Lecture #30 page 1 Kinetics: Reaction Rates, Orders, Half Lives aA + bB → cC + dD Rate of Reaction: Rate = − 1 d[A] 1 d[B] 1 d[C ] 1 d[D] =− = = a dt b dt c dt d dt N Experimentally ⇒ Rate = k∏ Ciγi i=1 Where k = rate constant Ci = Concentration of Reactant “i” γi = Order of reaction with respect to reactant “i” ∑ γi i = Overall rate of reaction Lecture #30 I) page 2 Zero Order Reactions (rare) A → products − d[A] =k dt {k is in [moles/(liter sec)]} [A] = -kt + [A]o [A] t1/2 = [A]o/(2k) [A]o [A]o/2 t1/2 t Lecture #30 page 3 II) First Order Reactions A → products − d[A] = k[A] dt [A] = [A]o e-kt {k is in [1/sec]} ln[A] = -kt + ln[A]o ln[A] ln[A]o Slope = -k t t1/2 = (ln 2) / k = 0.693/k k = (0.693)/(t1/2) Lecture #30 page 4 III) Second Order Reactions a) Second order in one component A → products − d[A] = k[A] 2 dt 1 1 = + kt [A] [A]o 1/[A] Slope = k 1/[A]o t t1/2 = 1/(k[A]o) Lecture #30 page 5 b) First order in each of two components A +B → products − d[A] = k[A][B] dt kt = [A][B]o 1 ln [A]o − [B]o [A]o [B] [A]o ≠ [B]o Special cases: 1 1 = + kt [A] [A]o i) [A]o = [B]o ⇒ [A] = [B] This is like 2nd order in one component ii) [B]o <<[A]o ⇒ [B] = [B]oe-k’t where k’ = [A]ok This is pseudo 1st order Lecture #30 Determining Orders of Reactions I) Getting the data a) Quench the reaction, measure concentrations b) For gas phase, measure pressure vs. time c) Spectroscopically follow reactants/products Etc… II) Analyzing the data A) Reactions with one reactant: A → products a) Plot or analyze [A] ln[A] 1/[A] … vs. t vs. t vs. t and find which gives a straight line. b) Half-life method: measure t1/2 vs. [A]o 1st order → t1/2 ∝ [A]o0 2nd order → t1/2 ∝ [A]o-1 etc…. page 6 Lecture #30 page 7 c) Multiple lifetimes (t3/4 and t1/2) (at t3/4, [A]=[A]o/4 ) 1st order → t3/4 = (2ln2)/k ⇒ 2nd order → t3/4 t3/ 4 =2 t1 / 2 t = 3/([A]ok) ⇒ 3/ 4 = 3 t1 / 2 B) Reactions with more than one reactant: e.g. A + B + C → products a) Initial Rate Method For [A]o For [A]o/ Δ[A] = Ro ≈ k[A]oα [B]oβ [C]oγ Δt t=0 Δ[A] / Δt = Ro/ ≈ k[A]o/ α [B]oβ [C]oγ t=0 Experimentally determine If 2 [A]o/ = [A]o then, if if if if ⎛ [A]o ⎜ = / Ro ⎜⎝ [A]o/ Ro Ro Ro/ Ro Ro/ Ro Ro/ Ro Ro/ etc… ⎞ ⎟ ⎟ ⎠ α =1 ⇒ α = 1 = 2 ⇒ α=½ =2 ⇒ α=1 =4 ⇒ α=2 Lecture #30 b) Flooding or Isolation page 8 (goal is to try to make problem look like a onereactant system) take [A]o << [B]o , [C]o e.g. flood system with B and C Then [B] ~ [B]o and [C] ~ [C]o So that − d[A] ≈ k'[A] α dt Where k' = k[B]oβ [C]oγ The reaction then becomes pseudo α-order with one reactant.

Lecture 30: Kinetics - Reaction Rates, Orders, Half Lives

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