Metal are extracted from their ores by a wide variety of techniques. The most common ores are oxides (MnO 2 ,Al 2 O 3 ,SnO 2 ), sulfides (PbS, ZnS), chlorides (NaCl, KCl, CaCl 2 , MgCl 2 ), and phosphates (Ca 3 (PO 4 ) 2 ). Most metals are obtained by direct treatment of their ores with chemical agents but the extraction of certain other requires electrolysis. An example of the former type of process is the extraction of iron form its oxide, described by the following equation : Fe 2 O 3 + 3C → 2Fe + 3CO

The relative case of extraction of a metal from its oxide can be estimated using the Ellingham diagram, which is show in figure. This diagram plots the free energies of formation of various oxides per mole of consumed oxygen as a function of absolute temperature. Electrolytic extraction proceeds in three steps (see equation). In the first step, the crystalline lattice of the ore is thermally disintegrated to form a liquid containing free metal cations. In the second step, the metal cations are stabilized by solvating them with some thermally stable non-aqueous solvent (NAS). In the final step, an applied electric potential reduces the cations to neutral atoms.

Step-1 : Ore(s) → M n+ ( l )

Step-2 : M n+ ( l ) + NAS → M n+ (solvent)

Step-3 : M n+ (solvated) + ne – → M

Extraction of a metal is usually preceded by enrichment of the ore. Some ores can be concentrated after pulverization by the use of specific collectors such as salt of organic acids and bases, which make the ores hydrophobic and thus separable from hydrophilic admixtures. Other enrichment techniques include density separation and magnetic separation.

(i) If for a certain ore the free energies of steps-3 and 2 were 248.50 and –250.25kJ, respectively, which of the following would determine the rate of extraction ?