First-Order Half-Life

For a first-order reaction, the rate is proportional to the amount of reactant still present, so the concentration decays exponentially with time. Half-life is the time needed for the amount to drop to one-half its current value, and when you solve the first-order integrated rate law for that condition, the concentration terms cancel out, leaving t_{1/2} = 0.693/k. That constant comes from ln 2, which appears because "half" means the ratio 1/2 in the exponential expression.

Use this formula when a reaction is known or assumed to be first order and you are given the rate constant k, or need to compare how long different first-order processes take to halve. It is common in kinetics, radioactive decay, drug elimination, and decomposition reactions that follow first-order behavior.

• Using the formula for zero-order or second-order reactions, where half-life depends on concentration
• Forgetting that k must have reciprocal-time units, such as s^{-1}, min^{-1}, or h^{-1}
• Confusing half-life with the time for complete disappearance of the reactant