Concept of Activation Energy

For a reaction to occur, reactant molecules must collide with each other. Only those collisions result in product formation which have energy equal or more than a certain minimum energy. This energy is called the threshold energy. This implies that there is an energy barrier between reactants and products which must be crossed before products can be formed. The energy required for crossing the energy barrier comes from the kinetic energy of reacting molecules. Hence, the minimum extra energy over and above the average potential energy of the reactants, which must be supplied so that the reactants are able to cross over the energy barrier is called the activation energy (E_a).

Activation energy = (Threshold energy) - (Average energy of the reactants)

= E_T - E_R -------------(18)

The concept of activation can be easily visualized from the below figure.

fig 6.11 - Illustration of energy barrier

and activation energy involved in a reaction

Each reaction has a characteristic value of energy of activation. At a given temperature, a reaction with low activation energy will proceed faster than a reaction with high energy of activation. This can be easily determined from the Arrhenius equation. The exponential value is larger for a low E_a as compared to the value of the exponential with high E_a. In other words, if low E_a is E_a1 and high E_a is E_a2, then k₁ greater than k₂ where the indices 1 and 2 represent reaction 1 and reaction 2 respectively.

Activation energy is low for fast reactions.

Activation energy is high for slow reactions.

Example 11:

The rate constants of reaction at 700 K and 760 K are 0.011M^-1s^-1 and 0.105 M^-1s^-1 respectively. What are the values of 'A' and 'Ea'?

Suggested answer:

Arrhenius equation is ln k= ln A^{-Ea / RT}

T₁ = 700K, T₂ = 760K, k₁ = 0.011M^-1s^-1, k₂ = 0.105 M^-1s^-1

Substitution of these values in the equation gives

= 166.311 KJ / mol

ln A = 24.06

A = 2.8 x 10¹⁰ M^-1 s^-1

Example12:

What is the activation energy of a reaction whose rate quadruples when the temperature is raised from 293 K to 313 K.

Suggested answer:

or, E_a = 52.85 KJ / mol

Example 13

For a reaction with activation energy of 55 KJ/mol, by what factor will the rate constant go up with a rise in temperature from 300 K to 310 K.

Suggested answer:

where k₂ is the rate constant at 310k and k₁ is the rate constant at 300k.

This example shows that for a 10^o rise in temperature near the room temperature results in doubling of the rate of the reaction.