Kinetics of acid-catalyzed aldol condensation reactions

13 Pages·2007·0.28 MB·English

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AtmosphericEnvironment41(2007)6212–6224
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Kinetics of acid-catalyzed aldol condensation reactions of
aliphatic aldehydes
(cid:2)
Mia T. Casalea, Aviva R. Richmana, Matthew J. Elroda, , Rebecca M. Garlandb,c,1,
Melinda R. Beaverb,c, Margaret A. Tolbertb,c
aDepartmentofChemistryandBiochemistry,OberlinCollege,Oberlin,OH44074,USA
bDepartmentofChemistryandBiochemistry,UniversityofColorado,Boulder,CO80309,USA
cCIRES,UniversityofColorado,Boulder,CO80309,USA
Received29September2006;receivedinrevisedform21December2006;accepted3April2007
Abstract
Field observations of atmospheric aerosols have established that organic compounds compose a large fraction of the
atmospheric aerosol mass. However, the physical/chemical pathway by which organic compounds are incorporated into
atmospheric aerosols remains unclear. The potential role of acid-catalyzed reactions of organic compounds on acidic
aerosolshas beenexploredasapossible chemical pathwayfortheincorporationoforganic materialintoaerosols. Inthe
present study,ultraviolet–visible (UV–vis) spectroscopywas used tomonitor the kineticsofformation ofthe productsof
theacid-catalyzedaldolcondensationreactionofarangeofaliphaticaldehydes(C –C ).Theexperimentswerecarriedout
2 8
atvarioussulfuricacidconcentrationsandarangeoftemperaturesinordertoestimatetherateconstantsofsuchreactions
on sulfuric acid aerosolsunder troposphericconditions. Therateconstants weregenerally foundtodecrease asthechain
lengthofthealiphaticaldehydeincreased(exceptforacetaldehyde,whichhadanunusuallysmallrateconstant),increase
asafunctionofsulfuricacidconcentrationaspredictedbyexcessaciditytheory,andshowednormalArrheniusbehavior
asafunctionoftemperature.Whilethekineticdataaregenerallyconsistentwithpreviouslaboratoryreportsofaldehyde
reactivityinvarioussulfuricacidmedia,thealdolcondensationreactionsinvolvingaliphaticaldehydesdonotappearfast
enough to be responsible for significant transfer of organic material into atmospheric aerosols.
r 2007 Elsevier Ltd. All rights reserved.
Keywords:Troposphere;Organicaerosols;Acid-catalyzedreactions;Kinetics
1. Introduction scattering and absorbing incoming solar radiation,
leading to a net cooling at the surface. Indirectly,
It is now recognized that tropospheric aerosols aerosols impact climate by serving as cloud con-
play an important role in the global climate system. densation nuclei (CCN). The optical and hygro-
Tropospheric aerosols directly affect climate by scopic properties, cloud condensation ability and
chemical reactivity of aerosols are impacted by
heterogeneous reactions, as all of these properties
(cid:2)
Correspondingauthor.Tel.:[phone].
depend on composition. Field measurements indi-
E-mailaddress:[email protected](M.J.Elrod).
1MaxPlanckInstituteforChemistry,BiogeochemistryDepart- catethatambientaerosolscanbecomposedofupto
ment,P.O.Box3060,55020Mainz,Germany. 80% by mass organic compounds (Saxena and
1352-2310/$-seefrontmatterr2007ElsevierLtd.Allrightsreserved.
doi:10.1016/j.atmosenv.2007.04.002
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Hildemann,1996;Middlebrooketal.,1998;Molnar elevated, Brock et al. (2003) found that the particle
et al., 1999; Turpin et al., 2000). growth exceeded that which could be explained by
Organic compounds may be transferred from the SO oxidation alone. However, Zhang and Wexler
2
vapor phase to the aerosol phase by physical (2002) found no significant difference in the organic
processes such as dissolution and condensation. compositionofaerosolswhethertheambientsulfate
However, it has been difficult to rationalize the high aerosols were acidic or neutralized.
organic content of aerosols by invoking only Because of the well-known acid-catalyzed aldol
physical mechanisms. For example, it is clear that condensation reaction for aldehydes, there have
manyatmosphericallyabundantorganiccompounds been a number of laboratory studies in which the
are not sufficiently soluble to partition significantly incorporation of gaseous aldehydes into acidic
into aerosols. Recently, chemical mechanisms have solutions as compared to non-acidic solutions have
been explored as a means by which the transfer beeninvestigated(IraciandTolbert,1997;Jangand
of organic compounds from the gas phase to the Kamens, 2001; Jang et al., 2002; M. Jang, et al.,
aerosol phase may be enhanced. In particular, 2003; M.S. Jang, et al., 2003; Michelsen et al., 2004;
acid-catalyzed reactions of organic compounds on Liggio et al., 2005; Zhao et al., 2005; Surratt et al.,
tropospheric aerosols have been investigated in 2006). Similar studies have been performed for
this context, as these reactions are postulated ketones (M. Jang, et al., 2003; M.S. Jang, et al.,
to lead to enhanced uptake of organic compounds 2003; Esteve and Noziere, 2005), acrolein and a-
by aerosols (Jang et al., 2002; Zhang and Wexler, pinene (Czoschke et al., 2003; Iinuma et al., 2004;
2002). Tolocka et al., 2004) and isoprene (Limbeck et al.,
Thereareseveraltypesofacid-catalyzedreactions 2003). Many of these studies have concluded that
of carbonyl-containing organic compounds that are the occurrence of accretion reactions are necessary
well known in bulk solutions (Carey and Sundberg, toexplaintheuptake oforganicmaterialinto acidic
1990;VollhardtandSchore,1994).Forexample,the media (Jang and Kamens, 2001; Jang et al., 2002;
acid-catalyzed aldol condensation reaction of alde- Czoschke et al., 2003; M. Jang, et al., 2003; M.S.
