kinetics
Collision theory, rate laws & orders, integrated rate forms, mechanisms, Arrhenius.
rate & collision theory · factors & catalysis · rate laws & orders · integrated forms · mechanisms · Arrhenius
Rate & collision theory
Rate. For \(a\mathrm{A}\to p\mathrm{P}\): rate \(=-\dfrac{1}{a}\dfrac{\dd[\mathrm{A}]}{\dd t}=\dfrac{1}{p}\dfrac{\dd[\mathrm{P}]}{\dd t}\); units usually \(\mathrm{mol\,dm^{-3}\,s^{-1}}\).
Collision theory. Successful collisions need \(E\ge E_a\) and correct orientation.
Maxwell–Boltzmann. Higher \(T\) flattens and right-shifts the distribution; a larger fraction of molecules exceeds \(E_a\).
Factors & catalysis
Factors. Higher concentration/pressure increases collision frequency; greater surface area exposes more particles; higher temperature increases both collision frequency and the fraction with \(E\ge E_a\).
Catalyst. Lowers \(E_a\); does not change \(\Delta H\), \(K\), or the equilibrium composition; speeds forward and reverse reactions equally.
Rate laws & orders
Rate equation. \(r=k[\mathrm{A}]^m[\mathrm{B}]^n\); orders \(m,n\) are experimental, not stoichiometric coefficients unless the step is elementary; overall order \(m+n\); units of \(k=(\mathrm{mol\,dm^{-3}})^{1-\text{order}}\,\mathrm{s}^{-1}\).
Initial rates. Doubling \([\mathrm{A}]\) changes the rate by \(2^m\); log method \(m=\dfrac{\log(r_2/r_1)}{\log([\mathrm{A}]_2/[\mathrm{A}]_1)}\).
Trap. Rate-law orders come from data or the mechanism's RDS, never from the balanced overall equation unless the reaction is a single elementary step.
Integrated forms
| Order | Rate vs \([\mathrm{A}]\) | Half-life | Linear plot |
|---|---|---|---|
| 0 | \(r=k\) | \(t_{1/2}=[\mathrm{A}]_0/2k\) | \([\mathrm{A}]\) vs \(t\), slope \(-k\) |
| 1 | \(r=k[\mathrm{A}]\) | \(t_{1/2}=\ln 2/k\) | \(\ln[\mathrm{A}]\) vs \(t\), slope \(-k\) |
| 2 | \(r=k[\mathrm{A}]^2\) | \(t_{1/2}=1/k[\mathrm{A}]_0\) | \(1/[\mathrm{A}]\) vs \(t\), slope \(k\) |
Mechanisms
Molecularity. Elementary steps are unimolecular, bimolecular, or termolecular; the rate-determining step controls the rate.
Consistency. A mechanism must sum to the overall equation and predict the observed rate law. Intermediates are made then consumed; catalysts are consumed then regenerated.
Arrhenius
Equation. \(k=Ae^{-E_a/RT}\); \(\ln k=-E_a/RT+\ln A\).
Plots. Plot \(\ln k\) vs \(1/T\): gradient \(-E_a/R\), intercept \(\ln A\). Two-temperature form: \(\ln(k_2/k_1)=-\dfrac{E_a}{R}\left(\dfrac{1}{T_2}-\dfrac{1}{T_1}\right)\).