12888
J. Phys. Chem. 1996, 100, 12888-12896
Environmental Chemistry (Gas and Gas-Solid Interactions): The Role of Physical Chemistry Mario J. Molina* and Luisa T. Molina Department of Earth, Atmospheric and Planetary Sciences and Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
David M. Golden SRI International, Menlo Park, California 94025 ReceiVed: January 12, 1996; In Final Form: April 11, 1996X
This paper reviews two physical chemistry topics related to atmospheric chemistry. First, we describe semiempirical models, based on thermochemistry and transition state theory, which are employed to estimate gas phase reaction rates over a wide range of temperatures and pressures. We also review briefly the experimental techniques utilized for measurements of elementary reaction rate constants, which provide the primary input to these models. We then address chemical reactions which take place in the atmosphere on the surface of solid, ice-like aerosol particles, discussing some current views on the mechanisms of these reactions and describing some laboratory techniques for the study of these heterogeneous processes.
I. Introduction Processes of importance in environmental chemistry include those occurring homogeneously in condensed phase or in the gas phase and heterogeneously at the interface between two phases. In this paper we will address two topics in connection with atmospheric chemistry: (1) gas phase chemical kinetics and thermochemistry and (2) gas-solid (heterogeneous) chemistry. Semiempirical theory is well established for the first subject, and we review this herein. For gas-solid chemistry we must rely much more on direct experimental findings while the theory develops. We discuss some of these findings in this paper. Gas phase reactions in the two lowest atmospheric layerssthe troposphere and the stratospheresare dominated by free radical processes. The production of radicals in the atmosphere is initiated mostly by solar photodissociation of closed-shell molecules; however, some radicals such as the nitrogen oxides (NO and NO2) are generated at the earth’s surface by combustion and by biological processes. Gas phase reactions between closed-shell species are in general too slow to matter at atmospheric temperatures; such reactions, however, may occur rapidly on the surface or in the interior of cloud and aerosol particles. Gas phase reactions with environmental consequences occur not only in the atmosphere but also inside the chamber of an internal combustion engine. Hence, an important goal in environmental chemistry is to develop quantitative models to predict reaction rate parameters applicable over a wide range of temperatures and pressures. This range often falls beyond that for which experimental data exist, so that it is frequently necessary to fit and to extrapolate from the rate data at hand. Even for simple bimolecular abstraction reactions, conventional Arrhenius expressions are generally valid only for a temperature range covering a few hundred degrees. For other reactions additional complications often arise, such as pressure dependence of the rate constants and multichannel chemically activated pathways. Compilations and evaluations of rate constants for reactions of importance in the stratosphere have X
Abstract published in AdVance ACS Abstracts, June 15, 1996.
S0022-3654(96)00146-3 CCC: $12.00
been published periodically;1,2 these evaluations are currently being extended to include tropospheric reactions. II. Homogeneous Gas Phase Processes In the following sections we discuss a few methods that have been developed to address some of the complications mentioned above with gas phase kinetics that allow accurate computation and numerical representation of rate constants based on experimental data. In the absence of data, these same techniques can be used to estimate rates of unstudied reactions. These estimates can be a great help in determining reaction mechanisms or focusing experimental resources on the most important reactions in a complex system. II.A. Thermochemistry. Thermochemistry underlies methods for understanding chemical kinetics. In many chemical models the reactions need to be considered in both the forward and reverse directions. Since the rate constants are related through the equilibrium constant, a data base of thermochemical values ensures consistency in this process and, of course, obviates the need for half of the rate constants in those models. Many codes calculate reverse rate constants automatically from the forward rate constant and the equilibrium constant computed from such a thermochemical data base. Conventional canonical transition state theory considers the rate constant in terms of differences in thermochemical properties of the “transition state” and the reactant(s). A good understanding of the thermochemical values for stable species is required in order to extrapolate to transient stable species, such as free radicals, as well as to values for constructs, such as transition states. II.A.1. Additivity Rule. Our objective is to obtain values 0 for ∆HT0 , ∆ST0 , and ∆Cp,T for chemical reactions. We describe here the most commonly employed methods, which are fundamentally empirical and which are based on extrapolation and codification of experimental data. Theoretical methods, discussed elsewhere in this issue, are rapidly improving and serving as useful sources of data where measurement is difficult to perform. © 1996 American Chemical Society
Environmental Chemistry
J. Phys. Chem., Vol. 100, No. 31, 1996 12889
Given the chemical reaction
aA + bB + ... a pP + qQ + ...
(1)
a change in some thermodynamic property Φ is given as follows:
∆Φ ) pΦP + qΦQ + ... - aΦA - bΦB - ...