hydes results in the conversion of two aldehyde Jang, et al., 2003; Kalberer et al., 2004; Tolocka et
molecules into a single molecule that has a carbon al., 2004; Jang et al., 2005). However, the actual
backbone made up of the sum of the carbon atoms identification of specific molecular products (which
in the reactant aldehydes. Barsanti and Pankow are needed to prove which accretion reactions are
(2004) have termed any such carbon backbone occurring) has been difficult. Garland et al. (2006)
building processes (of which the aldol condensation recently used a suite of analytical approaches
reaction is but one) as accretion reactions, since the (aerosol mass spectrometry, FTIR and UV–vis
end result is the formation of larger molecules from spectroscopy, 1H NMR and GC/MS) to directly
smaller ones. The net result of these types of show that hexanal undergoes aldol condensation
reactions is the formation of relatively less volatile reactions on sulfuric acid aerosols under laboratory
products (which helps prevent the physical transfer conditions. However, high hexanal concentrations
oforganicmaterialbackintothegasphase),andthe were used in the study, and no kinetics data were
dissolution of more reactant to maintain the availabletoestimatethelikelihoodofsuchreactions
solubility equilibrium (the ‘‘enhanced’’ solubility on tropospheric sulfuric acid aerosols. There have
effect). also been several other experiments in which the
SomefieldstudieshavenotedthatwhenbothSO heterogenous interaction of gaseous aldehydes with
2
and volatile organic compound (VOC) concentra- sulfuric acid surfaces has been probed. Michelsen
tions are high, there appears to be additional et al. (2004) studied the interaction of gaseous
particle growth, perhaps indicating that acid-cata- acetaldehyde with a film of sulfuric acid using a
lyzed reactions are causing the accretion of organic Knudsen cell apparatus as a function of H SO
2 4
compoundsintoaerosols(Brock etal.,2003;Chu et composition and temperature. They found evidence
al., 2004). Brock et al. (2002) found that in power for acetaldehyde reaction in the observation of the
plant plumes where SO concentrations are high apparent enhanced solubility of acetaldehyde under
2
and the VOCs concentrations are low, the observed certain conditions. On the other hand, Zhao et al.
particle growth can be accounted for by SO (2005) found only reversible uptake of octanal on
2
oxidation alone. However, in a different air parcel sulfuric acid films, which suggests that aldol
where both SO and VOC concentrations were condensation reactions for octanal are possibly
2
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6214 M.T.Casaleetal./AtmosphericEnvironment41(2007)6212–6224
quite slow. Noziere and Esteve (2005,2006) studied irreversibly and an a,b-unsaturated carbonyl com-
the UV–vis spectra of H SO solutions exposed to pound is formed.
2 4
several different carbonyl-containing compounds Baigrie et al. (1985) carried out the first extensive
(including the aldehydes acetaldehyde, propanal kinetics study of the acid-catalyzed aldol reaction
and butanal), and concluded that several sequential for the self-reaction of any aldehyde in their bulk
aldol condensation reactions were occurring. Acet- solution study of the acetaldehyde aldol reaction as
one has also been found to undergo aldol con- a function of sulfuric acid concentration at room
densation on highly acidic H SO surfaces to form temperature. They found that crotonaldehyde
2 4
mesityl oxide, and ultimately, 1,3,5-trimethyl ben- (the a,b-unsaturated carbonyl compound formed
zene (Duncan et al., 1999). in reaction 4) became the dominant product of
In chemical synthesis situations, aldol condensa- the reaction for H SO compositions equal to
2 4
tion reactions are widely utilized to build molecules 60wt% and higher. Under all conditions studied,
with larger carbon backbones. However, base the kinetics were observed to be second order in
catalysis is the preferred synthetic route for a acetaldehyde, confirming that reaction 3 is the
variety of reasons (Carey and Sundberg, 1990; rate-limiting step in the mechanism. The rate
Vollhardt and Schore, 1994), and thus the mechan- constants were found to increase as a function of
ism and kinetics of the acid-catalyzed aldol con- acidity, and because of the highly non-ideal nature
densation reaction has received considerably less ofthesolutions,thekineticsresultswereinterpreted
study. However, it has been established that the with the aid of excess acidity theory. In a further
mechanism given in Fig. 1 (shown for acetaldehyde, study of the acetaldehyde aldol self-reaction,
but easily generalized for any aldehyde) is operative Esteve and Noziere (2005) used a rotating wetted-
in the acid-catalyzed aldol condensation of alde- wall reactor to estimate the bulk rate constant for
hydes (Noyce and Snyder, 1959). Reactions 1 and 2 acid-catalyzed reaction of acetaldehyde for two
are fast, while reaction 3 is slow and known to be different sulfuric acid compositions. Noziere
the rate-limiting step in the process. Under high and Esteve (2005); Noziere et al. (2006) also studied
acidity conditions, reaction 4 occurs quickly and the kinetics of formation of subsequent products
(larger than crotonaldehyde) in the acetaldehyde
system as a function of acid strength (75–96wt%
H SO ) and temperature (273–314K). Kinetics
2 4
measurements have also been carried out for the
acid-catalyzed reactions of the following ketones:
acetone (Duncan et al., 1999; Esteve and Noziere
2005), 2-butanone, 2,4-pentanedione (Esteve and
Noziere, 2005), and methyl vinyl ketone (Noziere
et al., 2006).
