A first-order gas-phase reaction A ( g ) 2 B ( g ) + C ( g ) is carried out in a rigid vessel starting with pure gas A . The total pressure of the system after a very long time ( t ) is 600 mm Hg . If the half-life of the reaction is 15 minutes , the time required for the total pressure of the system to reach 500 mm Hg is:

Step-by-step solution

Let the initial pressure of pure gas A be P₀ . The reaction is A ( g ) 2 B ( g ) + C ( g ) . At t = 0 , the pressure is P₀ . At t , all of A has reacted. 1 mole of A produces 3 moles of gaseous products. Total pressure at infinite time, P_ = 3P₀ . Given P_ = 600 mm Hg , so 3P₀ = 600 P₀ = 200 mm Hg . Let x be the decrease in pressure of A at time t . Partial pressure of A at time t , P_A = P₀ - x Partial pressure of B at time t , P_B = 2x Partial pressure of C at time t , P_C = x Total pressure at time t , P_t = (P₀