentration
changed during a decay.
N2O5 was synthesized at room temperature by oxidizing NO2
with O3 produced from O2 carrier gas and a UV photolysis
source (Jelight Co., PS-3001-30). To remove H2O vapor from
the O2 carrier gas, a P2O5 trap was placed immediately upstream
of the ozonizer and reaction tube. N2O5 was injected into the
flow at concentrations of 5 × 1012-1 × 1014 molecules/cm3
via a 6 mm o.d. movable injector by passing a carrier gas of
30-50 sccm of N2 through a trap containing solid N2O5 which
was kept at -50-70 °C. To reduce the formation of HNO3 in
the trap, the carrier gas for the N2O5 passed through a P2O5
trap prior to entering the N2O5 trap. We checked that the N2
carrier gas was saturated with the vapor pressure of N2O5 at
the temperature of the trap by passing the flow through a 50
cm long absorption cell and by measuring the absorption signal
at 254 nm due to N2O5. The partial pressure of N2O5 measured
by the absorption measurements was within 7% of that
calculated by assuming the flow was saturated with N2O5. The
walls of the flow tube were coated with halocarbon wax to
minimize N2O5 wall loss, and they were washed and dried
between kinetics runs.
-
N2O5 Detection. N2O5 was detected as NO3 by chemical
ionization mass spectrometry (CIMS) using the I- reagent ion:
I- + N2O5 f NO3- + INO2. This detection scheme has been
used before to selectively monitor N2O5 in the presence of
HNO3, which is believed to not react with I-.18,19 As shown
in Figure 2, the entire flow from the aerosol reaction tube passes
into the CIMS source where it mixes with a much larger flow
of N2 at a pressure of 120 Torr. The pressure drop from the
750 Torr aerosol flow tube to the lower pressure CIMS source
Results
Typical decays of N2O5 as a function of injector distance for
a variety of aerosol surface areas for 17 wt % sulfuric acid

N2O5 Hydrolysis on Aerosols
J. Phys. Chem. A, Vol. 101, No. 5, 1997 875
Figure 6. First-order rate constant for N2O5 reaction due to aerosol
reaction as a function of total aerosol surface area for 17 wt % sulfuric
acid aerosols: squares, data from long flow tube; circles, data from
short flow tube.
Figure 5. Semilog plot of N2O5 signal as a function of injector position
for a variety of 17 wt % sulfuric acid aerosol surface areas and for
wall loss.
the average total aerosol surface area measured during the decay.
Two sets of data, one set obtained with the long flow tube and
an additional one with the short flow tube, are shown in Figure
6. As indicated below, for the scatter within the individual sets
of measurements, the two sets of data yield statistically
indistinguishable average values of the uptake coefficient. Thus,
we feel confident in reporting uptake coefficients performed
using both the longer and shorter flow tubes. The scatter in
plots such as Figure 6 is believed to arise from a number of
sources including variable wall losses during a set of measure-
ments, random errors in the experimental first-order decays, and
variability in the total aerosol surface area during the decay.
With respect to this latter point, typical 1σ precisions for the
surface area measured during a decay were on the order of (5%.
To convert first-order rate constants to gas-liquid uptake
coefficients, eq 4 is used to connect the regime where gas-phase
loss is in the kinetic limit to that where it is in the gas-phase
diffusion limit:25
aerosols are shown in Figure 5. Within experimental error, the
decays are first order. Note that there is a loss of N2O5 due to
wall reaction in the absence of aerosols, where the wall decay
was measured immediately after performing kinetics experi-
ments with aerosols in the flow tube. It was observed that larger
wall losses were somewhat correlated with higher relative
humidities in the flow tube, with observed first-order wall-loss
rate constants of roughly 0.1 s-1
.