As discussed above, the kinetics literature for the
acid-catalyzed reactions of the aldehydes is primar-
ily focused on the studies of the acetaldehyde
system. In particular, studies concerning the effect
of the molecularity of the aldehydes on the rate
constant and the acid and temperature dependence
of the rate constant for aldehydes other than
acetaldehyde are lacking. In the present study,
UV–vis spectroscopy was used to monitor the
kinetics of formation of the products in the bulk
phase acid-catalyzed aldol condensation reaction of
a range of linear aliphatic aldehydes (C –C ).
2 8
Theexperimentswerecarriedoutatvarioussulfuric

acid compositions and a range of temperatures in
order to estimate the rate constants of such
reactions on sulfuric acid aerosols under tropo-
Fig. 1. Acid-catalyzed aldol condensation mechanism for acet-
aldehyde. spheric conditions.
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2. Experimental transient, locally high concentrations of aldehyde)
to the sulfuric acid solution and vigorously mixing
In concentrated H SO (and in H O) the strong for several minutes to ensure solution homogeneity.
2 4 2
p-p* (e(cid:2)10,000cm(cid:3)1M(cid:3)1) transition arising from For example, a typical acetaldehyde experiment
the C ¼ O chromophore for aliphatic aldehydes involved adding 100ml of a 1.5M acetaldehyde
occurs at peak wavelengths less than 200nm, while solution to 50ml of 75wt% sulfuric acid, resulting
the very weak n-p* (e(cid:2)15cm(cid:3)1M(cid:3)1) transition in a 3(cid:4)10(cid:3)3M acetaldehyde in 75wt% H SO
2 4
occurs around 270nm (Lambert et al., 1987). solution. A small portion of the reaction mixture
Therefore, the reactant aldehydes are not easily was then added to either a 1mm or 1cm pathlength
monitored using standard UV–vis spectroscopy. quartz cuvette, and the reaction system was
However, the dehydrated aldol condensation pro- continuously monitored in the cuvette by UV–vis
ducts for the reactions of aliphatic aldehydes spectroscopy. As mentioned above typical initial
are a,b-unsaturated aldehydes (the product of aldehyde concentrations were on the order of
reaction 4 in Fig. 1) which have strong p-p* 10(cid:3)3M, which provided sufficient UV–vis absor-
(e(cid:2)10,000cm(cid:3)1M(cid:3)1) transitions at wavelengths of bance values and convenient initial rates. For the
at least 245nm in concentrated sulfuric acid. roomtemperatureexperiments,thetemperaturewas
According to the Woodward rules (Lambert et al., 29571K. For the temperature dependence experi-
1987), the peak wavelengths for hydrated aldol ments, the 50ml sulfuric acid solution was either
condensation products (the reactant in reaction 4, precooled or preheated to the appropriate tempera-
Fig. 1) are not expected to shift significantly from ture before the addition of the aldehyde solution,
the parent aldehyde wavelengths. Therefore, the and the cuvette was maintained at the desired
experiments described here specifically concern the temperature by the automated temperature control
kinetics of the formation of the dehydrated aldol system of the UV–vis spectrometer. The lowest
condensation product (as opposed to the overall temperature achieved ((cid:3)241C) was dictated by the
loss of the parent aldehyde or the production of limitedcapabilitiesoftherefrigerationsystemofthe
hydrated products). For this reason, it was neces- temperature control system.
sary to perform experiments at sulfuric acid
concentrations of 60wt% and higher to ensure 3. Results and discussion
complete dehydration of all aldol reaction products
(Baigrie et al., 1985). 3.1. Identification of reaction products
The Beer’s law molar extinction coefficients—to
allowforconversionoftheUV–visabsorbancedata The aldol condensation reaction products of
into absolute production concentrations—were di- acetaldehyde (crotonaldehyde) and butanal (2-ethyl-
rectly determined in 75wt% H SO for crotonalde- 2-hexenal)arecommerciallyavailable.Thespectraof
2 4
hyde (the acetaldehyde aldol condensation product) thesetwo products wereinvestigatedinconcentrated
and 2-ethyl-2-hexenal (the butanal aldol condensa- sulfuric acid solutions in order to identify their
tion product) by preparing dilute solutions in characteristic peak wavelengths and to determine
75wt% H SO and measuring the absorbance at their Beer’s law molar extinction coefficients. In
2 4
the appropriate peak wavelength. The spectra were 75wt% H SO , crotonaldehyde has a peak absor-
2 4
collected quickly, to avoid any possible acid- bance at 245nm and e¼ 9280cm(cid:3)1M(cid:3)1. Similarly,
catalyzed reaction. in 75wt% H SO , 2-ethyl-2-hexenal has a peak
2 4
Aqueous solutions of the aldehydes were pre- absorbance at 266nm and e¼ 11960cm(cid:3)1M(cid:3)1.
