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For the following reaction of first-order N 2 O 5 ( g ) → 2 NO 2 ( g ) + 1 / 2 O 2 ( g ) , if the total pressure of the system after 20 minutes is 220   mm and after a very long time, total pressure is 400   mm , then t 1 / 2 for the reaction is

Options

  1. A66 . 6 20 log 8 3
  2. B2 . 303 20 log 4 3
  3. C2 . 303 20 log 20 3
  4. D6 log 4 / 3

Correct answer

D. 6 log 4 / 3

Step-by-step solution

After a very long time, the reaction can be assumed to be completed. Thus, for the given reaction, N 2 O 5 → 2 NO 2 + 1 2 O 2 t = 0 P 0 0 0 t = 20   mins P 0 - p 2 p p 2 t → ∞ 0 2 P 0 P 0 2 According to the question, after a very long time, 2 P 0 + P 0 2 = 400 ⇒ 5 2 P 0 = 400 ⇒ P 0 = 160   mm And, after 20 minutes, P 0 - p + 2 p + p 2 = 220   mm ⇒ 160 + 3 2 p = 220 ⇒ 3 2 p = 60 ⇒ p = 40   mm Now, we know that, k = 0 . 693 t 1 / 2 Applying the integ

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