6.3 Potential energy surfaces and reaction coordinates

Potential energy surfaces map out how energy changes as reactants transform into products during a chemical reaction. They're the key visual tool for understanding why some reactions are fast and others are slow, because they show the energy barriers a reaction must overcome. This section covers how to read these diagrams, what the reaction coordinate actually represents, and how to extract both kinetic and thermodynamic information from a single graph.

Potential Energy Surfaces

Potential energy diagram interpretation

A potential energy diagram is a graph that tracks the energy of a reacting system from start to finish.

• The x-axis is the reaction coordinate, which represents the progress of the reaction from reactants to products.
• The y-axis is the potential energy of the system at each point along that path.

Reactants sit at the left side of the diagram, typically at a local energy minimum. Products sit at the right side, also at a local minimum. The difference in height between these two points tells you about the thermodynamics of the reaction.

The transition state is the highest energy point along the minimum energy pathway connecting reactants to products. It represents a fleeting, unstable arrangement of atoms where old bonds are partially broken and new bonds are partially formed. You'll never isolate a transition state in a flask; it exists only at the very top of the energy barrier.

Reaction coordinate concept

The reaction coordinate isn't a single physical distance or angle. It's a composite variable that tracks the collection of bond-breaking and bond-forming events as the reaction proceeds. Think of it as the path of least resistance through a mountain pass: the system follows whatever combination of atomic motions requires the least energy to get from reactants to products.

This concept is crucial for understanding reaction mechanisms. A mechanism describes the step-by-step sequence of bond changes that convert reactants into products, including any intermediates (real, isolable species that exist in energy valleys between steps) and transition states (energy maxima that the system passes through but never lingers at).

Potential energy surface and kinetics

The shape of the potential energy surface directly controls how fast a reaction proceeds.

• Activation energy (the height of the barrier) is the dominant factor. A tall barrier means few molecules have enough energy to react at a given temperature, so the reaction is slow. A short barrier means many molecules can clear it, so the reaction is fast.
• Steepness of the curve near the transition state also matters. A narrow, steep barrier means the energy changes rapidly as the system moves through the transition state, which can influence how quickly molecules pass over the barrier.
• Multiple peaks on a diagram indicate a multi-step mechanism. Each peak is a separate transition state, and the valley between two peaks is a reactive intermediate. The overall reaction rate is typically governed by the step with the highest-energy transition state (the rate-determining step).

Thermodynamics and Kinetics

Activation energy from diagrams

You can extract both kinetic and thermodynamic quantities from a single potential energy diagram. Here's how to read each one:

1. Activation energy ($E_a$): Measure the energy difference between the reactants and the transition state (the peak). This is the minimum energy the system needs to reach the transition state and proceed to products.

2. Enthalpy change ($\Delta H$): Measure the energy difference between the reactants and the products.

   • If products are lower in energy than reactants: $\Delta H < 0$ (exothermic).
   • If products are higher in energy than reactants: $\Delta H > 0$ (endothermic).

3. Reverse activation energy: For the reverse reaction, $E_a$ is measured from the products up to the same transition state. In an exothermic reaction, the reverse $E_a$ is always larger than the forward $E_a$ by exactly $|\Delta H|$.

The relationship between $E_a$ and $\Delta H$ tells you about both the speed and the favorability of a reaction:

• Small $E_a$, negative $\Delta H$: Fast and thermodynamically favorable. The reaction proceeds easily and releases energy.
• Large $E_a$, positive $\Delta H$: Slow and thermodynamically unfavorable. The reaction needs a lot of energy input and the products are less stable than the reactants.
• Small $E_a$, positive $\Delta H$: Fast but thermodynamically uphill. The reaction can proceed quickly if energy is supplied, but the products are higher in energy.
• Large $E_a$, negative $\Delta H$: Thermodynamically favorable but kinetically slow. The reaction wants to happen energetically, but the barrier is too high for most molecules to clear at room temperature. Combustion of wood is a classic example: very favorable thermodynamically, but it won't ignite without a match.