Carbon Reduction Method in Extraction of Metals

To determine which metals are NOT extracted using carbon-based reduction, let us evaluate each option based on metallurgical principles and thermodynamic stability:

1. Tin from $\text{SnO}_2$ (Cassiterite):

   • Tin oxide ($\text{SnO}_2$) is moderately stable and can be reduced to metallic tin using carbon (coal/charcoal) in a reverberatory furnace at around $1200\text{--}1300^\circ\text{C}$: $\text{SnO}_2 + 2\text{C} \xrightarrow{\Delta} \text{Sn} + 2\text{CO}$
   • Therefore, carbon-based reduction is used for extracting tin.

2. Iron from $\text{Fe}_2\text{O}_3$ (Hematite):

   • Hematite ($\text{Fe}_2\text{O}_3$) is reduced in a blast furnace using coke (carbon) and carbon monoxide ($\text{CO}$): $\text{Fe}_2\text{O}_3 + 3\text{C} \xrightarrow{\Delta} 2\text{Fe} + 3\text{CO}$
   • Therefore, carbon-based reduction is used for extracting iron.

3. Aluminium from $\text{Al}_2\text{O}_3$ (Alumina):

   • Aluminium has a very high affinity for oxygen ($\Delta G_f^\circ$ of $\text{Al}_2\text{O}_3$ is extremely negative).
   • Reduction of $\text{Al}_2\text{O}_3$ with carbon requires extremely high temperatures ($> 2000^\circ\text{C}$), at which aluminium forms aluminium carbide ($\text{Al}_4\text{C}_3$) rather than metallic aluminium.
   • Instead, aluminium is extracted by the Hall-Héroult electrolytic reduction process.
   • Therefore, carbon-based reduction is NOT used for extracting aluminium.

4. Magnesium from $\text{MgCO}_3 \cdot \text{CaCO}_3$ (Dolomite):

   • Highly electropositive metals like magnesium cannot be practically reduced by carbon because magnesium forms carbides at high temperatures and recombines with $\text{CO}$ upon cooling.
   • Commercially, magnesium is extracted using the Pidgeon process (silicothermic reduction using ferrosilicon, $\text{FeSi}$) or through the electrolysis of fused $\text{MgCl}_2$.
   • Therefore, carbon-based reduction is NOT used for extracting magnesium.

Thus, the method of carbon-based reduction is NOT employed for the extraction of aluminium (C) and magnesium (D).

Correct Options: (C) and (D)