Energy, Activation

the difference between the values of the average energy of particles (molecules, radicals, ions) that participate in an elementary act of a chemical reaction and the average energy of all the particles in the reacting system.

Activation energy varies widely for different chemical reactions, from a few joules per mole to about 10 J/mole. For the same chemical reaction, the value of the activation energy depends on the form of the distribution functions of the molecules with respect to the energies of their translational motion and with respect to the internal degrees of freedom (electronic, vibrational, rotational). Activation energy should be differentiated as a statistical quantity from the threshold energy, the minimum energy that must be attained by a pair of colliding particles for a given elementary reaction to occur.

According to concepts of the theory of absolute reaction rates, activation energy is the difference between the average energy of activated complexes and the average energy of the initial molecules.

The idea of activation energy originated in the 1870’s and 1880’s as a result of research by J. Van’t Hoff and S. Arrhenius regarding the influence of temperature on the rate of a chemical reaction. The constant k of the rate of a reaction is related to the activation energy E by the Arrhenius equation:

k = k₀e^–E/RT

where R is the gas constant, T is the absolute temperature in °K, and k₀ is a constant called the pre-exponential, or frequency, factor of the rate constant. The equation, based on the molecular-kinetic theory, was later derived in statistical physics with consideration of a number of simplifying assumptions, one being that activation energy is independent of temperature. This assumption is valid for practical purposes and for theoretical calculations over comparatively narrow temperature ranges.

Activation energy can be found from experimental data by several methods. In one technique, the kinetics of a reaction are studied at different temperatures (for information on the various methods, seeREACTION RATE, CHEMICAL). A graph is plotted in coordinates of In k versus 1/T; according to the Arrhenius equation, the slope of the straight line on the graph is equal to E. For single-space reversible reactions, the activation energy of the reaction in the forward or reverse direction can be calculated if the activation energy of the reaction in the other direction is known, and the temperature dependence of the equilibrium constant is obtained from thermodynamic data. The temperature dependence of activation energy must be considered for more exact calculations.

The activation energy of complex reactions is a combination of the activation energies of the elementary stages. Sometimes the concept of “apparent” activation energy is used in addition to the true activation energy, determined from the Arrhenius equation. For example, if the rate constants of heterogeneously catalytic reactions are determined from changes in the volumetric concentrations of the initial substances and the products, then the apparent activation energy differs from the true value by the magnitude of the thermal effects that accompany processes of adsorption and desorption of the reacting substances on the surface of the catalyst. Determination of the activation energy is a very complex problem in nonequilibrium systems, for example, in plasma chemical systems. However, the formal application of the Arrhenius equation is possible in some cases.

The concept of activation energy is the most important concept of chemical kinetics; values are listed in special handbooks, and they are used in chemical technology to calculate the rate constants of reactions under various conditions.