Define half-life. Derive expressions for the half-life of zero and first order reactions, and explain what a pseudo first order reaction is, with an example.

1. 1 · Define in one line. Half-life (t½) is the time for the reactant concentration to fall to half its initial value.
2. 2 · Zero order. Put [R] = [R]₀/2 in k = ([R]₀ − [R])/t: t½ = [R]₀/2k, proportional to [R]₀.
3. 3 · First order. Put [R] = [R]₀/2 in k = (2.303/t) log([R]₀/[R]): t½ = 2.303 log 2/k = 0.693/k, independent of [R]₀.
4. 4 · Sketch to compare. On a [R] vs t curve for first order, mark t½, 2t½, 3t½ at [R]₀/2, [R]₀/4, [R]₀/8: equal time gaps.
5. 5 · Pseudo first order. One reactant in large excess: CH₃COOC₂H₅ + H₂O → CH₃COOH + C₂H₅OH (H⁺); rate = k[CH₃COOC₂H₅].
6. 6 · Close in one line. So first order reactions such as radioactive decay have a constant half-life.

Scoring tip: State the log 2 = 0.3010 value you use; the 0.693 comes from 2.303 × 0.3010.