# Arrhenius Equation: The Dependence Of Rate Constant On Temperature

We all know that most of the chemical reaction rates increase with an increase in temperature. It has been observed that for every 10oC rise in temperature, the rate of reaction gets doubled. Until 1889, there was no fixed way to relate the variation of the rate of a reaction with temperature. In 1889, the Swedish chemist, Svante Arrhenius proposed an empirical equation that related the rate constant of a chemical reaction with temperature.

## What is Arrhenius equation?

Arrhenius equation is a formula used to express the temperature dependence reaction rates. It was proposed in the year 1889 by Svante Arrhenius. With the help of this equation let us understand the dependence of rate constant on temperature occurring in chemical reactions.

## Arrhenius Equation:

k = Ae-(EA/RT)

Where,
k= rate constant of the reaction
A= Arrhenius Constant
Ea= Activation Energy
R= Universal Gas Constant
T=Temperature in absolute scale

The term Ea is called the activation energy. It is the minimum amount of energy that the reacting molecules must possess so that the effective collisions may result in the formation of products. It is also sometimes referred to as the Activation Energy Barrier, and the reacting molecules must cross this barrier to collide effectively and form products. Arrhenius equation is used extensively in an industry by process engineers and reactor designers to model reaction kinetics.

## Arrhenius Equation Derivation:

Consider the equation-

k =Ae-(EA/RT)

If we take to log on both sides of the equation, the resulting equation will be as follows:

ln k = ln A – EA/RT          ……….. (1)

Now let us compare this equation with the equation of a straight line that is y=mx+c, where the m= slope of the line and c= y-intercept.

So we have:
y = ln k
x = 1/T
m =-EA/R
c = ln A

## Dependence Of Rate Constant On Temperature

So a plot of ln k on the y-axis and 1/T on the x-axis will give a straight line with its slop equal to –EA/R and y-intercept equal to ln A.

The following figure is the Arrhenius Equation graph showing the plot of ln k Vs 1/T.

Arrhenius Equation graph

Arrhenius Equation plays a very important role in the study of reaction. It gives the dependence of rate constant on temperature for a chemical reaction and provides us with a method to quantify the variation in reaction rate with temperature.

Let us now consider a reaction has activation energy Ea is occurring at a temperature T1 and has a rate constant k1. Assume that the temperature of the reaction is now altered, and it is now T2. No, we have to calculate the rate constant k2 at temperature T2.

As per Arrhenius Equation, for first condition:

ln K1 = ln A -{(EA/R)*(1/T1)} ……………. (2)

For second condition:

ln K2 = ln A – {(EA/R)*(1/T2)} ……………. (3)

Subtracting Equation (2) from equation (3) we will get,

ln K2 – ln K1 = {(EA/R)*(1/T2)} – {(EA/R)*(1/T1)}

ln K2/K1 = EA/R{(1/T1) – (1/T2)}

The above equation can be used to determine the rate constant k2 at temperature T2. Equation (1) is referred to as the Arrhenius Equation in logarithmic form.

## Frequently Asked Questions on Arrhenius Equation

### What is Arrhenius factor ?

In the equation k =Ae-(EA/RT) the pre-exponential factor ‘A’ is the Arrhenius factor. It is also known as frequency factor which represents the frequency of collisions between reactant molecules.

### Who formulated Arrhenius equation ?

It was formulated by a Swedish chemist by name Svante Arrhenius in the year 1889.

### What is Arrhenius plot?

Arrhenius plot helps in displaying the logarithm of a reaction rate constant which is plotted against inverse temperature (1/T).

### What are the factors affect the rate of reaction?

Some factors that affect the rate of reaction are: Catalyst, The concentration of a reactant, Temperature, The pressure of a reactant.