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JEE MainChemistryChemical Kinetics

For a first-order gas-phase reaction A(g) B(g) + 2C(g) , the total pressure of the reaction mixture at time t is P_t . After a very long time ( t ), the reaction goes to completion and the total pressure becomes P_ . The expression for the rate constant k is:

Options

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

Correct answer

D. 1 t ( 2P_ 3(P_ - P_t) )

Step-by-step solution

The given reaction is A(g) B(g) + 2C(g) . Let the initial pressure of A at t = 0 be P_i . At t = 0 : P_A = P_i , P_B = 0 , P_C = 0 . At time t , let the decrease in pressure of A be x . P_A = P_i - x P_B = x P_C = 2x Total pressure P_t = (P_i - x) + x + 2x = P_i + 2x Thus, x = P_t - P_i 2 At t , the reaction is complete, so all of A is consumed. P_A = 0 P_B = P_i P_C = 2P_i Total pressure P_ = 0 + P_i + 2P_i = 3P_i Therefore, the initial pressure is P_i = P_ 3 . The partial pressure of A at time t is: P_A = P_i - x

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