The rates of many atmospheric reactions are accelerated by the absorption of
light by one of the reactants. For example, consider the reaction between
methane and chlorine to produce methyl chloride and hydrogen chloride:
Reaction 1: \(\mathrm{CH}_{4}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g})
\longrightarrow \mathrm{CH}_{3}
\mathrm{Cl}(\mathrm{g})+\mathrm{HCl}(\mathrm{g})\)
This reaction is very slow in the absence of light. However,
\(\mathrm{Cl}_{2}(g)\) can absorb light to form \(\mathrm{Cl}\) atoms:
$$
\text { Reaction 2: } \mathrm{Cl}_{2}(g)+h v \longrightarrow 2 \mathrm{Cl}(g)
$$
Once the \(\mathrm{Cl}\) atoms are generated, they can catalyze the reaction of
\(\mathrm{CH}_{4}\) and \(\mathrm{Cl}_{2}\), according to the following proposed
mechanism:
Reaction 3: \(\mathrm{CH}_{4}(\mathrm{~g})+\mathrm{Cl}(\mathrm{g})
\longrightarrow \mathrm{CH}_{3}(\mathrm{~g})+\mathrm{HCl}(\mathrm{g})\)
Reaction 4: \(\mathrm{CH}_{3}(\mathrm{~g})+\mathrm{Cl}_{2}(g) \longrightarrow
\mathrm{CH}_{3} \mathrm{Cl}(g)+\mathrm{Cl}(g)\)
The enthalpy changes and activation energies for these two reactions are
tabulated as follows:
$$
\begin{array}{lll}
\hline \text { Reaction } & \Delta H_{\mathrm{ran}}^{\circ}(\mathrm{kJ} /
\mathrm{mol}) & E_{a}(\mathrm{~kJ} / \mathrm{mol}) \\
\hline 3 & +4 & 17 \\
4 & -109 & 4
\end{array}
$$
(a) By using the bond enthalpy for \(\mathrm{Cl}_{2}\) (Table \(8.4\) ), determine
the longest wavelength of light that is energetic enough to cause reaction 2
to occur. In which portion of the electromagnetic spectrum is this light
found? (b) By using the data tabulated here, sketch a quantitative energy
profile for the catalyzed reaction represented by reactions 3 and 4. (c) By
using bond enthalpies, estimate where the reactants,
\(\mathrm{CH}_{4}(g)+\mathrm{Cl}_{2}(g)\), should be placed on your diagram in
part (b). Use this result to estimate the value of \(E_{a}\) for the reaction
\(\mathrm{CH}_{4}(g)+\mathrm{Cl}_{2}(g) \longrightarrow\)
\(\mathrm{CH}_{3}(g)+\mathrm{HCl}(g)+\mathrm{Cl}(g) .\) (d) The species
\(\mathrm{Cl}(g)\) and
\(\mathrm{CH}_{3}(\mathrm{~g})\) in reactions 3 and 4 are radicals, that is,
atoms or molecules with unpaired electrons. Draw a Lewis structure of
\(\mathrm{CH}_{3}\), and verify that is a radical. (e) The sequence of reactions
3 and 4 comprise a radical chain mechanism. Why do you think this is called a
"chain reaction"? Propose a reaction that will terminate the chain reaction.
