How is the half-life of a first order reaction determined?

The half-life of a first order reaction is determined from the rate constant ( k ). In first order kinetics, the half-life is a unique property that does not depend on the initial concentration of the reactant. Instead, it is calculated using the equation:

[

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

]

This shows that the half-life is directly proportional to the natural logarithm of 2 (approximately 0.693) and inversely proportional to the rate constant. As ( k ) increases, the half-life decreases, indicating that the reaction occurs more quickly. This fundamental relationship is a characteristic feature of first order reactions, making the rate constant the key determinant of their half-life.

The other options refer to concepts that do not directly influence the half-life of a first-order reaction, such as activation energy, initial concentration, or temperature change, which instead could affect the rate constant or other dynamics of the reaction but not the half-life in this specific case.