pared by adding pure aldehyde to deionized water While the peak wavelengths shifted as a function of
and vigorously mixing for several hours to ensure acid strength, the Beer’s law molar extinction
complete dissolution. For the larger aldehydes, the coefficients varied by less than 10% over the acid
concentrations of these aqueous solutions were and temperature range of the experiments.
determined by their water solubility. The sulfuric Fig. 2 shows several spectra collected as a function
acid solutions were prepared by dilution of con- oftimeforanacetaldehydereactionsystemin75wt%
centrated (96wt%) H SO with deionized water. H SO at 295K at a relatively high initial acetalde-
2 4 2 4
The kinetics experiments were typically performed hyde concentration (6.8(cid:4)10(cid:3)3M) carried out in a
by adding the aqueous solution of the aldehyde 1mm cuvette. At early times, it is readily apparent
(diluted aldehyde solutions were used to avoid that crotonaldehyde (with a peak wavelength of
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creasedalkylchainlengthwillcausearedshiftfrom
crotonaldehyde (the acetaldehyde aldol product) to
1.2 hr
2.6 2-methyl-2-pentenal (the propanal aldol product).
2.4 However, the additional lengthening of the alkyl
2.2 chain in the parent aldehydes will not lead to an
2.0 additional red shift in the dehydrated aldol con-
1.8 densation products (Lambert et al., 1987), as the
ce 1.6 0.8 hr nature of the alkyl group has a much smaller effect
ban 1.4 onthepeakwavelength(becauseitisnotpartofthe
or 1.2
s chromophore electronic system) than does the size
Ab 1.0
0.4 hr of the conjugated system (which is part of the
0.8 19 hr
chromophore electronic system).
0.6 16 hr
0.4
10 hr
0.2
3.2. Integrated rate law analysis and reaction
0.0
efficiency
200 250 300 350 400 450 500
Wavelength (nm)
Data were collected at the peak absorption
Fig.2. UV–visabsorptionspectraatdifferentreactionstimesfor
wavelength for each system as a function of time,
the acetaldehyde reaction system at [acetaldehyde] ¼
0 and the absorption values were converted to
6.8(cid:4)10(cid:3)3M,75wt%H SO and295K.
2 4
absolute aldol product concentration via Beer’s
Law. Fig. 3 shows such a plot for an acetaldehyde
245nm) is a major product of the reaction. At later
(3(cid:4)10(cid:3)3M) kinetics run in 75wt% H SO and
times, the crotonaldehyde peak goes off scale, but a 2 4
295K carried out in a 1mm cuvette. At the lower
newpeakat364nmisobservedtogrowin.According
initial acetaldehyde concentration used in this run
to the Woodward rules for a,b-unsaturated carbonyl
(as compared to the data shown in Fig. 2), the
compounds (Lambert et al., 1987) the later time
245nmabsorptionpeakstaysonscale(A ¼ 1.2),
product is likely to have either three additional units max
and the crotonaldehyde concentration can be
of conjugation in an aliphatic structure, or two
calculated according to Beer’s law at all times. As
additional units of conjugation as part of a ring
mentioned above, acetaldehyde does have a weak
structure. The latter possibility has been suggested as
n-p* transition in this range that could potentially
a possible product of crotonaldehyde self reaction via
complicate the conversion of absorbance data to
a Michael addition mechanism (McIntosh et al.,
crotonaldehyde concentration. However, using the
1980). In our work to determine Beer’s law molar
initial acetaldehyde concentration of 3(cid:4)10(cid:3)3 and
extinction coefficients for crotonaldehyde in H SO
2 4
solutions, we noted that these solutions eventually
showed small absorptions at 364nm. Noziere and 0.0014
Esteve have also noted this absorption in their study
0.0012
ofacetaldehydereactionsinsulfuricacid(Noziereand
Esteve,2005;Noziereetal.,2006),buthaveattributed 0.0010
M)
it to additional aldol condensation reactions of e] ( 0.0008
d
products with acetaldehyde. A detailed study of this y
h
e
crotonaldehydeself-reactioniscurrentlyunderwayin ald 0.0006
n
our labs. oto 0.0004
Cr
All other aldehyde reaction systems in this study [
0.0002
showed similar product behavior. The peak wave-
length for the aldol products for all other systems 0.0000
was 266nm (the Beer’s law molar extinction
-0.0002
coefficient was assumed to be the same as for 0 50000 100000 150000 200000 250000
2-ethyl-2-hexenal for the purposes of the kinetics Time (s)
analysis) and a later time product was also always
Fig. 3. Experimental data (circles) and second-order kinetics fit
observed at 364nm in 75wt% H SO . Again, the
2 4 (line) of the aldol condensation reaction of acetaldehyde at
Woodward rules accurately predict that the in- [acetaldehyde] ¼3(cid:4)10(cid:3)3M,75wt%H SO and295K.