The Reynolds number for flow conditions in this work was
typically between 90 and 100. As a result, the entrance length
which is conventionally used to describe the point at which fully
developed laminar flow is developed, i.e., the distance at which
the center line velocity of the flow reaches 1.99 times the value
of the bulk velocity, is on the order of 16 cm.22 For the longer
flow tube used here, which was employed for all the ammonium
sulfate studies and for the studies of 17 and 67 wt % sulfuric
acid, all decays were monitored starting at a distance of 20 cm
from the downstream end of the flow tube. That is, laminar
flow was fully established for the entire length of the decay.
For the shorter flow tube, which was employed for the 40 and
59 wt % sulfuric acid studies, we used only a 10 cm entrance
length. However, given the asymptotic nature by which laminar
flow approaches a steady-state velocity profile, we feel confident
that this was sufficient length to allow a close approximation
to fully developed flow to be attained. In particular, it can be
calculated for our flow conditions that the center line velocity
after a 10 cm entrance length will already be 1.94 as large as
the bulk flow velocity.22
These entrance lengths not only allow the flow to approximate
fully developed laminar conditions, but they also give time for
mixing of N2O5 from the injector into the bulk flow. The time
for mixing to occur via molecular diffusion to a level where
there are no more than 5% inhomogeneities in the flow occurs
in a distance of roughly 15 cm for our flow conditions.23 It is
likely that mixing into the bulk in fact occurs much faster than
this via turbulent mixing processes, given the presence of the
injector and the fact that N2O5 is being injected into the flow
tube carrier gas.
γNiπdi2V
kir )
(4)
3γ(1 + 0.38Kn)
Kn(1 + Kn)
4 +
where kIi is the first-order rate constant due to aerosol size di,
V is the mean molecular velocity for N2O5, and Kn, the Knudsen
number, equals 6Dg/diV. Dg is the diffusion coefficient for N2O5
in the carrier gas. Because eq 4 assumes a monodisperse aerosol
distribution, we have evaluated the majority of our data by taking
the size of the aerosols, di, to be at the maximum of the surface
area density distribution for the large aerosols, i.e., those larger
than about 0.5 µm. Since our aerosol distribution of large
aerosols is clearly not monodisperse, we have validated this
assumption, by also performing the full calculation for a few
test cases using a measured aerosol size distribution. In
particular, for these cases we determine the uptake coefficient
by solving eq 5
kI ) kI
(5)
∑
i
The injector distances shown in Figure 5 are converted into
reaction times using the bulk flow velocity and a standard
correction, developed by Brown,24 to account for non-plug-flow
conditions. The overall N2O5 loss observed in the presence of
aerosols, along with the loss of N2O5 in the absence of aerosols
due to wall reaction, were used as input for this calculation.
The first-order-loss rate coefficients, kI, due to aerosol loss alone
for 17 wt % sulfuric acid aerosols are plotted in Figure 6 versus
i
for the uptake coefficient, where each individual kIi is calculated
from eq 4 for every aerosol size measured by the optical particle
counter. The uptake coefficient calculated in this manner, which
takes into account the polydisperse nature of our aerosols, agrees
with the uptake coefficient calculated by assuming a monodis-
perse distribution to better than 5%.

876 J. Phys. Chem. A, Vol. 101, No. 5, 1997
Hu and Abbatt
TABLE 1: Uptake Coefficients for N2O5 on H2SO4 Aqueous
Aerosols
RH (%)
90.0
H2SO4 compn (wt %)
17
uptake coeffa
no. of expts
0.023 ( 0.004b
0.021 ( 0.004c
0.024 ( 0.004d
0.038 ( 0.012d
0.060 ( 0.020d
0.050 ( 0.008c
15
8
7
5
7
58.5
19.5
8.5
40
59
66
5
a Data at 297 ( 1 K. b Data from both short and long flow tubes.
c Data from long flow tube. d Data from short flow tube.
