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A gaseous first-order reaction A(g) B(g) + C(g) takes place in a closed vessel. The initial pressure of the system is P₀ . The total pressure of the system is 1.5 P₀ at time t₁ , and 1.875 P₀ at time t₂ . The ratio t₂ t₁ is:

Options

  1. A1.25
  2. B2
  3. C3
  4. D4

Correct answer

C. 3

Step-by-step solution

Let the initial pressure of A(g) be P₀ . The reaction is: A(g) B(g) + C(g) At t = 0 : P₀ , 0 , 0 At time t : P₀ - p , p , p The total pressure at time t is P_t = (P₀ - p) + p + p = P₀ + p . Therefore, the decrease in pressure of A is p = P_t - P₀ . The partial pressure of A remaining at time t is: P_A = P₀ - p = P₀ - (P_t - P₀) = 2P₀ - P_t At time t₁ , the total pressure is P_t = 1.5 P₀ . The partial pressure of A at t₁ is: P_A = 2P₀ - 1.5 P₀ = 0.5 P₀ = P₀ 2 Since the pressure of A has halved, t₁ corresponds to exa

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