For a binary system, the excess Gibbs free energy of components 1 and 2 at \(30^{\circ} \mathrm{C}\) is given by \(\frac{G^{\mathrm{E}}}{R T}=0.500 x_{1} x_{2}\). The vapour pressures of components 1 and 2 are given by

\[ \ln P_{1}^{\text {Sat }}=11.92-\frac{4050}{T} \quad \text { and } \quad \ln P_{2}^{\text {Sat }}=12.12-\frac{4050}{T} \]

where \(P_{1}^{\text {Sat }}\) and \(P_{2}^{\text {Sat }}\) are in bar and \(T\) is in \(\mathrm{K}\). Calculate the composition of the azeotrope.