$1-$ Using Maxwell$$s Relationships Express the Volume Dependence of the Chemical Potential $($i$.$e$.$ Molar Gibb$$s Free Energy on Volume at Constant Temperature, and evaluate it for Perfect and vdWaals Gases.

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$2-$ Normal Freezing Point of Gallium $($Ga$)$ is $+29\mathrm{.}76$ oC and the Enthalpy of Fusion at that temperature is $5\mathrm{.}59$ kJ$/$mol$.$

$[$forG $0($Ga$($s$))=0$ kJ$/$mol$,$ Molar Entropy of the Solid and Liquid Ga are $+40\mathrm{.}83$ and $59\mathrm{.}25$ J$/$K$.$mol, and Densities of Solid and Liquid Ga are; $5\mathrm{.}907$ and $6\mathrm{.}093$ g$/$cm$3$; respectively$]$

i$-$ By making suitable approximations, calculate the Molar Gibbs Free Energy of the Liquid and the Solid Ga at the Normal Freezing Point.

ii$-$ What is the Freezing Point under $100\mathrm{.}0$ atm? $[$Assume that both Solid and Liquid Ga are incompressible, i$.$e$.$ volume does not change with pressure.$]$

iii$-$Without doing any calculations, describe how you would find the Molar Gibbs Free Energy of the Liquid and the Solid Ga under $100\mathrm{.}0$ atm and at the new Freezing Point you find in $($ii$).$

$3-$ Partial Pressures of Acetone and Carbon Disulfide at $308\mathrm{.}35$ K are given.

i$-$ Is this an Ideal Solution?

ii$-$ What are the compositions of the Vapor Phase for Liquid Mixtures of $0\mathrm{.}250,0\mathrm{.}500$ and $0\mathrm{.}750$ Mole Fractions of CS$2?$

iii$-$ Estimate the Chemical Potential of Liquid Acetone for the Liquid Mixture of $0\mathrm{.}500$ Mole Fraction of CS$2$ at $308\mathrm{.}35$ K$,$ by using the below given exerimental data and assuming the gases obey the Perfecet Gas Law? $(15$ pts$)$

$[$For Acetone$($l$)$forG$0=-155\mathrm{.}4$ kJ$/$mol and Sm $0=200\mathrm{.}4$ J$/$K$.$mol $]$