Write the balanced chemical equations for the following reactions:
$(a)$ Chlorine is passed over dry slaked lime.
$(b)$ Sodium bicarbonate reacts with dilute hydrochloric acid.
$(c)$ Sodium bicarbonate is heated.

(N/A) When chlorine is passed over dry slaked lime $(Ca(OH)_2)$,it forms bleaching powder $(CaOCl_2)$ and water $(H_2O)$. The balanced equation is: $Ca(OH)_2 + Cl_2 \rightarrow CaOCl_2 + H_2O$
$(b)$ When sodium bicarbonate $(NaHCO_3)$ reacts with dilute hydrochloric acid $(HCl)$,it produces sodium chloride $(NaCl)$,water $(H_2O)$,and carbon dioxide $(CO_2)$. The balanced equation is: $NaHCO_3 + HCl \rightarrow NaCl + H_2O + CO_2$
$(c)$ When sodium bicarbonate $(NaHCO_3)$ is heated,it undergoes thermal decomposition to form sodium carbonate $(Na_2CO_3)$,water $(H_2O)$,and carbon dioxide $(CO_2)$. The balanced equation is: $2NaHCO_3 \xrightarrow{\Delta} Na_2CO_3 + H_2O + CO_2$