(2)
Atom AdditiVity. A simple disproportionation reaction of diatomic molecules may be written
A2 + B2 a 2AB
(3)
If the property Φ is in reality an atomic property, then any property for which ∆Φ ) 0 obeys the law of atomic additivity. It is very unlikely that thermochemical quantities would obey such a simple law, but the uncertainty limits might be adequate. Atom additivity is totally unsatisfactory for the estimation of enthalpies and only of marginal value in estimation of entropy and heat capacity. Bond AdditiVity. A next level in the hierarchy that can be used for estimation of thermochemical properties is envisaged in terms of the reaction
A-X-A + B-X-B a 2A-X-B
(4)
If for this reaction, ∆Φ ) 0 ( δ, the law of bond additivity is obeyed. Properties are associated with the chemical bonds, which are the same on both sides of the equation. Bond additivity requires in general a much greater data base than the atom additivity contributions. Group AdditiVity. The next step in the additivity hierarchy is defined through the reaction
A-XY-A + B-XY-B a A-XY-B + B-XY-A
(5)
If for this case ∆Φ ) 0 ( δ, then law of group additivity is obeyed, and properties are associated with an atom and its ligands. This is usually a very useful level of approximation. The data base required is relatively large, but still accessible. Sometimes combinations of bond and group additivity are necessarily employed, if the data base is limited. It is sufficient to tabulate group contributions to ∆Hf0 and S0 0 at 298 K and Cp,T at various temperatures. ∆H0 and ∆S0 can then be calculated for chemical reactions at temperatures different than 298 K from a knowledge of the heat capacity. It is also necessary to point out that all the additivity contributions for entropy are for intrinsic entropy, rather than for real symmetry-corrected entropy. This is understood in 0 - R ln σ, where σ is the rotational symmetry terms of Sint number for the molecule. The external rotational symmetry correction takes into account that if all rotational permutations were weighted equally, then indistinguishable configurations would be counted more than once. Finally, for molecules exhibiting optical activity, there is an entropy of mixing correction term of R ln n, where n is the number of optical isomers. The overall correction to group additivity entropies is therefore given by 0 - R ln σ/n ST0 ) ST,intrinsic
(6)
Tables of additivity parameters and a discussion of additivity and structural concepts may be found in Thermochemical Kinetics3 (see also ref 4). II.A.2. Structural Estimates of Entropy and Heat Capacity. Statistical Thermodynamics. If molecular properties such as molecular weight, bond lengths, bond angles, and molecular
frequencies are known, the entropy and heat capacity may be calculated using the rigid rotor harmonic oscillator (RRHO) model. In most cases the ideal gas approximation is valid. This method, more time-consuming than group additivity, is also generally more accurate if the molecular parameters are known. To the extent that some inputs must be estimated (e.g., vibrational frequencies, rotational barriers, etc.), it becomes in effect a more detailed additivity scheme. A major advantage, however, is that the same techniques may be applied to transition states, hence allowing the estimation of A factors, modeling of multichannel systems, etc. Molecular Model Compounds. The structural considerations make it apparent that model compounds offer another estimation method. Consider, for example, the n-butane molecule: it is similar in many ways to CH3OCH2CH3, or CH3NH-CH2CH3, or CH3CH2CH2OH. The changes are simple to make and due almost entirely to symmetry and H motions. The most difficult estimate involves changing rotational barriers, but this turns out to be a small effect. Many of the preceding comments are a prologue to the estimation of free radical and transition state properties. Many radicals can be thought of as being derived from molecules by removal of a hydrogen atom. That is, if we wish to have the properties of the radical R•, we may ask how we expect it to differ from the molecule R-H. II.B. Gas Phase Kinetics. II.B.1. Bimolecular Metathesis Reactions. Rate Constant Formats from Transition State Theory. Bimolecular metathesis reactions are cast into the simplest transition state theory (TST) representation. Recognizing that the TST expression for the rate constants is given by3,4
k(T) )
kT exp(∆ST‡ /R) exp(-∆HT‡ /RT) ) h ‡ kT Q (T) exp(-∆H‡0/RT) (7) h Q(T)
we use expressions of the form3,4
k(T) ) ATB exp(-C/T)
(8)
where the parameters A, B, and C may be related to molecular properties of the reactants and the transition state: ‡ A ) [k/h(300)〈∆C‡p/R〉] exp[(∆S0‡ 300 - 〈∆Cp〉)/R]
(9a)
B ) (〈∆C‡p〉 + R)/R
(9b)
C ) [∆H‡300 - 〈∆C‡p〉(300)]/R
(9c)
‡ ‡ + ∆Cp,300 )/2 〈∆C‡p〉 ) (∆Cp,T
(10)
where
∆S0‡ 300 is the entropy change from reactants to transition state at 300 K, referred to a standard state of 1 atm. k, h, and R have their usual meanings as Boltzmann’s constant, Planck’s constant, and the gas constant (in the same units as ∆S and ∆Cp), respectively. If eqs 9a, 9b, and 9c are used in eq 8, the rate constant will have units of atm-1 s-1 (multiply by 1.362 × 10-22 T to convert to cm3 molecule-1 s-1). Modeling and Extrapolating H Atom Abstraction Reactions. Several authors have used various schemes for estimating transition state properties. The methods herein are closely related to those described by Benson3 and reiterated recently in
12890 J. Phys. Chem., Vol. 100, No. 31, 1996
Molina et al.
Figure 1. Reduced rate constant versus reduced pressure for a unimolecular process.
several publications;4-7 the methods have also been illustrated for a series of H atom metathesis reactions.8 Theoretical methods are beginning to be very helpful in determining the properties of the transition state. In the absence of help in these cases, the structure of the transition state is chosen by choosing the X-H-R angle to be linear or close to linear and fixing the X-H and the R-H bond distances to be approximately 0.3 Å greater than their values in the species X-H and R-H. The frequencies may be chosen from the list of normal and partial bond frequencies in Thermochemical Kinetics,3 or added in a consistent manner. Internal rotations may also be treated as described by Benson,3 with barriers being chosen as in normal molecules except for those involving rotation around the partial bonds of the transition state, where barriers of zero are always assigned. These methods have also been applied9 to a series of reactions in which OH radicals abstract a hydrogen alone from various halogenated alkanes. Many of these molecules are proposed replacements for the ozone-depleting molecules CFCl3 (CFC11) and CF2Cl2 (CFC-12). The reactions with OH determine their tropospheric lifetimes. The reported expressions are consistent with most of the existing experimental data.3,4 The important generality is that a self-consistent approach needs to be used, and no single reaction is treated in isolation. II.B.2. Single Channel Unimolecular Reactions. Falloff and the Lindemann Mechanism. If the simple Lindemann mechanism is used to describe a unimolecular decomposition k1
XY + M {\ } XY* + M k -1
k-a
XY* 98 X + Y
(11) (12)
and we write k-1[M] ) βω, where ω is collision frequency and (0 < β e 1) is the collision efficiency, then
kuni )
K1βωk-a , where K1 ) k1/k-1 βω + k-a
(13)
In the limits ω f ∞ and ω f 0, ∞ 0 kuni ) K1k-a; kuni ) K1βω
(14)
Following Troe,10-13 we define the reduced pressure ∞ Pr ≡ k0un/kuni
(15)
and the reduced rate constant,
kr ≡
kuni ∞ kuni
)
Pr 1 + Pr
(16)
If we were to plot log kr vs log Pr, we would find the universal function displayed in Figure 1 and labeled “Lindemann falloff”.
