$(a)$ Balance the chemical equation:
$Fe(s) + H_2O(g) \rightarrow Fe_3O_4(s) + H_2(g)$
$(b)$ Identify the type of reaction in the equation given below:
$Na_2SO_4(aq) + BaCl_2(aq) \rightarrow BaSO_4(s) + NaCl(aq)$

(N/A) To balance the equation $Fe(s) + H_2O(g) \rightarrow Fe_3O_4(s) + H_2(g)$:
$1$. Balance $Fe$: $3Fe(s) + H_2O(g) \rightarrow Fe_3O_4(s) + H_2(g)$
$2$. Balance $O$: $3Fe(s) + 4H_2O(g) \rightarrow Fe_3O_4(s) + H_2(g)$
$3$. Balance $H$: $3Fe(s) + 4H_2O(g) \rightarrow Fe_3O_4(s) + 4H_2(g)$
The balanced equation is $3Fe(s) + 4H_2O(g) \rightarrow Fe_3O_4(s) + 4H_2(g)$.
$(b)$ The reaction $Na_2SO_4(aq) + BaCl_2(aq) \rightarrow BaSO_4(s) + NaCl(aq)$ is a double displacement reaction because there is an exchange of ions between the reactants to form new products.