Q.i. Obtain the relationship between $\Delta G^0$ of a reaction and the equilibrium constant.

For a reaction aA + bB to cC + dD at conditions away from equilibrium, the Gibbs energy change is given by ΔG = ΔG0 + RT ln Q, where ΔG0 is the STANDARD Gibbs energy change (with all reactants and products in their standard states) and Q is the REACTION QUOTIENT -- an expression in the same form as the equilibrium constant, but built from the actual (non-equilibrium) concentrations Qc = [C]^c[D]^d / [A]^a[B]^b or, for gas-phase reactions, partial pressures Qp = (PC^c PD^d) / (PA^a PB^b). When a reaction reaches equilibrium, ΔG becomes exactly zero and Q takes on its special equilibrium value, the equilibrium constant (Kc or Kp); substituting these into the general equation gives 0 = ΔG0 + RT ln K, which rearranges to the key relation connecting thermodynamics and chemical equilibrium: ΔG0 = -RT ln K = -2.303 RT log10 K. This single equation lets the equilibrium constant of a reaction be calculated directly from its standard Gibbs energy change (or vice versa), linking how FAR a reaction proceeds (K) to how FAVOURABLE it is thermodynamically (ΔG0) -- a large negative ΔG0 corresponds to a large K (reaction goes essentially to completion), while a large positive ΔG0 corresponds to a very small K (reaction barely proceeds).