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First order gas phase reaction A B + C p_i = initial pressure of gas A, p_t = total pressure of the reaction mixture at time t Expression of rate constant ( k ) is

Options

  1. A1 t p_i 2p_i - p_t
  2. B1 t 2p_i p_i - p_t
  3. C1 t p_i 3p_i - 2p_t
  4. D1 t 3p_i 4p_i - p_t

Correct answer

A. 1 t p_i 2p_i - p_t

Step-by-step solution

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

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