Two cases: (a) Rate = k[A]^2 (single reactant): Integrated: 1/[A] = 1/[A]_0 + kt. Plot: 1/[A] vs t is linear with slope = +k. Half-life: $t_1$/2 = $\frac{1}{k[A]_0}$ — inversely proportional to initial concentration. (b) Rate = k[A][B] (two reactants, equal initial concentrations): same integrated form. For unequal concentrations: k = ($\frac{2.303}{t(a-b}$))log((b(a-x))/(a(b-x))), where a = [A]_0, b = [B]_0, x = amount reacted. Second order reactions: $t_1$/2 doubles when initial concentration is halved. This dependence of $t_1$/2 on [A]_0 distinguishes second order from first order.