Energy diagrams Knowledge-Based Study

Study notes

1. What is an Energy Diagram?

   A reaction energy diagram (also called a potential energy profile or reaction coordinate diagram) visually represents the energy changes that occur as reactants transform into products during a chemical reaction.

   • Vertical Axis (y-axis): Represents potential energy (enthalpy, $H$), typically measured in kilojoules per mole (kJ/mol).
   • Horizontal Axis (x-axis): Represents the reaction coordinate or reaction progress, tracing the geometric pathway of bond breaking and bond forming from initial reactants to final products.

   By examining an energy diagram, one can determine whether a reaction releases or absorbs thermal energy, evaluate the activation energy required to initiate the process, and identify temporary high-energy species formed along the pathway.

   Enthalpy Change ($\Delta H$)

   The overall enthalpy change of a reaction is defined as the difference between the enthalpy of the products and the enthalpy of the reactants:

   $\Delta H = H_{\text{products}} - H_{\text{reactants}}$

   1. Exothermic Reactions

   • The products reside at a lower potential energy than the reactants ($H_{\text{products}} < H_{\text{reactants}}$).
   • Energy is released to the surroundings, yielding a negative enthalpy change ($\Delta H < 0$).
   • The diagram displays a downward net step from left to right.

   2. Endothermic Reactions

   • The products reside at a higher potential energy than the reactants ($H_{\text{products}} > H_{\text{reactants}}$).
   • Energy is absorbed from the surroundings, yielding a positive enthalpy change ($\Delta H > 0$).
   • The diagram displays an upward net step from left to right.

   The Energy Barrier

   Molecules must collide with sufficient kinetic energy to overcome electrostatic repulsions and weaken existing chemical bonds. This required threshold is the activation energy ($E_a$).

   • Forward Activation Energy ($E_{a,\text{fwd}}$): The energy difference between the reactants and the peak of the energy barrier.
   • Transition State (Activated Complex): The chemical species located at the absolute peak of the curve. It represents an unstable, transient arrangement of atoms where old bonds are partially broken and new bonds are partially formed.
   • Reverse Activation Energy ($E_{a,\text{rev}}$): The energy difference between the products and the same transition state peak.

   The relationship connecting these quantities is given by:

   $\Delta H = E_{a,\text{fwd}} - E_{a,\text{rev}}$

   Notice that for an exothermic reaction, $E_{a,\text{rev}} > E_{a,\text{fwd}}$, whereas for an endothermic reaction, $E_{a,\text{fwd}} > E_{a,\text{rev}}$.

   Effects of a Catalyst

   A catalyst increases the rate of a chemical reaction by providing an alternative reaction pathway with a lower activation energy.

   • A catalyst lowers the energy of the transition state, thereby reducing both $E_{a,\text{fwd}}$ and $E_{a,\text{rev}}$ by the exact same amount.
   • A catalyst never alters the potential energy of the reactants or products; therefore, the overall enthalpy change ($\Delta H$) remains entirely unchanged.

   Multi-Step Reaction Diagrams

   Many chemical reactions proceed via multiple elementary steps:

   • Each elementary step possesses its own peak (transition state) and activation barrier.
   • Dips or local minima between peaks represent reaction intermediates—detectable, semi-stable species formed in one step and consumed in a subsequent step.
   • The step possessing the highest individual activation barrier relative to its immediate reactant or intermediate state serves as the rate-determining step (RDS).