Chemical Kinetics and Reaction Mechanisms

Pseudo First-Order Kinetics 15.4

  • Consider a rate law with more than one component:
    Rate = -\frac{d[A]}{dt} = k [A] [B]^2 [C]^3
  • To simplify, we can work under pseudo-first order conditions.
  • If [B] >> [A] and [C] >> [A], then the kinetics will appear as:
    Rate = k' [A]
  • Where k' = k [B]^2 [C]^3
  • Key Points:
    • [B] and [C] stay relatively constant compared to [A].
    • [A] is the limiting factor.
    • The simplified rate constant is: k = \frac{k'}{[B]^2 [C]^3}

Reaction Mechanisms

  • CH3Cl + Br^- \rightarrow CH3Br + Cl^-
  • Mechanism 1:
    CH3Cl + Br^- \rightarrow CH3Br + Cl^-
    Rate = -\frac{d[CH3Cl]}{dt} = k [CH3Cl] [Br^-]
  • Mechanism 2:
    1. CH3Cl \rightarrow CH3^+ + Cl^- (slow)
    2. CH3^+ + Br^- \rightarrow CH3Br (fast)
      Rate = -\frac{d[CH3Cl]}{dt} = k [CH3Cl]
  • The rate law is based on the rate-determining step (RDS).

Pseudo First-Order Kinetics Example Problem

  • Reaction: BrO3^- + 5Br^- + 6H^+ \rightarrow 3Br2 + 3H_2O
  • Rate law: Rate = -\frac{d[BrO3^-]}{dt} = k[BrO3^-][Br^-][H^+]^2
  • Conditions:
    • [BrO3^-]0 = 0.0010 M
    • [Br^-] = 2.0 M
    • [H^+] = 1.5 M
  • Assumption:
    • Assume pseudo-first order kinetics: Rate = k'[BrO_3^-]
  • Given slope from plot ln[BrO_3^-] vs time is -0.087 s^{-1}, therefore k' = 0.087 s^{-1}.
  • k' = k [Br^-] [H^+]^2
  • k = \frac{k'}{[Br^-][H^+]^2} = \frac{0.087 s^{-1}}{(2.0 M)(1.5 M)^2} = 0.019 M^{-2}s^{-1}

Reaction Mechanisms 15.6

  • A reaction mechanism is the step-by-step process by which reactants evolve to products.
  • Very rarely is the reaction mechanism reflected in the overall balanced equation.
  • Intermediates are formed and consumed during the reaction.
  • Example: NO2 + CO \rightarrow NO + CO2 Mechanism:
    1. NO2 + NO2 \rightarrow NO_3 + NO
    2. NO3 + CO \rightarrow NO2 + CO_2

Rate Determining Step

  • The rate law is determined by the rate-determining step (RDS) of the reaction mechanism.
  • The RDS is the slowest step and therefore is the observable step.
  • Rate Law stoichiometry of RDS.
  • Example:
    2NO2 + F2 \rightarrow 2NO2F Rate = -\frac{d[NO2]}{dt} = k [NO2] [F2]
  • Mechanism:
    1. NO2 + F2 \rightarrow NO_2F + F (slow)
    2. F + NO2 \rightarrow NO2F (fast)
  • The sum of the elementary steps gives the overall balanced equation confirming it is a good mechanism
  • The first step is the rate-limiting step, determining the overall reaction rate.

Mechanisms Example

  • CH3Cl + Br^- \rightarrow CH3Br + Cl^-
  • Mechanism 1: CH3Cl + Br^- \rightarrow CH3Br + Cl^- Rate = -\frac{d[CH3Cl]}{dt} = k [CH3Cl] [Br^-]
    • Pseudo 1st order
  • Mechanism 2:
    1. CH3Cl \rightarrow CH3^+ + Cl^- (slow)
    2. CH3^+ + Br^- \rightarrow CH3Br (fast)
      Rate = -\frac{d[CH3Cl]}{dt} = k [CH3Cl]
    • Reflected in data
  • Based on the graphs:
    • Mechanism 1 is 1st order in CH_3Cl and 0th order in Br^-.
    • Mechanism 2 is 1st order in CH_3Cl.

Determining Rate Law and Mechanism

  • Reaction: H2(g) + 2BrCl(g) \rightarrow 2HCl(g) + Br2(g)
  • Experimental Rate Law: Rate = k [H_2] [BrCl]
  • Proposed Mechanism:
    1. H_2 + BrCl \rightarrow HCl + HBr (slow)
    2. HBr + BrCl \rightarrow HCl + Br_2 (fast)
  • The intermediate in this mechanism is HBr.
  • The sum of the elementary steps gives the overall balanced equation verifying the mechanism. The first step is the rate-determining step. (✓ Mechanism)