(a) Derive the relation between standard Gibbs energy change \(\Delta G^{0}\) and equilibrium constant \(K\).

(b) The water gas shift reaction \[ \mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightarrow \mathrm{CO}_{2}+\mathrm{H}_{2} \]
is carried out under the following conditions: The reactants are \(2 \mathrm{~mol}\) of \(\mathrm{H}_{2} \mathrm{O}\) and \(1 \mathrm{~mol}\) of \(\mathrm{CO}\). The temperature is \(1100 \mathrm{~K}\) and pressure is 1 bar. Data given: \(\ln K=0\). Find the equilibrium composition of the components.