Answer: The rates of many atmospheric reactions are

Chapter , Problem 122IE

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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: \(\mathrm{CH}_{4}(g)+\mathrm{Cl}_{2}(g) \rightarrow \mathrm{CH}_{3} \mathrm{Cl}(g)+\mathrm{HCl}(g)\)

This reaction is very slow in the absence of light. However, \(\mathrm{Cl}_{2}(g)\) can absorb light to form \(\mathrm{Cl}\) atoms:

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

Once the \(\mathrm{Cl}\) atoms are generated, they can catalyze the reaction of \(\mathrm{CH}_{4} \text { and } \mathrm{Cl}_{2}\), according to the following proposed mechanism:

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

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

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, \(\mathrm{CH}_{4}(g)+\mathrm{Cl}_{2}(g)\), should be placed on your diagram in part (b). Use this result to estimate the value of \(\mathrm{E}_{a}\) for the reaction

\(\mathrm{CH}_{4}(g)+\mathrm{Cl}_{2}(g) \rightarrow \mathrm{CH}_{3}(g)+\mathrm{HCl}(g)+\mathrm{Cl}(g)\).

(d) The species \(\mathrm{Cl}(g) \text { and } \mathrm{CH}_{3}(g)\) 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 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.

Equation Transcription:

       

     

       

 

   

     

   

   

     

   

   

     

Text Transcription:

CH_4(g)+Cl2(g) \rightarrow  CH_3Cl(g)+HCl(g)      

Cl_2(g)    

Cl      

Cl_2(g)+hv \rightarrow  2Cl(g)  

Cl    

CH_4   and  Cl_2    

CH_4(g)+Cl(g) \rightarrow  CH_3(g)+HCl(g)    

CH_3(g)+Cl_2(g) \rightarrow  CH_3Cl(g)+Cl(g)

Cl_2  

CH_4(g)+Cl_2(g)      

E_a    

CH_4(g)+Cl_2(g) \rightarrow  CH_3(g)+HCl(g)+Cl(g)  

Cl(g) and CH_3(g)    

CH_3