Solved: The rates of many atmospheric reactions are accelerated by the absorption of

Chapter 20, Problem 14.124

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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 Cl atoms:

Reaction 2: \(\mathrm{Cl}_{2}(\mathrm{g})+h v \longrightarrow 2 \mathrm{Cl}(\mathrm{g})\)

Once the Cl atoms are generated, they can catalyze the reaction of CH4 and Cl2, according to the following proposed mechanism:

Reaction 3: \(\mathrm{CH}_{4}(\mathrm{g})+\mathrm{Cl}(\mathrm{g}) \longrightarrow \mathrm{CH}_{3}(\mathrm{g})+\mathrm{HCl}(g)\)

Reaction 4: \(\mathrm{CH}_{3}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{g}) \longrightarrow \mathrm{CH}_{3} \mathrm{Cl}(\mathrm{g})+\mathrm{Cl}(\mathrm{g})\)

The enthalpy changes and activation energies for these two reactions are tabulated as follows:

(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, \(\mathrm{CH}_{4}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g})\), should be placed on your diagram in part (b). Use this result to estimate the value of \(E_{a}\) for the reaction \(\mathrm{CH}_{4}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) \longrightarrow \mathrm{CH}_{3}(\mathrm{g})+\mathrm{HCl}(g)+\mathrm{Cl}(g)\). (d) The species Cl(g) and CH3(g) in reactions 3 and 4 are radicals, that is, atoms or molecules with unpaired electrons. Draw a Lewis structure of \(\mathrm{CH}_{3}(\mathrm{g})\), and verify that it is a radical. (e) The sequence of reactions 3 and 4 comprises a radical chain mechanism. Why do you think this is called a “chain reaction”? Propose a reaction that will terminate the chain reaction.