Arrhenius Rate of Constant and Temperature

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,

• k signifies the rate of constant of a chemical reaction
• A signifies the pre-exponential factor which in the words of collision theory is described as the frequency of rightly oriented collisions between the species that react with each other.
• e defines the base of the natural logarithm, which is called Euler's number.
• Ea signifies the activation energy of the chemical reaction that takes place.
• R represents the universal gas constant
• T represents the absolute temperature related to the reaction (in Kelvin)

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 (K₈) present in the Arrhenius equation. The Arrhenius equation was formalized by the Swedish chemist called Svante Arrhenius in the year of 1889.

Is the process of catalysis accounted for, by the Arrhenius equation?

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.

Arrhenius plot

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.

Effect of temperature

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.

Effect of a catalyst on rate constant

A catalyst increases the rate of a reaction by decreasing the activation energy needed for the reaction to take place.

Real-life examples

• Milk turns sour much faster when kept in an open environment than keeping it in a refrigerator.
• During summers, butter becomes rancid much faster than in winters.
• Eggs boil faster at sea level but take a lot of time in the mountains.
• Cold-blooded animals like reptiles become lethargic during winter.