Atmospheric Photochemistry

According to Planck's law, the energy of one photon of frequency v is hv. In atmospheric photochemistry, the photon that is a reactant in a chemical reaction is written as hv, for example, for the photolysis of N02,

Photon energy can be expressed per mole of a substance by multiplying hv by Avogadro's number, 6.022 x 1023 molecules mol-1:

The energy4 associated with a particular wavelength X is as follows, with X in nm:

Typical ranges of wavelengths and energies in the portion of the electromagnetic spectrum of interest in atmospheric chemistry are

Typical Wavelength or Range Typical Range of Name of Wavelengths, nm Energies, kJmol"1

Visible

Red

700

170

Orange

620

190

Yellow

580

210

Green

530

230

Blue

470

250

Violet

420

280

Near ultraviolet

400-200

300-600

Vacuum ultraviolet

200-50

600-2400

4 A traditional unit used by chemists for expressing energies associated with molecules is kcalmol The conversion factor between kJmol-1 and kcalmol"1 is (kJmol-1) x 0.2390 = kcalmol-1

4 A traditional unit used by chemists for expressing energies associated with molecules is kcalmol The conversion factor between kJmol-1 and kcalmol"1 is (kJmol-1) x 0.2390 = kcalmol-1

Photon energies can be compared with bond energies of molecules. The energy contained in photons of wavelengths near the red end of the visible spectrum is comparable to the bond energies of rather loosely bound chemical species. For example, in the ozone molecule, the O—02 bond energy is about 105 kJ mol"1; in N02. the O—NO bond energy is about 300 kJ mol-1 (which corresponds to a wavelength of about 400 nm). The lowest energy photons that are capable of promoting chemical reaction lie in the visible region of the electromagnetic spectrum. Wavelengths at which chemical change can occur correspond roughly to the energies at which electronic transitions in molecules take place. Absorption of radiation can occur only if an upper energy level of the molccule exists that is separated from the lower level by an energy equal to that of the incident photon. Small molecules generally exhibit intense electronic absorption at wavelengths shorter than do larger molecules. For example, N2 and H2 absorb significantly at wavelengths less than JOOnm, while 02 absorbs strongly for X < 200nm, H20 for >v < 180nm, and C02 for?. < 165nm.

Photo dissocia lion of 02 Let us estimate the maximum wavelength of light at which the photodissociation of 02 into two ground-state oxygen atoms occurs;

The enthalpy change for this reaction is A H ~ 498.4 kJ mol 1, which is z in (4.35)-.

Thus, 02 cannot phoiodissociate at wavelengths longer than about 240 nm. The primary step of a photochemical reaction may be written

where A* is an electronically cxcited state of the molecule A. The cxcited molecule A' may subsequently partake in

Collisionai deactivation A* + M—> A + M Ionization A*—^ A+ + e

The quantum yield for a specific process involving A* is defined as the ratio of the number of molecules of A undergoing that process to the number of photons absorbed. Since the total number of A moleculcs formed equals the number of photons absorbed, the quantum yield c|>, for a specific process i, say, dissociation, is just the fraction of the A* molecules that participate in path i. The sum of the quantum yields for all possible processes must equal 1. The rate of formation of A* is equal to the rate of photon absorption and is written

where jA, having units s 1, is the first-order rate constant for photolysis or the so-called specific absorption rate; jA is normally taken to be independent of [A]. The rate of formation of B; in step 1 is

where (j^ is the quantum yield of step 1.

Photodissociation of a molecule can occur when the energy of the incoming photon exceeds the binding energy of the particular chemical bond. Thus the excited species A* can lie energetically above the dissociation threshold of the molecule. One or more of the products of photodissociation may themselves be electronically excited. Consider the photolysis of ozone:

Various combinations of electronic states are possible for the products O and 02 depending on the wavelength of incident radiation. The lowest energy pair of excited products is O('D) + 02(1 Ag), which form at an expected threshold wavelength of about 305 nm. As noted in Chapter 3, the singlet-D oxygen atom, O^D), is the most important electronically excited species in the atmosphere. (Henceforth we will have no need to distinguish electronically excited states of molecular oxygen; we will simply indicate all oxygen molecules emerging from photodissociation of 03 as 02.) Recall that the reaction of O('D) with water vapor is a source of OH radicals in the entire atmosphere, and 0(' D) reaction with N20 is the principal source of NO* in the stratosphere.

To calculate the rate of a photochemical reaction we need to know the number of photons absorbed per unit volume of air containing a given concentration [A] (molecules cm-3) of an absorbing molecule A.

The number of photons absorbed by a molecule A in a wavelength region X to X + dX is the product of its absorption cross section cta(^) (cm2 molecule"1), the spectral actinic flux I(X) (photons cm-2 s_1 nm-1), and the number concentration of A (molecules cm-3):

To calculate the rate of photolysis of A we need to multiply this expression by the quantum yield for photolysis, <|>a(^)- Thus the rate of photolysis in the wavelength region X to X + dX is aA(X)^A(X)I(X)dX[A]

The total photolysis rate of A is the integral of this expression over all possible wavelengths rXl / '

[A] molecules cm

where Xi and X2 are, respectively, the shortest and longest wavelengths at which absorption occurs. For the troposphere, for example, ~k\ = 290 nm.

The quantity in brackets has already been identified as the first-order photolysis rate constant:

/•À.2

7A= / cta {X,T)$A(X,T)I(X)dX

(4.39)

A,

The integral in (4.39) is often approximated for computational purposes by a summation over small wavelength intervals

i where the overbar denotes an average over a wavelength interval AX,- centered at A,. The width of the wavelength intervals AX, is usually dictated by the available resolution for the actinic flux I(X). A typical size of AX, is 5 nm from 290 nm to over 400 nm, and lOnm beyond 400 nm. Values of cr(X) and <j)(X) may not be available on precisely the same intervals as for /(X), so some interpolation may be necessary.

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