0 2 4
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Beer’s law molar extinction coefficient for this Inthiscase,theinitialrateofthealdolproduction
transition of e(cid:2)15cm(cid:3)1M(cid:3)1, the maximum absor- is measured as a function of the initial aldehyde
bance due to acetaldehyde under these conditions is concentration. Fig. 4 shows a set of initial rates
only 0.004, which is insignificant compared to the experiments for the butanal system at 75wt%
absorption values (A ¼ 1.2) observed in the H SO and 295K. To linearize the determination
max 2 4
experiments. of the rate order n, logarithms are taken of both
AswillbeconfirmedinSection3.3,thereactionis sides of Eq. (3):
second order in the reactant aldehyde:
(cid:2) (cid:3)
d½aldol(cid:5)
1d½aldehyde(cid:5) d½aldol(cid:5) log ¼ nlog½aldehyde(cid:5)þlog k. (4)
(cid:3) ¼ ¼ k½aldehyde(cid:5)2. (1) dt
2 dt dt
The kinetics curve can be directly fit by the
Fig.5showstherateorderanalysisforthedatain
integrated second-order product rate law arising
Fig. 4. From these experiments, a rate order of 1.95
from Eq. (1) above (the solid line in Fig. 3):
was determined, thus confirming the expected rate
(cid:3)1 ½aldehyde(cid:5) order of 2 as given in Eq. (1). Rate constants were
½aldol(cid:5) ¼ þ 0. (2)
t ð2=½aldehyde(cid:5) Þþ4kt 2 calculated via Eq. (3) from measurements of the
0
initial rate and [aldehyde] . Typically, at least three
0
ThefitisshownasthesolidlineinFig.3andisin
kinetics runs (with different initial aldehyde con-
excellent agreement with the data, resulting in a
centrations to confirm the rate order of the process)
bimolecular rate constant of 1.2(cid:4)10(cid:3)3M(cid:3)1s(cid:3)1.
were carried out for each combination of parent
However, this method for determining rate con-
aldehyde, H SO concentration and temperature.
2 4
stants was extremely time-consuming (data were
The statistical error (1s) for the entire data set of
collected for 3 days to construct Fig. 3). Section 3.3
rate constants was 14%. The sources of systematic
describesanalternativeinitialratesmethodthatwas
error in the determination of the rate constants are
used to more efficiently determine rate constants.
expected to arise from linearly dependent uncer-
However, the data in Fig. 3 provide unique
tainties in Beer’s law molar extinction coefficients
information on the reaction. As the reaction has
(10%, as discussed above) used to calculate the
been followed virtually to completion in Fig. 3, it is
initial rates, and in the initial concentration of the
possible to estimate the final concentration of the
aldehydes (10%, as estimated from the volumetric
aldol product crotonaldehyde. Therefore, using the
precision used in the preparation of the solutions)
stoichiometry of the reaction and the initial con-
used to calculate the bimolecular rate constants
centration of acetaldehyde, it is possible to deter-
themselves.
mine the aldol yield of the reaction. The
crotonaldehyde concentration at the longest time is
about 0.0013M, and the initial acetaldehyde con-
0.00012
centration was 0.003M. According to the stoichio-
metry of the reaction (two acetaldehyde molecules
0.00010
react for every crotonaldehyde molecule formed), a
M)
rceraoctotinoanldyeiheyldde.ofTh1e0r0e%fores,hothueldolbesaedrvetod 0cr.0o0to15naMl- nal] ( 0.00008
e
dehyde yield of the reaction is greater than 85%. ex 0.00006
h
2-
yl-
3.3. Initial rates and aldehyde rate order analysis eth 0.00004
2-
[
In order to expedite the determination of rate 0.00002
constants, an initial rates method was used. In the
initial rates method, the kinetics of the reaction are 0.00000
0 200 400 600 800 1000 1200
monitored before the reaction has proceeded
Time (s)
significantly such that the following approximation
holds: Fig. 4. Initial rates measurements for the aldol condensation
reaction of butanal at 75wt% H SO and 295K. Circles:
d½aldol(cid:5) 2 4
¼ k½aldehyde(cid:5)n ¼ k½aldehyde(cid:5)n. (3) [butanal]0¼1.0(cid:4)10(cid:3)3M, squares: [butanal]0¼5.0(cid:4)10(cid:3)4M,
dt 0 triangles:[butanal] ¼2.5(cid:4)10(cid:3)4M.
0
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6218 M.T.Casaleetal./AtmosphericEnvironment41(2007)6212–6224
the aldehyde rate order but that is instead applied
-7.0
here to find the effective H+ rate order (the slope,
m, in Eq. (5)) for the acid-catalyzed process. The
-7.2
intercept, b, in Eq. (5) represents the value of log k
ate) -7.4 at infinite dilution (X ¼ 0). Values for CH+ and X
nitial r -7.6 (fCoroxvaarnioduYs aHte2sS,O1497s8o)l,utainodnsahpaavreambeeetenrizceodmfpoilremd
og (i -7.8 forawhasbeendeterminedforH2SO4solutions(Shi
l et al., 2001). For example, in the previous study of
theacetaldehydesystem,whenthedatawereplotted
-8.0
according to Eq. (5), a slope of 0.95 was obtained,
-8.2 affirming the expectation that the acid catalysis is
first order in [H+] for the aldol condensation
-3.6 -3.5 -3.4 -3.3 -3.2 -3.1 -3.0 -2.9
mechanism (Baigrie et al., 1985).
