Consider the binary liquid mixture of benzene and cyclohexane at $298K.$ Benzene has a boiling point of $80\mathrm{.}1C,$ and cyclohexane has a boiling point of $80\mathrm{.}75C.$

a$)$ At $x_{\text{b}\text{e}\text{n}\text{z}\text{e}\text{n}\text{e}}=0\mathrm{.}2,$ the mixture has an excess enthalpy of $+350\frac{J}{m}ol.$ Find the molar Gibbs energy of mixing assuming a regular mixture $)=(0.$

b$)$ Benzene and cyclohexane experience an azeotrope when at $x_{\text{b}\text{e}\text{n}\text{z}\text{e}\text{n}\text{e}}=0\mathrm{.}553$ and $77\mathrm{.}45C.$ Draw the temperature$-$composition diagram of the azeotrope.

c$)$ Why does this mixture result in a low$-$boiling azeotrope?