$(40$pts$)$ Using Pb$-$Sn eutectic phase diagram answer following questions: Use atomic $\%!x_{Sn}=at\frac{\%}{100}!$

a$)(15)$Calculate the Henryian activity coefficient of $Pb$ and $Sn$ at the solubility limit at $250C$ assuming liquid solution obeys Regular solution model. $R=8\mathrm{.}314\frac{J}{m}ol.K$

b$)(10)$Calculate and draw activity of $Pb$ and $Sn$ vs$.$ mol fraction of $x_{Sn}$ at $250C.$

c$)(15)$Plot schematically

i$)G^m$ vs$.x_{Sn}$ curve for solid $($ and $)$ and liquid solution at $T($Eutectic$)$ and $\frac{300}{x}C.x$ is the last digit of the your S$.$number. If it is zero take it$,$ one.

ii$)$ Activity of $Sn$ and $Pb$ vs$.x_{Sn}$ at $T($Eutectic$)$ and $\frac{300}{x}C.$