Final answer:
The half-life of a first-order reaction can be determined using the formula t₁₂ = 0.693/k, showing that half-life is constant and solely dependent on the rate constant k for first-order kinetics.
Step-by-step explanation:
To find the half-life of a first-order reaction, you can use the formula derived from the integrated rate law, which states that the half-life (t₁₂) is inversely proportional to the rate constant (k) of the reaction. The formula is written as t₁₂ = 0.693/k. This relationship indicates that for first-order reactions, the half-life is constant and does not depend on the initial concentration of the reactant. This is a characteristic feature of first-order kinetics.
Moreover, if we observe the behavior of first-order reactions over multiple half-lives, we find that the amount of reactant left after n half-lives is (1/2)n times the initial concentration. This means that after one half-life, half of the reactant remains; after two half-lives, a quarter remains, and so on.
Example:
If you know the rate constant for the decomposition of hydrogen peroxide in water at 40 °C, you can calculate the half-life by simply plugging the rate constant value into the t₁₂ = 0.693/k formula.