6.2 Transition state theory fundamentals

Transition State Theory explains how chemical reactions occur through an activated complex. This high-energy intermediate forms when reactants collide with enough energy, determining the reaction rate. Understanding this process helps predict and control reaction speeds.

The theory postulates a quasi-equilibrium between reactants and the activated complex. It differs from collision theory by focusing on the complex's formation and decomposition. Calculating rate constants and understanding activation energy's role are key aspects of this theory.

Transition State Theory Fundamentals

Activated complex in reactions

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• High-energy, unstable intermediate formed during a chemical reaction when reactant molecules collide with sufficient energy and proper orientation
• Located at the highest point on the reaction coordinate diagram, representing the maximum potential energy
• Critical point in a reaction pathway that determines the rate of the reaction
  • Point at which the reactants are partially converted into products
  • Rate of the reaction depends on the concentration of the activated complex and the rate at which it decomposes into products (products could be molecules like H2O or NH3)

Transition state theory postulates

• Reactants and activated complex are in quasi-equilibrium
  • Concentration of the activated complex is proportional to the concentrations of the reactants
• Activated complex can convert into products or revert back to reactants
  • Rate of product formation depends on the rate of decomposition of the activated complex
• Activated complex passes through the transition state only once, does not oscillate back and forth around the transition state
• Differs from collision theory:
  • Considers formation of an activated complex, while collision theory does not
  • Assumes quasi-equilibrium between reactants and activated complex, while collision theory does not consider equilibrium
  • Focuses on decomposition of activated complex into products, while collision theory emphasizes collision frequency and orientation of reactant molecules (like two billiard balls colliding)

Rate constant calculation methods

• Arrhenius equation relates rate constant ($k$) to activation energy ($E_a$) and temperature ($T$): $k = A e^{-E_a/RT}$
  • $A$ is pre-exponential factor or frequency factor, represents frequency of collisions with proper orientation
  • $R$ is universal gas constant (8.314 J mol$^{-1}$ K$^{-1}$)
• To calculate rate constant:
  1. Determine activation energy ($E_a$) and pre-exponential factor ($A$) experimentally or from literature
  2. Substitute values of $E_a$, $A$, $R$, and $T$ (in Kelvin) into Arrhenius equation
  3. Solve equation for $k$, the rate constant

Activation energy and reaction rates

• Activation energy ($E_a$) is minimum energy required for reactants to form activated complex
  • Higher activation energy means fewer reactant molecules will have sufficient energy to form activated complex
• Rate of chemical reaction is inversely proportional to activation energy
  • As activation energy increases, rate of reaction decreases because smaller fraction of reactant molecules will have enough energy to overcome activation energy barrier
• Relationship between activation energy and reaction rate is exponential, as described by Arrhenius equation
  • Small change in activation energy can lead to significant change in rate constant and reaction rate (doubling $E_a$ could decrease rate by factor of 10)