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JEE Main201815 Apr 2018Morning ShiftChemistryChemical KineticsActual

N ₂ O ₅ decomposes to NO ₂ and O ₂ and follows first order kinetics. After 50 minutes, the pressure inside the vessel increases from 50 ~mm ~Hg to 87.5 ~mm ~Hg . The pressure of the gaseous mixture after 100 minutes at constant temperature will be ______.

Options

  1. A136.25 ~mm ~Hg
  2. B106.25 ~mm ~Hg
  3. C175.0 ~mm~Hg
  4. D116.25 ~mm ~Hg

Correct answer

B. 106.25 ~mm ~Hg

Step-by-step solution

N ₂ O ₅ 2 NO ₂+ 1 2 O ₂ array llll At t =0 & 50 & 0 & 0 At t =50 ~min & 50- p ₁ & 2 p ₁ & p ₁ 2 array Total pressure at 50 minutes aligned &=50- p ₁+2 p ₁+ p ₁ 2 =87.5 &50+ 3 p ₁ 2 =87.5 & 3 p ₁ 2 =37.5 & p ₁= 37.5 2 3 =25 aligned At t =100 ~min 50- p ₂ 2 p ₂ p ₂ 2 50 minutes is half life period For 100 minutes i.e. for 2 half lives 50-p₂=12.5 p ₂=37.5 ~mm of Hg Total pressure at 100 minutes =50- p ₂+2 p ₂+ p ₂ 2 =50+ 3 p ₂ 2 =50+ 3 2 37.5=50+56.25=106.25 ~mm of Hg

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