Quick Recap — Kinetics Calculations

  • First order: k=2.303tlog⁡[A]0[A]k=\dfrac{2.303}{t}\log\dfrac{[A]_0}{[A]}; t1/2=0.693kt_{1/2}=\dfrac{0.693}{k}; 75% done =2 t1/2=2\,t_{1/2}, 87.5% =3 t1/2=3\,t_{1/2}, 99.9% =10 t1/2=10\,t_{1/2}.
  • Zero order: [A]=[A]0−kt[A]=[A]_0-kt; completion time =[A]0/k=[A]_0/k; t1/2=[A]0/2kt_{1/2}=[A]_0/2k.
  • Rate-constant units by order: 0 →\to mol L−1^{-1}s−1^{-1}; 1 →\to s−1^{-1}; 2 →\to L mol−1^{-1}s−1^{-1}; 3 →\to L2^2mol−2^{-2}s−1^{-1}.
  • Arrhenius: log⁡k2k1=Ea2.303R(1T1−1T2)\log\dfrac{k_2}{k_1}=\dfrac{E_a}{2.303R}\left(\dfrac{1}{T_1}-\dfrac{1}{T_2}\right).