Arrhenius Equation and Activation Energy

Arrhenius Equation

For a chemical reaction with rise in temperature by 10°, the rate constant is nearly doubled.

The temperature dependence of the rate of a chemical reaction is given by Arrhenius equation,

where,

A = frequency or Arrhenius factor or pre-exponential factor,

R = gas constant and

E_a = activation energy

Taking log on both sides, we get,

The graph of ln k and  is a straight line.

In the Arrhenius equation, when T → ∞ or E_a = 0 then

k = Ae⁰ = A,

and the rate of reaction becomes independent of temperature

Activation Energy (E_a)

The additional amount of energy, required by the reactant so that their energy (E_R) becomes equal to the threshold value is known as activation energy.

E_a = E_T - E_R

Lower the activation energy, faster is the reaction.

Different reactions have different rates because their activation energies are different.

Larger the value of E_a, smaller the value of rate constant and greater is the effect of a given temperature rise on k.

Activated complex (or transition state)

Activated complex is the highest energy unstable intermediate between the reactants and products and gets decomposed immediately (having very short life), to give the products. In this state, bonds of reactant are not completely broken while the bonds of products are not completely formed.

Example

H₂ (g) + I₂ (g) → 2HI (g)