2.8:
Effect of Temperature Change on Reaction Rate
A reaction's rate law defines the relationship between a reactant concentration and the reaction rate in terms of a rate constant, ‘k’.
The rate constant describes the relationship between temperature and kinetic parameters relating to the collision, orientation, and activation energy of reacting molecules via the Arrhenius equation. ‘A’ is a constant called the Arrhenius factor or frequency factor. ‘e’ is an exponential factor integrating activation energy measured in joules-per-mole, the gas constant, and the temperature in kelvin.
The parameters’ temperature dependence can be explained with the collision model, which states that reacting molecules should collide with sufficient energy in the correct orientation to initiate a chemical reaction.
The frequency factor constitutes two components—the collision frequency and the orientation factor. The collision frequency is the number of molecular collisions per unit time, whereas the orientation factor describes the probability of collisions with a favorable orientation.
Still, only a small fraction of collisions leads to a reaction. This is because the reacting molecules have to overcome an energy barrier, called the activation energy, to transform into products.
Only those molecules colliding with sufficient kinetic energy will have enough potential energy to bend, stretch, or break bonds to transform into a high-energy intermediate called the transition state, or the activated complex. The short-lived, unstable activated complex loses energy to form stable products, whose total energy is lower than that of the reactants.
The exponential factor in the Arrhenius equation represents the fraction of successful collisions resulting in products. An increase in temperature influences both the frequency factor and the exponential factor.
At elevated temperatures, molecules move faster, more forcefully, and with higher thermal energies, leading to more favorable collisions.
For most reactions, a temperature increase results in higher frequency and exponential factors, leading to a rise in the rate constant, consequently translating to an accelerated reaction rate.
2.8:
Effect of Temperature Change on Reaction Rate
The Arrhenius equation,
relates the activation energy and the rate constant, k, for many chemical reactions.
In this equation, R is the ideal gas constant, which has a value 8.314 J/mol·K, T is the temperature in kelvin, Ea is the activation energy in joules per mole, e is the constant 2.7183, and A is a constant called the frequency factor, which is related to the frequency of collisions and the orientation of the reacting molecules.
The frequency factor, A, reflects how well the reaction conditions favor correctly oriented collisions between reactant molecules. An increased probability of effectively oriented collisions results in larger values for A and faster reaction rates.
The exponential term, e−Eₐ/RT, describes the effect of activation energy on the 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—a lower activation energy results in a more significant fraction of adequately energized molecules and a faster reaction.
The exponential term also describes the effect of temperature on the reaction rate. A higher temperature represents a correspondingly greater fraction of molecules possessing sufficient energy (RT) to overcome the activation barrier (Ea). This yields a higher value for the rate constant and a correspondingly faster reaction rate.
The minimum energy necessary to form a product during a collision between reactants is called the activation energy (Ea). The difference in activation energy required and 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 molecules, the reaction will occur slowly, since only a few fast-moving molecules will have enough energy to react. If the activation energy is much smaller than the molecules' average kinetic energy, a large fraction of molecules will be adequately energetic, and the reaction will proceed rapidly.
Reaction diagrams are widely used in chemical kinetics to illustrate various properties of a reaction of interest. It shows how a chemical system's energy changes as it undergoes a reaction, converting reactants to products.
This text is adapted from Openstax, Chemistry 2e, Section 12.5: Collision Theory.