Problem $1($modified Gaskell $9\mathrm{.}2)(30\text{'})$

According to Gaskell's textbook Appendix A Table A$\mathrm{.}4,$ the standard vapor pressure of Mn:

$lnp(atm)=-\frac{33440}{T}-3\mathrm{.}02lnT+37\mathrm{.}68$ at the temperature range $x_{Mn}=0\mathrm{.}5KMn1\mathrm{.}50gMn1atmMnMn{x}_{Mn}Fe-Mn1863K1517K.$

When $1$ mole $of$ Argon gas $is$ bubbled through a large volume $ofanFe-Mn$ melt $of{x}_{Mn}=0\mathrm{.}5at1863K$ evaporation $ofMn$ into the $Ar$ causes the mass $of$ the melt $to$ crease $by1\mathrm{.}50g.$ The mixing gas $(ArMn)$ leaves the melt $at$ a pressure $of1$atm. Please calculate:

$(a).$ What $is$ the partial pressure $ofMnin$ the $Ar-Mn$ mixing gas.

$(b).$ What $is$ the activity and activity coefficient $ofMnin$ the liquid alloy.

$(c).$ Please schematically draw the vapor pressure $ofMnas$ a function $of{x}_{Mn}in$ the $Fe-Mn$ melt $at1863K.$