Respuesta :
1) Balance the chemical equation.
[tex]PbO_2+Mn^{2+}\rightarrow Pb^{2+}+MnO^-_4_{}[/tex]Step 1: Assign oxidation numbers
PbO2: Pb (+4) and O (-2)
Mn2+: Mn (+2)
Pb2+: Pb (+2)
MnO4-: Mn (+7) and O (-2)
Step 2: Figure out what's being reduced and what's being oxidized.
Mn has been oxidized. It changed from (+2) to (+7)
Pb has been reduced. It changed from (+4) to (+2)
Step 3: Write half-reaction
Oxidation half-reaction
[tex]Mn^{2+}\rightarrow MnO^-_4[/tex]Reduction half-reaction
[tex]PbO_2\rightarrow Pb^{2+}_{}[/tex]Step 4: Balance all elements EXCEPT for hydrogen and oxygen
Oxidation half-reaction
[tex]Mn^{2+}\rightarrow MnO^-_4[/tex]Reduction half-reaction
[tex]PbO_2\rightarrow Pb^{2+}_{}[/tex]Step 5: Balance oxygens. We do so by adding water molecules to the half-reactions as needed.
Oxidation half-reaction
[tex]Mn^{2+}+4H_2O\rightarrow MnO^-_4[/tex]Reduction half-reaction
[tex]PbO_2\rightarrow Pb^{2+}_{}+2H_2O[/tex]Step 6: Balance hydrogens. We do so by adding protons (H+) to the half-reactions as needed.
Oxidation half-reaction
[tex]Mn^{2+}+4H_2O\rightarrow MnO^-_4+8H^+[/tex]Reduction half-reaction
[tex]PbO_2+4H^+\rightarrow Pb^{2+}_{}+2H_2O[/tex]Step 7: Balance charges. We do so by adding electrons
Oxidation half-reaction
[tex]Mn^{2+}+4H_2O\rightarrow MnO^-_4+8H^++5e^-[/tex]Reduction half-reaction
[tex]PbO_2+4H^++2e^-\rightarrow Pb^{2+}_{}+2H_2O[/tex]Step 8: Multiply half-reactions to make the number of electrons equal.
Oxidation half-reaction.
[tex]2\cdot(Mn^{2+}+4H_2O\rightarrow MnO^-_4+8H^++5e^-)[/tex]New oxidation half-reaction.
[tex]2Mn^{2+}+8H_2O\rightarrow2MnO^-_4+16H^++10e^-[/tex]Reduction half-reaction
[tex]5\cdot(PbO_2+4H^++2e^-\rightarrow Pb^{2+}_{}+2H_2O)[/tex]New reduction half-reaction
[tex]5PbO_2+20H^++10e^-\rightarrow5Pb^{2+}_{}+10H_2O)[/tex]Step 9: Cancel electrons and combine the half-reactions
Overall reaction
[tex]2Mn^{2+}+8H_2O+5PbO_2+20H^+\rightarrow2MnO^-_4+16H^++5Pb^{2+}+10H_2O[/tex]Step 10: Balance the chemical equation by reducing the number of water molecules and protons.
Overall reaction
[tex]2Mn^{2+}+5PbO_2+4H^+\rightarrow2MnO^-_4+5Pb^{2+}+2H_2O[/tex]2) The balanced chemical equation
Overall reaction
[tex]2Mn^{2+}+5PbO_2+4H^+\rightarrow2MnO^-_4+5Pb^{2+}+2H_2O[/tex].
