From the Ellingham diagram $($figure $1),$ estimate the molar values $($based on $Mg{O}_{(s)})$ for the following reactions. $(12$ points$)$

$500C$

a$.A{l}_2{O}_{3(s)}+3M{g}_{(s)}=2A{l}_{(s)}+3Mg{O}_{(s)},G(773K)=?$

b$.A{l}_2{O}_{3(s)}+3M{g}_{(1)}=2A{l}_{(1)}+3Mg{O}_{(s)},H(1273K)=?$

c$.A{l}_2{O}_{3(s)}+3M{g}_{(g)}=2A{l}_{(l)}+3Mg{O}_{(s)},S(1473K)=?$

$1200C$

Figure $1.$ The Ellingham diagram for selected oxides.