Detailed study of HOCl + HCl → Cl2 + H2O in sulfuric acid

Article abstract of DOI:10.1021/jp9633153

Reactive uptake coefficients for HOCl as a function of [HCl] were measured in a rotating wetted-wall flow reactor for several sulfuric acid solutions containing between 49 and 67 wt % H₂SO₄ at 220 and 250 K. The solubility of HOCl in sulfuric acid solutions at 220 and 250 K was also measured. Using these measured solubilities, calculated HCl solubilities, and estimated diffusivities for HOCl, the second-order rate coefficients (k^II) in the liquid were extracted. At 250 K, k^II increases with increasing acid concentration, from 3 × 10⁵ M^-1 s^-1 at 49 wt % acid to 5 × 10⁶ M^-1 s^-1 at 67 wt %. It is suggested that the reaction may involve an initial protonation of HOCl, followed by reaction of H₂OCl⁺ with Cl^-.

Full text of DOI:10.1021/jp9633153

J. Phys. Chem. A 1997, 101, 4717-4725
4717
Detailed Study of HOCl + HCl f Cl2 + H2O in Sulfuric Acid
D. J. Donaldson,*,† A. R. Ravishankara,‡ and David R. Hanson*
Aeronomy Laboratory, National Oceanic and Atmospheric Administration, Boulder, Colorado, and
CooperatiVe Institute for Research in EnVironmental Sciences, UniVersity of Colorado, Boulder, Colorado
ReceiVed: October 24, 1996; In Final Form: January 17, 1997X
Reactive uptake coefficients for HOCl as a function of [HCl] were measured in a rotating wetted-wall flow
reactor for several sulfuric acid solutions containing between 49 and 67 wt % H2SO4 at 220 and 250 K. The
solubility of HOCl in sulfuric acid solutions at 220 and 250 K was also measured. Using these measured
solubilities, calculated HCl solubilities, and estimated diffusivities for HOCl, the second-order rate coefficients
(kII) in the liquid were extracted. At 250 K, kII increases with increasing acid concentration, from 3 × 105
M-1 s-1 at 49 wt % acid to 5 × 106 M-1 s-1 at 67 wt %. It is suggested that the reaction may involve an
initial protonation of HOCl, followed by reaction of H2OCl+ with Cl-.
Introduction
ω is the mean molecular speed, Dl is the liquid phase diffusion
coefficient, k is the first-order loss rate coefficient, and HX is
The reactive uptake of HOCl onto ice and sulfuric acid
solutions doped with HCl is thought to play a significant role
in the activation of chlorine in the stratosphere.1
the (effective) Henry’s law constant for molecule X. The
function f(a/l) ) coth(a/l)-l/a depends upon the ratio of the
radius a of the liquid particle to the “reactodiffusive length” l
) (Dl/k)1/2 of X;6 in the bulk experiments described here, f(a/l)
) 1.
HOCl + HCl f H2O + Cl2
(R1)
The reaction of HOCl with HCl in 60 wt % sulfuric acid has
been studied previously3,4 using the same methods as those
employed here. The rate coefficient for R1 in ∼60 wt % sulfuric
1.6 × 105 M-1 s-1) and 251 K (kII ) 1.4 × 106 M-1 s-1). These
results suggest an activation energy of ∼5 kcal mol-1 for the
reaction at this acid concentration. Earlier studies of Cl2
hydrolysis in solutions, with [H+] < 0.1 M, derived a value for
the third-order rate coefficient of 1.8 × 104 M-2 s-1 for the
process
This reaction has been investigated in the laboratory by a number
of groups.2-5 Sources of HOCl in the stratosphere include
heterogeneous hydrolysis of ClONO2
acid was determined at two temperatures, 200-205 K (kII
)
ClONO2 + H2O f HNO3 + HOCl
and the gas phase process,
ClO + HO2 f HOCl + O2
(R2)
(R3)
Reactions such as R1 and R2 are important in the stratosphere
because they transform reservoirs for active chlorine into more
photochemically labile chlorine.
H+ + Cl- + HOCl f H2O + Cl2
(R1′)
Accurate parameterization of the rates of these reactions is
needed in atmospheric models to calculate the reaction prob-
ability, γ. Ideally, such models use a framework based on a
mechanistic understanding of the reactions to predict the reaction
probability as a function of temperature, water partial pressure,
trace gas concentrations, and aerosol size. We have recently
outlined a framework for such models6a which is briefly
described here.
The uptake of a gas phase species into solution is governed
by its physical solubility and by reaction (reversible or irrevers-
ible) in solution. The competition between diffusion of the
species and its consumption Via reaction will determine its
distribution in the liquid phase. Analytical solutions of the
continuity equation, including diffusion and reaction, have been
worked out for many systems of interest.6b,c In the general case
of a spherical droplet of radius a, γ for species X is given by6a
at 293 K.5a,b HCl is thought to be present primarily as Cl- in
the 49-67 wt % solutions,14 and the concentration of Cl(-I)
in solution is equal to [Cl-] + [HCl]. To simplify the
discussion, we use [HCl] to denote [Cl(-I)].
There is a lack of measurements of R1 in strong sulfuric acid
solutions and the second-order liquid phase rate coefficient for
R1 (kII) is currently assumed to be independent of the acid
content of the liquid.7 The results presented below show that
this assumption is not valid.
Here, we examine the reaction of HOCl with HCl (R1) in
detail. Measurements of HOCl solubilities and reaction prob-
abilities for R1 over a wide range of sulfuric acid concentrations
(50-75 wt %) at 250 and 220 K are presented. A possible
reaction mechanism is suggested, and a formulation of kII as a
function of acid content is presented. An improved methodol-
ogy for calculating γ for reaction 1 is also presented.
1
γ
1
R
ω
)
+
(1)
Experimental Section
4RTHX kD f(a/l)
x
1
(a) Procedure. The bulk uptake measurements were per-
formed using the rotating wetted-wall (RWW) flow reactor
(inner diameter of 1.84 cm), described in detail previously.8
Approximately 1 mL of sulfuric acid solution was placed inside
the RWW. During an experiment, the acid concentration was
kept constant by maintaining a partial pressure of water equal
to the vapor pressure of water for that acid concentration.9a,14
where R is the mass accommodation coefficient for species X,
† Permanent address: Department of Chemistry, University of Toronto,
Toronto, Ontario Canada M5S 1A1.
‡ Also at Department of Chemistry and Biochemistry, University of
Colorado, Boulder, CO.
X Abstract published in AdVance ACS Abstracts, May 1, 1997.
S1089-5639(96)03315-4 CCC: $14.00 © 1997 American Chemical Society

4718 J. Phys. Chem. A, Vol. 101, No. 26, 1997
Donaldson et al.