TABLE 2: Uptake Coefficients for N2O5 on (NH4)2SO4
Aqueous Aerosols
RH (%) (NH4)2SO4 compn (wt %) uptake coeffa no. of expts
93.5
83.0
68.5
50.0
20
40
60
80
0.017 ( 0.002
0.023 ( 0.004
0.053 ( 0.006
0.044 ( 0.008
5
5
7
5
Figure 7. Uptake coefficient for N2O5 on sulfuric acid aqueous
solutions and water surfaces as a function of relative humidity: filled
triangles, this work (297 K); filled circle, Fried et al.10 (293 K); open
triangles, Mozurkewich and Calvert9 (293 K); open squares, Van Doren
et al.30 (282 K); filled square, Lovejoy and Hanson12 (298 K); open
circle, George et al.31 (277 K).
a Data at 297 ( 1 K.
thus validating the correction procedure for non-plug-flow
conditions to this degree of accuracy. Similarly, we have no
method to check the accuracy of the gas-phase diffusion
correction, but the dominant source of error in this regard is
most likely to arise from incorrectly determining the peak of
the aerosol surface area distribution. Assuming an inaccuracy
of 10% in our ability to size the aerosols, this corresponds to a
relatively small potential error of 2% for uptake coefficients of
0.02 and 5% for uptake coefficients of 0.05. The final source
of potential systematic error, which we believe to be on the
order of (25% as described above, arises from the measurement
of the total aerosol surface areas in the flow tube.
It should be noted that there is the possibility that HNO3
formed as a result of reaction 1 will be strongly partitioned from
the gas phase to the aerosol, thus affecting the composition of
the aerosols being studied. This is of most concern to the
ammonium sulfate studies because the Henry’s law solubility
of HNO3 into such solutions is extremely high.28 For the
maximum gas-phase concentrations of HNO3 expected to be in
the flow tube for a gas-phase concentration of N2O5 of 7 ×
1012 molecules/cm3, it is calculated that the maximum dissolved
concentration of HNO3 which could arise in the aerosols is 0.3
M, assuming the nitric acid is fully partitioned to the condensed
phase. This liquid-phase concentration estimate is valid only
for a few runs where small total aerosol volumes were used,
≈8 × 10-8 cm3/cm3. Most of the kinetics studies used
significantly larger aerosol volumes, and the estimated concen-
tration of HNO3 in the aerosols is thus smaller than 0.3 M. Along
the same line of thought, the partial pressures of N2O5 used in
the 40 and 59 wt % sulfuric acid studies were very high (≈1 ×
1014 molecules/cm3), which will have produced high concentra-
tions of HNO3 in the gas phase. However, the Henry’s law
constant for HNO3 in sulfuric acid solutions of this composition
is sufficiently low that very little HNO3 is expected to be have
been partitioned to the aerosols.29 One advantage of using large
aerosols in this experiment is that aerosol volumes are cor-
respondingly high, making these potential interferences of
relatively minor importance.
Figure 8. Uptake coefficient for N2O5 on ammonium sulfate aerosols
as a function of relative humidity: filled circle, this work (297 K);
filled square, Mozurkewich and Calvert9 (293 K).
For this work we have used a diffusion coefficient for N2O5
in the carrier gas of 0.10 cm2/s for our total pressures of 750
Torr in the flow tube. This value was calculated using standard
Lennard-Jones parameters taken from refs 26 and 27. The
calculated value for the diffusion coefficient is not significantly
affected by the presence of variable amounts of water vapor in
the flow. The size of the diffusion correction relative to the
uptake coefficients which would be calculated in the kinetic
limit is on the order of 10-50%, depending upon the size of
the aerosols and the size of the uptake coefficient.
