Reaction profiles and the energy barrier
A reaction profile (energy diagram) plots the potential energy of the reacting system against the progress of the reaction. It shows three key features:
- Reactant energy — the starting level, set as the reference.
- Transition state (activated complex) — the peak of the profile. The activated complex is an unstable arrangement of atoms at the point where old bonds are partially broken and new bonds are partially formed. It cannot be isolated.
- Product energy — the final level. If products are lower in energy than reactants, the reaction is exothermic (ΔH < 0); if higher, it is endothermic (ΔH > 0).
The activation energy is the vertical distance from the reactant energy level to the transition state peak. It is independent of ΔH — a highly exothermic reaction can still have a high activation energy and proceed very slowly without a catalyst.
For reaction rates and how activation energy determines how fast reactions proceed, see our reaction rates guide.
The Maxwell-Boltzmann distribution
At any given temperature, molecules in a gas or solution do not all have the same energy. The Maxwell-Boltzmann distribution shows the spread of molecular energies: a few molecules have very low energy, most have intermediate energy, and a tail of molecules has very high energy.
Only molecules with energy at or above Eₐ can react on collision. The activation energy therefore acts as a threshold — the area under the Maxwell-Boltzmann curve to the right of Eₐ represents the fraction of molecules capable of reacting.
When temperature increases:
- The distribution shifts to higher energies.
- The peak moves right and flattens.
- The area to the right of Eₐ increases substantially — a modest temperature rise can more than double the reaction rate.
When a catalyst is added:
- The distribution is unchanged (same temperature).
- Eₐ decreases — a larger fraction of molecules (larger tail area) now exceeds the barrier.
The Arrhenius equation
Svante Arrhenius (1889) quantified the relationship between temperature, activation energy and rate constant:
k = A · e−Eₐ/RT
Taking the natural log of both sides gives a linear form: ln k = ln A − Eₐ/RT. A plot of ln k against 1/T gives a straight line with slope −Eₐ/R, allowing Eₐ to be determined experimentally by measuring rate constants at different temperatures.
The exponential nature of the equation explains why even small decreases in Eₐ (e.g., from a catalyst) or small increases in temperature produce large increases in rate.
Biological significance: enzymes as activation energy reducers
Enzymes are the most effective catalysts known. The enzyme carbonic anhydrase catalyses the hydration of CO₂ (CO₂ + H₂O ⇌ H₂CO₃) at a rate of ~10⁶ reactions per second — a 10⁷-fold acceleration over the uncatalysed rate. It achieves this by:
- Binding both substrate molecules in the correct orientation (reducing the entropy cost of the transition state).
- Providing charged and hydrogen-bonding groups that stabilise the transition state — reducing Eₐ directly.
- Excluding water from the active site, avoiding competing side reactions.
Enzyme inhibitors — including many drugs — work by interfering with this Eₐ-lowering mechanism. See our enzymes guide for the full treatment of competitive and non-competitive inhibition.
For the connection between chemical kinetics and industrial catalysis (Haber process, Contact process), see our reaction rates guide and the catalyst glossary entry.