Kinetics and Rate Laws

$\text{Rate} = k[A]^m[B]^n$

Determined experimentally (NOT from balanced equation). Compare initial rates to find orders.

Plot all three; the one that gives a straight line indicates the order.

$k = Ae^{-E_a/RT}$ $\ln k = -\frac{E_a}{R}\cdot\frac{1}{T} + \ln A$

Plot $\ln k$ vs $1/T$: slope = $-E_a/R$, y-intercept = $\ln A$

Two-point form: $\ln\frac{k_2}{k_1} = \frac{E_a}{R}\left(\frac{1}{T_1} - \frac{1}{T_2}\right)$

• Elementary step: single molecular event
• Rate-determining step (RDS): slowest step
• Rate law comes from the RDS (or steps up to and including RDS)
• Intermediate: produced in one step, consumed in another (not in overall equation)
• Catalyst: consumed and regenerated; lowers $E_a$

• Homogeneous: same phase as reactants
• Heterogeneous: different phase (usually solid catalyst, gas/liquid reactants)
• Enzyme: biological catalyst (specific, lock-and-key)
• Catalysts provide alternative pathway with lower $E_a$; don't change $\Delta H$ or equilibrium position

• Rate law determined experimentally: $\text{Rate} = k[A]^m[B]^n$
• Integrated rate laws: linearise to determine order
• First order: constant $t_{1/2} = 0.693/k$
• Arrhenius: $\ln k$ vs $1/T$ gives $-E_a/R$ as slope
• RDS determines rate law; catalysts lower $E_a$