Following most experiments, a sample of the solutions was
titrated with a standardized NaOH solution; the acid content
was within 0.5 wt % of the concentration estimated from the
water partial pressure and temperature. Some acid samples were
used repeatedly: after a set of uptake measurements, the H2O
content of the liquid was varied (by setting a new partial pressure
of H2O and allowing sufficient time, ∼30 min, for the “stirred”
acid solution and the gas phase H2O to equilibrate) and a new
set of uptake measurements were performed. Several acid
concentrations were used in this study: 49, 52, 54, 56.5, 58,
62.5, 65, 67, 70, and 75 wt % at 250 K and 58, 60, 63, 67, 70,
and 75 wt % at 220 K (uncertainty of the H2SO4 content of the
solutions is (0.5 wt %.)
Gas phase first-order loss rate coefficients (kg) for HOCl were
measured in the wetted-wall flow reactor in an excess of HCl.
HOCl, prepared by reaction of HF with Ca(OCl)2 powder,3,4
was entrained in a flow of He and introduced into the main He
flow through a movable injector. By moving the injector, the
exposure to the solution was varied, and kg was obtained. HCl
and H2O were introduced into the main He flow upstream of
the rotating wetted wall. Because HCl was added to the
solutions from the gas phase, saturation of the solutions must
be ensured. By comparing [HCl] exiting the RWW to [HCl]
entering the RWW (monitored by diverting the HCl flow around
the RWW), we could determine when the solutions were
saturated. Note that excess gas phase HCl does not guarantee
that the liquid phase loss for HOCl is pseudo first-order
(discussed further below and in the Appendix.)
order loss rate conditions for HOCl were not achieved and
physical agitation of the solutions would be expected to
influence γ. Measurements when solution [HOCl] was greater
than 0.5 × [HCl] were not included in the analysis. From
simple modeling calculations (see Appendix) we predict less
than a 10% effect on the measured γ when [HOCl] is less than
0.5 × [HCl] (compared to the case when [HOCl] , [HCl].)
Nonreactive uptake (without HCl present) of HOCl in
H2SO4 solutions was also studied and HOCl solubility was
determined.3,4 The Henry’s law coefficient HHOCl was deter-
mined at 250 K for several acid concentrations by measuring
the total uptake of HOCl into a continuously stirred acid
solution.4 The parameter HHOCl(Dl)1/2 was determined at 220
K for three H2SO4 solutions by measuring the time-dependent
HOCl uptake onto quiescent liquids.3
Measurements of the reaction probability of HOCl on sulfuric
acid aerosol particles doped with HCl were performed at 250
K. The experimental procedure is identical to that described
by Hanson and Lovejoy4 except the aerosol particles were
composed of 67 wt % H2SO4 and ∼6 × 10-5 M HCl (i.e., the
aerosol particles were exposed to an HCl partial pressure of
∼1 × 10-6 atm) and γ for HOCl was measured as a function
of particle radius.
(b) Data Analysis. The measured decrease in [HOCl] as a
function of injector position was fitted to a first-order decay,
and then transformed into a loss rate coefficient (kg) using the
calculated average flow velocity in the flow reactor. This loss
rate was “corrected” for gas phase diffusional loss11a (typically
<20%, however, for bulk experiments with large uptakes, γ ∼
0.1, up to ∼150%). For bulk measurements γ was calculated11b
by dividing kg by ω/d where ω is the mean molecular speed
and d is the inner diameter of the flow reactor.12 For the aerosol
experiments γ was obtained by dividing kg by the first-order
collision rate with the aerosol particles.4 Gas phase diffusion
coefficients for HOCl-in-He and H2O (p(Torr) × Dg ) 339 and
81 Torr cm2 s-1, respectively, at 250 K) were estimated13 using
the Lennard-Jones parameters of ClO for HOCl.
HOCl, HCl, and Cl2 were monitored using a chemical
ionization mass spectrometer (CIMS), as described previ-
-
ously.3,4,10 SF6 was used as the ionic reagent in the CIMS
flow tube for most of the kinetic runs. The signal at 143 amu,
-
the SF5O- product ion formed in the SF6 + HOCl reaction,
was found to have a significant contribution from SF4Cl- when
[HCl] was large (this appeared to be due to a reaction between
SF5- and HCl; an ion-molecule reaction rate coefficient of 1.0
× 10-10 cm3 s-1 would explain our observations.) Therefore,
the F- + HOCl f ClO- + HF reaction was also used on
occasion to monitor HOCl. The chemical ionization mass
spectrometer was calibrated using known HCl concentrations,
The liquid phase first-order rate coefficient k is given by
kII[HCl] and [HCl] ) H*HClpHCl, where H*HCl is the effective
Henry’s law constant for HCl (see note 14 in ref 4 for an
explanation of effective Henry’s law constants.) Thus, from
-
and the SF5Cl-/SF6 signal ratio was used to calculate the
1/2
eq 1 and for γ , R, γ for HOCl is proportional to (pHCl
)
if
absolute HCl concentration.3,4 The range of HCl partial
pressures, pHCl, was ∼(3 × 10-10)-(3 × 10-7) atm. pHOCl
(typically 10-9 atm) was estimated by comparing the SF5O-
signal to the calibrated signal for HCl at 162 amu (SF5Cl-) and
applying the ∼5 factor difference in sensitivity (i.e., the ratio
of the reaction rate coefficients.10)
the reaction takes place in the bulk solution. Thus, plots of log
γ Vs log pHCl should yield slopes of 0.5. Alternatively, plots of
1/2
1/γ Vs 1/(pHCl
)
should be linear with intercepts equal to 1/R
(eq 1).
The inverse of the reaction probability 1/γ was found to be
linearly proportional to 1/(pHCl)
1/2. The slopes of these plots
The total pressure was typically 1 Torr, though measurements
at both larger (up to 3 Torr) and smaller (down to 0.5 Torr)
pressures were performed. The majority of the gas was He
while water partial pressure was a maximum of 0.2 Torr for 49
wt % acid at 250 K. The average flow velocity was typically
∼1000 cm s-1, and the total mass flow rate was in the range
3-4 std cm3 s-1. The RWW was rotated between 0 and ∼3
rpm for the reactive uptake measurements. No dependence on
rotation rate was observed for the measured reaction probabilities
except for low pHCl results for 67 wt % acid: at 250 K and for
pHCl ) 3 × 10-9 atm the reaction probability decreased by about
a factor of 2 when the RWW was stopped. A much smaller
decrease (∼15%) was observed at 250 K for pHCl ) 2 × 10-8
atm, and at higher pHCl γ did not depend on rotation rate. The
dependence on rotation rate is most likely due to the stirring of
the solution. In these cases, it was discovered that the solution
[HOCl] was larger than [HCl] and consequently pseudo-first-
were used to extract kII. Inserting k ) kIIH*HClpHCl and f(a/l)
) 1 into eq (1), the slopes of linear regressions to 1/γ Vs
1/2
1/(pHCl
)
are related to solubilities, Dl, and kII Via
ω
slope )
(2)
4RTHHOCl kIIH*HCl D1
x
The values of H*HCl were taken from the calculations of Carslaw
et al.14 Values of HHOCl were taken from the calculations of
Huthwelker et al.15 for acid concentrations less than 60 wt %,
and interpolated from the measured solubility data presented
here in the range 60-75 wt % (see below.) Values of Dl for
HOCl were taken to be 1.1 times that of Huthwelker et al.15
(this calculation for Dl was about 10% less than the measured
value for 60 wt % acid4). The values of all parameters used in
the analysis are listed in Table 1.

