Activation Energy and the Arrhenius Equation

OpenStax Chemistry 2e

The minimum energy necessary to form a product during a collision between reactants is called the (Ea). How this energy compares to the kinetic energy provided by colliding reactant molecules is a primary factor affecting the rate of a chemical reaction. If the activation energy is much larger than the average kinetic energy of the molecules, the reaction will occur since only a few fast-moving molecules will have enough energy to react. If the activation energy is much smaller than the average kinetic energy of the molecules, a large fraction of molecules will be adequately energetic and the reaction will proceed . The picture below shows how the energy of a chemical system changes as it undergoes a reaction converting reactants to products according to the equation A + B → C + D.

Reaction diagram for the exothermic reaction A + B ⟶ C + D. Source: OpenStax Chemistry 2e

These are widely used in chemical kinetics to illustrate various properties of the reaction of interest. Viewing the diagram from left to right, the system initially comprises reactants only, A + B. Reactant molecules with sufficient energy can collide to form a high-energy activated complex or . The unstable transition state can then subsequently decay to yield stable products, C + D. The diagram depicts the reaction’s activation energy, Ea , as the energy difference between the reactants and the transition state. Using a specific energy, the enthalpy, the enthalpy change of the reaction, ΔH, is estimated as the energy difference between the reactants and products. In this case, the reaction is (ΔH < 0) since it yields a decrease in system enthalpy.

The Arrhenius equation relates the activation energy and the , for many chemical reactions:

In this equation, R is the , which has a value 8.314 J/mol/K, T is temperature on the Kelvin scale, Ea is the activation energy in joules per mole, e is the constant 2.7183, and A is a constant called the , which is related to the frequency of collisions and the orientation of the reacting molecules.

Postulates of collision theory are nicely accommodated by the Arrhenius equation. The frequency factor, A, reflects how well the reaction conditions favor properly oriented collisions between reactant molecules. An increased probability of effectively oriented collisions results in larger values for A and .

The exponential term, e−Ea/RT, describes the effect of activation energy on reaction rate. According to kinetic molecular theory, the temperature of matter is a measure of the average kinetic energy of its constituent atoms or molecules. The distribution of energies among the molecules composing a sample of matter at any given temperature is described by the plot shown in the first picture below. Two shaded areas under the curve represent the numbers of molecules possessing adequate energy (RT) to overcome the activation barriers (Ea). A activation energy results in a greater fraction of adequately energized molecules and a faster reaction.

The exponential term also describes the effect of temperature on reaction rate. A higher temperature represents a correspondingly greater fraction of molecules possessing sufficient energy (RT) to overcome the activation barrier (Ea), as shown in the second picture below. This yields a greater value for the rate constant and a correspondingly faster reaction rate.

Molecular energy distributions showing numbers of molecules with energies exceeding (a) two different activation energies at a given temperature, and (b) a given activation energy at two different temperatures. Source: OpenStax Chemistry 2e

A convenient approach for determining Ea for a reaction involves the measurement of k at two or more different temperatures and using an alternate version of the Arrhenius equation that takes the form of a linear equation

Source: OpenStax Chemistry 2e