Related Formula
Δ G° = -nFE°cell$$\Delta G^{\circ} = -nFE^{\circ}_{\text{cell}}$$
For a spontaneous reaction, Δ G° < 0$\Delta G^{\circ} < 0$.
Core Logic
Due to the inert pair effect, the stability of the lower oxidation state (+2$+2$) increases down the group in Group 14. Therefore, Pb²⁺$Pb^{2+}$ is more stable than Pb⁴⁺$Pb^{4+}$. Conversely, for lighter elements like Sn, the +4$+4$ oxidation state is more stable than +2$+2$.
Let's evaluate the first reaction:
PbO₂ + Pb arrow 2PbO$$PbO_{2} + Pb \rightarrow 2PbO$$
Here, Pb⁴⁺$Pb^{4+}$ (PbO₂$PbO_2$) is being reduced to Pb²⁺$Pb^{2+}$ (PbO$PbO$), and Pb⁰$Pb^{0}$ is being oxidized to Pb²⁺$Pb^{2+}$. Since Pb²⁺$Pb^{2+}$ is the more stable state, this reaction is thermodynamically favorable (spontaneous). Thus, Δᵣ G°(1) < 0$\Delta_r G^{\circ}(1) < 0$.
Step 1: Evaluate Second Reaction
Now evaluate the second reaction:
SnO₂ + Sn arrow 2SnO$$SnO_{2} + Sn \rightarrow 2SnO$$
Here, Sn⁴⁺$Sn^{4+}$ (SnO₂$SnO_2$) is being converted to Sn²⁺$Sn^{2+}$ (SnO$SnO$). However, we know that Sn⁴⁺$Sn^{4+}$ is more stable than Sn²⁺$Sn^{2+}$. This means the formation of Sn²⁺$Sn^{2+}$ from Sn⁴⁺$Sn^{4+}$ is not favored. The reaction is non-spontaneous. Thus, Δᵣ G°(2) > 0$\Delta_r G^{\circ}(2) > 0$.
Pattern Recognition
Inert pair effect drives heavier elements to lower oxidation states (spontaneous, Δ G < 0$\Delta G < 0$) and lighter elements to higher oxidation states (making reduction to lower state non-spontaneous, Δ G > 0$\Delta G > 0$).
Chapter Mix
Class 11 Chemistry: p-Block Elements
Class 12 Chemistry: Thermodynamics