HOCl + HCl f Cl2 + H2O
J. Phys. Chem. A, Vol. 101, No. 26, 1997 4719
TABLE 1: Henry’s Law Solubilities and Parameters Used To Determine kII
250 K
220 K
H2SO4
wt %
measured HHOCl
HHOCl enhanced
Dl (ref 15)
H*HCl (ref 14),
measuredb
HHOClxDl
calculated,b,c
HHOClxDl
M atm-1 a
(Table 5)
10-7 cm2 s-1
M atm-1
H*HCl
49
52
54
56.5
58
60
62.5
63
65
67
3770
2900
2500
1980
1700
1500
1210
8.7
7.9
7.3
6.6
6.2
33800
13100
6800
2900
1740
1000
340
2500
(9)e
7.1
8.4
6.4
2.8 × 104
1.2 × 104
1400d
1100
4.9
(4.6)e
2.7
4.2
3500
1100
900
1000
1060
1000
940
4.2
3.6
130
60
2.6
70
75
0.9
0.73
a Estimated uncertainty is (25%. b In units of M atm-1 cm s-1/2. Estimated uncertainty in the measured values is (30%. c Calculated using the
enhanced HHOCl from Table 5 and Dl from Huthwelker.15 These values are 15-20% lower than the measured values. The measured values were
used in the calculation of kII in Table 2. d From ref 4. Actual conditions: 59.5 wt % and 251 K. e Extra- and interpolated from the measured values.
Figure 1. Results of nonreactive uptake experiment at 250 K, in 62.5
wt % sulfuric acid. Both an uptake (negative-going signal) and a
desorption (positive-going signal) measurement are shown. The inte-
grated area between the curves and the interpolated unperturbed signal
(dashed line) is proportional to the Henry’s law coefficient of HOCl.
A slow increase with time in [HOCl] from the source is evident.
Figure 2. Measured Henry’s law constants for HOCl in sulfuric acid,
as a function of acid concentration. The dashed line is from the model
of Huthwelker et al.15 and the solid line is a fit to the datassee text for
details.
enhancement factor ) 1 + 1.052 × exp(0.273 ×
(wp-65.66)) (3)
Results
where wp is wt % H2SO4. Thus HHOCl (solid line in the figure)
is obtained by multiplying the calculated values15 by eq 3. This
is a strictly empirical approach; our object is to obtain HHOCl
for a given H2SO4 content. The measured HHOClxDl at 220 K
and HHOClxDl calculated according to this procedure and Dl
taken from Huthwelker et al.15 are also listed in Table 1. The
enhancement factor is taken to be independent of temperature.
The calculated values (eq 3) lie within 15% of the measured
values at 220 K.
(b) Reactive Uptake and Kinetics of HOCl + HCl. The
measured first-order loss rates for HOCl were used to calculate
γ, as outlined above. The growth of Cl2 was consistent with
the observed loss of HOCl. A relatively large Cl2 background
arising from the HOCl source precluded extracting good kinetic
data from the Cl2 growth curves.
(a) Solubility of HOCl in H2SO4. Figure 1 displays a
representative nonreactive HOCl uptake experiment for 62.5 wt
% acid at 250 K. Several uptake and evaporation cycles for
HOCl were performed for a number of acid concentrations. In
all cases, HHOCl derived from uptake measurements was the same
as that derived from evaporation measurements. (Note that, in
some runs, the very first exposure of HOCl to the liquid resulted
in a large and irreversible uptake of HOCl, indicating the
presence of a small amount of a dissolved impurity in some of
the solutions.) The measured results are presented in Table 1
where the (25% uncertainty4 reflects the combined precision
and estimated systematic error. Shown in Figure 2 are the
measured values plotted Vs wt % at 250 K; the dashed line shows
the calculated values of Huthwelker et al.15 The measured HHOCl
in 62.5-70 wt % acid are higher than those calculated using
the model of Huthwelker et al.15 The measured values of
HHOClxDl at 220 K are also larger than the model prediction.
Figures 3 and 4 display representative plots of log γ Vs log
pHCl for 250 and 220 K, respectively. For the most part, γ varies
1/2
as pHCl as expected, with slopes of linear regressions to the
The measured values divided by the calculated values defines
an enhancement factor and a fit of this Vs H2SO4 content resulted
in the equation
data in the log-log plots ranging from 0.4-0.55. γ depends
on the sulfuric acid content, in general decreasing with increas-
ing H2SO4 concentration. Also, for a given pHCl and acid

4720 J. Phys. Chem. A, Vol. 101, No. 26, 1997
Donaldson et al.
TABLE 2: Liquid Phase Second-Order Rate coefficients
wt % slopea (250 K), kII (250 K),b slopea (220 K), kII (220 K),b
acid
eq 2
M-1 s-1
eq 2
M-1 s-1
49
52
54
56.5
58
60
62.5
63
65
67
0.0011
0.0018
0.0020
0.0041
0.0044
2.8 × 105
5.3 × 105
1.2 × 106
1.2 × 106
2.4 × 106
1.4 × 106 c
4.7 × 106
4.2 × 10-4
8.0 × 10-4
4.3 × 105
4.4 × 105
9.1 × 105
0.011
0.0016
0.018
0.04
7.5 × 106
4.9 × 106
a In units of atm-1/2 b Uncertainties are +100, -50%. c Fom ref 4.
.
Figure 3. Representative results showing the reactive uptake of HOCl
as a function of HCl pressure, at 250 K. The slopes of the 52, 62.5,
and 67 wt % data are 0.48, 0.55, and 0.43, respectively.
Figure 4. Results of reactive uptake experiments at 220 K. The slopes
of the 58, 60, and 63 wt % data are 0.46, 0.38, and 0.45, respectively.
Figure 6. The measured second-order rate coefficients for the HOCl
+ HCl reaction, plotted as a function of wt % H2SO4: 250 K, filled
circles; 220 K, dotted triangles. The open square is the measurement
at 251 K from ref 4. A linear regression to the data at 250 K is shown:
log10 kII ) 1.884 + 0.0747wp with wp in wt %.
and l ) 0.18 µm. The dashed curve is a fit with Γb fixed at
0.026, the value predicted from the 67 wt % bulk data at 250
K; this results in a value for l of 0.28 µm. Using this latter
value and the definition of l ) (Dl/k)1/2, the first-order loss rate
coefficient for HOCl is k ) Dl/l2 ) 460 s-1; dividing by the
estimated [HCl] (6 × 10-5 M) results in a second-order rate
coefficient in 67 wt % acid at 250 K of ∼8 × 106 M-1 s-1
.
