Lecture Notes on Rate Laws and Reactions

Rate Expressions vs Rate Laws

• Rate Expressions: Measure the rate of reaction.
• Rate Laws: Used to predict future reaction rates based on initial conditions (e.g., initial concentrations of reactants).
  • Allow predictions similar to laws of physics (e.g., gravity).

Rate Law Components

• General Form: For a reaction ( A + B \rightarrow C ), the rate law is based on reactant concentrations:
  • ( \text{Rate} = k[A]^x[B]^y )
• Components:
  • Rate Constant (k): Proportionality constant.
  • Orders (x, y): Exponents representing the order of reaction with respect to each reactant.
    • Overall Order: Sum of individual orders (e.g., ( x + y )).
  • Determination of Orders: Typically from experimental data, not coefficients except in Elementary reactions.

Elementary vs Non-Elementary Reactions

• Elementary Reactions:
  • Cannot be broken into simpler steps.
  • Orders can be determined from stoichiometric coefficients.
• Non-Elementary Reactions:
  • Complex pathways; orders derived experimentally.
• Multi-Step Pathways:
  • Overall reaction may involve several elementary steps.

Experimental Determination of Rate Laws

• Using Experimental Data: Identify how changes in concentration affect rate.
  • Compare trials where only one reactant concentration changes.
  • Calculate exponents by observing changes in rate.
• Example Trials:
  • Trial 1: Compare to find order of ( NO ) by keeping ( Cl_2 ) constant.
  • Trial 2: Compare to find order of ( Cl_2 ) by keeping ( NO ) constant.

Orders of Reaction

• Zero Order:
  • Rate unaffected by concentration changes.
• First Order:
  • Rate directly proportional to concentration.
• Second Order:
  • Rate proportional to square of concentration changes.
• Higher Orders (e.g., Third Order): Rare, higher impact on rate.

Practical Example and Calculation

• Calculation of Rate Constant (k):
  • Use experimental data to compute ( k ) with known rate and concentrations.
• Units of Rate Constant:
  • Depends on overall reaction order (e.g., ( M^{-2}s^{-1} ) for third order).
  • Units: Multiply together according to rate law equation.

Considerations in Rate Laws

• Elementary Reaction Hypothesis: Initial assumption about reaction type.
• Correlation to Experimental Data: Necessary to confirm elementary nature.
• Uncommon Reactions: More complex or involving multiple molecules (e.g., termolecular reactions).

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These notes cover the key concepts and methodologies for understanding and calculating rate laws in chemical reactions, focusing on the role of experimental data in determining the reaction orders and constants.