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JEE MainChemistryChemical Kinetics

A first-order gas-phase reaction follows the equation A(g) 2B(g) + C(g) . If the initial pressure of the system is P₀ and the total pressure of the reaction mixture at time t is P_t , the correct expression for the rate constant k is:

Options

  1. A1 t ( P₀ 2P₀ - P_t )
  2. B1 t ( 3P₀ 4P₀ - P_t )
  3. C1 t ( 2P₀ 3P₀ - P_t )
  4. D1 t ( 3P₀ - P_t 2P₀ )

Correct answer

C. 1 t ( 2P₀ 3P₀ - P_t )

Step-by-step solution

The given reaction is A(g) 2B(g) + C(g) . At t = 0 , the partial pressure of A is P₀ , and the pressures of B and C are 0 . At time t , let the decrease in the pressure of A be x . Pressure of A = P₀ - x Pressure of B = 2x Pressure of C = x The total pressure at time t is: P_t = (P₀ - x) + 2x + x = P₀ + 2x From this, we get: x = P_t - P₀ 2 The partial pressure of A at time t is: P_A = P₀ - x = P₀ - P_t - P₀ 2 = 3P₀ - P_t 2 For a first-order reaction, the rate constant k is given by: k = 1 t ( P₀ P_A ) Substituting

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