Write balanced chemical equations for the following:
$(a)$ Calcium carbonate reacts with hydrochloric acid.
$(b)$ Calcium oxychloride reacts with hydrochloric acid.
$(c)$ Sodium hydroxide reacts with zinc.

(N/A) Calcium carbonate reacts with hydrochloric acid to form calcium chloride,water,and carbon dioxide:
$CaCO_{3} + 2HCl \rightarrow CaCl_{2} + H_{2}O + CO_{2}$
$(b)$ Calcium oxychloride (bleaching powder) reacts with hydrochloric acid to form calcium chloride,water,and chlorine gas:
$CaOCl_{2} + 2HCl \rightarrow CaCl_{2} + H_{2}O + Cl_{2}$
$(c)$ Sodium hydroxide reacts with zinc to form sodium zincate and hydrogen gas:
$2NaOH + Zn \rightarrow Na_{2}ZnO_{2} + H_{2}$