log [butanal]
0 Fig.6showstheexcessacidityplot(carriedoutas
describedabove)fortheaciddependenceoftherate
Fig. 5. Rate order determination for the aldol condensation
reactionofbutanalfordatashowninFig.4. constant for aldol condensation for the butanal
system at 295K, from 62.5–88wt% H SO . The
2 4
3.4. Excess acidity analysis data are obviously fit well by the excess acidity
formalism, and a slope of 0.99770.015 was
The acid dependence of the aldol formation rate determined, again confirming that the acid catalysis
constants for the acetaldehyde system has been is first order in [H+]. Excess acidity analyses were
previously investigated and analyzed using the carried out for the 295K kinetic data for the other
excess acidity formalism (Baigrie et al., 1985). The aldehydesystems(foracetaldehyde,thepresentdata
excess acidity method accounts for the non-ideal were combined with the data from the previous
behavior of highly acidic solutions and is necessary investigation (Baigrie et al., 1985)) and the results
for the interpretation of acid-catalyzed kinetics are given in Table 1. The self-consistency of the
results under such conditions. The method has been analysis method is apparent in that all systems are
described in detail previously (Cox and Yates, characterized by a slope of unity (within the 95%
1979), and is related to the Hammett acidity confidence interval). As will be subsequently dis-
function, H (Hammett and Deyrup, 1932). The cussed, the parameters from the excess acidity
0
excess acidity formalism is an attempt to define a analysis can be used to predict rate constants for
linear relationship between the observed rate con-
stant and some acidity function for an acid-
catalyzed process, much like a pseudo first-order
rate constant can be linearly related to the 2
concentration of the excess reactant. The excess
acidity parameter, X, is best thought of as a 1
quantity analogous to pH for concentrated acidic
solutions. In their previous study of the acid-
0
catalyzed aldol condensation reaction of acetalde-
hyde, Baigrie et al. found a linear relationship
between (logk(cid:3)logC (cid:3)loga ) and X, where k is -1
H+ w
the bimolecular rate constant, C is the proton
H+
concentration, and aw is the activity parameter for -2
H O,suchthatthedatacouldbefittothefollowing
2
expression:
-3
3 4 5 6 7 8
ðlog k(cid:3)log C (cid:3)log a Þ ¼ mX þb. (5)
Hþ w
As X is analogous to log[H+], this analysis is
Fig.6. Excessacidityplotforthealdolcondensationreactionof
essentially a more sophisticated version of the
butanal at 295K. Compositions ranging from 62.5 to 88wt%
‘‘log–log’’ plotting exercise described above to find H SO arerepresentedonthisplot.
2 4
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M.T.Casaleetal./AtmosphericEnvironment41(2007)6212–6224 6219
Table1 0.18
60 wt%
Excessacidityparametersat295K
0.16 65 wt%
70 wt%
Aldehyde m7s(fromEq.(5)) b7s(fromEq.(5)) 0.14 75 wt%
80 wt%
Acetaldehyde 1.00370.049 (cid:3)7.3170.27 0.12 85 wt%
Propanal 0.95070.031 (cid:3)5.4770.17 1)
Butanal 0.99770.015 (cid:3)5.69170.084 1- s 0.10
PHeenxtaannaall 00..9967167700..002302 (cid:3)(cid:3)56..93307700..1118 -k (M 0.08
0.06
Heptanal 0.9970.15 (cid:3)6.3170.71
Octanal 1.00470.089 (cid:3)6.7270.42 0.04
0.02
0.00
the lower H SO concentrations that were not
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1 2 3 4 5 6 7 8 9
accessible in this study (due to the requirement that
Number of Carbons Atoms in Aldehyde
thedehydratedaldolproductbethedominantform)
but that are of interest in assessing the role of aldol Fig. 7. Dependence of the aldol condensation reaction rate
condensation reactions in tropospheric aerosols. constant on the reactant aldehyde and H SO concentration at
2 4
Because previous kinetic work (Noyce and Snyder, 295K.
1959) suggests that the dehydration step (Eq. (4) in
Fig. 1) is not rate-limiting, but rather that the rate
limiting step is the aldol formation (Eq. (3) in it is often used in atmospheric studies as the
Fig. 1), it should be possible to extrapolate the ‘‘prototype’’ aldehyde. From the point of view of
present data to lower H SO concentrations, where aldol reactivity, acetaldehyde is clearly not a repre-
2 4
the dehydrated aldol product is not formed. sentative aldehyde.
3.5. Aldehyde dependence 3.6. Temperature dependence
Thisstudyisthefirstsystematicexaminationofthe Temperature dependence measurements were
dependence of the aldol reaction rate constant for a made for the acetaldehyde, butanal, and hexanal
numberofdifferentaldehydes.Fig.7showsthe295K systems at 75wt% H SO to assess whether the
2 4
rate constants for each aldehyde system at a number temperature dependence of the rate constant varies
of different H SO compositions. As discussed in among the different aldehydes studied. Similar
2 4
Section3.4,theaciddependenceoftherateconstants measurements were made for the butanal system
can be precisely analyzed through the excess acidity at 65 and 85wt% H SO to assess whether the
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formalism. However, Fig. 7 shows the interesting temperature dependence of the rate constant varies
dependence of the rate constant on the alkyl chain among the different H SO compositions used.
