General Principles and Processes of Isolation of Elements: Key Formulae

1. Concentration of Ores

• Hydraulic Washing:
• • Based on differences in specific gravity of the ore and gangue.
• Magnetic Separation:
• • Used when either the ore or the gangue is magnetic.
• Froth Flotation Method:
• • $\text{Froth flotation method: Collectors and froth stabilizers are used to separate sulfide ores.}$
• Leaching (e.g., of Alumina):
• • ${\text{Al}}_2{\text{O}}_3+2\text{NaOH}+3{\text{H}}_2\text{O}\to 2\text{Na}[{\text{Al(OH)}}_4]$

2. Extraction of Metals from Concentrated Ore

• Calcination:
• • ${\text{Fe}}_2{\text{O}}_3\cdot x{\text{H}}_2\text{O}\stackrel{\Delta }{\to }{\text{Fe}}_2{\text{O}}_3+x{\text{H}}_2\text{O}$
• Roasting:
• • $2\text{ZnS}+3{\text{O}}_2\to 2\text{ZnO}+2{\text{SO}}_2$
  • $2{\text{Cu}}_2\text{S}+3{\text{O}}_2\to 2{\text{Cu}}_2\text{O}+2{\text{SO}}_2$

3. Thermodynamic Principles of Metallurgy

• Gibbs Free Energy:
• • $\Delta G=\Delta H-T\Delta S$
  • Ellingham Diagram: Used to predict the feasibility of a reduction process.
• Reduction of Metal Oxides:
• • $\text{MxO}+y\text{C}\to x\text{M}+y\text{CO}$
  • For example:
  • $\text{FeO}+\text{C}\to \text{Fe}+\text{CO}$

4. Electrochemical Principles of Metallurgy

• Electrolytic Reduction:
• • $\Delta G^{\circ }=-nF{E}^{\circ }$
• Electrolysis (e.g., Hall-Heroult Process for Aluminium):
• • Overall reaction:
  • $2{\text{Al}}_2{\text{O}}_3+3\text{C}\to 4\text{Al}+3{\text{CO}}_2$

5. Example Applications

• Extraction of Iron (Blast Furnace Reactions):
• • ${\text{Fe}}_2{\text{O}}_3+3\text{CO}\to 2\text{Fe}+3{\text{CO}}_2$
• Extraction of Copper (Reverberatory Furnace):
• • $2{\text{Cu}}_2\text{S}+3{\text{O}}_2\to 2{\text{Cu}}_2\text{O}+2{\text{SO}}_2$

6. Common Mistakes and Tips

• Incorrect unit conversions in thermodynamics: Always check the units when calculating $\Delta G$.
• Misinterpretation of the Ellingham Diagram: Remember that only reactions with negative $\Delta G$ are spontaneous.

Formula Explanation and Derivations

1. Gibbs Free Energy ($\Delta G$):
2. • Principle: Determines the spontaneity of a reaction. A negative $\Delta G$ indicates a spontaneous process.
   • Units: $\Delta G$ is measured in Joules (J) or kilojoules (kJ).
   • Conditions: Applicable at constant temperature and pressure.
2. Electrochemical Cell Potential ($E^{\circ }$):
3. • Principle: Related to the spontaneity of electrochemical reactions.
   • Derivation: Based on the Nernst equation.
3. Ellingham Diagram:
4. • Principle: Graphically represents the temperature dependence of the stability of compounds (primarily oxides).
   • Application: Used to select appropriate reducing agents for metallurgical processes.

Practice Problems

1. Calculate the $\Delta G$ for the reduction of FeO by CO at 1000 K.
2. Using the Ellingham diagram, determine at what temperature magnesium can reduce alumina.

This summary captures the critical formulae, explanations, derivations, and applications necessary for NEET UG Chemistry preparation from the specified chapter.