14.3 Transition state theory and activated complex

Transition state theory explains how reactions happen through high-energy activated complexes. It's all about molecules overcoming energy barriers to transform into products. This theory helps us understand why some reactions are fast and others are slow.

The activation energy and temperature are key players in determining reaction rates. By manipulating these factors, we can control how quickly reactions occur. This knowledge is crucial for optimizing chemical processes in various industries.

Transition State Theory

Key Concepts and Assumptions

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• Transition state theory explains the rates of elementary reactions by assuming that reactants must pass through a high-energy transition state or activated complex to form products
• The activated complex is a transient, unstable species formed when reactants collide with sufficient energy and proper orientation, representing the highest energy point along the reaction coordinate
• The activated complex is in equilibrium with the reactants, and its concentration determines the rate of product formation
• The difference in energy between the reactants and the activated complex is the activation energy ($E_a$), the minimum energy required for a reaction to occur

Factors Affecting Reaction Rate

• The rate of a reaction depends on the concentration of the activated complex, which in turn depends on the activation energy and temperature
• Higher concentrations of the activated complex lead to faster reaction rates, as more reactant molecules have sufficient energy to overcome the activation energy barrier
• Temperature increases the average kinetic energy of molecules, allowing a greater proportion of reactants to form the activated complex and proceed to products
• Catalysts lower the activation energy by providing an alternative reaction pathway, increasing the concentration of the activated complex and the reaction rate

Activation Energy and Rate

Relationship between Activation Energy and Reaction Rate

• The activation energy ($E_a$) is the energy barrier that reactants must overcome to form the activated complex and proceed to products
• A higher activation energy results in a slower reaction rate because fewer reactant molecules have sufficient energy to form the activated complex
• Lowering the activation energy, through the use of catalysts or by increasing temperature, increases the reaction rate by allowing more reactant molecules to form the activated complex

Maxwell-Boltzmann Distribution and Reaction Rates

• The Maxwell-Boltzmann distribution describes the distribution of molecular energies in a system and helps explain why increasing temperature leads to a greater proportion of molecules with energy equal to or greater than the activation energy
• At higher temperatures, the Maxwell-Boltzmann distribution shifts to the right, with a greater area under the curve above the activation energy, indicating a larger fraction of molecules with sufficient energy to react
• Catalysts shift the Maxwell-Boltzmann distribution by lowering the activation energy, allowing a greater proportion of molecules to have the required energy to form the activated complex at a given temperature

Arrhenius Equation Applications

Components of the Arrhenius Equation

• The Arrhenius equation, $k = Ae^{-E_a/RT}$, relates the rate constant ($k$) to the activation energy ($E_a$), pre-exponential factor ($A$), gas constant ($R$), and absolute temperature ($T$)
• The pre-exponential factor ($A$) represents the frequency of collisions between reactants and the probability of those collisions having the proper orientation for reaction
• The exponential term, $e^{-E_a/RT}$, represents the fraction of collisions with sufficient energy to overcome the activation energy barrier

Calculating Rate Constants and Activation Energies

• The Arrhenius equation can be used to calculate the rate constant ($k$) at a given temperature if the activation energy and pre-exponential factor are known
• By plotting $ln(k)$ vs. $1/T$, the activation energy can be determined from the slope ($-E_a/R$) of the resulting straight line, while the pre-exponential factor ($A$) can be determined from the y-intercept
• The Arrhenius equation allows for the prediction of rate constants at different temperatures, enabling the optimization of reaction conditions (temperature, catalyst choice) for desired outcomes

Collision and Orientation in Kinetics

Effective Collisions and Reaction Rates

• For a reaction to occur, reactant molecules must collide with sufficient energy (equal to or greater than the activation energy) and proper orientation
• The collision theory states that the rate of a reaction is proportional to the frequency of effective collisions between reactant molecules
• Effective collisions are those with sufficient energy and proper orientation to break existing bonds and form new bonds, leading to the formation of products
• Increasing the concentration of reactants leads to a higher frequency of collisions and, consequently, a faster reaction rate, as described by the rate law

Molecular Orientation and Steric Factors

• Molecular orientation is crucial because reactants must collide with the proper spatial arrangement for the necessary bonds to break and form, not all collisions with sufficient energy lead to reaction due to improper orientation
• Steric factors, such as the size and shape of reactant molecules, can affect the probability of collisions with proper orientation and impact the pre-exponential factor ($A$) in the Arrhenius equation
• Molecules with complex structures or bulky substituents may have a lower probability of effective collisions due to steric hindrance, resulting in a smaller pre-exponential factor and slower reaction rates
• Orientation effects can be particularly important in reactions involving asymmetric molecules or those with specific functional groups that must interact for the reaction to proceed (lock-and-key model in enzyme catalysis)