Examples of data analysis can be found in ref 4. Energy-Dependent Mechanisms. The Lindemann mechanism is too simple, however, in that it assumes that all excited molecules, XY*, are the same and that the product forming step, k-a, proceeds with a single rate. In fact, k1, k-1, and k-a are all functions of the energy of XY*. (At a still higher level of accuracy, these quantities also depend on J, the rotational quantum number.) We may still define kr and Pr as kuni/k∞uni and k0uni/k∞uni, respectively, and we notice that kr may be expressed as in the Lindemann representation, but with an additional term, leading to the function in Figure 1 labeled “RRKM falloff”:
kr )
Pr F 1 + Pr K
(17)
Still following Troe,10-13 we define FK (the “broadening parameter”) in terms of its central value Fc (i.e., its value at Pr ) 1, where kr ) 1/2k∞ for the Lindemann model). Using the simplest assumption of symmetric broadening about Pr ) 1,
FK ≡ FcX, where X ) [1 + (log Pr)2]-1
(18)
It is easy to see that if one uses available unimolecular rate theories, such as RRKM, one can calculate Fc, since at Pr ) 1, Fc ) 2kuni/k∞uni. Thus, using RRKM, it is only necessary to calculate kuni at pressures corresponding to Pr ) 1. Numerical Representation of Pressure and Temperature Dependence. The pressure dependence of the rate constants can thus be characterized in terms of three parameters: k0uni, k∞uni, and Fc. If the analysis is carried out over a temperature range, expressions for k0uni (T), k∞uni (T), and Fc(T) can be obtained. These are ∞ ) aTb exp(-c/T) kuni
(19)
0 kuni [M] ) a′Tb′ exp(-c′/T)
(20)
Fc ) a′′ exp(-b′′/T) + exp(-T/c′′)
(21)
The entire complex pressure and temperature dependence is thus accurately described by nine parameters.1 It is observed that the two pressure limiting rate constants can be fitted as a function of only two parameters each and that over the limited range of temperature applicable to the stratosphere the value of Fc can be taken as 0.6. In terms of computer modeling, this is a trivial number of coefficients, yet allows the confident extrapolation of the model over a wide range of conditions. Notice that in principle these parameters are pertinent to strong collision conditions (β ) 1). In fact, since atmospheric gases are generally weak colliders, and the value of β varies with the gas, the parameter values are adjusted slightly to incorporate the effects of weak collisions applicable to atmospheric conditions. Of course, kbi, the rate constant for the reverse (association) reaction, may be computed from kuni and the equilibrium constant. In order to obtain descriptions of reactions in the form of eqs 19-21, models must be developed which can be fit to the available experimental data on k0, k∞, and the falloff regime. Since these are empirical fits, not a priori calculations, overly sophisticated models are not necessary. They should be rigorous enough to adequately describe the actual behavior, and thus allow extrapolation, but the details are often not critical.
Environmental Chemistry
J. Phys. Chem., Vol. 100, No. 31, 1996 12891 The Association Reaction. Pursuing the Lindemann formulamay be written by analogy to the previous tion further, kassn bi discussion with the addition of the second pathway: assn kbi )
Figure 2. Representative reaction coordinate diagrams.
Examples of reactions of this type are found in Table 2 of the report from the NASA Panel for Data Evaluation.1 Of particular interest are reactions such as
Cl + NO2 f ClNO2 (ClONO)
(22)
ClO + NO2 f ClONO2 (ClOONO?)
(23)
OH + NO2 f HONO2 (HOONO?)
