In first-order reactions, what is true about the half-life?

In first-order reactions, the half-life is defined as the time required for the concentration of a reactant to decrease to half of its initial value. A key characteristic of first-order kinetics is that this half-life remains constant, regardless of the initial concentration of the reactant. This constant nature of the half-life is a direct consequence of the mathematical expression that describes first-order reactions, which can be expressed as:

[ k = \frac{0.693}{t_{1/2}} ]

where ( k ) is the rate constant and ( t_{1/2} ) is the half-life. Since the rate constant ( k ) is a fixed value for a particular reaction at a given temperature, the half-life calculated from it will also remain unchanged throughout the reaction.

This constancy helps simplify the analysis of first-order reactions and is a distinguishing trait when comparing them to reactions of other orders, where the half-life may depend on the concentration of reactants. Thus, recognizing that the half-life is constant is foundational to understanding first-order kinetics and its practical implications in various chemical processes.