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Order of Reaction

Consider this...

Question

Consider this reaction:
$2 N O_{2} (g) + O_{3} (g) ⟶ N_{2} O_{5} (g) + O_{2} (g)$
The reaction of nitrogen dioxide and ozone represented is first order in $N O_{2} (g)$ and in $O_{3} (g)$ . Which of these possible reaction mechanisms is consistent with the rate law?
Mechanism I: $N O_{2} (g) + O_{3} (g) ⟶ N O_{3} (g) + O_{2} (g)$ (slow)
$N O_{3} (g) + N O_{2} (g) ⟶ N_{2} O_{5} (g)$ (fast)
Mechanism II: $O_{3} (g) ⇌ O_{2} (g) + [O]$ (fast)
$N O_{2} (g) + [O] (g) ⟶ N O_{3} (g)$ (slow)
$N O_{3} (g) + N O_{2} (g) ⟶ N_{2} O_{5} (g)$ (fast)

I only

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II only

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Both I and II

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None of the above

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Solution

The correct option is B I only
Given that rate= $k [N O_{2}] [O_{3}]$
From mechanism I, rate= $k [N O_{2}] [O_{3}]$ .....[From slow reaction]
This is in accordance with the given rate.
From mechanism II, rate= $k [N O_{2}] [[O]]$ .....[From slow reaction]
Now, $k_{e q} = \frac{[O] . [O_{2}]}{[O_{3}]} => [O] = \frac{k_{e q} [O_{3}]}{[O_{2}]}$
rate $= k . k_{e q} \frac{[N O_{2}] [O_{3}]}{[O_{2}]}$
This is not consistent with the given rate.

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Similar questions

2 N O_{2 (g)} + O_{3 (g)} \to N_{2} O_{5 (g)} + O_{2 (g)}

N O_{2 (g)}

O_{3 (g)}

N O_{2} + O_{3} \to N O_{3} + O_{2}

N O_{3} + N O_{2} \to N_{2} O_{5}

O_{3} ⇌ O_{2} + O

N O_{2} + O \to N O_{3}

N O_{3} + N O_{2} \to N_{2} O_{5}

2 O_{3} (g) ⟶ 3 O_{2} (g)

O_{3} (g) k ⇌ O_{2} (g) + [O] (g)

O_{3} (g) + [O] k^{'} - -------- \to 2 O_{2} (g)

Δ H / k J

2 N_{2} (g) + 5 O_{2} (g) ⟶ 2 N_{2} O_{5} (s)

N_{2} (g) + 3 O_{2} (g) + H_{2} (g) ⟶ 2 H N O_{3} (a q) Δ H / k J = - 414.0

N_{2} O_{5} (s) + H_{2} O (I) ⟶ 2 H N O_{3} (a q) Δ H / k J = - 86.0

2 H_{2} (g) + O_{2} (g) ⟶ 2 H_{2} O (I) Δ H / k J = - 571.6

Δ H / k J

2 N_{2} (g) + 5 O_{2} (g) ⟶ 2 N_{2} O_{5} (s)

N_{2} (g) + 3 O_{2} (g) + H_{2} (g) ⟶ 2 H N O_{3} (a q); Δ H / k J = - 414.0

N_{2} O_{5} (s) + H_{2} O (l) ⟶ 2 H N O_{3} (a q); Δ H / k J = - 86.0

2 H_{2} (g) + O_{2} (g) ⟶ 2 H_{2} O (l); Δ H / k J = - 571.6

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