Potential energy diagrams Knowledge-Based Study

Study notes

1. Potential Energy Profiles of Single-Step Reactions

   A potential energy diagram illustrates the change in potential energy of a chemical system as reactants transform into products along the reaction coordinate.

   Key components of a single-step reaction profile include:

   • Reactants and Products: The baseline energy levels at the start and conclusion of the step.
   • Transition State (Activated Complex): The highest energy configuration along the reaction pathway, representing an unstable arrangement of atoms with partially formed and partially broken bonds.
   • Activation Energy (Ea): The minimum energy barrier that reacting species must overcome for a successful collision, defined as the energy difference between the transition state and the reactants: $E_{\text{a}} = E_{\text{transition state}} - E_{\text{reactants}}$.
   • Enthalpy Change ($\Delta H$): The difference between product energy and reactant energy: $\Delta H = E_{\text{products}} - E_{\text{reactants}}$. When products lie lower than reactants, the process is exothermic ($\Delta H < 0$); when products lie higher, it is endothermic ($\Delta H > 0$).

   Energy Diagrams for Complex Mechanisms

   Most chemical reactions do not proceed in a single elementary event but rather through a sequence of elementary steps termed a reaction mechanism. Each elementary step possesses its own discrete transition state and activation barrier.

   Distinctive features of multi-step energy profiles include:

   • Reaction Intermediates: Chemical species generated in one elementary step and consumed in a subsequent step. On an energy profile, intermediates correspond to local energy minima (valleys) located between successive transition states. Unlike transition states, intermediates possess fully formed chemical bonds and a measurable lifetime.
   • Number of Transition States: A reaction with n elementary steps exhibits n distinct energy peaks (transition states) and $n - 1$ local minima (intermediates).
   • Rate-Determining Step (RDS): The slowest elementary step governs the overall reaction rate. In an energy diagram, the rate-determining step corresponds to the elementary step whose transition state presents the highest energy barrier relative to the preceding valley (or initial reactant state).

   Catalysis and Reaction Coordinates

   A catalyst increases the rate of a chemical reaction without being permanently consumed in the overall process. It achieves this by providing an alternative reaction pathway involving different elementary steps and intermediate species.

   Key thermodynamic and kinetic consequences depicted on an energy diagram:

   • Lowered Activation Energy: The alternative catalytic pathway possesses transition states with lower potential energies than the uncatalyzed pathway, yielding a smaller effective activation energy ($E_{\text{a, cat}} < E_{\text{a, uncat}}$).
   • Equal Acceleration of Forward and Reverse Rates: Because the barrier is lowered equally relative to the catalyzed transition state, both forward and reverse reaction rates increase proportionally.
   • Invariance of $\Delta H$: The initial energy of the reactants and the final energy of the products remain unchanged. Thus, a catalyst has no effect on the reaction enthalpy ($\Delta H$), equilibrium position, or overall reaction thermodynamics.