Why do the following reactions proceed differently? `Pb_(3)O_(4)+8HClrarr3PbCl_(2)+Cl_(2)+4H_(2)O` and `Pb_(3)O_(3)+4HNO_(3)rarr 2Pb(NO_(3))_(2)+PbO_(2)+2H_(2)O`

Explanation

`Pb_(3)O_(4) -= 2overset((+2))(Pb)O.overset((+4))(Pb)O_(2)`. In `PbO_(2)`, lead is present in +4 oxidation state, whereas the stable stable state of lead is +2. `PbO_(2)` thus can act as an oxidant and therefore, can oxidise `Cl^(-)` ion on HCl into Chloine. We may also keep in mind that PbO is a basic oxide.
The reaction `Pb_(3)O_(4) + 8HCl rarr 3PbCl_(2) + Cl_(2) + 4H_(2)O` can be splitted into acid-base reaction `(2PbO + 4HCl rarr 2PbCl_(2) + 2H_(2)O)` and redox reaction `(PbO_(2) + 4HCl rarr PbCl_(2) + Cl_(2) + 2H_(2)O. PbO_(2)` can not oxidise `NO_(3)^(-)`.
Hence the reaction `Pb_(3)O_(4) + 4HNO_(3) rarr 2Pb(NO_(3))_(2) + PbO_(2) + 2H_(2)O` is only acid-base reaction.