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To explain:
Which of the following mechanisms is for thermal decomposition of NO2 and which is for the photochemical decomposition of NO2?
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Answer to Problem 13.109QA
Solution:
Mechanism a is the photochemical decomposition of NO, while mechanism b and c are thermal decomposition of NO2.
Explanation of Solution
1) Concept:
We are calculating the rate law for slow step for each given mechanism. If it is the same as the given rate of thermal decomposition of NO2, then that mechanism is for thermal decomposition of NO2. If it is same as the given rate of photochemical decomposition of NO2, then that mechanism is for photochemical decomposition of NO2.
2) Given:
thermal decomposition of NO2, Rate=k[NO2]2
photochemical decomposition of NO2, Rate=k[NO2]
a. NO2(g)→NO(g)+O(g)…slow
O(g)+NO2(g)→NO(g)+O2(g)…fast
b.NO2(g)+NO2(g)→N2O4(g)…fast
N2O4(g)→NO(g)+NO3(g)…slow
NO3(g)→ NO(g)+O2(g)…fast
c.NO2(g)+NO2(g)→NO(g)+NO3(g)…slow
NO3(g)→ NO(g)+O2(g)…fast
3. Calculations:
Rate law for mechanism a:
Rate1=ka[NO2]
Here Ka is the rate constant for slow step of reaction a. This rate is the same as the given rate of photochemical decomposition of NO2. Therefore, mechanism a is the mechanism of photochemical decomposition of NO2.
Rate law for mechanism b:
Rate2=kb[N2O4]
Here, N2O4 is the intermediate formed in the step (1) (fast), so we need to write the rate law for both forward and backward reaction of step (1):
Rate1=k1[NO2][NO2]=k-1[N2O4]
Here k1 is the rate constant of forward reaction, and k-1 is the rate constant of backward reaction.
Rearranging above rate equation for [N2O4], we get
[N2O4]=k1[NO2][NO2]k-1=k1k-1[NO2]2
Plugging the value of [N2O4] in Rate2 equation, we get
Rate=kb.k1k-1[NO2]2
Rate=k[NO2]2
where, k=kb.k1k-1
This rate of mechanism b is the same as the given rate of thermal decomposition of NO2. Therefore, mechanism c is the mechanism of thermal decomposition of NO2.
Rate law for mechanism c:
Rate=kc[NO2][NO2]
Rate=kc[NO2]2
Here Kc is the rate constant for slow step of mechanism c. This rate is the same as the given rate of thermal decomposition of NO2. Therefore, mechanism c is the mechanism of thermal decomposition of NO2.
Conclusion:
Mechanism a is the photochemical decomposition of NO2, while mechanism b and c are thermal decomposition of NO2.
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Chapter 13 Solutions
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