(24)
ka
(25)
-a
βω
XY* + M 98 XY + M
(26)
kb
XY* 98 C + D
(27)
A particularly interesting example of such a process is the important reaction of OH with CO: OH + CO
ka k–a
HOCO*
kb
H + CO2
(29)
βω k-a + kb
(30)
Prassn )
krassn )
assn kbi
) assn,∞
kbi
Prassn βω ) k-a + kb + βω 1 + Passn
(31)
r
Again, taking energy dependence into account
Reaction 22 yields both indicated products. The extended ClONO is less stable, but produced equally rapidly due to its higher density of states. For this reaction the entropy and enthalpy considerations are balanced. There was some suggestion that reaction 23 would exhibit the same sort of behavior, but no evidence for the formation of products other than chlorine nitrate (ClONO2) has been found.1 In the case of reaction 24, there is some data14 indicating that the rate constants values recommended by the NASA Panel for Data Evaluation1 are somewhat in error. The shape of the rate constant vs pressure curve suggests formation of isomers such as HOONO at high pressure. II.B.3. Multichannel Unimolecular (Complex Mode) Reactions. Thermally Stable Intermediates. Figure 2 shows representative reaction coordinate diagrams for various types of reactions. Multichannel unimolecular reactions, also referred to as complex mode reactions, are represented in Figure 2c. Here, the association reaction produces the excited species XY*. This species will decompose if proper localization of the excess energy occurs prior to collisional stabilization. As there may be several reactive surfaces, the decomposition products may be other than the starting species. Since these other reactions are energetically accessible due to the release of energy in the initial association, they are known as chemical activation processes. For a system with two reactive surfaces, ignoring thermal dissociation of XY (that is, the reverse of reaction 26), the Lindemann mechanism is
} XY* X + Y {\ k
kaβω k-a + kd + βω
(28)
βω
HOCO
This reaction has been well studied due to its importance in the atmosphere and in combustion processes. Parameters that describe most of the existing data in terms of eqs 19-21 can be found in the NASA Panel for Data Evaluation publication.1
krassn )
Prassn 1 + Prassn
(Frassn)x
(32)
Chemical ActiVation. For the chemical activation process, the Lindemann mechanism yields ca ) kbi
kakb k-a + kb + βω
(33)
βω k-a + kb
(34)
Prca )
krca
Prca βω ) ) k-a + kb + βω 1 + Pca
(35)
r
Once again, taking energy dependence into account yields
krca )
Prca
x (Fca c ) 1 + Prca
(36)
Notice that for this case the low-pressure limit of the bimolecular rate constant is independent of pressure, while the high-pressure limiting bimolecular rate constant is best expressed as a firstorder constant multiplied by the pressure. The rate constant for production of C (and/or D) is just the chemical activation rate constant, kca, if XY does not thermally decompose:
kc )
1 d[C] ca ) kbi [X][Y] dt
(37)
While this may seem to be a large number of parameters to define this system, it must be remembered that they may be derived from more than one type of experiment and that some rate constants are sensitive to only a few of these parameters. In any case, no alternate representation of data for this type of systems has been proposed which adequately predicts the values of the rate constants over wide temperature and pressure ranges. II.C. Experimental Techniques. An important goal in atmospheric chemistry is to accurately measure in the laboratory elementary reaction rate constants; another important goal is to measure in the atmosphere the concentrations of the many species of interest. There are a number of techniques which have much in common for both sets of measurements; we present here a brief description only of the most common laboratory methods. Much emphasis in modern techniques for kinetics studies has been placed on direct measurements, where the concentration
12892 J. Phys. Chem., Vol. 100, No. 31, 1996 of the reactants and/or products is monitored as a function of time. An important requirement for this type of measurement is high sensitivity and selectivity in order to minimize complications arising from secondary reactions. Indirect and relative rate measurements are, however, still very useful in special cases, particularly when the reaction mechanism is well established or when direct techniques are not available. The two direct techniques which have yielded most of the kinetic information relevant to atmospheric chemistry are flash (or laser) photolysis and fast (or discharge) flow. In the former, the reactant mixture is prepared by directing a short pulse of light onto a reaction cell containing suitable photolytic precursors, while the concentration of the reacting species is measured in real time, usually on a time scale of milliseconds and employing optical techniques such as fluorescence. In the discharge-flow method, the measurements are carried out at steady state; the free radical reactant is most often prepared by flowing a suitable precursor through a microwave discharge cavity and is then rapidly mixed with the other reactants downstream in a flow tube. The reaction timesusually millisecondssis adjusted by means of a movable injector, and the mixture is monitored downstream with a variety of techniques such as resonance fluorescence, mass spectrometry, or laser magnetic resonance.15 These methods are complementary to those employed for investigations of chemical dynamics (e.g., molecular beams in high-vacuum chambers). For atmospheric purposes it is best to measure rate constants at moderate pressures in order to ensure proper thermalization of the reactants; chemistry of excited species sometimes leads to artifacts in laboratory kinetics studies. Of course, such chemistry is of fundamental importance and is being carefully investigated, as described in a separate paper in this issue;16 however, with a few notable exceptions (e.g., reactions of O 1D) it is not directly applicable to the atmospheric environment. The flash photolysis and the fastflow techniques have been optimized for accurate thermal rate constant measurements, and the results agree well for those reactions that have been successfully studied with the two techniques; however, even for simple reactions it is difficult to determine absolute rate constants to better than about (20%. A major advantage of the flash photolysis technique is that it allows rate constants to be measured over a wide range of temperatures and pressures, with little interference from wall effects. On the other hand, certain reactant mixtures are very difficult to prepare cleanly using photolysis only; this is the case, for example, for radical-radical reactions or when one of the reactants is photolytically very labile. Furthermore, a fast analytical scheme needs to be employed, as the measurements are carried out in real time. The fast-flow technique allows a wide range of species to be generated and accurately monitored: the primary radicals produced by a microwave discharge can be cleanly interconverted to other radicals before mixing with the other reactants, and the radical concentrations can be measured using various titration schemes. Furthermore, the analytical technique can be relatively slow, since the reaction mixture is probed under steady-state conditions. However, the overall pressure range accessible to the conventional flow technique is rather small, namely about 1-10 Torr. The reason is that the reactants must have a well-defined residence time in the flow tube, and at moderate pressures (with laminar flow) molecules travel much faster down the center of the tube than close to the walls; at sufficiently low pressures they diffuse rapidly, sampling all radial positions, and hence effectively move at the average velocity. Another disadvantage of the low-pressure requirement
Molina et al.
