Activation energy is the key to understanding chemical reactions. It's the energy barrier reactants must overcome to form products. This concept explains why some reactions happen quickly, while others need a push from catalysts or higher temperatures.

Determining activation energy involves measuring reaction rates at different temperatures. By plotting this data and using the Arrhenius equation, we can calculate the activation energy. This helps predict reaction speeds and design more efficient chemical processes.

Activation Energy and Its Determination

Role of activation energy

• Minimum energy required for reactants to overcome energy barrier and form products in a chemical reaction
  • Reactant molecules must collide with sufficient energy to break existing bonds and form new bonds (bond breaking and formation)
  • Higher activation energy means slower reaction rate as fewer collisions have enough energy to overcome barrier (reaction rate)
• Determines rate of a chemical reaction
  • Catalyst can lower activation energy increasing reaction rate without being consumed (catalysis)

Activated complex and energy relationship

• High-energy unstable intermediate formed during a chemical reaction
  • Point of highest potential energy along reaction coordinate (transition state)
  • Formed when reactants have enough energy to overcome activation energy barrier (energy barrier)
• Difference in energy between reactants and activated complex is activation energy
• Short-lived and quickly decomposes into products or back into reactants
  • Higher concentration of activated complex leads to faster reaction rate (reaction rate)

Methods for determining activation energy

• Arrhenius equation relates rate constant ($k$) of a reaction to activation energy ($E_a$) and temperature ($T$)
  • $k = A e^{-E_a/RT}$ where $A$ is pre-exponential factor and $R$ is gas constant
• Reaction rate measured at different temperatures to determine activation energy experimentally
  1. Measure reaction rate at various temperatures
  2. Calculate rate constant ($k$) for each temperature using rate law
  3. Plot natural logarithm of rate constant ($\ln k$) against inverse of temperature ($1/T$) known as Arrhenius plot
  4. Slope of Arrhenius plot equal to $-E_a/R$ allowing activation energy to be calculated
• Other methods include
  • Collision theory relates activation energy to fraction of collisions with sufficient energy to overcome barrier (collision frequency)
  • Transition state theory calculates activation energy based on difference in Gibbs free energy between reactants and activated complex (Gibbs free energy)

Calculation of activation energy

• Arrhenius equation rearranged to solve for activation energy
  • $E_a = -R \cdot \text{slope}$ where slope determined from Arrhenius plot of $\ln k$ vs. $1/T$
• Units for activation energy typically kJ/mol or J/mol (energy units)