$word_{count}$: 230

Zero order: [A] = [A]0 - kt. Linear plot: [A] vs t (slope = -k). Half-life: $t_1$/2 = [A]$\frac{0}{2k}$, proportional to [A]_0. Rate constant decreases when [A]_0 is lower. Examples: surface reactions at saturation, photochemical reactions. First order: ln[A] = ln[A]_0 - kt, equivalently k = $\frac{2.303}{t}$log([A]_0/[A]). Linear plot: ln[A] vs t (slope = -k). Half-life: $t_1$/2 = 0.693/k, independent of [A]_0. After n half-lives: fraction remaining = $\frac{1}{2}$^n. This is the most common and most tested order. Examples: radioactive decay, N2O5 decomposition. For gases: k = $\frac{2.303}{t}$log($\frac{P_0}{2P_0 - P_t}$) for A -> B + C. Second order (rate = k[A]^2): 1/[A] = 1/[A]_0 + kt. Linear plot: 1/[A] vs t (slope = +k). Half-life: $t_1$/2 = $\frac{1}{k[A]_0}$, inversely proportional to [A]_0. Each successive half-life is twice the previous. Determining order from data: test all three linear plots — whichever gives a straight line identifies the order. Alternatively: if $t_1$/2 is constant (first order), proportional to [A]_0 (zero), or proportional to 1/[A]_0 (second). General: $t_1$/2 proportional to [A]_0^(1-n).