Appendix Free Radicals

Free radicals are characterized by an odd number of electrons, an unpaired electron in the outer valence shell. These species are exceptionally reactive, as they are always seeking to pair off their lone election. Free radicals play a central role in atmospheric chemistry in both the stratosphere and the troposphere. Important radicals include, for example, OH and H02 (both stratosphere and troposphere) and CI and CIO (stratosphere).

One can represent the bonding in molecules using the Lewis dot structure, in which lines represent a pair of bonded electrons and dots represent other electrons. The hydrogen and methane molecules are represented by

Oxygen and nitrogen molecules are

The triple bond between the two nitrogen atoms makes N2 an exceptionally stable molecule. The hydroxyl (OH) radical has the structure

NO and N02, important throughout the atmosphere, are actually radicals. Their electronic structures are


3.1a What are the lifetimes of CHF2C1 (HCFC-22) and CH2C1CF3 (HCFC-133a) by reaction with OH in the troposphere? Assume an average OH concentration of [OH] = 106 molecules cm and an average tropospheric temperature of T — 250 K. Reaction rate constants are (Sander et al. 2003):

&0H+CHF2C1 = 1-05 x 10"12 exp(— 1600/T) cm3 molecule"1 s"1 &OH+CH2CICF3 = 5.6 x 10"13 exp(-1100/r) cm3 molecule"1 s"1

3.2a The termolecular reaction

is quite important in atmospheric chemistry. Plot the reaction rate coefficient of this reaction as a function of pressure, specifically, [M], at 300 K. Consider the pressure range from 0.1 to lOatm. At 1 atm, where does the reaction rate constant lie in the transition between third- and second-order kinetics? The expression for the reaction rate coefficient is given in Table B.2.

3.3a Calculate the lifetime of O atoms against the reaction

at the Earth's surface at 298 K. The third-order rate constant for this reaction is 4.8 x 10 33 cm6 molecule 2s '. How does this lifetime change at 25 km altitude?

3.4B The reaction rate coefficient at 298 K of the reaction

is 2.8 x 10~16 cm3 molecule-1 s Estimate the rate coefficient with reference to collision theory and on this basis, determine the fraction of collisions that lead to reaction. Assume molecular radii for CHF3 and OH of 2.1 x 10_8cm and 2.0 x 10"8 cm, respectively.

3.5b The reaction of OH and CIO has two channels:

OH + CIO —y H02 + CI k = 7.4 x 10"12 exp (270/7) HC1 + 02 k = 3.2 x 10"13 exp (320/7)

Why is the A factor for the second channel so much lower than the first? Note that for both radicals OH and CIO, the unpaired election that reacts is on the O atom.

3.6a What is the first-order rate coefficient of N2Os reacting heterogeneously by

at 298 K in a population of particles, all of which have 0.2 pm diameter, of overall number concentration 1000 cm-3? The reaction efficiency y can be taken as 0.1.

Alkylperoxynitrates, R02N02, can be presumed to decompose according to the following mechanism:

Let us assume that a sample of R02N02 decomposes in a reactor and its decay is observed. We desire to estimate k\ from that rate of disappearance. To analyze the system we assume that both R02 and N02 are in pseudo-steady state and that [R02] — [N02]. Show that the observed first-order rate constant for R02N02 decay is related to the fundamental rate constants of the system by

Thus, given k0bS and values for k2 and ¿3, k\ can be determined. Consider the following reaction system:

The concentrations of B and C are zero at t = 0.

a. Derive analytical expressions for the exact dynamic behavior of this system over time. Show mathematically under what conditions the pseudo-steady-state approximation (PSSA) can be made for [B].

b. Use the PSSA to derive a simpler set of equations for the concentrations of A,

The most important oxidizing species for tropospheric compounds is the hydroxyl (OH) radical. A standard way of determining the OH rate constant of a compound is to measure its decay in a reactor in the presence of OH relative to the decay of a second compound, the OH rate constant of which is known. Consider two compounds A and B, A being the one for which the OH rate constant is to be determined and B the reference compound for which its OH rate constant is known. Show that the concentrations of A and B in such a reactor obey the following relation:


[A]0_*a, JB], where [A]0 and [B]0 are the initial concentrations, [A], and [B], are the concentrations at time f, and kA and ka are the OH rate constants. Thus, plotting yields a straight line with slope kA /k^. Knowing kg allows one to calculate kA from the slope.

3.10c Once released at the Earth's surface, a molecule diffuses upward through the troposphere and at any time may be removed by chemical reaction with other species, by absorption into particles and droplets, or by photodissociation. If the removal processes are rapid relative to the rate of diffusion, the species will not get mixed uniformly in the troposphere before it is removed. If, on the other hand, removal is slow relative to the rate of diffusion, the species may have a uniform tropospheric concentration.

Consider a species A whose removal from the atmosphere can be expressed as a first-order reaction, that is, RA = —kAcA. If the removal of A is the result of reaction with background species B, then kA can be a pseudo-first-order rate constant that includes the concentration of B in it. The intrinsic rate constant is given by the Arrhenius expression kA = A0exp(-Ea/RT).

Let us assume that the vertical concentration distribution of A can be represented generally as cA = ca0 exp(—HAz) by analogy to the exponential decrease of pressure with altitude, p = poexp(-Hz). Show that the tropospheric lifetime of A over the tropospheric height Hr is given by

The tropospheric temperature profile can be approximated by T(z) = To — olz, where 7o = 293 K and a = 5.5 K km-1. Show that the ratio of the lifetime of species A at altitude z to that at the Earth's surface is

%T _ [1 - cxp(—HAHT)] exp(-Ea/RT0) xo Ha exp[~Ea/R(T0 - t*z)] exp{-HAz)dz

Let us apply the foregoing theory to some trace atmospheric constituents whose principal removal reactions are with the OH radical. Consider CH3C1, CHF2C1, CH3SCH3, and H2S. For the purpose of the calculation assume that the OH radical concentration is 106 molecules cm"3, independent of height. Place the computed values of ij/io for these species on a plot of x^/x0 versus kA at surface conditions. Discuss.


Atkinson, R. et al. (2004) IUPAC Subcommittee on Gas Kinetic Data Evaluation for Atmospheric

Chemistry, Benson, S. W. (1976) Thermochemical Kinetics, 2nd ed., Wiley, New York. Laidler, K. J. (1987) Chemical Kinetics, 3rd ed., Harper & Row, London. Pilling, M. J., and Seakins, P. W. (1995) Reaction Kinetics, Oxford Univ. Press, Oxford, UK.

Sander, S. P., Friedl, R. R., Golden, D. M., Kurylo, M. J., Huie, R. E., Orkin, V. L., Moortgat, G. K., Ravishankara, A. R., Kolb, C. E., Molina, M. J., and Finlayson-Pitts, B. J. (2003) Chemical Kinetics and Photochemical Data for Use in Atmospheric Studies, Evaluation no. 14, Jet Propulsion Laboratory Publication 02-25 (available at

Troe, J. (1983) Specific rate constants k(E,J) for unimolecular bond fissions, J. Chem. Phys. 79, 6017-6029.

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  • Jens Mehler
    How does methane contribute to global warming a level chem free radicals?
    8 months ago

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