2 4
length of the parent aldehyde. In particular, the Fig. 8 shows an Arrhenius analysis of the results
75wt% H SO 295K rate constant dramatically of the 75wt% H SO experiments. It is clear that
2 4 2 4
increases from acetaldehyde (1.61(cid:4)10(cid:3)3M(cid:3)1s(cid:3)1) normal Arrhenius behavior is observed over the
to butanal (84.9(cid:4)10(cid:3)3M(cid:3)1s(cid:3)1), and then gradually range of temperatures studied ((cid:3)24 to 421C).
decreasesasthealkylchainlengthensfurther.Therise Table 2 contains the Arrhenius parameters deter-
in the reactivity from the C to the C aldehyde is mined for all temperature dependence experiments.
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probably related to the fact that the b-carbon in Withinthe95%confidenceinterval,nodifferencein
acetaldehyde is a primary carbon atom (–CH ), the temperaturedependence of the rate constant for
3
whereas the b-carbon for the other systems is a thedifferentH SO compositionswasobtained,but
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secondary carbonatom (–CH –). Presumably,oneof a statistically meaningful decrease in the activation
2
the intermediates in the aldol condensation mechan- energy was determined as the alkyl chain of the
ism is destabilized if the reaction occurs at a primary parent aldehyde lengthened. Assuming Arrhenius
b-carbon.ThedecreaseinreactivityfromtheC toC behavior holds, the parameterization of the tem-
4 8
aldehydeisnotaseasilyrationalized.Inanycase,itis perature dependence of the rate constant deter-
important that the present study indicates that minedhereallowsthepredictionofrateconstantsat
acetaldehyde is an unusually unreactive aldehyde, as temperatures below the lowest directly used in the
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6220 M.T.Casaleetal./AtmosphericEnvironment41(2007)6212–6224
-1
-2
-3
-4
-5
k
n
l -6
-7
-8
-9
-10
0.0031 0.0032 0.0033 0.0034 0.0035 0.0036 0.0037 0.0038 0.0039
1/T (1/K)
Fig.8. Arrheniusanalysisofthetemperaturedependenceofthealdolcondensationreactionrateconstant(circles:acetaldehyde;squares:
hexanal;triangles:butanal)at75wt%H SO .
2 4
Table2 X ¼ 1:07(cid:4)10(cid:3)3(cid:4)ðwt%H SO Þ2(cid:3)1:34(cid:4)10(cid:3)2
2 4
Arrheniusparameters
(cid:4)ðwt%H SO Þþ3:34(cid:4)10(cid:3)1. ð7Þ
2 4
Aldehyde wt%H SO (cid:3)E /R7s(K) lnA7s
2 4 a
The 298K water activity (a ) has been previously
w
Acetaldehyde 75 (cid:3)68807200 16.6870.69 parameterized as a function of water mole fraction
Butanal 65 (cid:3)55807650 14.572.2 (Y ) (Shi et al., 2001):
75 (cid:3)62507270 18.4170.93 w
85 (cid:3)64707940 19.773.2 ðwt%H SO Þ
Hexanal 75 (cid:3)51307250 13.0770.86 Yw ¼ hðwt%H SO Þþ½100(cid:3)2ðwt%4H2SO4Þ(cid:5)(cid:6)MH2SO4i, (8)
2 4 MH2O
present experiments ((cid:3)241C); such temperatures where MH2SO4 and MH2O are the molar mass of
are often relevant in the upper troposphere. sulfuric acid and water, respectively.
(cid:4)
log a ¼ log exp½0:00305(cid:4)ð(cid:3)69:775(cid:4)Y
w w
3.7. Parameterization of kinetic data
(cid:3)18253(cid:4)Y2 þ31072:2(cid:4)Y3
w w
In order to improve the utility of the present (cid:3)25668:8(cid:4)Y4(cid:5)(cid:6)(cid:7). ð9Þ
w
kinetics data, several parameterizations were deter-
From the excess acidity analysis for each alde-
mined to allow the calculation of aldol condensation
hyde (the slope, m, and intercept, b, values given in
rateconstantsforanyaldehyde,H SO composition,
2 4 Table 1 obtained by analysis according to Eq. (5))
and temperature. The excess acidity parameters, log
and the values of X, logC and loga (para-
C and X were taken from Cox and Yates (1978) H+ w
H+ meterized above), the rate constant for each aldol
and wereseparately fitto a second-orderpolynomial
condensationreactionat295Kforany wt%H SO
expression as a function ofwt% H SO : 2 4
2 4 can be calculated:
log C ¼ (cid:3)2:62(cid:4)10(cid:3)4 (cid:4)ðwt%H SO Þ2
Hþ 2 4 kð295KÞ ¼ 10ðmXþbþlog CHþþlog awÞ. (10)
þ3:79(cid:4)10(cid:3)2 (cid:4)ðwt%H SO Þ
2 4
Rate constants at other temperatures can be
(cid:3)2:58(cid:4)10(cid:3)1, ð6Þ
calculatedbyusingthe295Krateconstantcalculated
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M.T.Casaleetal./AtmosphericEnvironment41(2007)6212–6224 6221
above(anychangesintheapparentrateconstantdue the finding of Garland et al. (2006) that H SO
2 4
to the temperature dependence of C and a are aerosols exposed to hexanal under such conditions
H+ w
subsumed in the Arrhenius analysis), and the (cid:3)E /R are composed of as much as 88% organic by mass.