This compares favorably (within a factor of 2) with the result
derived from the bulk measurements. A more accurate com-
parison between the bulk and aerosol measurements is not
warranted (as was done in ref 4.) Accurately measuring l g
∼0.3 µm is difficult because our present technique for sizing
of the particle samples (UV light extinction measurements
between 0.2 and 0.4 µm) becomes uncertain above rs ) 0.6
µm.
Figure 5. Measured reaction probability on 67 wt % H2SO4 particles
at 250 K plotted against particle radius. The dashed and dotted curves
are fits of the data to eq 4.
concentration, γ is larger by almost an order of magnitude at
220 K than it is at 250 K. Uptake experiments performed with
70 and 75 wt % acid showed small losses for HOCl, and pseudo-
first-order loss rate conditions for HOCl in solution could not
be ensured (note that the solubility of HOCl is much greater
than the solubility of HCl in these solutions.) A portion of the
low pHCl data for the 62.5, 63, 65, and 67 wt % solutions was
also not included in the analysis (at 220 K, none of the 65 and
67 wt % data was acceptable).
The measured γ on 67 wt % sulfuric acid aerosol is plotted
as a function of particle size (surface-area-weighted mean
radius,8 rs) in Figure 5. γ increases nearly linearly with rs for
small particles and approaches a limiting value for large rs. This
is expected according to eq 1 which reduces to
Shown in Table 2 and Figure 6 is kII calculated as described
above using the parameters listed in Table 1. The values of
the slopes (eq 2) are also listed in Table 2. Note the strong
dependence of kII on [H2SO4] at 250 K in the 49-67 wt %
range. The measured rate coefficients at 220 K are also
consistent with this trend.
The uncertainties in kII are (+100, -50%) and were estimated
by summing (in quadrature) the estimated errors in the values
2
of (HHOCl
)
(+56, -36%), H*HCl (+30, -23%), Dl (+33,
-25%), and pHCl (+25, -20%). Twice the precision in
measuring γ a number of times n (i.e., ∼2 × (15%/n1/2) ) 9%
for n ∼ 10) is small compared to this estimated uncertainty.
The uncertainties in the calculated H*HCl and Dl for HOCl were
estimated by comparing to measured values (HCl solubilities
from 45-60 wt % of refs 3 and 4 and HOCl diffusivity of ref
4 at 60 wt %.) Note that the uncertainties in the calculated
H*HCl and Dl are not known outside of these ranges. We cannot
γ ≈ Γb f(rs/l)
Γb ) (4RT/ω)HHOCl(Dlk)1/2
(4a)
(4b)
when Γbf(rs/l) , R ∼1 (and a ) rs). The solid curve is a fit to
the data according to eq 4 resulting in values of Γb ) 0.019

HOCl + HCl f Cl2 + H2O
J. Phys. Chem. A, Vol. 101, No. 26, 1997 4721
assess the possible additional uncertainty in these quantities until
a comparison to measurements over a wide range of conditions
is made.
kII with acid content suggests that the reaction may involve a
protonation step followed by reaction with Cl- (we now
explicitly denote the dissolved HCl as Cl-.) This is the pathway
k4, k-4
HOCl + H+ 7
8 H2OCl+
(R4)
Discussion
(a) HOCl Solubility. Our measured solubilities for HOCl
are greater than those predicted by the model of Huthwelker et
al.15 for acid content >60 wt %. The model is a fit to
measurements at acid concentrations less than 60 wt % and
predicts a steady decrease in HHOCl with increasing acid
concentration. The model considers only the physical solubility
of HOCl; protonation is not included. The higher measured
values could be partly due to protonation of HOCl at high acid
concentrations. We define a thermodynamic protonation equi-
librium constant Keq to be the inverse of the H2OCl+ acid
constant:
k5
H2OCl+ + Cl- 98 Cl2 + H2O
(R5)
denoted (4) f (2) f (1) by Eigen and Kustin.5a Note that the
hydrolysis of Cl2 (reverse of R5) can be neglected for the
conditions of our experiment. According to this mechanism,
the HOCl loss rate in the liquid is
d
[HOCl] ) -k4[HOCl][H+] + k-4[H2OCl+]
(7)
dt
Assuming a steady state for [H2OCl+],
k4[HOCl][H+]
[H2OCl+]
a
f
H2OCl
+
+
H2OCl
Keq
)
)
(5)
[H2OCl+]ss )
(8)
+
aHOClaH
fHOClfH
+
+
[HOCl][H ]
k-4 + k5[Cl-]
where ai and fi represent the activity and molar activity
coefficient, respectively, of component i. An effective Henry’s
law constant H*HOCl can be defined which is a function of acid
strength
and solving for the pseudo-first-order loss rate coefficient for
HOCl, we obtain
k4[H+]
k-4 + k5[Cl-]
k )
k5[Cl-]
(9)
H*HOCl ) ([HOCl] + [H2OCl+])/pHOCl ) HHOCl (1 +
[H+]KeqfH+fHOCl/fH OCl+) (6)
2
Under the conditions of the present experiments, it is likely that
k-4 . k5[Cl-]. The maximum Cl- concentration in our
experiments can be estimated from the maximum possible value
of H*HClpHCl ) (104)(10-8) ) 10-4 M. Taking a diffusion-
limited value for k5 (∼3 × 108 M-1 s-1 at 250 K in 50-70 wt
% H2SO4), we obtain a maximum value for k5[Cl-] of ∼3 ×
If Keq is sufficiently small, protonation is not important until
high acid concentrations; this is apparently the case for HOCl
in concentrated H2SO4.
Although protonated HOCl has not been detected in solution,
it has been reported in the gas phase Via mass spectrometry,17
and its existence in/on amorphous solids has been inferred from
infrared spectra of matrix-isolated ClONO2/H2O mixtures.18 On
the basis of these spectra, Sodeau et al.18 proposed H2OCl+ as
an intermediate in chlorine nitrate hydrolysis. An alternative
interpretation, consistent with the present work, is that some of
the HOCl formed in the hydrolysis is protonated by H+ from
dissociated HNO3 product. Protonated HONO has also been
reported in sulfuric acid solutions of 70-90 wt % acid.19 It is
likely that HOCl becomes protonated to some extent in strong
acid solutions.
