Activation energy
Activation energy explains how a reaction can be thermodynamically favorable yet slow. Molecules do not move directly from reactants to products: they pass through high-energy configurations along a reaction pathway.
Barrier versus reaction energy
The forward activation energy Eₐ is the energy gap between reactants and the highest relevant barrier along the pathway. The reaction enthalpy or free-energy change compares reactants with products.
large negative ΔG does not imply small Eₐ
Diamond converting to graphite is thermodynamically favorable under ordinary conditions but kinetically extremely slow because the atomic network must reorganize through a large barrier.
Arrhenius equation
k = A e−Eₐ/RT
k is the rate constant, A is a pre-exponential factor containing collision/orientation information, R is the gas constant and T is absolute temperature. Because T sits in an exponential, modest heating can change k dramatically.
A useful linear form is ln k = ln A − Eₐ/(RT); plotting ln k against 1/T gives a slope of −Eₐ/R when Arrhenius behavior is valid.
Catalysts and reaction mechanisms
A catalyst participates in elementary steps and is regenerated overall. By stabilizing different intermediates or transition configurations, it creates a route with a smaller highest barrier.
The catalyst accelerates both forward and reverse reactions. It cannot make an unfavorable equilibrium favorable; it only helps the system approach the same equilibrium faster.
Enzymes are highly selective catalysts because their active sites bind particular molecular arrangements and stabilize specific reaction pathways.
Transition state and molecular orientation
“Having enough energy” is not sufficient for every collision. Reactants must also approach with a geometry that can rearrange bonds. The transition state is not an isolable ordinary molecule; it is the highest-energy region along a chosen reaction coordinate.
In multistep mechanisms, each elementary step has its own barrier. The slowest influential step is often associated with the largest free-energy barrier, but coupled steps can make simple “rate-determining step” language approximate.
Temperature sensitivity and safety
Because rate constants can rise exponentially with temperature, heat released by an exothermic reaction can accelerate the reaction further. Industrial reactors therefore require heat removal, mixing and kinetic data—not just thermodynamic calculations.
Activation energy inferred from an Arrhenius plot is an effective parameter over the measured temperature range. If the mechanism changes with temperature, a single straight line may fail.
Activation barriers in real measurements
Two-temperature estimate
The Arrhenius equation can be written between two temperatures: ln(k₂/k₁) = −Eₐ/R(1/T₂ − 1/T₁). This removes the unknown pre-exponential factor A and lets an effective activation energy be estimated from two rate constants.
Because the temperature must be in kelvin, a seemingly small Celsius change can produce a substantial exponential rate change.
Barrier height is a free-energy concept in detailed kinetics
Elementary-reaction theory often replaces a simple potential-energy barrier with an activation free energy ΔG‡. Transition-state theory gives a rate scale proportional to exp(−ΔG‡/RT), showing that entropy of activation can matter as well as enthalpy of activation.
Two pathways with similar energetic peaks can therefore have different rates if one transition configuration is much more constrained.
Catalysts can change the entire sequence
A catalyst need not merely “lower one hump.” It may create new intermediates and several smaller elementary barriers. Heterogeneous catalysts adsorb reactants on surfaces; acid catalysts transfer protons; enzymes position substrates and stabilize charge development.
Comparing catalyzed and uncatalyzed profiles should preserve the same initial and final thermodynamic states. Only the path changes.
Worked example: why 10 K can matter
Take an effective activation energy of 80 kJ mol⁻¹. The Arrhenius ratio between 298 K and 308 K is k₂/k₁ = exp[(Eₐ/R)(1/298 − 1/308)], which is about 2.85.
A ten-kelvin rise nearly triples the rate constant in this example. The familiar laboratory observation that “warming speeds reactions” is therefore an exponential kinetic effect, not merely slightly faster molecular motion.
Exercises
Thermodynamics versus kinetics
A reaction has ΔG < 0 but does not occur noticeably. Give one likely explanation.
Solution
It may have a large activation barrier, so the rate is extremely small.
Catalyst
Does a catalyst change ΔG°?
Solution
No. It changes the pathway and barrier, not the free-energy difference between reactants and products.
Arrhenius plot
What is the slope of ln k versus 1/T?
Solution
−Eₐ/R.