Chapter 2, Problem 30E

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: CH₄ (g) + C1₂ (g) → CH₃ C1 (g) + HC1 (g)
This reaction is very slow in the absence of light. However, C1₂ (g) can absorb light to form C1 atoms:

Reaction 2: C1₂ (g) + hv → 2C1 (g)
Once the C1 atoms are generated, they can catalyze the reaction of CH₄ and C1_2, according to the following proposed mechanism:

Reaction 3: CH₄ (g) + C1 (g) → CH₃ C1 (g) + HC1 (g)
Reaction 1: CH₃ (g) + C1₂ (g) → CH₃ C1 (g) + C1 (g)
The enthalpy changes and activation energies for these two reactions are tabulated as follows:

Reaction	ΔH0(KJ/mol)	Ea (KJ/mol)
3	+4	17
4	--109	4

By using the bond enthalpy for C1₂ (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, CH₄ (g) + C1₂ (g), should be placed on your diagram in part (b). Use this result to estimate the value of E_a for the reaction CH₄ (g) + C1₂ (g) → CH₃ C1 (g) + C1 (g). (d) The species C1 (g) and CH₃ (g) in reactions 3 and 4 are radicals, that is. Atoms or molecules with unpaired electrons. Draw a Lewis structure of CH₃, and verify that it is 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.