Note that the enhancement in the solubility over that
calculated using a simple Setchenow dependence15 is not likely
to be due only to protonation (i.e., the last term in parentheses
in eq 6 is likely to be small compared to one.) If the
enhancement in the HOCl solubility were entirely due to
protonation, then the concentrations of [H2OCl+] and [HOCl]
would be approximately equal in 65 wt % acid (where from
Figure 2 the enhancement factor is ∼2.) The overall rate
coefficient kII would then be expected to be about one-half of
the diffusion-limited value of 3 × 108 M-1 s-1 (assuming the
rate coefficient for H2OCl+ + Cl- is diffusion limited, see R4
and R5 below.) Because the measured kII in 65 wt % acid is
much lower than the diffusion limited value, HOCl is not likely
to be primarily in protonated form in these solutions. The reason
the measured HHOCl is greater than the predicted values15 may
be due to a rejection of higher order terms in the model.15
(b) Kinetic Analysis and Mechanistic Implications. The
results shown in Figure 6 indicate a strong dependence of the
reaction rate coefficient on acid concentration at 250 K. At
this temperature, there is a 20-fold increase in kII as the acid
concentration increases from 49 to 65 wt %. The increase in
+
+
104 s-1. Since we expect k4/k-4 ) Keq fH fHOCl/fH OCl , 1
2
(see below) and k4 to be large, k-4 is almost certainly .3 ×
104 s-1. Thus we can simplify the expression above to
k4[H+]
k ≈
k5[Cl-]
(10)
k-4
This equation yields a straightforward dependence for k and γ
on [Cl-] and on [H+], as is observed for 49-67 wt % solutions.
Note that if k-4 were not .k5[Cl-], this straightforward
dependence would not have been observed. From this expres-
sion, the values of kII ) k/[Cl-] in Figure 6 and Table 2 are
given by
k4[H+]
kII ≈
k5
(11)
k-4
A similar expression can be derived assuming an initial attack
by Cl- on HOCl, as proposed by Eigen and Kustin5a and for
much lower acid concentrations (the pathway they denote as
(4) f (3) f (1)):
HOCl + Cl- 7k6, k-68 HOCl2
(R6)
(R7)
-
k7
HOCl2- + H+ 98 Cl2 + H2O
The first-order rate coefficient for HOCl loss is
k6[Cl-]
k-6 + k7[H+]
k )
k7[H+]
(12)

4722 J. Phys. Chem. A, Vol. 101, No. 26, 1997
Donaldson et al.
For kII ) k/[Cl-] and k-6 . k7[H+], this reduces to
k6
kII ≈
k7[H+]
(13)
k-6
This is the same form as kII (eq 11) derived for the protonation
mechanism (R4-R5). Note that Eigen and Kustin5a considered
the protonation mechanism to be too slow to contribute to their
measurements on the basis of thermodynamic calculations20 that
suggested the “extreme unlikelihood” of finding H2OCl+ in
solution. That argument might not be valid in the strong acid
solutions studied here. Note that our kinetic results do not help
us choose between these two mechanisms. It is reasonable,
however, to suggest that R4-R5 is a likely pathway in strong
acids.
The dependence of kII on acid content can be understood by
using the concept of the effective acidity in strong acid solutions,
first proposed by Hammett.21 Much work has been carried out
on the reactions of organic weak bases in strong acids (such as
sulfuric acid),22,23 and these reactions typically follow a mech-
anism similar to that given by R4-R5. Our analysis of the
variation of kII with acidity is based on this body of work.
First, we introduce the ratio k4/k-4 ) [H2OCl+]/[H+][HOCl]
) Kc (the concentration equilibrium constant37) into the expres-
sion for the thermodynamic protonation constant of HOCl (eq
5):
Figure 7. Logarithm of kII/[H+] at 250 K plotted against the “X”
parameter, a universal acidity function. A linear regression line and
the 95% confidence limits are also shown (symbols as in Figure 6.)
See text for details. Also shown (dashed lines) are the diffusion limited
reaction rate coefficients (kd.l.)/100, kd.l. ) 4πR*Dl(6 × 1020 M-1 s-1
,
for R* ) 6 × 10-8 cm and Dl taken from Huthwelker et al.15 (lower
curve) and that from Williams and Long16 (upper curve) normalized
to 6 × 10-7 cm2 s-1 for 59.5 wt % acid at 250 K.4
Note that the 95% confidence levels indicate an uncertainty in
the intercept of a factor of 5 (+400, -80%).
Making the reasonable assumption that R5 is diffusion-limited
(k5 ) 3 × 108 M-1 s-1), the value of Keq at 250 K is ∼10-5
M-1. Alternatively, because k5 is less than or equal to 3 × 108
M-1 s-1, our error limits imply a lower limit to Keq of
(1/5)1800/3 × 108 ) 10-6 M-1. This corresponds to an ideal
solution, [H+] ) 0, upper limit to ∆G0 of +7 kcal mol-1 for
the protonation reaction R4 at 250 K. This value is higher than
that for methanol protonation (the ∆G0 for the protonation of
aqueous CH3OH calculated from data in ref 27 is +1.2 kcal
mol-1) consistent with a smaller proton affinity for HOCl (an
ab-initio determination of the gas phase proton affinity of
HOCl28 is 153 kcal mol-1; ∼20 kcal mol-1 smaller than that
for methanol.29)
[H2OCl+]
k4
f
f
H2OCl
+
+
H2OCl
Keq
)
)
(14)
+
fH+fHOCl k-4 fH+fHOCl
[HOCl][H ]
Replacing eq (14) in eq (11) and taking logarithms,
fH+f
kII ) Keq HOCl[H+]k5
(15)
f
+
H2OCl
fH+f
log kII ) log Keq + log
HOCl + log [H+] + log k5 (16)
f
+
H2OCl
Following the “excess acidity” analysis of Cox and Yates,24-26
These arguments are consistent with the reaction mechanism
involving an initial protonation followed by reaction of H2OCl+
with Cl-. Reaction of H2OCl+ with molecular HCl, expected
to be present in the most acidic solutions, could also occur.
fH+f
f
fH+f
log
HOCl ) m* log
B* ) m*X
(17)
fB*H
+
+
H2OCl
(c) Temperature Dependence and Comparison to Previous
Measurements. For the 58, 60, and 63 wt % results, there is
about a factor of 4 difference between the kII values at 250 and
220 K resulting in an estimate for the effective activation energy
of 5 kcal mol-1 for the overall reaction, essentially the same as
that estimated for 60 wt % between 202 and 250 K(∼5 kcal
mol-1.)3,4
where B* represents a hypothetical standard reference base. This
states that the ratios of activity coefficients for protonation
reactions in strongly acidic media are simply related to one
another, Via the parameter m*. Note that m* as used here is
slightly different from that defined by Cox and Yates.24,25 Using
this definition of X and rearranging,
Using an effective activation energy of 5 kcal mol-1, we
estimate the 293 K, [H+] f 0 empirical rate coefficient to be
Keqk5 ∼ 104 M-2 s-1 (using Keqk5 ) 1800 at 250 K). This is of
the same magnitude as the 293 K third-order reaction rate
constant given by Eigen and Kustin5a for low acid concentrations
(1.8 × 104 M-2 s-1). However, given the large uncertainty in
the intercept in Figure 7 and the large differences in reaction
conditions between the present work and that of ref 5, this
agreement may be fortuitous.
