# Two point arrhenius equation, Easy derivation, 3 application

Two point Arrhenius equation, Arrhenius equation definition, derivation, applications such as calculation of activation energy and frequency factor, and some related topic have been discussed here.

## Arrhenius equation definition

The effect of temperature on the rate of a chemical reaction can be explained quantitatively. Arrhenius derived a simple relationship between rate constant k and temperature of the reaction system, which is called as Arrhenius equation.

Arrhenius equation can be expressed as

k=A e –Ea/RT

Where, A= a constant which is also known as frequency factor or Arrhenius factor of the reaction, which can be determined experimentally.

Ea= activation energy of reaction

k= rate constant

T= temperature of the system in Kelvin

R= gas constant

## what is frequency factor in arrhenius equation

The frequency factor A in the Arrhenius equation is also known as Arrhenius factor or pre-exponential factor, which represents the frequency of collisions between the molecules in the reaction

## Two point arrhenius equation

From Arrhenius equation,

k=A e –Ea/RT

Taking natural logs on both sides of the above equation, we get,

ln k = ln A – Ea/RT

Or, ln k= -Ea/RT + ln A

At two different temperatures T1 and T2, the corresponding values of rate constants k1 and k2 are known respectively then, we can write as:

Subtracting equation (i) from the equation (ii), we get. This equation (iii) is known as the two-point Arrhenius equation. This form of the Arrhenius equation is very useful in calculating activation energy if experimental rate constants are given.

## Arrhenius equation derivation

Let us consider a chemical reaction

Where k1 and k2 are the rates constant for forwarding reaction and backward reaction respectively. These can be related with equilibrium constant kc as

kc= k1/k2

According to Vant Hoff’s relation, the change in equilibrium constant kc with temperature can be given as:

Putting the values of kc and ◬E in the above equation, we get

This equation can be split into the following two equations.

Where C1 and C2 are constant and whose value can be set to zero. From equations (i) and (ii), it is clear that the rate constant is related to the energy of reactants. Therefore, for a general reaction like

the above equation can be written as:

On integration, we obtain the following expression.

ln k = – E/RT + C ( Where C= Integration constant)

This equation is similar to Hood’s equation, therefore can be written as,

k=A e –Ea/RT

This is the expression of Arrhenius equation.

## Activation energy calculation from arrhenius equation

The activation energy of a particular chemical reaction can be calculated by using the Arrhenius equation.

According to the Arrhenius equation,

k=A e –Ea/RT

Taking ln on both sides, we get,

ln k = ln A – Ea/RT

On rearrangement, we have,

In k= -Ea/RT + ln A. This equation is in the form of y= mx+c. So, When ln k is plotted against 1/T, a straight line is obtained and the activation energy Ea can be calculated from the slope of the straight line.

## how to calculate frequency factor in arrhenius equation

The frequency factor or Arrhenius factor can be determined by plotting In k versus 1/T. When the plot is drawn, a straight line is obtained having an intercept equal to In A. Hence, the frequency factor is calculated from the intercept of the straight line as shown in the figure.

## Importance of arrhenius equation

The importance of the Arrhenius equation is listed below:

1. Arrhenius equation relates rate constant with the temperature and hence it can be used to study the effect of temperature on the reaction rate quantitatively.
2. Arrhenius equation can be used to calculate the activation energy of a particular chemical reaction.
3. This equation can be used to determine the frequency factor of a reaction, experimentally.

• K. J. Laidler, Chemical Kinetics, Harper and Row, New York, 1988
• G. K. Vemulapalli, Physical Chemistry, Prentice-Hall of India Pvt. Ltd., New Delhi,1997.
• P. Atkins and J. de Paula, Atkins’ Physical Chemistry, (10th Edition), Indian edition, Oxford University Press, 2014
• https://en.wikipedia.org/wiki/Arrhenius_equation

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