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COMEDK2024ChemistryChemical KineticsActual

Given below a first order reaction in the gas phase A ( g ) B ( g )+ C ( g ) If the initial pressure of the system is P _ i and the total pressure at t seconds is P _ t , the rate constant k for the reaction is:

Options

  1. Ak = 2.303 t P _ i (2 P _ i + x )
  2. Bk = 2.303 t P _ i P _ t
  3. Ck = 2.303 t P _ i ( P _ i + x )
  4. Dk = 2.303 t P _ i (2 P _ i - P _ t )

Correct answer

D. k = 2.303 t P _ i (2 P _ i - P _ t )

Step-by-step solution

The reaction is A ( g ) B ( g ) + C ( g ) . At t = 0 , the 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 . Then the pressures of B and C are x each. The pressure of A becomes P_i - x . The total pressure P_t at time t is the sum of the partial pressures of all gases: P_t = (P_i - x) + x + x = P_i + x From this, 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 c

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