Reaction Mechanisms and Rate Laws

Introduction to Reaction Mechanisms

• Reaction Mechanism: A step-by-step pathway by which a particular reaction occurs.
• Elementary Reactions: Individual steps in a reaction mechanism.

Example of a Reaction Mechanism

1. Step 1: ( A + B \rightarrow C + D )
   • Rate Law: ( \text{Rate} = k_1[A][B] )
   • Rate Constant: ( k_1 )
2. Step 2: ( D + E \rightarrow F + B )
   • Rate Law: ( \text{Rate} = k_2[D][E] )
   • Rate Constant: ( k_2 )

Identifying Catalysts and Intermediates

• Catalyst: Consumed first, then produced later.
• Intermediate: Produced first, then consumed later.
• Example:
  • Catalyst: B (consumed first, then produced)
  • Intermediate: D (produced first, then consumed)

Overall Reaction

• Combine steps, cancelling intermediates and catalysts.
• Example: Overall Reaction ( A + E \rightarrow C + F )

Molecularity of Elementary Reactions

• Unimolecular Reaction: Involves one molecule as reactant.
  • Example: ( A \rightarrow B )
  • Rate Law: ( \text{Rate} = k[A] )
• Bimolecular Reaction: Involves two molecules.
  • Example: ( A + A \rightarrow B ) or ( A + B \rightarrow C )
  • Rate Law: ( \text{Rate} = k[A]^2 ) or ( \text{Rate} = k[A][B] )
• Termolecular Reaction: Involves three molecules.
  • Rare due to statistical difficulty of three molecules colliding.
  • Example: ( A + B + C \rightarrow D )
  • Rate Law: ( \text{Rate} = k[A][B][C] )

Determining Rate Law for Overall Reaction

• Depends on the slowest step (rate-determining step).
• Example Reaction: ( O_3 + NO_2 \rightarrow NO_3 + O_2 ) (slow)
  • Overall Reaction: ( O_3 + 2NO_2 \rightarrow N_2O_5 + O_2 )
  • Rate Law: ( \text{Rate} = k[O_3][NO_2] )

Example Problem Analysis

• Steps:
  1. ( 2H_2O_2 \rightarrow 2H_2O + O_2 )
  2. Slow step (first step) determines rate.
• Catalyst: ( I^- ) (consumed then produced)
• Intermediate: ( IO^- ) (produced then consumed)
• Overall Reaction: ( 2H_2O_2 \rightarrow 2H_2O + O_2 )
• Rate Law for Overall Reaction: ( \text{Rate} = k[H_2O_2] )

Key Concepts

• Catalyst Function: Provides alternative pathway, lowers activation energy.
• Elementary Reaction Orders: Determined by stoichiometric coefficients.
• Rate Laws: Depend on slowest elementary step in mechanism.