Figure 3. Schematic representation of atmospheric pressure flow apparatus for measurements of the reaction probability for ClONO2 + HCl on ice aerosols.53
is that the wall collision frequency is high, so that secondary reactions on the tube walls often interfere with the measurements, particularly at low temperatures. In addition, for termolecular reactions, as well as for complex mode processes, the rates need to be directly measured at higher pressures. For these reasons the flow technique has been modified in recent years to extend its range of applicability to higher pressures.17,18 If the pressure is increased sufficiently turbulent flow develops, and the gas mixture at the core of the flow travels at a nearly uniform velocity, thus providing well-defined reaction times. A challenge working at the higher pressures has been to develop suitable high-sensitivity analytical techniques to compensate for the higher dilution. One such technique involves chemical ionization at moderate pressures, followed by extraction of the product ions into a conventional high-vacuum mass spectrometry chamber.19,20 An example of a flow tube apparatus using this technique is shown schematically in Figure 3. In fact, such chemical ionization schemes have been previously utilized to monitor trace species in the atmosphere.21,22 In particular, the OH radical has been successfully measured at ground level at concentrations of about 106 molecules cm-3 by first converting it in a flow system to isotopically labeled H2SO4, which is then selectively monitored by chemical ionization mass spectrometry; this method yields results in good agreement with those obtained with a long-path laser absorption technique.23 In the stratosphere, OH has been measured using balloon platforms with laser-induced fluorescence techniques.24 III. Heterogeneous Chemistry and Kinetics Heterogeneous processes in the troposphere involve predominantly reactions on liquid cloud droplets, although chemistry on ice crystals and on solid aerosols is also of importance. In this section we focus mainly on the stratosphere, where the importance of heterogeneous processes has been dramatically illustrated by the annual appearance of the “ozone hole” during the Antarctic spring.25,26 A detailed review of laboratory studies of heterogeneous atmospheric chemistry has been published recently.27 III.A. Stratospheric Processes. Heterogeneous reactions on particle surfaces in polar stratospheric clouds (PSCs) convert chlorine reservoir molecules into easily photolyzed active chlorine species which lead to ozone destruction. In addition, heterogeneous reactions remove odd nitrogen species which would normally sequester active chlorine in stable reservoir molecules.
Environmental Chemistry
J. Phys. Chem., Vol. 100, No. 31, 1996 12893
The following reactions are considered to be key contributors to polar ozone depletion:
ClONO2 + H2O f HOCl + HNO3
(38)
ClONO2 + HCl f Cl2 + HNO3
(39)
HOCl + HCl f Cl2 + H2O
(40)
These are chlorine activation reactions; the most important one is reaction 39, which converts ClONO2 and HClsthe two most abundant stable chlorine reservoir speciessinto the much more easily photolyzed species Cl2. When the sunlight returns during the Antarctic spring, photolysis releases chlorine atoms which destroy ozone via catalytic cycles. In addition, reactions 38 and 39 generate nitric acid, most of which remains in condensed phase. This scavenging of odd nitrogen by PSCs reduces the ability of the ClONO2 reservoir to sequester active chlorine. While the Antarctic ozone hole is startling and obvious, more subtle changes are occurring in the stratospheric ozone layer on a global scale. Both ground-based and satellite measurements indicate that global ozone concentrations have decreased by about 5% per decade at mid-latitudes.26 Measurements of a variety of speciessincluding free radicalssin the lower stratosphere combined with laboratory investigations and model calculations show that the following heterogeneous reaction plays a key role in determining the chemical balance at midlatitudes:26
N2O5 + H2O f 2HNO3
(41)
The substrate for heterogeneous chemistry in the stratosphere is made of aerosols or cloud particles, which exist predominantly at altitudes between about 10 and 25 km. The “background” aerosol layer consists mainly of droplets of aqueous sulfuric acid with an average diameter of ∼0.1 µm and a number density of 1-10 cm-3, providing a surface area of roughly 1 µm2 cm-3.28 Major volcanic eruptions may increase this background area by 1 or 2 orders of magnitude. The composition of the particles depends on the temperature and the partial pressure of water vapor:29 at mid-latitudes and low latitudes it ranges between about 60 and 80 wt % sulfuric acid for typical stratospheric conditions (210-240 K and ∼5 parts per million by volume water vapor). The particles become less concentrated as the temperature decreases or the water vapor increases, and at high latitudes they form polar stratospheric clouds (PSCs); the aerosols rapidly swell at first, absorbing not only water vapor but also nitric acid vapor, reaching compositions such as 30 wt % H2SO4 and 30 wt % HNO3 at ∼195 K.30,31 These droplets are highly supercooled and may eventually freeze to form crystalline hydrates. The two most common PSCs are type I and type II; the former have particle diameters in the 0.5-2 µm range, exist at temperatures 2-5 K above the frost point of water, and are generally believed to consist of nitric acid trihydrate (NAT). However, some recent laboratory and field observations suggest that on many occasionssparticularly in the northern hemispheressuch particles are actually liquid.32,33 Type II PSCs consist of ice particles and condense at temperatures below the ice frost point, growing into significantly larger crystals (10 µm or more). Numerous laboratory experiments have shown that reactions 38-40 occur efficiently on water ice and on nitric acid trihydrate.34-39 These reactions have also been studied on sulfuric acid surfaces by several different groups;40-44 they are very slow on the relatively concentrated sulfuric acid solutions
