The Arrhenius equation is a formula that gives a relation between the rate constant of a chemical reaction, the absolute temperature, and the A-factor. The A-factor is also known as the pre-exponential factor. It can be observed as the frequency of structured collisions that take place between reactant particles. It gives insight into the dependence on the rates of reaction of absolute temperature. We usually write the expression of the Arrhenius equation as:
Where,
If the activation energy is defined in terms of energy per reactant molecule, then the universal gas constant should be altered with the Boltzmann constant (K_{8}) present in the Arrhenius equation. The Arrhenius equation was formalized by the Swedish chemist called Svante Arrhenius in the year of 1889.
The primary purpose of a catalyst is to lower the activation energy to match the required amount needed for a reaction. Hence, the lowered activation energy that is done by the catalyst can be replaced into the Arrhenius equation so that the rate constant can be obtained for the catalyzed reaction.
The exponential part of the Arrhenius equation (-Ea/RT) shows an exponential increase in the value of the rate of constant for any kind of decrease in the activation energy. The rate of a chemical reaction is directly proportional to the rate of constant of that reaction. The decrease in activation energy gives an outcome with an exponential rise in the reaction rate.
It is necessary to observe that the rates of uncatalyzed reactions are more importantly influenced by temperature than the rates of those reactions that are catalyzed. This is due to the activation energy present in the numerator of the term -Ea/RT and the absolute temperature is present in the denominator. The activation energy of the catalyzed reaction is comparatively low, it acts on the temperature of the rate constant that occurs more in the associated uncatalyzed reaction.
When logs are taken on the two sides of the equation, the Arrhenius equation is written as -
The Arrhenius plot for the decomposition of nitrogen dioxide is shown above in the picture.
ln k = ln (Ae_{-Ea/RT})
When solving the equation furthermore, we get:
ln k = ln (A) + ln (e_{-Ea/RT})
ln k = ln (A) + (-Ea/RT) = ln (A) – (Ea/R) (1/T)
As we can see that ln(A) is a constant, the equation that associates to that of a straight line (y = mx + c) whose slope (m) is -Ea/R. When we plot the logarithm of the rate constant (ln K) on the Y-axis and the opposite of the absolute temperature (1/T) is marked on the X-axis, that graph is termed an Arrhenius plot.
In a chemical reaction, the rate constant and temperature are directly proportional to each other. The rate of reaction increases exponentially with the temperature. As the temperature in the chemical reaction increases, the rate constant also increases. The kinetic energy of the reaction increases along with the temperature. As we increase the temperature, the kinetic energy in the number of molecules becomes greater than the activation energy. The rate of the overall reaction gets increased, whereas the activation energy gets decreased.
A catalyst increases the rate of a reaction by decreasing the activation energy needed for the reaction to take place.