Reaction Coordinates and Activation Energy

Introduction

A mechanism proposes an order of bond changes; an energy diagram shows the barriers and intermediate states along that proposed path. Reactants cross transition-state peaks to reach products, sometimes pausing at local minima corresponding to intermediates. The height of a barrier influences rate, while the difference between starting and final states concerns thermodynamics. These are related but distinct pieces of information.

Core explanation

Plot energy vertically and reaction progress horizontally. The horizontal reaction coordinate is not necessarily literal time; it represents progress through molecular geometries along a pathway. A one-step concerted reaction such as an ideal SN2 substitution has one major peak, its transition state. A two-step SN1 path can show a first peak for leaving-group ionisation, a carbocation valley, and a second peak for nucleophile capture. The valley represents a species with a finite lifetime in the model; the peaks are not stable compounds that can be bottled.

Activation energy for a step is the energy difference from its starting state to its transition state in a simple enthalpy-like diagram. More accurately, reaction rates at a temperature relate to activation free-energy barriers, which incorporate entropy as well as energy. A lower barrier generally means a faster elementary step under comparable conditions. Raising temperature usually increases the fraction of molecular encounters able to cross a barrier, but it does not automatically alter the equilibrium preference in the same way.

The reaction energy difference between reactants and products indicates whether products are lower or higher in energy under the defined conditions. A product can be thermodynamically favoured but form slowly if the barrier is high. Conversely, a reaction can proceed quickly to a less stable product under kinetic control if its path is easier. A catalyst changes the pathway and lowers one or more barriers; it does not generally change the energies of starting and final states or the equilibrium constant.

For a multi-step path, the highest absolute peak is not always the correct simple rate-determining description. The relevant barrier is measured from the preceding intermediate or reactant state, and steady-state kinetics can involve several steps. At introductory level, one often identifies the slow step by its particularly large barrier relative to its immediate starting state. In SN1, ionisation can be slow because forming separated ions costs energy; a solvent that stabilises ions can reduce that barrier. The second capture step may then be faster.

An intermediate can sometimes be detected, trapped, or inferred from products such as rearranged skeletons. A transition state cannot be isolated as a stable molecule, though its structure can be inferred indirectly from kinetics, isotope effects, and computation. Reaction-coordinate diagrams are therefore representations of a model to test, not direct photographs of molecules moving along a line.

Step-by-step reasoning

1. Mark reactants, products, each peak, and each intervening valley. 2. Count peaks to identify proposed elementary steps. 3. Measure each barrier from its immediately preceding minimum. 4. Compare reactant and product levels for thermodynamic change. 5. Connect rate and catalyst claims to barrier heights, not just final energy.

Visual explanation

Draw a one-peak SN2 curve and a two-peak SN1 curve. Label transition states at peaks, a carbocation intermediate in the SN1 valley, and separate arrows for activation barrier and overall energy change.

Real-world analogy

A route over mountains may lead downhill overall but require climbing a high pass first. Destination height tells final stability; pass height controls how difficult the journey is.

Real-world example

A reaction becomes faster with a catalyst while product equilibrium stays essentially the same. The energy diagram shows a lower-barrier route with unchanged reactant and product levels.

Why?

Why is a transition state shown as a peak rather than a valley? It is a high-energy configuration that must be crossed, while a valley corresponds to a relatively persistent intermediate.

Common misconception

“A strongly exothermic reaction must be fast.” It can still have a high activation barrier and proceed slowly without an appropriate catalyst or initiation.

Worked example

Imagine reactants at 0 arbitrary energy units, a first transition state at 80, a carbocation intermediate at 30, a second transition state at 50, and products at −20. The first forward barrier is 80 units, while the second is 50−30 = 20 units. The overall product energy change is −20 units. The model therefore suggests slow initial ionisation despite an overall energy-lowering reaction. Do not equate the product's −20 value with its activation barrier.

Quick check

1. On a reaction-coordinate diagram, what does a valley between two peaks represent? Answer: A reaction intermediate, a local minimum between elementary barriers.

Exam focus

Measure barrier heights from their starting minima and distinguish activation free energy from overall product stability. Label axes and do not treat horizontal distance as elapsed time.

Advanced insight

Different mechanisms can have crossing free-energy profiles as conditions change. Solvent, concentration, and temperature may change which pathway has the lowest effective barrier and observed rate.

Summary

Reaction-coordinate diagrams show transition-state peaks, intermediate valleys, and product energies. Barrier heights inform rates, whereas reactant–product differences describe thermodynamic preference under the stated conditions.

Practice questions

1. How many transition-state peaks does a simple one-step SN2 path show? Answer: One peak for its concerted transition state. 2. Does a catalyst normally change the equilibrium constant solely by lowering a barrier? Answer: No. It accelerates approach to equilibrium through a lower-barrier path. 3. Can a lower-energy product form slowly? Answer: Yes, if the pathway to it has a large activation barrier.