6.9 Describing a Reaction: Energy Diagrams and Transition States

Energy Diagrams and Transition States

Energy diagrams for organic reactions

Energy diagrams (also called reaction profiles) plot the potential energy of a reacting system against the reaction coordinate, which tracks progress from reactants to products.

• The x-axis is the reaction coordinate, representing how far along the reaction has progressed.
• The y-axis is the potential energy of the system at each point.

The energy levels of reactants and products sit at different heights on the diagram. The difference between them tells you whether the reaction is exergonic (energy released, products lower) or endergonic (energy absorbed, products higher).

The transition state is the highest-energy point along the pathway from reactants to products. It's not a real molecule you can isolate; it's a fleeting arrangement of atoms where old bonds are partially broken and new bonds are partially formed. Transition states are drawn in brackets with a double-dagger symbol ($\ddagger$).

Why does the transition state matter? Its structure influences both the reaction rate and the stereochemical outcome of the products. The Hammond postulate connects the structure of the transition state to whichever species (reactant or product) it's closer to in energy. For an exergonic step, the transition state resembles the reactants; for an endergonic step, it resembles the products.

Activation energy ($E_a$) is the energy difference between the reactants and the transition state. It represents the minimum energy barrier that must be overcome for the reaction to proceed. A higher $E_a$ means a slower reaction, because fewer molecules have enough energy to clear that barrier at a given temperature.

Activation energy and reaction rates

Reaction rate depends on what fraction of molecules have enough kinetic energy to reach the transition state. The Arrhenius equation captures this relationship:

$k = Ae^{-E_a/RT}$

• $k$ = rate constant
• $A$ = pre-exponential factor (accounts for collision frequency and proper orientation)
• $E_a$ = activation energy
• $R$ = gas constant
• $T$ = absolute temperature (in Kelvin)

Two practical takeaways from this equation:

• Higher $E_a$ → smaller $k$ → slower reaction. The exponential relationship means even modest increases in $E_a$ can dramatically slow a reaction.
• Higher temperature → larger fraction of molecules with enough energy to cross the barrier → faster reaction. A common rough estimate is that reaction rates roughly double for every 10°C increase, though this varies.

Reactions with very high activation energies are essentially "forbidden" at room temperature. Catalysts address this by providing an alternative pathway with a lower-energy transition state. The catalyst doesn't change $\Delta G$ for the reaction; it only lowers $E_a$, making the reaction faster.

Types of organic reaction profiles

Exergonic reactions have products at lower energy than reactants ($\Delta G < 0$). These are thermodynamically favorable. Combustion of glucose is a classic example.

Endergonic reactions have products at higher energy than reactants ($\Delta G > 0$). These are non-spontaneous under standard conditions and require energy input. In biological systems, endergonic reactions are often coupled to exergonic ones (like ATP hydrolysis) to drive them forward.

Not all energy diagrams show a single smooth hill. Many organic reactions proceed through intermediates, which are real (though often short-lived) species that sit in energy valleys between two transition states. Each step in the mechanism has its own transition state and its own $E_a$. For example, an $S_N1$ reaction passes through a carbocation intermediate, so its energy diagram has two humps with a valley in between.

Thermodynamics and Kinetics in Organic Reactions

The spontaneity of a reaction depends on both enthalpy ($\Delta H$, the heat absorbed or released) and entropy ($\Delta S$, the change in disorder), combined through the Gibbs free energy equation:

$\Delta G = \Delta H - T\Delta S$

A reaction can be enthalpically unfavorable but still spontaneous if the entropy increase is large enough (and vice versa). Temperature plays a decisive role in tipping the balance.

Transition state theory builds on these ideas by treating the transition state as a special, high-energy species in quasi-equilibrium with the reactants. The rate of reaction then depends on how easily and how often molecules reach that transition state geometry. For complex reactions involving multiple bonds changing simultaneously, the full energy landscape is a multidimensional potential energy surface, though for most organic chemistry purposes, the simplified two-dimensional reaction coordinate diagram captures the essential features.