Step 1: Identify Metal X:
Sphalerite is the ore Zinc Blende (\(\text{ZnS}\)). So, metal X is Zinc (Zn).
Step 2: Properties of Zinc:
Zinc is a metal with a relatively low boiling point (\(\text{b.p.} \approx 907^\circ\text{C}\)).
Common impurities like iron, lead, etc., have much higher boiling points.
Step 3: Select Purification Method:
Distillation is the method used for refining low boiling volatile metals like Zinc (Zn) and Mercury (Hg). The impure metal is heated, and pure metal vapors are condensed, leaving non-volatile impurities behind.
Comparison:
- Poling: Used for Copper (removal of oxides).
- Zone Refining: Used for Semiconductors (Si, Ge) for ultra-high purity.
- Vapour Phase Refining: Mond's Process (Ni), Van Arkel (Ti, Zr).
Final Answer:
Distillation.