6.4 Comparing collision theory and transition state theory

Chemical reactions happen when molecules collide or form an activated complex. Collision theory focuses on the frequency and energy of these collisions, while transition state theory examines the formation of an activated complex at the reaction's energy peak.

Both theories explain how temperature affects reaction rates using exponential equations. They help us understand factors like activation energy, molecular orientation, and catalysts. Transition state theory provides a more detailed picture of reaction mechanisms and molecular structure's role.

Collision Theory and Transition State Theory

Collision vs transition state theory

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• Collision theory explains reactions occur when reactant molecules collide with enough energy (activation energy, $E_a$) and proper orientation
  • Collision frequency and energy distribution of collisions determine reaction rate
  • Arrhenius equation relates rate constant ($k$) to temperature ($T$): $k = Ae^{-E_a/RT}$, where $A$ is pre-exponential factor, $R$ is gas constant
• Transition state theory states reactants form an activated complex (transition state) at highest energy point along reaction coordinate
  • Activated complex is in equilibrium with reactants
  • Reaction rate depends on concentration of activated complex
  • Eyring equation: $k = \frac{k_BT}{h}e^{-\Delta G^‡/RT}$, where $k_B$ is Boltzmann constant, $h$ is Planck's constant, $\Delta G^‡$ is Gibbs free energy of activation
• Both theories consider energy barrier (activation energy) reactants must overcome and relate rate constant to temperature using exponential functions
• Collision theory focuses on collision frequency and energy distribution, while transition state theory emphasizes formation and concentration of activated complex

Strengths and weaknesses of theories

• Collision theory strengths:
  • Provides simple, intuitive explanation for factors affecting reaction rates (concentration, temperature, activation energy)
  • Explains role of molecular orientation in successful collisions
• Collision theory weaknesses:
  • Does not consider detailed molecular structure of reactants and products
  • Assumes all collisions with sufficient energy lead to successful reactions
  • Does not provide complete picture of reaction mechanism
• Transition state theory strengths:
  • Provides more detailed description of reaction mechanism
  • Considers molecular structure and geometry of activated complex
  • Allows calculation of rate constants using statistical mechanics
  • Explains role of entropy in formation of activated complex
• Transition state theory weaknesses:
  • Assumes activated complex is in equilibrium with reactants
  • Does not account for possibility of non-equilibrium effects
  • Requires knowledge of molecular structure and vibrational frequencies of activated complex, which can be difficult to obtain experimentally

Application in reaction kinetics

• Determining effect of temperature on reaction rate
  • Use Arrhenius equation (collision theory) or Eyring equation (transition state theory) to calculate change in rate constant with temperature
• Comparing reaction rates for different reactions
  • Use activation energy and pre-exponential factor (collision theory) or Gibbs free energy of activation (transition state theory) to compare rates of different reactions
• Investigating effect of catalysts on reaction rates
  • Both theories explain role of catalysts in lowering activation energy and increasing rate constant
  • Transition state theory provides insights into specific interactions between catalyst and reactants in activated complex
• Analyzing effect of molecular structure on reaction rates
  • Transition state theory better suited for understanding how molecular structure and geometry influence formation and stability of activated complex, and consequently, reaction rate