Collision Theory and Activation Energy

Plot energy against reaction progress. The rise from reactants to the peak is the forward activation energy; the fall from the peak to products is the reverse activation energy. Their difference is ΔH, negative for an exothermic reaction and positive for an endothermic one. The species at the peak is the transition state, which cannot be isolated.

Suppose reactants are at 20 kJ/mol, a transition state at 95 kJ/mol and products at −10 kJ/mol on one common energy reference. Then E_a,f = 95 − 20 = 75 kJ/mol, E_a,r = 95 − (−10) = 105 kJ/mol and ΔH = −10 − 20 = −30 kJ/mol. Barriers are measured up from the relevant starting state; reaction enthalpy compares the endpoints. The horizontal coordinate is a reaction pathway, not elapsed time, so the width of a peak does not report the reaction duration.

At any temperature, molecular energies are spread over a wide distribution. Raising the temperature flattens and broadens the curve, shifting the peak to higher energy, and the area beyond the activation energy grows sharply. That growing tail, not a faster average speed alone, is what makes reactions accelerate so strongly with temperature.

For equal particle numbers, the total area under each energy distribution is the same. Heating lowers the peak height and broadens the distribution, but the area to the right of a fixed E_a line grows. The peak energy is not the energy of every particle, and some successful collisions occur below the mean energy of a hotter sample if they meet the same threshold. On a catalyst comparison at the same T, keep the distribution fixed and draw a lower threshold for the alternative pathway; do not redraw it as if the catalyst heated the sample.

Higher concentration or pressure increases collision frequency. Greater surface area on a solid increases the number of exposed particles available to collide. Higher temperature increases both frequency and, far more importantly, the fraction of collisions with sufficient energy. A catalyst lowers the activation energy so a larger fraction of existing collisions succeeds.

Compressing a gas by reducing volume at fixed T raises its concentration, often increasing collisions per volume. Adding an inert gas at fixed volume does not raise the reactant partial concentrations. Stirring can improve contact or remove a diffusion limitation, but it does not itself lower a molecular activation barrier. Powdering a solid changes exposed surface, while adding more of an already excess pure solid without changing accessible area need not produce the same effect.

A catalyst provides an alternative pathway with a lower barrier and is regenerated by the end. In a simple common-transition-state diagram it lowers both barriers equally; more generally it accelerates both directions consistently with the same equilibrium constant and unchanged reaction thermodynamics.

A one-peak diagram makes the endpoint relation E_a,f − E_a,r = ΔH especially clear: lowering that shared peak lowers both barriers by the same amount. Real catalysis can introduce several peaks and intermediate valleys, so the effective observed activation energies need not be represented by one identical numerical lowering. The general result is stronger and simpler: a catalyst changes the route and speeds equilibration, while leaving the reaction's ΔG°, ΔH and equilibrium constant at the same temperature unchanged. It cannot make an unfavorable net reaction favorable by itself.