What's the relationship between rate constant and temperature?

The rate constant of a reaction generally increases with temperature, as described by the Arrhenius equation.

The relationship between the rate constant (k) and temperature (T) is given by the Arrhenius equation: k = Ae^(-Ea/RT), where A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin. This equation shows that the rate constant increases exponentially with temperature.

The Arrhenius equation is derived from the concept that molecules must overcome a certain energy barrier, known as the activation energy, to react. At higher temperatures, more molecules have the kinetic energy needed to overcome this barrier, leading to an increase in the rate of reaction. This is reflected in the rate constant, which is a measure of the speed of a reaction.

The pre-exponential factor (A) in the Arrhenius equation is a measure of the frequency of collisions between molecules. It is generally assumed to be constant for a given reaction, although in reality it can vary slightly with temperature. The activation energy (Ea) is also typically constant for a given reaction.

The exponential term in the Arrhenius equation, e^(-Ea/RT), is known as the Boltzmann factor. It represents the fraction of molecules that have enough energy to overcome the activation energy barrier. As the temperature increases, the Boltzmann factor increases, meaning that a larger fraction of molecules can react. This leads to an increase in the rate constant.

In summary, the rate constant of a reaction is strongly dependent on temperature. According to the Arrhenius equation, it increases exponentially with temperature due to an increase in the fraction of molecules that have enough energy to react. This is a fundamental concept in chemical kinetics, which is the study of the rates of chemical reactions.