Define Gibbs Free energy and hence Derive the Relationship between Equilibrium Constant and Gibbs free energy and hence Calculate ΔG ^o for conversion of oxygen to ozone 3/2 O₂ (g) ——> O₃ (g) at 300 K, if K_p for this conversion is 9.4710^-29.

Gibbs free energy:
It is the standard free energy which is equal to the difference in free energies of formation of the products and reactants both in their standard states. It is denoted by ΔG^o.
Relationship between Free Energy and Equilibrium Constant

When equilibrium has not been attained, the free energy change of the reaction in any state is denoted as ΔG which is related to the standard free energy change of the reaction, ΔG^o.

ΔG = ΔG^o + RT InQ
Where Q is the reaction quotient

When equilibrium is attained, there is no further free energy change i.e. ΔG = 0 and Reaction quotient Q becomes equal to equilibrium constant. Hence the above equation will become as shown below:

ΔG^o = –RT In K_eq

Or ΔG^o = –2.303 RT log K_eq

In case of galvanic cells. Gibbs energy change ΔG is related to the electrical work done by the cell.

ΔG = -nFE_cell
Where, n = no. of moles of electrons involved
F = the Faraday constant
E = emf of the cell

If reactants and products are in their standard states then
ΔG^o =nFE^o_cell
3/2 O₂ (g) ——> O₃ (g)
Now, ΔG^o = –2.303 RT log K_p

Where R = 8.314 J/K mol, K_p = 9.4710^-29, T = 300K

Hence Gibbs energy, ΔG^o = 160971 J/mol = 160.971 KJ/mol