which exist at stratospheric compositions and temperatures typical of mid-latitudes. In contrast, reaction 41 occurs very fast on such concentrated sulfuric acid solutions and hence affects the partitioning of NOx in the mid-latitude stratosphere. This in turn affects the partitioning of chlorine between active and inactive species through the formation of ClONO2, leading to ozone depletion at those latitudes, as mentioned above. The solubility of trace species like HNO3 and HCl in sulfuric acid solutions is an important issue. Reactions 38, 39, and 41 generate HNO3, and its solubility determines to what extent this product is dissolved or released into the gas phase. The measured solubility of HNO3 in concentrated sulfuric acid is small enough that at mid-latitudes most of the stratospheric nitric acid will be in the gas phase.30,45 The solubility of HCl in sulfuric acid determines the efficiency of reactions 40 and 41; it is several orders of magnitude smaller than HNO3 solubility.44,46 This implies that very little HCl is present in the midlatitude sulfate aerosol, thus explaining that reactions 40 and 41 are not important at those latitudes. However, the situation changes drastically at high latitudes: as the sulfuric acid droplets become dilute, the HCl solubility increases sharply, with a corresponding increase in the rates of reactions 39 and 40.44,47,48 The net result is that in the stratosphere, at temperatures below a threshold value of about 195 K, chlorine activation reactions become extremely efficient, taking place either on liquid or on solid aerosol particles. The next sections discuss laboratory methods for quantifying the rates of heterogeneous reactions of possible atmospheric importance and the mechanisms of such reactions. III.B. Definitions. If a gaseous species, C, is taken up in interaction with a simple uniform surface of area A, the rate of loss or uptake of that species per unit volume may be described in terms of a first-order surface loss rate constant, kSI, or in terms of the “uptake coefficient,” γ, which is the fractional number of collisions leading to loss; for reactive uptake γ is referred to as the “reaction probability”. Since the number of collisions, ω, of a gaseous species of concentration [C] and average velocity Vj with a surface of area A is given approximately by gas kinetic theory as
ω ) VjA[C]/4
(42)
the loss rate of C per unit volume is
-d[C]/dt ) γVjA[C]/4V
(43)
and the first-order loss rate constant is
γ A ksI ) Vj 4 V
(44)
Values of γ have been reported using a variety of experimental methods and have been interpreted in terms of physical models to yield reactivities of gaseous species with atmospheric particulate. III.C. Experimental Techniques. A variety of experimental techniques have been used and can be divided into two categories: Knudsen cells and flow tubes. Knudsen cells are low-pressure reactors in which the reactive surface is static. The time scale of Knudsen cell experiments ranges from a few seconds to hundreds of seconds. Flow tubes tend to operate on a faster time scale, determined by the residence time in the flow tube and the position of a movable injector. The reactive surface can be on the flow tube wall, either static or flowing, or can be in the form of droplets or aerosol particles. The techniques all involve the exposure of gaseous molecules of interest to surfaces that may interact by simple physical or
12894 J. Phys. Chem., Vol. 100, No. 31, 1996 by reactive uptake. As will become clear, the experimental techniques are capable of simulating only a partial set of atmospheric conditions; it is necessary to rely on some understanding of the physics and chemistry involved in order to extrapolate to the actual conditions that are applicable in the atmosphere. The uptake efficiency need not be constant with time, unless the surface is continuously being renewed. A heterogeneous interaction on a solid surface could result in the adsorbate or its reaction products accumulating on the surface. This could lower the number of available surface sites and thereby decrease the net uptake efficiency. On liquid surfaces, solubility limitations can lead to time-dependent uptake coefficients. As the surface layer of the liquid saturates with gas, reevaporation starts to compete with adsorption, and the net uptake efficiency decreases with time. III.C.1. Knudsen Cell Reactor. Heterogeneous reaction rates and solubilities of trace species can be measured using a Knudsen cell reactor.49 The experimental apparatus consists of two chambers separated by a valve. The material of interest is placed in the bottom chamber, which can be cooled to stratospheric temperatures. The gas phase species is introduced into the top chamber which has a small escape aperture leading to a differentially pumped mass spectrometer detection system. The concentration in the top chamber is kept low enough that molecular flow applies, so the residence time in the top chamber is determined by the size of the escape aperture. When the valve between the two chambers is opened, loss of the gas phase species to the surface competes with escape through the aperture and is observed as a decrease in the mass spectrometer signal. Loss of molecules to the surface can be due to uptake by the surface, reaction on the surface, and diffusion into the bulk. III.C.2. Wall-Coated Flow Tubes. As described above, flow tube techniques have been a standard technique in the measurement of homogeneous rate constants for radicalmolecule and radical-radical reactions for a long time. An extensive literature exists on this method, and this literature has always included discussion of wall loss of reactants species, since such processes compete with the homogeneous loss of interest. On the other hand, it is possible to determine uptake efficiencies by coating a flow tube reactor with a surface of interest. The experiments relevant to atmospheric heterogeneous chemistry are performed with both solid and liquid surfaces using some variant of the generic apparatus.15 The most common technique for the detection of gaseous species is mass spectrometry; some groups have used direct molecular beam sampling and electron impact ionization,35,37 while others have employed chemical ionization schemes.38,39 For certain species, particularly atoms and small radicals, optical methods have also been used. III.C.3. Droplet Train Flow Tube. An interesting experiment involves generating a train of liquid droplets in a flow tube and measuring the uptake of gaseous species in contact with these droplets using both mass spectrometric and optical techniques, as described in a separate article in this issue.50 These experiments are similar to the flow tube experiments described above, except that the area of the surface corresponds to the droplet area. This technique has been extended recently to the measurement of small (less than 0.001) values of the uptake coefficient, by bubbling gas through a liquid.51 III.C.4. Entrained Aerosol Flow Tube. For the study of reactions directly on aerosol particles, several workers have devised experiments that are yet another variant on the flow tube technique.41,52-54 The particles are entrained in the main
