6.10 Describing a Reaction: Intermediates

Reaction Intermediates and Energy Diagrams

Reaction intermediates in organic chemistry

In a multistep reaction, intermediates are the species that form after the starting material but before the final product. They're produced in one step and consumed in the next, which is why you can't usually isolate them.

• The number of intermediates is always one fewer than the number of steps. A two-step reaction has one intermediate; a three-step reaction has two.
• Intermediates are often highly reactive species: carbocations, carbanions, or radicals. They can also be neutral but still reactive molecules.
• A classic example: when an alkene reacts with bromine, a bromonium ion forms as an intermediate. That bromonium ion then reacts further (say, with water) to give the final product.

Understanding what the intermediate is and how it behaves is central to figuring out a reaction mechanism. If you can identify the intermediate, you can usually reason through the rest of the pathway.

Energy diagrams for two-step reactions

Energy diagrams plot the potential energy of all species in a reaction as the reaction progresses. The x-axis is the reaction coordinate (think of it as a timeline of bond-breaking and bond-forming), and the y-axis is potential energy.

For a two-step reaction, the diagram has two peaks and one valley between them:

1. The first transition state (peak 1) sits between the reactants and the intermediate.
2. The intermediate appears as a valley (local energy minimum) between the two peaks. It's lower in energy than either transition state, but typically higher in energy than the reactants or products.
3. The second transition state (peak 2) sits between the intermediate and the products.

Transition states are energy maxima where bonds are partially broken and partially formed. They're not real isolable species; they exist only at the top of each energy hill.

Two key quantities you can read directly from the diagram:

• Overall activation energy ($E_a$): the energy difference between the reactants and the highest transition state on the diagram. This controls how fast the overall reaction proceeds.
• Overall free energy change ($\Delta G$): the energy difference between the reactants and the products. This tells you whether the reaction is thermodynamically favorable.

Activation energy in multistep reactions

The step whose transition state is highest in energy is the rate-determining step (RDS). It acts as a bottleneck because the reaction can't go faster than its slowest step.

• For example, in an $S_N1$ reaction, the rate-determining step is formation of the carbocation, because that transition state has the highest activation energy.
• You can also read the activation energy for each individual step off the diagram: it's the energy gap between the starting point of that step (reactant or intermediate) and its transition state.

For thermodynamics, the overall $\Delta G$ equals the sum of the free energy changes for every step:

$\Delta G_{overall} = \Delta G_1 + \Delta G_2 + \cdots + \Delta G_n$

Each step can be individually favorable ($\Delta G < 0$) or unfavorable ($\Delta G > 0$). What matters for the overall reaction is the sign of $\Delta G_{overall}$. A negative value means the reaction is thermodynamically favorable; a positive value means it's not.

Kinetics and thermodynamics in reaction analysis

These two concepts answer different questions about a reaction:

• Kinetics asks how fast? It depends on activation energies and transition state heights. A reaction with a low $E_a$ is fast; a reaction with a high $E_a$ is slow.
• Thermodynamics asks how far? It depends on $\Delta G$. A large negative $\Delta G$ means the reaction strongly favors products at equilibrium.

A reaction can be thermodynamically favorable but kinetically slow (large negative $\Delta G$, but high $E_a$), or the reverse. The energy diagram lets you see both features at once.

Hammond's postulate bridges kinetics and thermodynamics by connecting the structure of a transition state to whatever stable species (reactant, intermediate, or product) is closest to it in energy. If a transition state is high in energy and close in energy to the intermediate, its structure will resemble that intermediate. This is useful because you can't observe transition states directly, but you can reason about intermediate stability, and Hammond's postulate lets you use that reasoning to predict reaction rates and selectivity.