Wang and Margerum5b measured the temperature dependence
of Keqk5 (their k-1) from 273 to 303 K and obtained 6.5 kcal
mol-1 for an effective activation energy for Keqk5. Using this
activation energy, the extrapolation of their results to 250 K
results in a value of 2400 M-2 s-1 for Keqk5. This is in good
agreement with our value extrapolated to [H+] ) 0. Wang and
log kII ) log Keq + m*X + log[H+] + log k5 (18)
(log kII-log[H+]) ) (log Keq + log k5) + m*X
log(kII/[H+]) ) log(Keqk5) + m*X
(19)
A semilog plot of (kII/[H+]) Vs X should yield a straight line
with Keqk5 as intercept. Such a plot is shown for the 250 K
data in Figure 7, with values of X and [H+] taken from Cox
and Yates.24,25b The fit to a straight line is good, albeit over a
fairly small range of X, implying that the mechanistic assump-
tions behind the analysis are valid. The resulting slope m* )
0.5 is in the range predicted for protonation on oxygen.24,25a
The intercept from this plot yields a value of ∼1800 for Keqk5.

HOCl + HCl f Cl2 + H2O
J. Phys. Chem. A, Vol. 101, No. 26, 1997 4723
TABLE 3: Comparison with Previously Reported Rate
Coefficients
TABLE 4: Parameters and Equations for Calculating
Reaction Probability of HOCl onto Sulfuric Acid Particles
wt %
rate
extrapolated
valuea
parameter
expression
ref
H2SO4 T, K coefficient
lit. value
ref
R
Dl
aH2O
H*HCl
kII
1.0
4
1.0 × 104 M-2 s-1 1.8 × 104 M-2 s-1 5a
b
9 × 10-9 b
0
0
34
59.5
60
293
250
274
251
202
Keqk5
Keqk5
kII
1800 M-2 s-1
2400 M-2 s-1 c
5b
4
4
pH O/10(9.217-2190/(T-12.7))
7, 38
7, 38
this work
2
6 × 104 M-1 s-1
8 × 104 M-1 s-1
3.49
exp(6250/T - 10.414) × (aH O
exp(2.303 × (6.08 - 1050/T2
+ 0.0747wp))c
)
kII
2.1 × 106 M-1 s-1 1.4 × 106 M-1 s-1
kII
2.2 × 105 M-1 s-1 1.6 × 105 M-1 s-1
3
k
wp
HrootD
adivl
f
Γcalc
γ
kIIH*HClpHCl
s-1
a Obtained from the fit of log10 kII Vs wt % shown in Figure 6 along
with a 5 kcal mol-1 effective activation energy (see Table 4). b For the
reaction sequence R4-R5 with Keq from eq 14. Also could be the
analogous expression for the reaction sequence R6-R7. See text for
details. c Extrapolated to 250 K.
see Table 5
wt % H2SO4
Table 6
this work
6a, 7
this work
6a, 7
HHOCl(D1)1/2 d
rp(k/D1)1/2
1/tanh(adivl) - 1/adivl
2.25 × 10-5(T52.5k)1/2 × HrootD
1/(R-1 + (Γcalc f)-1
)
Margerum also presented evidence for an acid-assisted mech-
anism
a Input parameters are pHCl, pH O, rp in atm, mbar, and cm,
respectively. b Dl varies with T and a2cid content; however, for a given
HA + HOCl + Cl- f A-‚H2OCl+‚Cl- f A- + H2O +
pH O, these variations approximately cancel resulting in a constant Dl
2
for wp as a function of T. Dl ) 9 × 10-9 is predicted for stratospheric
conditions from the relation Dl ) constT/viscosity15 with the constant
determined for 59.5% acid at 251 K.4 Note that the calculated γ is
insensitive to the value of Dl for stratospheric conditions. c Note that
this expression for kII is not valid beyond 65 wt % acid. The calculated
γ for atmospheric conditions using this expression (Figure 8), however,
is e10-4 and is not significant for atmospheric conditions. d Formu-
lation for HHOCl from Huthwelker et al.15 along with the enhancement
at high acid content shown here are detailed in Table 6.
Cl2 (R8)
-
The HSO4 ion was identified as one of the acids HA. Note
that the extrapolation to [H+] ) 0 in Figure 7 also involves
extrapolation to [HSO4-] ) 0. The transition state, A-‚
H2OCl+‚Cl-, is described by Wang and Margerum as involving
a proton transfer to HOCl as Cl+ is transferred to Cl-. They
point out that a sequence similar to R6-R7 is a two-step analog
to R8. The reverse of R8, the base-assisted hydrolysis of Cl2,
was originally proposed by Lifshitz and Perlmutter-Hayman5c
as a two-step process similar to the reverse of R6-R7. An
alternative is that a sequence similar to R4-R5 is also a two-
step analog to R8. As Wang and Margerum stated, one cannot
determine which mechanism is operating from kinetics alone.
However, it appears that the protonation mechanism R4-R5
should not be rejected from consideration.
Shown in Table 3 are the comparisons discussed above for
[H+] ) 0 and comparison of the previously reported values for
kII in strong sulfuric acid solutions with values obtained by
extrapolating the present results to the same conditions. The
values of the extrapolated kII are -25, +50, and +35% different
than the previously reported values. As all these measurements
are accurate to approximately +100/-50%, these discrepancies
are not consequential. Indeed, the agreement is remarkable
considering the extent of extrapolation (∼15 wt % and ∼25
K).
Figure 8. The predicted reactive uptake coefficient for HOCl + HCl
on 0.2 µm aerosol particles, assuming pH O ) 3.0 × 10-4 mbar and
2
pHCl ) 10-10 atm. The short-dashed curve shows the variation of sulfuric
acid aerosol composition with temperature (right axis) under these
conditions (ref 9 and Table 4). The solid curve is the calculated reaction
probability for HOCl + HCl using Tables 4, 5, and 6. The dash-dot
curve is γ calculated as for the solid curve except assuming kII ) 1.6
× 105 M-1 s-1 independent of acid content.
(d) Atmospheric Implications. The parameters determined
here allow a calculation of the reaction probability for HOCl
onto stratospheric sulfuric acid aerosols. Recent measurements4
of the reaction probability of HOCl on 34 wt % sulfuric acid
suggest that the mass accommodation coefficient R is close to
unity, and we take R ) 1 independent of temperature and H2-
SO4 content. kII was taken to be a function of wt % (as
determined at 250 K; see Figure 6) and a 5 kcal/mole effective
activation energy was employed (see Table 4.) The solubility
of HOCl was taken to be that of Huthwelker et al.15 with the
additional enhancement at high acidities (eq 3). Figure 8
displays the values of γ calculated using the equations and
parameters in Tables 4-6 for 0.2 µm radius particles over a
range of stratospherically important temperatures, assuming
reaction probability for cold polar lower stratospheric conditions
is significantly less than the previous calculation, which was
based on an invalid assumption (kII independent of [H2SO4]).
Note also that the HCl solubilities of Carslaw et al.14 are higher
than the HCl solubility given in Table 4 for cold conditions
(H2SO4 content <50 wt %), and using them results in a higher
calculated γ.
