Differential rate law Describe the relationship between reaction rate and concentration of species ★ Integrated rate law Describe how concentration of each species is changing with time Example A ( Reactant) > B(Product) zero order. d[A]/dt=k[Ay° first order d[al/dt =k[Al second order:-d[a]/dt=k[A]2
Ì Differential Differential rate law — Describe Describe the relationship relationship between reaction rate and concentration of species. Ì Integrated rate law — Describe how concentration of each species is chang g in with time Example: A (Reactant) → B (Product) zero order: −d[A] / dt = k [A]0 fi t d d[A] / dt k [A]1 first order: −d[A] / dt = k [A]1 second order: −d[A] / dt = k [A]2 11
Zero order First Order Second order d[aldt= k[ajo-d[aldt =k[a] -d[Aldt= k[AJ d[AF-kdt [A]d[]_-kdt LAJ dAl k dt A Jo JIAyO JAI JIAJOJA 0 [A]==kt+[Alo n[A]=-kt+ In(Al o 1/A]= kt+ 1/Alo In(Alo In[A] slope k slope =-k [A [Alo'*kt
Zero Order First Order Second Order −d[A]/dt = k[A] 0 −d[A]/dt = k[A] −d[A]/dt = k[A] 2 [A] [A] ∫ ∫ = − [A] t 0 0 d[A] k dt ∫ ∫ = − [A] [A} t 0 0 k dt [A] d[A] ∫ ∫ = − [A] [A} t 0 2 0 k dt [A] d[A] [A] = −k t + [A] 0 ln[A] = − kt + ln[A] 0 1/[A]= kt + 1/[A] 0 12 [A]= [A] 0·e-kt