Write the balanced chemical equation for each of the following cases:
$(a)$ Magnesium is treated with very dilute $HNO_3$.
$(b)$ Aluminium powder is added to $Fe_2O_3$.
$(c)$ Zinc sulphide is roasted.

(N/A) Magnesium reacts with very dilute nitric acid to produce magnesium nitrate and hydrogen gas:
$Mg(s) + 2HNO_3(aq) \longrightarrow Mg(NO_3)_2(aq) + H_2(g)$
$(b)$ Aluminium powder reacts with iron$(III)$ oxide in a thermite reaction to produce iron and aluminium oxide:
$Fe_2O_3(s) + 2Al(s) \longrightarrow 2Fe(l) + Al_2O_3(s) + \text{Heat}$
$(c)$ Zinc sulphide is roasted in the presence of oxygen to produce zinc oxide and sulphur dioxide gas:
$2ZnS(s) + 3O_2(g) \xrightarrow{\Delta} 2ZnO(s) + 2SO_2(g)$