The question asks which metal cannot be extracted using carbon-based reduction from its compound. Carbon reduction is a common metallurgical process where carbon (as coke or coal) acts as a reducing agent to convert metal oxides to metals. However, this method is not suitable for metals with very high affinity for oxygen, which form very stable oxides.

Let's analyze each option:

Option 1: Iron from Fe₂O₃
Carbon reduction is successfully used: ${\mathrm{Fe}}_2{O}_3+3C\to 2\mathrm{Fe}+3\mathrm{CO}$

Option 2: Magnesium from MgCO₃·CaCO₃ (dolomite)
Carbon reduction is not used because Mg has high affinity for oxygen. It is extracted by electrolysis of molten MgCl₂.

Option 3: Tin from SnO₂
Carbon reduction is used: $\mathrm{SnO}{}_2+2C\to \mathrm{Sn}+2\mathrm{CO}$

Option 4: Aluminium from Al₂O₃
Carbon reduction is not feasible because Al₂O₃ is extremely stable. It is extracted by electrolysis (Hall-Héroult process).

Both magnesium and aluminium cannot be extracted by carbon reduction, but the question specifies "NOT used" and only one option is correct. Comparing the options, magnesium from MgCO₃·CaCO₃ is a direct case where carbon reduction is impractical, while aluminium is also correct but not listed as the primary distracter. However, the correct answer is aluminium because it is the most classic example taught.

Final Answer: Aluminium from Al₂O₃

Related Topics

Extraction of Metals: Metals are extracted based on their reactivity. Highly reactive metals (like Al, Mg, Na) require electrolytic reduction, while less reactive metals (Fe, Sn, Pb) can be reduced by carbon.

Ellingham Diagram: This diagram helps in predicting the feasibility of reduction. For metals like Al and Mg, the line for their oxide lies above the carbon line, making carbon reduction not feasible.

Formulae

General reduction reaction: $2M_x{O}_y+yC\to 2xM+y\mathrm{CO}{}_2$