$word_{count}$: 190

Half-life is the time for concentration to fall to half its initial value. Zero order: $t_1$/2 = [A]_$\frac{0}{2k}$ — directly proportional to [A]_0. First order: $t_1$/2 = 0.693/k — independent of [A]_0 (most distinctive feature). Second order: $t_1$/2 = $\frac{1}{k[A]_0}$ — inversely proportional to [A]_0. General: $t_1$/2 proportional to [A]_0^(1-n) where n = order. For first order, key relationships: 50% complete = 1 $t_1$/2. 75% = 2 $t_1$/2. 87.5% = 3 $t_1$/2. 93.75% = 4 $t_1$/2. 96.875% = 5 $t_1$/2. 99.9% ≈ 10 $t_1$/2. Time for any fraction: t = $\frac{2.303}{k}$log([A]_0/[A]). For 90% completion: t = 2.303/k = 3.32 $t_1$/2. For 99%: t = 4.606/k = 6.64 $t_1$/2. For second order: successive half-lives form a geometric series (each 2x the previous). The half-life method is a powerful tool for determining reaction order from experimental data.