Molina et al. carrier gas and are treated similarly to a gaseous reactant in the conventional flow tube apparatus; however, an important difference is that the pressure needs to be significantly higher to prevent the particles from settling and collecting at the tube walls. In one such experiment the aerosol particles are made by atomizing a mist from a solution containing an inorganic salt and then drying the droplets in a diffusion dryer.41 This polydisperse aerosol is charged, and the charged particles are separated into a monodisperse fraction for introduction into the reaction tube, which operates under laminar flow conditions. Gaseous species may be detected in the usual ways, and postreaction analysis of the particles is also performed. A recent extension of this technique54 has been employed to study the reaction of N2O5 with sulfuric acid aerosols. Using this complex approach to produce monodisperse aerosols has led to the conclusion that the reaction probability is not particularly size dependent, indicating that it takes place at the surface. Another experiment utilizes the turbulent-flow approach, described above for gas phase studies; in this case it has been used to investigate the ClONO2 + HCl reaction directly on ice particles with diameters in the 1-5 µm range53 (see Figure 3). The results agree reasonably well with those obtained using the low pressure flow technique with an ice film deposited on the tube walls, indicating that no significant artifacts are introduced by working with such films. III.D. Mechanisms for Heterogeneous Chlorine Activation Reactions. As discussed above, laboratory measurements have shown that the chlorine activation reactions 39 and 40 are remarkably efficient, requiring only a few collisions of the reactant ClONO2 or HOCl molecule with ice exposed to HCl vapor. Clearly, the reaction proceeds through sequential rather than simultaneous collisions of the reactants with the surface; hence, at least one of the reactantssmost likely HClshas a high affinity for the condensed phase. Previous measurements had shown that HCl is only sparingly soluble in ice; more recent investigations have indicated, however, that monolayer amounts of HCl are taken up by the ice surface under temperature and HCl partial pressure conditions similar to those prevailing in the polar stratosphere.39,55 There are several papers in the literature proposing a physical adsorption mechanism for these heterogeneous reactions, assuming the presence of conventional active sites, Langmuirtype adsorption isotherms, etc.56 However, physical adsorption is expected to incorporate only negligible amounts of HCl on the ice surface,57,58 even allowing for a very strong hydrogen bond. These expectations led early on to the suggestion that reaction 39 should not occur on ice under stratospheric conditions of temperature and HCl partial pressure and that the results of laboratory measurements were dominated by spurious grain boundary effects.57,59 The high affinity of HCl for the ice surface can be explained by assuming that the HCl solvates, forming hydrochloric acid, as is the case with liquid water. This process is exothermic by ∼18 kcal/mol; in contrast, a hydrogen bond of HCl with ice is estimated to be only 5 kcal/mol.57 Solvation can occur because the surface layers of ice are disordered, with the water molecules having much larger mobility there than in the bulk crystal. This behavior leads to the formation of a quasi-liquid layer on the ice surface which can be experimentally observed at temperatures down to about 240 K.60 The presence of HCl strongly depresses the freezing point (a 9 m HCl solution freezes at ∼190 K), so that formation of a quasi-liquid HCl solution layer appears plausible under polar stratospheric conditions.58 Furthermore, the large reaction probabilities for the ClONO2 or HOCl plus
Environmental Chemistry HCl reactions can be understood with the quasi-liquid layer model: the mechanism for these reactions most likely involves “quasi-aqueous” ions. In contrast, adsorbed molecular HCl is expected to behave rather similarly to gaseous HCl and hence should react very slowly: in the gas phase, only upper limits to the HCl + ClONO2 rate have been determined.61 The interaction of HCl with ice has also been investigated using FTIR spectroscopy,62 as well as temperature-programmed desorption.63 Although some of these results were obtained at rather low temperatures in high-vacuum chambers, they suggest that HCl dissociates on the ice surface under stratospheric conditions. These experiments also show that at relatively high HCl partial pressures and low temperatures crystalline HCl hydrates are readily formed; in the stratosphere, however, the conditions fall outside the thermodynamic stability regime for any such hydrates.58 Laboratory measurements of the uptake of HCl by NAT have also been conducted.35,39 For NAT, however, an additional parameter that needs to be taken into account is its H2O vapor pressure: at any given temperature it can have a range of values, whereas for water-ice it has, of course, only one value. Observations show that when the H2O vapor pressure of NAT approaches that of ice its surface takes up as much HCl as ice, whereas the amount decreases by more than 2 orders of magnitude as the H2O vapor pressure drops. The reaction probabilities for reactions 39 and 40 behave accordingly: they have large values when the H2O vapor pressure of NAT is within a factor of ∼3 of that of ice.35,39 It appears that the uptake as well as the reaction probabilities is controlled by the availability of water at the surface. IV. Summary and Vision of the Future Laboratory studies, together