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Metal extraction from oxides is fundamentally a reduction process governed by Gibbs free energy: Delta G = Delta H - TDelta S. A reaction is feasible when Delta G is negative. The Ellingham diagram plots Delta G of oxide formation (per mole O2) versus temperature.
Key features: (1) Most metal oxide lines slope upward because oxidation consumes gas (decreases entropy, Delta S negative). (2) A metal whose oxide-formation line lies BELOW can reduce the oxide whose line lies ABOVE. (3) At melting/boiling points, slope changes due to entropy change from phase transitions.
The carbon line is special. C + O2 -> CO2 has nearly zero slope (1 mol gas -> 1 mol gas, Delta S approximately 0). But 2C + O2 -> 2CO has a negative slope (1 mol gas -> 2 mol gas, Delta S positive). At high temperatures, the carbon line drops very low, making carbon an excellent reducing agent.
The aluminium line (4Al + 3O2 -> 2Al2O3) is very low — Al can reduce Fe2O3, Cr2O3, Mn3O4 (thermite reactions) but NOT MgO, CaO, Na2O (whose lines are even lower). This hierarchy determines which reducing agent is used for each metal: electrolysis for Na/K/Ca/Mg/Al, carbon for Zn/Fe/Sn/Pb, self-reduction for Cu.