Final answer:
The half-life of a first-order reaction is calculated using the equation t₁₂ = 0.693/k which indicates that, regardless of concentration, the reactant concentration halves every fixed interval. For a second-order reaction with a rate constant of 0.0576 L mol⁻¹ min⁻¹ and an initial concentration of 0.200 mol L⁻¹, the half-life is 18 minutes.
Step-by-step explanation:
The half-life of a reaction indicates the time required for the concentration of a reactant to decrease to half of its initial value. In the case of first-order reactions, the half-life is directly related to the rate constant (k) of the reaction, as described by the equation t₁₂ = 0.693/k. If we have a first-order reaction with a half-life of 2.0 ages, it implies that every 2.0 ages, the concentration of the reactant will be reduced by half.
For a second-order reaction with a given rate constant and initial concentration, we can calculate the half-life using the appropriate second-order half-life equation, which when applied to a reaction initiated with an initial concentration of 0.200 mol L⁻¹ and a rate constant of 0.0576 L mol⁻¹ min⁻¹, yields a half-life of 18 minutes. This means that it takes 18 minutes for the concentration of the reactant to decrease by half.