Complete and balance the following chemical equations:
$(a)$ $Ca(OH)_{2} + Cl_{2} \longrightarrow$
$(b)$ $CaSO_{4} \cdot 1/2 H_{2}O + H_{2}O \longrightarrow$
$(c)$ $Na_{2}CO_{3} \cdot 10H_{2}O \xrightarrow{\text{air}} \dots$

(N/A) $Ca(OH)_{2} + Cl_{2} \longrightarrow CaOCl_{2} + H_{2}O$ (Bleaching powder is formed).
$(b)$ $CaSO_{4} \cdot 1/2 H_{2}O + 1 \frac{1}{2} H_{2}O \longrightarrow CaSO_{4} \cdot 2H_{2}O$ (Gypsum is formed).
$(c)$ $Na_{2}CO_{3} \cdot 10H_{2}O \xrightarrow{\text{air}} Na_{2}CO_{3} \cdot H_{2}O + 9H_{2}O$ (Efflorescence occurs,forming sodium carbonate monohydrate).