$1.$ Discuss the methodology of constructing a fugacity chart for a binary system and its practical applications.

$-$ What are the key differences between ideal and non$-$ideal solutions, and how are these differences quantified?

$-$ Explain how the concept of partial molar volume is related to the activity coefficient and excess free energy.

$-$ Discuss the application of the Gibbs$-$Duhem equation in the analysis of ternary systems.