a
values (given in Table 2) from the appropriate JangandKamens(2005)studiedtheheterogeneous
Arrhenius analysis: interaction of octanal vapor with various seed
aerosols at 298K with the H SO composition
(cid:8)(cid:3)E (cid:2)1 1 (cid:3)(cid:9) 2 4
kðTÞ¼ kð295KÞ(cid:4)exp a (cid:4) (cid:3) . controlled by the relative humidity of the smog
R T 295K
chamber. Using octanal concentrations of about
(11) 260ppb, the aerosols were observed to increase in
volume by as much as factor of 2 over the 1h
3.8. Comparison to previous work timescale of the experiment. Zhao et al. (2005) have
measured the Henry’s law constant for octanal in
Thepresentfindingthatdehydratedaldolproducts 67wt% H SO at 296K and determined a value of
2 4
are formed efficiently for a variety of saturated 2300Matm(cid:3)1. Assuming a H SO composition of
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aliphatic aldehydes in concentrated H SO solutions 67wt% for the highest acidity experiments by Jang
2 4
is in agreement with earlier studies on acetaldehyde and Kamens, an octanal aerosol concentration
byBaigrieetal.(1985)andNoziereandEsteve(2005) of 6.0(cid:4)10(cid:3)4M is calculated for these conditions.
and a study of the interaction of hexanal with actual Using the present kinetics data (and the parameter-
H SO aerosolsbyGarlandetal.(2006).Asdiscussed izationsgivenabove),thebimolecularrateconstantis
2 4
above,anextensivekineticdatasetforacid-catalyzed about 2.9(cid:4)10(cid:3)3M(cid:3)1s(cid:3)1, and the reaction rate can
aldol condensation self-reactions exists only for be calculated: 2.9(cid:4)10(cid:3)3M(cid:3)1s(cid:3)1(cid:4)[6.0(cid:4)10(cid:3)4M]2,
acetaldehyde(Baigrieetal.,1985;EsteveandNoziere, which is equal to 1.0(cid:4)10(cid:3)9Ms(cid:3)1. Therefore, for a
2005).Thepresentrateconstantsfortheacetaldehyde 1hexperiment,thepresentkineticsresultspredictthat
self-reaction are about 50% higher than the rate the reaction has proceeded about only 1% toward
constantsdeterminedat65,75,and85wt%inBaigrie completion, and does not appear to provide support
et al., but somewhat lowerthan thevaluedetermined for aldol condensation reactions as the explanation
by Esteve and Noziere for 85wt% H SO . for the large growth in organic mass observed in the
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Garland et al. (2006) studied the heterogeneous Jang and Kamens experiments. Similarly, Esteve and
interaction of hexanal vapor with H SO aerosols Noziere (2005) have used their kinetics data for
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with compositions between 30 and 96wt% and at acetone to show that the acid-catalyzed reactions of
298K. They report evidence for reaction at all acetone are too slow to be responsible for increased
H SO compositions, with increasing reaction evi- organic mass observed in aerosols in smog chamber
2 4
dent at the highest acidities. Typical reaction experiments. Esteve and Noziere also asserted that
conditions were as follows: 7Torr hexanal, 75wt% since atmospheric conditions are much less favorable
H SO and a reaction time of 13min. In order to for such acid-catalyzed reactions than smog chamber
2 4
calculate the acid phase hexanal concentration, the conditions, the reactions of ketones with sulfuric acid
appropriate Henry’s law coefficient is required. aerosolsareprobablynotresponsibleforhighorganic
Unfortunately, there have been no measurements content of tropospheric aerosols.
of this quantity for hexanal in H SO solutions.
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However, if a conservative value of 100Matm(cid:3)1 3.9. Roleofaldehydealdolcondensationreactionson
(roughly the value determined by Esteve and atmospheric sulfuric acid aerosols
Noziere (2005) for acetaldehyde in 70wt %
H SO and at 298K) is assumed, a hexanal While it is clear that acid-catalyzed accretion
2 4
concentration of 1.0M is calculated. Using the reactions involving aldehydes have been observed in
present kinetics data (and the parameterizations many laboratory experiments, these experiments
given above), the bimolecular rate constant is about typically use higher aldehyde concentrations (most
1.8(cid:4)10(cid:3)2M(cid:3)1s(cid:3)1, and the reaction rate can be often, much higher) than those observed in the
calculated: 1.8(cid:4)10(cid:3)2M(cid:3)1s(cid:3)1(cid:4)[1.0M]2, which is atmosphere in order to drive the reactions to occur
equal to 1.8(cid:4)10(cid:3)2Ms(cid:3)1. Therefore, for a 780s on a reasonable time scale. Obviously, kinetic data
experiment, the present kinetics results predict that are needed to extrapolate from such laboratory
thereactionwillgotocompletionseveraltimesover conditionstothoseoftheatmosphere,particularlyas
undertheseconditions.Thisresultisconsistentwith a function of H SO composition and temperature.
2 4