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Understanding Reaction Dynamics and Approximations

Apr 10, 2025

Lecture on Reaction Dynamics and Steady-State Approximations

Overview of U Model Reactions

  • U Model Reactions: Involves three reactions:
    1. A + A ā†’ A* + A (Rate constant: KF)
    2. A* ā†’ A (Rate constant: KB)
    3. A* ā†’ Products (Rate constant: KF')*

Rate Equations

  • Rate equations can be written for species A and A*.
  • Attempt to eliminate A* to find equations in terms of only A.
  • Resulting equations can be complex and difficult to solve due to their non-linear second-order nature.

Steady-State Approximations

  • Quasi Steady-State Approximation (QSSA): Assume DCA*/DT ā‰ˆ 0.
    • A* is produced quickly but consumed slowly.
    • Considered as a snapshot or freeze-frame scenario where intermediate concentration remains mostly constant.
  • Using QSSA, derive simplified equations:
    • Derive expression for CA* in terms of CA and substitute to get a simpler equation for DCA/DT.*

Reaction Order Analysis

  • Aim: Determine if reactions behave as first or second order.
    • Analyze the reaction set as a global reaction involving intermediates.
  • Express DCA/DT and analyze:
    • Depending on pressure, reaction may exhibit first or second-order characteristics.

Effects of Pressure on Reaction Order

  • High Pressure:
    • Backward reaction predominates (second reaction - bimolecular).
    • Reaction behaves like a first-order.
  • Low Pressure:
    • Third reaction (unimolecular) predominates.
    • Reaction behaves like a second-order.
  • Important to compare terms with unity to deduce reaction order.

Application to HBr Reaction

  • Global Reaction: H2 + Br2 ā†’ 2HBr
    • Experiments indicate complexities not aligned with molecular level reactions.
  • Observed reaction rate:
    • DC(HBr)/DT involves a non-linear dependency on the concentration of Br2 and inversely on the concentration of HBr.
    • Exhibits self-inhibition as the concentration of HBr increases.

Explanation via Mechanism

  • Proposed Mechanism:
    • Involves multiple chain initiation, propagation, and termination steps.
    • Demonstrates the role of intermediates and reverse reactions in affecting reaction rates.

Partial Equilibrium Approximation

  • An alternate approach to steady-state approximation.
  • Focus on fast reversible reactions.
    • Exploit equilibrium to establish algebraic relations for intermediate concentrations.
  • Example template reactions provided to demonstrate approach:
    • Use equilibrium constants to express intermediates in terms of stable species concentrations.

Next Steps

  • Continued discussion on eliminating intermediates using equilibrium constants in next class.

Note: This lecture covers advanced concepts in reaction dynamics, including the use of mathematical approximations to simplify complex reaction systems. Understanding these approximations is crucial for analyzing the behavior of chemical reactions under varying conditions.

Full transcript