Photolysis Frequency (s1)
Figure 2.1 Daytime average photolysis frequencies versus pressure for selected species. The rates are for typical mid-latitude conditions. The O, photolysis rate is the sum of the rates of the O('P) and O('D) product channels. The rates are calculated by the photolysis routine from the Goddard three-dimensional Chemical Transport Model .
2.1.2 Second-order reactions
A second-order reaction is one with two reactants, such as the reaction between chlorine monoxide (CIO) and atomic oxygen (O):
and whose rate is the product of a rate constant and the concentrations of the reactants:
Second-order reaction rate constants have units of cubic centimeters per molecule per second (cm* molecule 1 s ' ), and are generally functions of temperature. Unlike first-order reactions, the abundances of the reactants in Equation (2.8) must be expressed in number density units, [f there are no other sources or sinks of the reactants or products, then by the conservation of mass,
Temperature dependence of reactions Svante Arrhenius first suggested in 1887 that second-order rate constants vary exponentially with inverse temperature. The functional form of a second-order rate constant is often written
The pre-exponential factor A, which has the same units as the rate constant, is related to the fraction of collisions between the reactants that results in a successful reaction. Reactions in which essentially every collision results in a reaction have A factors of -10 10 cm' molecule 1 s Reactions in which the reactants must have very specific orientations only occur for a small fraction of the collisions, and can have A factors as small as 10 17 cm1 molecule 1 s
In addition to this constraint on orientation, there is also in general a repulsive force between the reactants that must be overcome for a reaction to take place. This is expressed in Equation (2.10) as Ea, the "activation energy" of the reaction. The term exp(-7i.,/(/? 7')), where R is the gas constant and 7" is the temperature (K), is proportional to the number of molecules whose average translational kinetic energy exceeds the threshold E.r It is these molecules that are able to surmount the repulsive force and react.
E, can be as large as 20 kJ mol '. For these reactions, the rate constant will increase by -50-70% for a 10 K increase in stratospheric temperature. Other reactions, especially those involving a molecule with an unpaired electron (known as a radical), have an £a of zero. Some second-order reactions even have negative activation energies or show a dependence on pressure in addition to temperature. These reactions are more complicated than simple two-body bimolecular reactions, and involve the formation of reaction intermediates prior to formation of the products.
The NASA Panel for Data Evaluation [51 publishes tables of A factors and E JR for virtually every second-order reaction of stratospheric interest. This indispensable resource is widely used by stratospheric modelers.
dt dl dt dt
2.1.3 Association reactions
An association or three-body reaction is one in which two reactants combine to form a single product molecule. An example of such a reaction is the formation of chlorine nitrate (CIONO,)
These reactions typically take place in two steps. First, the reactants collide to form an excited intermediate molecule:
where the asterisk signifies an excited state. The CIONO,* molecule contains too much internal energy for it to exist for more than a few vibrational periods, and two things can subsequently happen to it. First, the CIONO,* molecule can collide with a third body, denoted M, but generally N, or O,, which carries away some of the internal energy of the excited molecule, thereby stabilizing it:
Alternatively, it can decompose back into CIO and NO ,, in which case there is no net reaction:
If the pressure is sufficiently high, in other words [M| is large, then every excited intermediate that is formed will collide with a third-body M, and form the stable molecule. In this case, the formation rate of CIONO, is equal to the rate of formation of the excited intermediate CIONO,*. This is known as the "high-pressure limit" of the reaction. At low pressures, [Mj is small and the excited intermediate CIONO,* usually decomposes back to CIO and NO,. In this case, the formation rate of CIONO, is set by the collision rate between CIONO,* and M. This is known as the "low-pressure limit". At pressures between these limits the rate of the reaction is set by a combination of the two processes.
