Differential rate Law?

automobile-produced smog is NO2, a brown gas that irritates mucous membranes. Consider the following reaction mechanism for the gas phase reaction of NO with O2 to produce NO2, with an indication of the speed of each step. The general form of the differential rate law is rate = k [NO]m[O2]n. 

step 1— NO + O2 → NO2 + O_____(slow);  

k

1

 

step 2— O2 ↔ 2 O _______________ (fast equilibrium);   

k

2

 (forward),  

k

2

 (reverse)

step 3— O + NO → NO2 __________(fast);  

k

3

  

Choose the answer below that provides the correct rate law expression, with the rate constant defined in terms of the rate constants of the mechanism steps.

   

k

1

 [NO]2   

   

k

2

 [NO]2 

   

k

1

k

2

 [NO]2 

   

k

1

 [NO] [O2]

   

k

2

 [NO] [O2]

   

k

1

k

2

 [NO] [O2]

   

k

1

k

2

 [NO]2 [O2]

   

\( k_1 k_{-2} \) [NO]2 [O2]

   

k

1

k

2

k

2

 [NO]2 [O2]

   

\( {{k_1 k_{-2}}\over{k_2}} \) [NO]2 [O2]

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