The uptake coefficients which we report for N2O5 hydrolysis
on a range of compositions of sulfuric acid and ammonium
sulfate aerosols are given in Figures 7 and 8 and in Tables 1
and 2. The errors listed in the figures and tables reflect 1σ
precisions. Potential systematic errors could arise from a variety
of sources including the treatment of non-plug-flow conditions
in the flow reactor, the correction made to account for gas-
phase diffusion, and the measurement of the aerosol surface
areas in the flow tube. Although we have no a priori method
to test the Brown correction procedure for non-plug-flow
conditions,24 it can be noted that Lovejoy and Hanson have
performed uptake coefficient measurements using pulsed injec-
tion of N2O5 to experimentally determine reaction times.12 These
workers have found that the pulsed studies agree with those
from the more conventional steady-state experiments to 4%,
Discussion
Confidence in the present set of uptake coefficient measure-
ments comes from comparison to other results in the literature
for sulfuric acid at low relative humidities. In particular, other
measurements of the N2O5 hydrolysis reaction probability on
either sulfuric acid or ammonium sulfate surfaces which were

N2O5 Hydrolysis on Aerosols
J. Phys. Chem. A, Vol. 101, No. 5, 1997 877
performed relatively close to room temperature are included in
Figures 7 and 8. Included in the comparison are data from a
variety of experimental techniques: aerosol flow tube measure-
ments from Mozurkewich and Calvert,9 Fried et al.,10 and
Lovejoy and Hanson11,12 and droplet train experiments of Van
Doren et al.30 and George et al.31 Agreement for the sulfuric
acid studies at low relative humidities is quite good. In
particular, our results at 8.5 and 19.5% relative humidity fall
within the error limits of the studies of Van Doren et al., Fried
et al., and Lovejoy and Hanson. It should be noted that the
Fried et al. experiment represents the latest version of the
Mozurkewich and Calvert aerosol kinetics study, which initially
reported the larger uptake coefficients on sulfuric acid shown
in the figures.
e.g., γ < 0.003 for relative humidity of 25%. Similarly, in some
of our ammonium sulfate experiments we lowered the relative
humidity below 40% under conditions of high aerosol surface
area, and we observed very small loss of N2O5, corresponding
to γ e 0.01. Although this reaction probability limit is highly
uncertain because the particles are solid under these conditions
and our aerosol scattering calibrations are not necessarily
appropriate, it nevertheless appears as though N2O5 is quite
unreactive on dry particles.
For photochemical modeling within the boundary layer these
results indicate that the reaction probability will be dependent
upon the ambient relative humidity. For example, for sulfuric
acid aerosols close to room temperature, the appropriate reaction
probability for the N2O5 hydrolysis is on the order of 0.025 for
high relative humidity conditions, e.g., those corresponding to
sulfuric acid aerosols of ≈20 wt % composition. For lower
relative humidities and more concentrated sulfate aerosols, the
data support a somewhat larger reaction probability near 0.05.
At high relative humidities, the N2O5 uptake coefficient has
not previously been measured on sulfuric acid solutions.
However, for comparison sake, we have included in Figure 7
results measured on pure water surfaces by both Van Doren et
al. and George et al. at 282 and 277 K, respectively. From the
figure it appears as though uptake coefficients on dilute sulfuric
acid solutions are similar to those measured on water surfaces.
It should be noted that both the Van Doren et al. and George et
al. studies report a substantial negative temperature dependence
to the uptake coefficient on water (for example, from Van Doren
Acknowledgment. This work has been supported financially
by both the Atmospheric Chemistry Program at the National
Science Foundation and the SASS Program at NASA. The
authors thank John Seeley for guiding us in the design of our
CIMS instrument, Greg Huey for suggesting the use of the Po-
210 ion source, and Dennis O’Brien for writing some of the
data acquisition software.
et al.30 γN O ) 0.040 ( 0.005 at 282 K and 0.061 ( 0.004 at
271 K), so a comparison to our measurements performed at
297 K on dilute sulfuric acid may not be entirely appropriate.
2
5
References and Notes
The most intriguing aspect of the data in Figure 7 is that the
N2O5 uptake coefficient is somewhat higher at lower relative
humidities than at high relative humidities. This behavior is
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opposite direction.8 The relative independence of the uptake
coefficient upon acid composition has been observed previ-
ously,8,32 and it implies that water does not play a direct, reactive
role in the rate-determining step for the reaction. Rather, the
rate-determining step for the reaction appears to be either that
involved in the ability of the surface to accommodate N2O5 or
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