At first sight this looks like an exponential multiplied by a factor that is linear in temperature. However, free energy is itself a temperature dependent quantity. The free energy of activation is the difference of an enthalpy term and an entropy term multiplied by the absolute temperature. The pre-exponential factor depends primarily on the entropy of activation. The overall expression again takes the form of an Arrhenius exponential (of enthalpy rather than energy) multiplied by a slowly varying function of T. The precise form of the temperature dependence depends upon the reaction, and can be calculated using formulas from statistical mechanics involving the partition functions of the reactants and of the activated complex. Limitations of the idea of Arrhenius activation energy Both the Arrhenius activation energy and the rate constant k are experimentally determined, and represent macroscopic reaction-specific parameters that are not simply related to threshold energies and the success of individual collisions at the molecular level. Consider a particular collision (an elementary reaction) between molecules A and B. The collision angle, the relative translational energy, the internal (particularly vibrational) energy will all determine the chance that the collision will produce a product molecule AB. Macroscopic measurements of E and k are the result of many individual collisions with differing collision parameters. To probe reaction rates at molecular level, experiments are conducted under near-collisional conditions and this subject is often called molecular reaction dynamics. Another situation where the explanation of the Arrhenius equation parameters fall short is in heterogeneous catalysis, especially for reactions that show Langmuir-Hinshelwood kinetics. Clearly, molecules on surfaces do not "collide" directly, and a simple molecular cross-section does not apply here. Instead, the pre-exponential factor reflects the travel across the surface towards the active site. There are deviations from the Arrhenius law during the glass transition in all classes of glass-forming matter. The Arrhenius law predicts that the motion of the structural units (atoms, molecules, ions, etc.) should slow down at a slower rate through the glass transition than is experimentally observed. In other words, the structural units slow down at a faster rate than is predicted by the Arrhenius law. This observation is made reasonable assuming that the units must overcome an energy barrier by means of a thermal activation energy. The thermal energy must be high enough to allow for translational motion of the units which leads to viscous flow of the material. See also