Introduction to Carbon Reduction Method

The carbon-based reduction method, also known as smelting, is a pyrometallurgical process used to extract metals from their oxide ores. In this method, carbon (in the form of coke) acts as a reducing agent at high temperatures. The feasibility of this process for a given metal oxide is determined by thermodynamics, which can be visualized using an Ellingham diagram. For the reduction to be spontaneous, the Gibbs free energy change ($\Delta G$) for the overall reaction must be negative.

General reaction: $M_xO_y + C \rightarrow xM + CO/CO_2$

This method is generally effective for moderately reactive metals whose oxides are less stable than carbon monoxide or carbon dioxide at achievable temperatures (e.g., Fe, Sn, Zn, Pb). However, it is not suitable for highly reactive metals (e.g., Na, K, Mg, Al) because their oxides are extremely stable (have very large negative Gibbs free energy of formation). Reducing these oxides with carbon would require impractically high temperatures, often leading to undesirable side reactions like carbide formation.

Let's analyze each option:

Step 1: Analyze option A - tin from $SnO_2$

Tin (Sn) is a moderately reactive metal. Its primary ore is cassiterite ($SnO_2$). Tin is commercially extracted by smelting $SnO_2$ with carbon (coke) in a reverberatory furnace at about 1200-1300 °C.

$SnO_2(s) + 2C(s) \xrightarrow{\Delta} Sn(l) + 2CO(g)$

Since the carbon reduction method is used for the extraction of tin, this option is incorrect.

Step 2: Analyze option B - iron from $Fe_2O_3$

The extraction of iron from its ore, hematite ($Fe_2O_3$), is a classic example of carbon-based reduction. The process is carried out in a blast furnace where coke (carbon) serves as both a fuel and a reducing agent. The carbon first burns to form carbon monoxide (CO), which is the primary reducing agent.

$C(s) + O_2(g) \rightarrow CO_2(g)$ $CO_2(g) + C(s) \rightarrow 2CO(g)$

The reduction of iron oxide occurs in several steps: $3Fe_2O_3 + CO \rightarrow 2Fe_3O_4 + CO_2$ $Fe_3O_4 + CO \rightarrow 3FeO + CO_2$ $FeO + CO \rightarrow Fe + CO_2$

Direct reduction by carbon also occurs at higher temperatures: $FeO + C \rightarrow Fe + CO$. Since the carbon reduction method is central to iron extraction, this option is incorrect.

Step 3: Analyze option C - aluminium from $Al_2O_3$

Aluminium (Al) is a highly reactive metal. Its oxide, alumina ($Al_2O_3$), is extremely stable with a highly negative Gibbs free energy of formation ($\Delta G_f^\circ$). According to the Ellingham diagram, the line for the formation of $Al_2O_3$ is far below the lines for the formation of CO and $CO_2$. This means that reducing $Al_2O_3$ with carbon requires a very high temperature (above 2000 °C), which is not economically feasible. Furthermore, at such high temperatures, aluminium reacts with carbon to form aluminium carbide ($Al_4C_3$).

Therefore, carbon reduction is NOT used for aluminium extraction. Instead, aluminium is extracted by the Hall-Héroult process, which involves the electrolysis of a molten mixture of alumina ($Al_2O_3$) and cryolite ($Na_3AlF_6$). Thus, option C is a correct answer.

Step 4: Analyze option D - magnesium from $MgCO_3.CaCO_3$

Magnesium (Mg) is a highly reactive alkaline earth metal. The ore mentioned is dolomite ($MgCO_3.CaCO_3$). The first step is calcination to obtain the oxides:

$MgCO_3.CaCO_3(s) \xrightarrow{\Delta} MgO(s) + CaO(s) + 2CO_2(g)$

Like alumina, magnesium oxide ($MgO$) is very stable. The carbon reduction of $MgO$ is thermodynamically unfavorable except at extremely high temperatures (above 2000 °C).

$MgO(s) + C(s) \rightleftharpoons Mg(g) + CO(g)$

The reaction is reversible, and since magnesium is volatile at these temperatures, it is difficult to prevent the reverse reaction upon cooling.

Therefore, the carbon reduction method is NOT used for magnesium extraction. The main industrial methods are:

1. Dow Process: Electrolysis of molten $MgCl_2$.
2. Pidgeon Process: Thermal reduction of calcined dolomite with ferrosilicon (FeSi) under vacuum, not carbon.

Thus, option D is also a correct answer.

Conclusion

The carbon-based reduction method is not used for the extraction of highly reactive metals like aluminium and magnesium due to the high stability of their oxides. Therefore, the correct options are C and D.