In the MacArthur-Forrest cyanide process for silver extraction:

• Leaching (Oxidation): The crushed silver ore is treated with a dilute solution of $\text{NaCN}$ in the presence of atmospheric oxygen ($\text{O}_2$), which acts as the oxidising agent:
  $$4\text{Ag} + 8\text{CN}^- + 2\text{H}_2\text{O} + \text{O}_2 \rightarrow 4[\text{Ag}(\text{CN})_2]^- + 4\text{OH}^-$$
• Precipitation (Reduction): Zinc dust is added to reduce the dicyanoargentate(I) complex to metallic silver, where $\text{Zn}$ acts as the reducing agent:
  $$2[\text{Ag}(\text{CN})_2]^- + \text{Zn} \rightarrow [\text{Zn}(\text{CN})_4]^{2-} + 2\text{Ag}$$

Matching metallurgical processes with corresponding metals:

• Electrolytic reduction (Hall-Héroult process): Used for extraction of Aluminium ($\text{Al}$) from purified $\text{Al}_2\text{O}_3 \rightarrow$ (A)-(III).
• Bessemerization: Used in the converter for Copper ($\text{Cu}$) extraction to produce blister copper by auto-reduction $\rightarrow$ (B)-(IV).
• Smelting: Reduction in blast furnace using coke and limestone is famously applied to Iron ($\text{Fe}$) $\rightarrow$ (C)-(I).
• Reduction from oxide: Reduction of $\text{ZnO}$ with coke in vertical retort process is used for Zinc ($\text{Zn}$) $\rightarrow$ (D)-(II).

Matching minerals to their principal constituent metals:

• Siderite: Iron carbonate ($\text{FeCO}_3$) $\rightarrow$ Iron (II).
• Malachite: Basic copper carbonate ($\text{CuCO}_3\cdot\text{Cu(OH)}_2$) $\rightarrow$ Copper (III).
• Calamine: Zinc carbonate ($\text{ZnCO}_3$) $\rightarrow$ Zinc (IV).
• Bauxite: Hydrated aluminium oxide ($\text{AlO}_x(\text{OH})_{3-2x}$, $0 \lt x \lt 1$) $\rightarrow$ Aluminium (I).

The Van Arkel method is a vapour phase refining technique used for removing all oxygen and nitrogen impurities from metals like Zirconium ($\text{Zr}$) and Titanium ($\text{Ti}$):

$$\text{Zr (impure)} + 2\text{I}_2 \xrightarrow{870\text{ K}} \text{ZrI}_4\text{ (volatile)}$$ $$\text{ZrI}_4 \xrightarrow{2075\text{ K, Tungsten filament}} \text{Zr (pure)} + 2\text{I}_2$$

Nickel ($\text{Ni}$) is refined by the Mond process, Copper ($\text{Cu}$) by electrolytic refining, and Tin ($\text{Sn}$) by liquation.