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JEE MainChemistryChemical Kinetics

A first-order gas-phase reaction A ( g ) 2 B ( g ) + C ( g ) is carried out in a closed vessel, starting with pure A . Let the total pressure of the system at time t be P _ t and the total pressure at infinite time be P _ . Which of the following expressions is correct for the rate constant k ?

Options

  1. Ak = 1 t 2 P _ 3 P _ - P _ t
  2. Bk = 1 t P _ 2( P _ - P _ t )
  3. Ck = 1 t 2 P _ 3( P _ - P _ t )
  4. Dk = 1 t P _ 2 P _ -3 P _ t

Correct answer

C. k = 1 t 2 P _ 3( P _ - P _ t )

Step-by-step solution

Let the initial pressure of A be P ₀ . array lccc & A ( g ) & 2 B ( g ) + & C ( g ) t =0 & P ₀ & 0 & 0 t = t & P ₀- x & 2 x & x t = & 0 & 2 P ₀ & P ₀ array At infinite time, the total pressure is: P _ = 2 P ₀ + P ₀ = 3 P ₀ P ₀ = P _ 3 At time t , the total pressure is: P _ t = ( P ₀ - x ) + 2 x + x = P ₀ + 2 x x = P _ t - P ₀ 2 The partial pressure of reactant A at time t is: P _ A = P ₀ - x = P ₀ - P _ t - P ₀ 2 = 3 P ₀ - P _ t 2 Substitute P ₀ = P _ 3 into the expression for P _ A : P _ A = 3 ( P _ 3 ) - P _ t 2

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