The rate of an association reaction is often written as rate = ¿*[X]| YJ (2.15)
where k* is the effective second-order rate constant (with units of cm ' molecule 1 s ' ) for the three-body reaction, and [X] and [Y| are the abundances of the reactants in molecules per cubic centimeter. It must be remembered that for these reactions, k*
depends not only on temperature but also on pressure. The NASA Panel for Data Evaluation publishes tables of kinetic data and a formula for calculating the effective second-order rate constant k* of a reaction given the temperature and pressure (see DeMore et al. , pp. 8-11).
Thermal decomposition Thermal decomposition occurs when a molecule splits into fragments following nonreactive collisions with other molecules—usually N2 or 02. An example is the thermal decomposition of the chlorine monoxide dimer (ClOOCI):
This reaction is the opposite of a three-body association reaction. First, collisions between ClOOCI and M transfer energy to ClOOCI and create the excited intermediate ClOOCI*. This excited intermediate can either collide with another M and have some internal energy taken out, leading to the restabilization of the intermediate, or the excited intermediate can fall apart into fragments:
At stratospheric temperatures, this type of reaction breaks bonds in only the most weakly bound molecules (such its ClOOCI).
The rate of reaction (2.16) is generally written as a first-order process:
where kx is the thermal decomposition rate constant with units of inverse seconds. In practice, k' must be calculated from the rate of the association reaction and the equilibrium constant between the reactant and products (see DeMore et al. , Table 3).
Heterogeneous reactions Reactions can also occur on the surfaces of liquid and solid particles. For example, an important heterogeneous reaction in the stratosphere is
Much like association reactions, this simple-looking reaction actually represents a far more complicated process 129-32]. Typically, one of the reactants is first absorbed onto/into the particle (in this case, HC1). Then, reactions occur as the other reactant (in this case, ClONO,) collides with the particle. Because of this, heterogeneous reactions are usually written as a first-order loss process for the constituent that reacts on collision:
where is a first-order rate constant with units of inverse seconds. Using simple collision theory, we can write kH as k" (2.21)
V is the thermal velocity of the molecule, in this case C10N02. For a typical molecule at stratospheric temperatures, V is several hundred meters per second. A is the particle surface area per unit volume, also known as the surface area density (abbreviated SAD), y, called the reactive uptake coefficient, is the fraction of collisions between the reactant and the particle that result in a reaction, /is therefore dimen-sionless and always between 0 and 1. In general, vis a function of temperature, pressure, particle radius, water vapor abundance, and the gas phase abundance of the absorbed constituent (in this example, HQ) [29,33].
There are two general types of particles in the stratosphere: sulfate aerosol and polar stratospheric clouds (PSCs). Sulfate aerosol particles are the more common. First characterized by Junge et al. , these particles are liquid, and their composition varies with temperature (Figure 2.2). Above -215 K, H2S04 makes up 70-80% of the mass of the aerosol, with water making up virtually all of the remainder. As the particles cool, they absorb water vapor, decreasing the relative abundance of H,SO,. At temperatures below -200 K, the particles absorb significant amounts of UNO, [35,36], The majority of the aerosol particles in the stratosphere are found in the lower stratosphere in the so-called "Junge layer".
Aerosol particles are initially formed ("nucleated") in rising tropical air masses . This produces large numbers (~ 1 (P particles cm ') of extremely small (a few angstroms in radius) H2S04/H20 particles [39|. Then, on a time-scale of a day or so, these particles coagulate, resulting in the formation of fewer (10"-UK particles cm '), larger particles. A binary phase droplet, such as these H2S04/H20 particles, can, in general, achieve equilibrium with the vapor phase of one of its components, but not both. Because of the much greater abundance of H>0 compared to H2S04 in the stratosphere, these H,S04/H20 particles are in equilibrium with respect to water, but are subsaturated with respect to H2S04. H2S04 produced in the stratosphere from the oxidation of sulfur-bearing species is therefore rapidly absorbed by the particles. This causes the composition of the aerosol particles to change, and to regain equilibrium the particle absorbs water. Through this process, and coagulation, the
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