State the conditions under which the following metals react with water. Write the equation for each reaction:
$(a)$ $Na$
$(b)$ $Mg$
$(c)$ $Fe$

(N/A) $Na$ reacts vigorously with cold water.
$2Na(s) + 2H_2O(l) \rightarrow 2NaOH(aq) + H_2(g)$
$(b)$ $Mg$ does not react with cold water but reacts with hot water.
$Mg(s) + 2H_2O(l) \rightarrow Mg(OH)_2(aq) + H_2(g)$
$(c)$ $Fe$ does not react with cold or hot water but reacts with steam.
$3Fe(s) + 4H_2O(g) \rightarrow Fe_3O_4(s) + 4H_2(g)$