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JEE MainChemistryChemical Kinetics

A first-order gas-phase reaction A ( g ) B ( g ) + C ( g ) is carried out in a closed vessel, starting with pure A . The half-life of the reaction is t _ 1/2 . If the total pressure of the system at infinite time is P _ , what will be the total pressure of the system at time t = 2 t _ 1/2 ?

Options

  1. A5 4 P _
  2. B1 8 P _
  3. C7 4 P _
  4. D7 8 P _

Correct answer

D. 7 8 P _

Step-by-step solution

Let the initial pressure of A be P ₀ . array lccc & A ( g ) & B ( g ) + & C ( g ) t =0 & P ₀ & 0 & 0 t = & 0 & P ₀ & P ₀ array At infinite time, the total pressure is: P _ = P ₀ + P ₀ = 2 P ₀ P ₀ = P _ 2 At time t = 2 t _ 1/2 , two half-lives have passed. The remaining pressure of A will be: P _ A = P ₀ 2² = P ₀ 4 The decrease in pressure of A is x = P ₀ - P ₀ 4 = 3 P ₀ 4 . At this time, the pressures of the gases are: P _ A = P ₀ - x = P ₀ 4 P _ B = x = 3 P ₀ 4 P _ C = x = 3 P ₀ 4 The total pressure at t = 2 t _ 1

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