X 2 Y is a first order reaction where 1.0 ~mol / L of the reactant yields 0.4 ~mol / L of Y in 200 minutes. Calculate the half-life period of the reaction in minutes.

Step-by-step solution

The reaction is X 2 Y . Let the initial concentration of X be [A]₀ = 1.0 mol/L . At time t = 200 minutes , the concentration of Y formed is 0.4 mol/L . From the stoichiometry, the amount of X consumed is 1 2 [ Y ] = 0.4 2 = 0.2 mol/L . The concentration of X remaining at t = 200 minutes is [A]_t = [A]₀ - 0.2 = 1.0 - 0.2 = 0.8 mol/L . For a first order reaction, the rate constant k is given by k = 2.303 t ( [A]₀ [A]_t ) . k = 2.303 200 ( 1.0 0.8 ) = 2.303 200 (1.25) 2.303 0.0969 200 0.001115 min ⁻¹ . The half-life p