A gas-phase decomposition reaction X(g) Y(g) + 2Z(g) takes place in a rigid vessel at a constant temperature. The half-life of the reaction is found to be independent of the initial pressure. If the initial pressure of X is 200 mm Hg and the total pressure of the mixture after 40 minutes is 560 mm Hg , the half-life of the reaction is: (Given: 2 = 0.30 ; 3 = 0.48 )

Step-by-step solution

Since the half-life is independent of the initial pressure, the reaction follows first-order kinetics. Let the initial pressure of X be P₀ = 200 mm Hg . The reaction is: X(g) Y(g) + 2Z(g) At t = 0 : 200 mm Hg 0 + 0 At t = 40 min : (200 - x) x + 2x The total pressure at t = 40 min is: P_ total = (200 - x) + x + 2x = 200 + 2x Given P_ total = 560 mm Hg : 200 + 2x = 560 2x = 360 x = 180 mm Hg The partial pressure of reactant X remaining after 40 minutes is: P_t = 200 - 180 = 20 mm Hg Using the first-order integrated r