Final answer:
The half-life is the duration for the concentration of a reactant to reduce to half its initial value. For second-order reactions, a special equation utilizing the rate constant and initial concentration calculates the half-life. In first-order reactions, including radioactive decay, half-life is determined using t₁/₂ = 0.693/k, where k is the rate constant.
Step-by-step explanation:
The half-life of a reaction refers to the time required for the concentration of a reactant to decrease to half of its initial value. For a second-order reaction with a starting concentration of 0.200 mol L¹ and a rate constant of 0.0576 L mol¹ min¹, the half-life can be calculated using a specific mathematical equation for second-order reactions. Similarly, the half-life of a first-order reaction, such as radioactive decay, can be determined using the equation t₁/₂ = 0.693/k, where k is the rate constant.
Additionally, for a first-order process, after n half-lives, the remaining amount of reactant or isotope can be calculated using (1/2)n times the initial concentration. The half-life for different orders of reactions and processes varies and is determined by their respective equations based on the reaction order and rate constants.