## K

2 h Pa

3. Mixing ratio.

(a) The VMR of O, in the upper stratosphere (3 hPa, 240 K) is 2 ppmv. What is the number density of O,?

(b) If a parcel of this air is moved to the lower stratosphere (50 hPa, 210 K), what is the VMR and number density of O, at the new location of the parcel? Assume that there are no chemical changes in the parcel.

4. VMR and MMR. There are really two types of mixing ratio: volume mixing ratio

(VMR) and mass mixing ratio (MMR). As described above, the VMR of constituent

X is the ratio of number density of X to the ambient number density: [X]/[M]. MMR

is, analogously, the ratio of the mass density of X to the ambient mass density: Px/Pm- Write an expression to convert from VMR to MMR for 110.

5. Pass the sunscreen! Assume column O, decreases by 50%. How does the number of 250 and 300 nm photons reaching the surface change? If you were a sunscreen manufacturer, would you be more concerned with changes in surface radiation at 250 or 300 nm? Assume that the absorption cross-section of O, is 1.15 x 10 17 cm2 and 3.4 x 10 cm3 at 250 and 300 nm, respectively, and column O, is 350 DU before it is halved.

Chapter 2 Fundamentals of Stratospheric Chemistry

Before we discuss the stratosphere in detail, we first review some of the fundamental concepts of atmospheric chemistry and stratospheric science.

### 2.1 Kinetics

Thermodynamics reveals whether a process will occur spontaneously or not. For example, at a pressure of 1 atrn, ice is stable below 273.15 K. At higher temperatures, thermodynamics reveals that ice will spontaneously convert to water. Common experience tells us that the time for an ice cube to melt at room temperature is a few minutes. Surprisingly, thermodynamics also tells us that the diamond form of carbon is unstable under typical atmospheric conditions and will spontaneously convert to graphite. Whoever said that "diamonds are forever" apparently did not look up the free energy of the various forms of carbon. In defense of the advertising executive who came up with the slogan, however, our daily experience tells us that the conversion from diamond into graphite is slow, occurring over time-scales much longer than advertising executives' careers. In other words, thermodynamics provides information about the eventual outcome of a process. But it provides no information about the rate of the process. For studies of the chemistry of the atmosphere, however, a knowledge of the rate of a process is crucial. In this section, we discuss what determines the rates of chemical reactions, a field referred to as chemical kinetics.

### 2.1.1 First-order reactions

A first-order reaction is one in which a reactant spontaneously transforms itself into one or more products. Examples of this include radioactive decay and isomerization. The rate of a first-order reaction is equal to the product of a rate constant and the abundance of the reactant X:

where k is the first-order rate constant for the reaction, and it has units of inverse seconds (s 1). [X], the abundance of X, can be expressed in either number density or VMR units. If [X J is expressed in number density (molecules cm '), then the rate has units of molecules per cubic centimeter per second (molecules cm ' s '). If f X] is expressed in volume mixing ratios (VMRs), then the rate is in VMR per second (VMR s"1).

If there are no other sources or sinks of X, then the time derivative of [X1 is equal to the instantaneous rate of the reaction:

The rate of a reaction is always a positive number, so the minus sign indicates that X is being consumed.

Rearranging and integrating Equation (2.2) with the initial condition that the concentration of X at t = 0 is [X]„ yields an expression for [X| as a function of time t:

Note that over any time interval 1/&, |X] is reduced by a factor of \jc (1/2.72 ~ 0.368). As a result, l/k is often referred to as the c-folding time or lifetime of X. The concept of lifetime will be discussed at length later in this chapter.

Photolysis Sunlight is composed of ultraviolet, visible, and near-infrared radiation similar to that emitted by a black body at -5700 K (see Goody and Yung , Appendix 9). These solar photons cany energies of 1 to a few electronvolts, enough to break bonds in many molecules. As a result, the absorption of solar photons by molecules in the atmosphere often results in the molecules being split into fragments. This process, known as photolysis, is an important process in the stratosphere. A typical photolytic reaction is the photolysis of nitric acid (HNO,):

where hv represents the energy of a photon.

Photolysis is usually treated as a first-order process, so that the rate at which a molecule is split into fragments is the product of a photolysis frequency (typically designated ./) and the concentration of the molecule. The rate of Equation (2.4) is:

./. of course, has units of inverse seconds.

The photolysis frequency./ at a given point in space and time is the integral of the product of the photon flux ¿/(A), the absorption cross-section a{X), and the quantum yield fi(A). The integral extends over the portion of the solar spectrum whose photons have sufficient energy to dissociate the molecule:

As indicated, all of the terms in the integral are generally functions of wavelength. The photon flux q(X) is also a function of many other variables, including the total amount of ozone located above the point, the albedo (reflectivity) of the surface, and solar zenith angle (SZA). The absorption cross-section a(A) will often vary with temperature. The quantum yield ft A), the fraction of photons absorbed that leads to fragmentation of the molecule, can also be a function of temperature. In most cases the quantum yield is nearly 1, but it is often less at wavelengths near the energetic cut-off for dissociation of the molecule. For more discussion of photolysis, see Brasseur and Solomon [27|, Chapter 4.

As mentioned above, the photolysis frequency is generally a strong function of the SZA. The SZA is the angle between the Sun and the point located directly over the observer's head (the zenith). Thus, an SZA of 0° means that the Sun is directly overhead, while an SZA of 90° means that the Sun is near the horizon. SZAs greater than -90° mean that the Sun is below the horizon, i.e. it's night-time. At night, photolysis does not occur. It should be noted that for an observer in the stratosphere the sun does not set exactly at 90° owing to the observer's great height above the surface. Instead, the Sun can still be seen several degrees past 90°, with the exact SZA of sunset depending on the observer's altitude.

Figure 2.1 shows altitude profiles of the daytime-averaged photolysis frequencies of several important trace constituents in the stratosphere. The change in the photolysis frequency with altitude provides information about the wavelength dependence of the absorption cross-section of the molecule. For example, NO, absorbs visible radiation (wavelengths between 400 and 900 nm) strongly. Because the atmosphere is essentially transparent to visible radiation, the radiation field is fairly constant with height, and the photolysis frequency for this constituent shows little altitude dependence. For species that absorb shorter-wavelength ultraviolet radiation, on the other hand, the photolysis frequency shows significant dependence on altitude. This arises because O, efficiently absorbs ultraviolet radiation, so there is more ultraviolet radiation above the ozone layer, leading to higher photolysis rates there than at lower altitudes. The photolysis frequency for UNO,, for example, decreases by more than 2 orders of magnitude as one descends from the upper to the lower stratosphere.

Note that the Earth, clouds, and atmosphere radiate similar to a black body at -200-300 K. These photons of terrestrial origin have wavelengths greater than ~4 pm and generally do not have enough energy to break bonds in molecules. The absorption of these photons can, however, excite rotational and vibrational modes in a molecule, and the interaction of these photons with the atmosphere has important consequences for the Earth's climate. 