Please answer all the questions clearly PS$=$ X$=2$ and Y$=4,0\mathrm{.}2$Y means $0\mathrm{.}24,5$XY means $5243)$ For a Ti$-$Cd binary solid solution, at $5$ X Y$^$C; activity coefficient $-$ molar fraction is expressed with the following equation

ln$\backslash$gamma $\_$c d$=0\mathrm{.}55-1\mathrm{.}10$ X$\_$c d$+0\mathrm{.}55$ X$\_$c d$^2$

a$)$ Using the Gibbs$-$Duhem relation calculate the activity of Titanium for X$\_$T$\_$i$=0\mathrm{.}2$ Y composition. b$)$ Calculate the mixing excess free energy of the solution. c$)$ Calculate the mixing free energy of the solution.