The initial protonation mechanism proposed here is not
dependent on sulfuric acid being the proton donor. In principle,
any strong acid could initiate a reaction, for example, aqueous
HNO3 Type I PSC particles would be expected to exhibit similar
chemistry. Also, the reactive uptakes of HOBr and HONO Via
reactions such as HOBr + HCl and HONO + HCl may also
proceed through such a mechanism. If [HNO3] is high, the
reaction H2OCl+ + NO3-/HNO3 f H2O/H3O+ + ClONO2
might take place, regenerating chlorine nitrate from HOCl. This
is analogous to the BrONO2 + H2O T HOBr + HNO3
pH O) 3 × 10-4 mbar and pHCl )10-10 atm. For these
2
conditions, a line is plotted to show temperature Vs wt %
H2SO4. The expected reaction probabilities are different than
those assuming kII is independent of acid content (dash-dot
curve in the figure). The overall conclusions regarding the
relative importance of the HOCl + HCl reaction under
stratospheric conditions are not altered (i.e., it is significant only
in solutions with acid content <∼60 wt %). Note that the

4724 J. Phys. Chem. A, Vol. 101, No. 26, 1997
Donaldson et al.
that the quantity kIIC2(x ) 0, t) was equal to 10 s-1. In one
run, kIIC2 was held fixed at 10 s-1 for all x and t, and a
reactodiffusive length of 2.00 × 10-4 cm was obtained for C1,
TABLE 5: Calculation of H2SO4 Content from T and pH O
.
2
Z ) ln(pH O, mbar)
2
wt %
wp
expression
ref
33
in excellent agreement with the theoretical value, l ) (4 × 10-7
/
(-14.0508 + 0.708928 × Z)T + 3578.6a
10)1/2 cm, indicating the gradient at the surface is the expected
value. In the next case, C2(x,t)0) was set equal to 2×C1(x,t)0)
and both were allowed to change (decrease) with time. The
gradient in C1 was about 10% less than it would have been if
C2 was fixed at a constant value. (Note that, in the absence of
surface reactions, γ is directly proportional to the gradient in
the liquid at the surface.) Even for the case where C2(x,t)0)
was equal to C1(x,t)0), the gradient in C1 was only about 20%
less than if C2 were not allowed to vary. Therefore, we conclude
that the measured reaction probability of component 1 is not
affected by more than 10% if it is known that C2 is at least 2
times C1. Also note that the gas phase concentration of
component 2 must be much greater than the gas phase
concentration of component 1. Then the condition that
C2(x)0,t) remains constant will be fulfilled.
45.5374 + 1.55981 × Z- 0.197298 × T
a A fit using the pH O Vs wt % data of Giauque et al.9 believed to be
more accurate at low2temperatures than the Gmitro and Vermeulen30
data that Steele and Hamill31 fitted to (see Massucci et al.32). Previous
wp equation from ref 6a Table 3 results in a bias of 1-2 wt % with
respect to the Giauque et al. data.9 Extreme caution should be exercised
in the use of this equation, i.e., only for 10-4 < pH O < 10-3 mbar, 40
< wp < 80, and 190 < T < 230 K. The maximu2m deviation of this
equation from the Giauque et al. data9 is 0.6 wt % with a root mean
square deviation of 0.3 wt % for 195 < T < 230 K. At 190 K, the
maximum deviation of this equation from the data9 is 0.9 wt %.
TABLE 6: Solubility of HOCl. From Huthwelker et al.15a
parameter
expression
notes and refs
m
10.196wp/(100 - wp)
(wp to molal) only for
pure sulfuric acid
solutions
Hhuth
rho
exp(6.4946 - m(-0.04107
+ 54.56/T) -5862 ×
(1/298.15 - 1/T))
(molal atm-1
)
References and Notes
(1) (a) Crutzen, P. J.; Muller, R.; Bruhl, Ch.; Peter, Th. Geophys. Res.
Lett. 1992, 19, 1113. (b) Cox, R. A.; et al. Geophys. Res. Lett. 1994, 21,
1439.
(2) (a) Hanson, D. R.; Ravishankara, A. R. J. Geophys. Res. 1991 96,
17307. (b) Hanson, D. R.; Ravishankara, A. R. J. Phys. Chem. 1992, 96,
2682. (c) Abbatt, J. P. D.; Molina, M. J. Geophys. Res. Lett. 1992, 96,
7674. (d) Abbatt, J. P. D.; Molina, M. J. J. Phys. Chem. 1992, 96, 7674-
7679. (e) Zhang, R.; Leu, M. T.; Keyser, L. J. Phys. Chem. 1994, 98, 13563.
(3) Hanson, D. R.; Ravishankara, A. R. J. Phys. Chem. 1993, 97, 12309.
(4) Hanson, D. R.; Lovejoy, E. R. J. Phys. Chem. 1996, 100, 6397.
(5) (a) Eigen, M.; Kustin, K. J. Am. Chem. Soc. 1962, 84, 1355. (b)
Wang, T. X.; Margerum, D. W. Inorg. Chem. 1994, 33, 1050. (c) Lifschitz,
A.; Perlmutter-Hayman, B. J. Phys. Chem. 1962, 66, 701.
1000 + C1m + C2m1.5 + C3m2 solution density
(kg m-3
)
C1
C2
C3
123.64 - 5.6 × 10-4T2
-29.54 + 1.814 × 10-4T2
2.343 - 1.487 × 10-3
-1.324 × 10-5T2
T
conversion (rho/1000)/(1+ m0.09808)
HM
HHOCl
(molal to molar)
(Hhuth) (conversion)
HM(1 + 1.052 exp(0.273
(wp - 65.66)))
enhancement factor at
high acidities (this work)
reaction.34 Note that the regeneration of ClONO2 from HOCl
and HNO3 is not expected to be important in the atmosphere
for the same reasons that regeneration of BrONO2 could be
ignored: the [H2O]/[HNO3] ratio is so large that the equilibrium
ratio [XONO2]/[HOX] is very small.
(6) (a) Hanson, D. R.; Ravishankara, A. R.; Solomon, S. J. Geophys.
Res. 1994, 99, 3615. (b) Danckwerts, P. V. Trans. Faraday Soc. 1951, 47,
1014. Danckwerts, P. V. Gas-Liquid Reactions; McGraw-Hill: New York,
1970. (c) Schwartz, S. E. in Chemistry of Multiphase Atmospheric Systems;
Jaeschke, W., Ed.; Springer-Verlag: New York, 1986; 451.
(7) Ravishankara, A. R.; Hanson, D. R. J. Geophys. Res. 1996, 101,
3885.
Acknowledgment. This work was funded in part by
NOAA’s Climate and Global Change Research program. We
thank Professors A. J. Kresge and Robin A. Cox for helpful
discussions about acidity functions, the reviewers for helpful
comments, and I. K. Kim for taking the 220 K 58 wt % data.
D.J.D. thanks NSERCC for a University Research Fellowship.
