$PbO$ and $PbO_2$ react with $HCl$ according to the following chemical equations:
$(i)$ $2PbO + 4HCl \to 2PbCl_2 + 2H_2O$
$(ii)$ $PbO_2 + 4HCl \to PbCl_2 + Cl_2 + 2H_2O$
Why do these compounds differ in their reactivity?

(N/A) In equation $(i)$,the oxidation number of the elements does not change,so this reaction is not a redox reaction. It is an acid-base reaction.
In equation $(ii)$,the oxidation number of $Pb$ decreases from $+4$ to $+2$ (reduction) and the oxidation number of $Cl$ increases from $-1$ to $0$ (oxidation). Thus,$PbO_2$ acts as an oxidising agent and $Cl^-$ is oxidised to $Cl_2$.