Rate equations

Rate equations and orders

The rate equation $\text{rate}=k[A]^m[B]^n$ has orders $m,n$ (0, 1 or 2) found by experiment, not from the equation. Initial-rates method: change one concentration at a time; doubling [A] doubles the rate (1st order), quadruples it (2nd order), or leaves it unchanged (zero order). Graphs: on a concentration–time graph, zero order is a straight line, first order has a constant half-life ($t_{1/2}=\frac{\ln2}{k}$). k increases with temperature (Arrhenius: $k=Ae^{-E_a/RT}$; $\ln k=\ln A-\frac{E_a}{RT}$). The rate-determining step (slowest step) contains the species in the rate equation.