Question

What is the difference between free energy and activation energy?

Answer 1

Free energy	Activation energy
The amount of energy which is available to perform the thermodynamic process is called free energy.	Activation energy somewhat works as an energy barrier which has to be overcome by the reactant to produce the products.
It is represented as $∆\mathrm{G}$, because free energy is also called Gibbs free energy.	It is represented as ${\mathrm{E}}_{\mathrm{a}}$.
They are not affected by catalysts.	They are affected by catalysts.
Mathematically it is represented as follows:$∆\mathrm{G}=∆\mathrm{H}-\mathrm{T}∆\mathrm{S}$; where $∆\mathrm{G}$is the change in Gibbs free energy, $∆\mathrm{H}$is the change in enthalpy, T is the temperature, $∆\mathrm{S}$is the change in entropy.	Activation energy can be represented as: $\mathrm{k}={\mathrm{Ae}}^{-\frac{\mathrm{Ea}}{\mathrm{RT}}}$; where k is the rate constant, A is the Arrhenius constant, R is the gas constant,${\mathrm{E}}_{\mathrm{a}}$ is the activation energy.