with field observations and modeling calculations, have clearly demonstrated the importance of heterogeneous processes in the atmosphere. Much remains to be learned, however, before heterogeneous chemistry can be placed on a firm theoretical foundation analogous to that which exists for gas phase kinetics. Laboratory techniques have evolved significantly in the past few years and are now capable of yielding values of the relevant reaction probabilities or γ’s under a variety of conditions. Some questions remain, though, about the extent to which laboratory substrates simulate the surfaces of actual atmospheric particles; for example, the identity and surface morphology of the various nitric acid and sulfuric acid hydrates which make up solid polar stratospheric cloud particles are not yet well established. Such questions can only be resolved by a close interplay between field and laboratory studies. Furthermore, uptake coefficients and reaction probabilities measured in the laboratory need to be understood in terms of “elementary processes”, which represent the behavior of the system at the molecular level, so that they may be used reliably in models aimed at predicting the behavior of the atmosphere for a variety of future scenarios. Thus, the heterogeneous process may be thought of as consisting of the combination of several physical and chemical steps, such as accommodation from the gas phase to the surface, subsequent reevaporation, diffusion on the surface or into the bulk, and possible reaction. Ideally, each of these steps should be investigated for all the important heterogeneous atmospheric reactions by developing suitable experimental techniques and by conducting experiments designed to measure the relevant parameters that characterize each step. Such information would facilitate additional developments at the elementary-step level of the theoretical foundations of this field. As mentioned above, the theoretical framework underpinning gas phase reactions is rather well developed, and yet chemical
J. Phys. Chem., Vol. 100, No. 31, 1996 12895 kinetics as applied to atmospheric chemistry is at present very much an experimental science. As a consequence of the limitations of the available experimental techniques, the pressure and temperature dependencies of many complex mode reactions have not been investigated under conditions appropriate to the lower stratosphere. More strikingly, the branching ratios for the various channelssand even the identity of the productssare often in question; an example is the production of HCl in the reactions between ClO and OH or HO2. Also, the possibility of formation of new species with relatively weak bonds in radical recombination reactions needs to be further investigated. Such species would be thermally unstable at room temperature and hence might not have been previously characterized, and yet they might be important at polar stratospheric temperatures; an example of such species is chlorine peroxide (ClOOCl).1,64 Also, for processes such as the photooxidation of all but the simplest hydrocarbons the details of the reaction mechanisms operating in the atmosphere are at best only qualitatively understood. In most cases only the reaction rate for the first step is knownse.g., attack by the hydroxyl radicalsand the reaction rates and branching ratios for the subsequent steps involving the intermediates in the photooxidation process remain to be investigated. More powerful experimental techniques need to be developed to enable such measurements. References and Notes (1) DeMore, W. B.; Sander, S. P.; Golden, D. M.; Hampson, R. F.; Kurylo, M. J.; Howard, C. J.; Ravishankara, A. R.; Kolb, C. E.; Molina, M. J. Chemical Kinetics and Photochemical Data for Use in Stratospheric Modeling, EValuation No. 11, JPL Publication, 94-26; Jet Propulsion Laboratory: Pasadena, CA, 1994. (2) Atkinson, R.; Baulch, D. L.; Cox, R. A.; Hampson, R. F., Jr.; Kerr, J. A.; Troe, J. J. Phys. Chem. Ref. Data 1992, 21, 1125. (3) Benson, S. W. Thermochemical Kinetics, 2nd ed.; Wiley: New York, 1976. (4) Golden, D. M.; Manion, J. A. Applications of Chemical Kinetics. In AdVances in Chemical Kinetics and Dynamics; Barker, J. R., Ed.; JAI Press: London, 1992; Vol. 1, p 187. (5) Cohen, N.; Westberg, K. R. Int. J. Chem. Kinet. 1986, 18, 99. (6) Cohen, N.; Benson, S. W. J. Phys. Chem. 1987, 91, 162. (7) Golden D. M. Gas Phase Homogeneous Kinetics. In NATO ASI Series; Moortgat, G. K., Ed.; Springer-Verlag: Heidelberg, 1994; Vol. 121, pp 69-92. (8) Stewart, P. H.; Rothem, T.; Golden, D. M. Tabulation of Rate Constants for Combustion Modeling. Twenty-Second Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, PA, 1988; p 943. (9) Cohen, N. Aerospace Report No. ATR-94-(8446)-1, 1994. (10) Troe, J. J. Chem. Phys. 1977, 66, 4758. (11) Troe, J. J. Phys. Chem. 1979, 83, 114. (12) Troe, J. Ber. Bunsen-Ges. Phys. Chem. 1983, 87, 161. (13) Troe, J. Ber. Bunsen-Ges. Phys. Chem. 1983, 87, 169. (14) Robertshaw, J. S.; Smith, I. W. M. J. Phys. Chem. 1982, 86, 785. (15) Howard, C. J. J. Phys. Chem. 1979, 83, 3. (16) Moore, C. B.; Smith, I. J. Phys. Chem. 1996, 100, 12848. (17) Seeley, J. V.; Jayne, J. T.; Molina, M. J. Int. J. Chem. Kinet. 1993, 25, 571. (18) (a) Keyser, L. F. J. Phys. Chem. 1984, 88, 4750. (b) Abbatt, J. P. D.; Demerjian, K. L.; Anderson, J. G. J. Phys. Chem. 1990, 94, 4566. (19) Seeley, J. V.; Meads, R. F.; Elrod, M. J.; Molina, M. J. J. Phys. Chem. 1996, 100, 4026. (20) Elrod, M. J.; Meads, R. F.; Lipson, J. B.; Seeley, J. V.; Molina, M. J. J. Phys. Chem. 1996, 100, 5808. (21) Eisele, F. L.; Tanner, D. J. Geophys. Res. 1991, 96, 9295. (22) Schlager, H.; Arnold, F. Geophys. Res. Lett. 1990, 17, 433. (23) Mount, G. H.; Eisele, F. L. Science 1992, 256, 1187. (24) Wennberg, P. O.; et al. ReV. Sci. Instrum. 1994, 65, 1858. (25) Solomon, S. ReV. Geophys. 1988, 26, 131. (26) WMO Scientific Assessment of Ozone Depletion: 1994. Global Ozone Research and Monitoring Project Report No. 37; World Meteorological Organization: Washington, DC, 1994. (27) Kolb, C. E.; Worsnop, D. R.; Zahniser, M. S.; Davidovits, P.; Keyser, C. F.; Leu, M.-T.; Molina, M. J.; Hanson, D. R.; Ravishankara, A. R.; Williams, L. R.; Tolbert, M. A. Laboratory Studies of Atmospheric Heterogeneous Chemistry. In AdVanced Series in Physical Chemistry:
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