(8) Lovejoy, E. R.; Huey, L. G.; Hanson, D. R. J. Geophys. Res. 1995,
100, 18775.
(9) (a) Giauque, W. F.; Hornung, E. W.; Kunzler, J. E.; Rubin, T. R.
J. Am. Chem. Soc. 1960, 82, 62. (b) McDonald, J. E. J. Geophys. Res.
1965, 70, 1553. (c) Gable, C. M.; Betz, H. F.; Maron, S. H. J. Am. Chem.
Soc. 1950, 72, 1445.
(10) Huey, L. G.; Hanson, D. R.; Howard, C. J. J. Phys. Chem. 1995,
99, 5001.
(11) (a) Brown, R. L. J. Res. Natl. Bur. Stand. (U.S.) 1978, 83, 1. (b)
Howard, C. J. J. Phys. Chem. 1979, 83, 3.
(12) With liquid present, d is 0.88-0.90 cm and with the stirring rod
present the effective inner diameter of the RWW flow reactor is (0.892-
0.252)1/2 ) 0.85 cm. Note that the presence of the ∼0.5 cm o.d. stirring rod
may significantly compromise the cylindrical symmetry requirement of the
diffusion correction procedure.11a This is expected to be important for large
corrections. In these experiments, there are only a small number of
measurements with corrections >20%. These have additional uncertainty
included in the extracted reaction probabilities.
(13) (a) Mason, E. A.; Monchick, L. J. Chem. Phys. 1962, 36, 2746.
(b) Monchick, L.; Mason, E. A. J. Chem. Phys. 1961, 35, 1676.
(14) Carslaw, K. S.; Clegg, S. L.; Brimblecombe, P. J. Phys. Chem.
1995, 99, 11557.
Appendix
A simple numerical procedure was used to solve simulta-
neously the equations
∂C
∂t
∂2C1
∂x2
1 ) D1
- kIIC2C1
- kIIC1C1
(20)
∂C
∂t
∂2C2
∂x2
2 ) D1
(15) Huthwelker, T.; Peter, Th.; Luo, B. P.; Clegg, S. L.; Carslaw, K.
S.; Brimblecombe, P. J. Atmos. Chem. 1995, 81, 21.
(16) Williams, L. R.; Long, F. S. J. Phys. Chem. 1995, 99, 3748.
(17) Egsgaard, H.; Carlsen, L. Int. J. Mass Spectrom. Ion Processes
1992, 113, 233.
(18) Sodeau, J. R.; Horn, A. B.; Banham, S. F.; Koch, T. G. J. Phys.
Chem. 1995, 99, 6258.
(19) Deschamps, J. M. R. C. R. Hebd. Seances Acad. Sci. 1957, 245,
where C1 and C2 are the concentrations of components 1 and 2
in the liquid. After about 1 s of simulated time, steady state
was achieved (with time step dt ) 10-6 s and dx ) 10-6 cm).
A similar scheme was used in the appendices of refs 3 and 35.
The finite-differencing scheme was forward time centered space,
which is stable for parabolic equations such as eq 20 with Dldt/
dx2 < 0.5.36 The concentration at the surface was fixed for
both C1 and C2, reflecting the fact that γ is much less than R
(R ≈ 1) for our experimental conditions. Dl was chosen to be
4 × 10-7 cm2 s-1 for both species, and kII was chosen such
1432.
(20) Bell, R. P.; Gelles, E. J. Chem. Soc. 1951, 2734. This early
thermodynamic calculation is highly uncertain involving many estimated
quantities including the solvation free energies ∆Gs for H2OCl+ and Cl-.

HOCl + HCl f Cl2 + H2O
J. Phys. Chem. A, Vol. 101, No. 26, 1997 4725
The estimate of ∆Gs(H2OCl+) of Bell and Gelles is likely to have an
uncertainty on the order of a few tens of kcal mol-1. Note that ∆Gs(Cl-)
has since been measured (Randles, J. E. B. Trans. Faraday. Soc. 1956, 52,
1573) to be about 13 kcal mol-1 more exothermic than the estimate Bell
and Gelles used.
(21) Hammett, L. P.; Deyrup, A. J. J. Am. Chem. Soc. 1932, 54, 2721.
(22) Rochester, C. H. Acidity Functions; Academic Press: New York,
1970.
(23) (a) Liler, M. Reaction Mechanisms in Sulphuric Acid; Academic
Press: New York, 1971. (b) Bagno, A.; Scorrano, G.; O’Ferrall, R. A. ReV.
Chem. Intermed. 1987, 7, 313.
(24) Cox, R. A.; Yates, K. J. Am. Chem. Soc. 1978, 100, 3861.
(25) (a) Cox, R. A.; Yates, K. Can. J. Chem. 1979, 57, 2944. (b) X
corrected for temperature as in Ibid. 1979, 57, 2960.
(33) Carslaw, K. S.; B. Luo; Peter, Th. Geophys. Res. Lett. 1995, 22,
1877. The equations developed in this reference for calculating wp H
have a wider range of applicability than that of Table 5 and can also be
used to estimate the HNO3 content of atmospheric sulfuric acid. The wp
obtained from Table 5 has a maximum of 1.0 wt % deviation from that
obtained from eq 10 of this reference for the range of conditions detailed
in Table 5.
2SO4
(34) Hanson, D. R.; Ravishankara, A. R.; Lovejoy, E. R. J. Geophys.
Res. 1996, 101, 9063.
(35) Hanson, D. R.; et al. J. Phys. Chem. 1992, 96, 4979.
(36) Press, W. H.; et al. Numerical Recipes in Pascal; Cambridge
University Press: New York, 1989.
(26) Cox, R. A. Acc. Chem. Res. 1987, 20, 27.
(27) Taft, R. W. In Progress in Physical Organic Chemistry; Taft, R.
E., Ed.; John Wiley: New York, 1983; Vol. 14.
(28) Francisco, J. S.; Sander, S. P. J. Chem. Phys. 1996, 102, 9615.
(29) Lias, S. G.; Bartmess, J. E.; Liebman, J. F.; Holmes, J. L.; Levin,
R. D.; Mallard, W. G. J. Phys. Chem. Ref. Data 1988, 17 (Suppl. No. 1).
(30) Gmitro, J. I.; Vermeulen, T. AIChE J. 1964, 10, 740.
(31) Steele, H. M.; Hamill, P. J. Atmos. Sci. 1981, 12, 517-528.
(32) Massucci, M.; Clegg, S. L.; Brimblecombe, P. J. Chem. Eng. Data
1996, 41, 765.
(37) Atkins, P. W. Physical Chemistry; W. H. Freeman and Company:
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Note that the aH O given by this expression are ∼10% different than that of
2
Massucci et al.32 The HCl solubilities obtained using this aH O and the
2
expression given in Table 4, however, are consistent with the current
measured solubilities. Alternatively, the HCl solubilities of Carslaw et al.14
*
can be used, which are up to a factor of 2 greater than HHCl given in Table
4.