For a certain reaction A Products , the plot of concentration [A] versus time t yields a straight line with a negative slope. If the initial concentration of the reactant is 0.5 M and the reaction goes to completion in 50 s , what is the half-life of this reaction?

Step-by-step solution

A plot of concentration [A] versus time t that yields a straight line with a negative slope indicates that the reaction follows zero-order kinetics. The integrated rate law for a zero-order reaction is: [A] = -kt + [A]₀ The reaction goes to completion when [A] = 0 . Substituting the given values ( [A]₀ = 0.5 M and t = 50 s ): 0 = -k(50) + 0.5 k = 0.5 50 = 0.01 M s ⁻¹ The half-life ( t_ 1/2 ) for a zero-order reaction is given by: t_ 1/2 = [A]₀ 2k Substituting the values: t_ 1/2 = 0.5 2 0.01 = 0.5 0.02 = 25 s Altern