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Qwestrum Engineering360 · Mining & Metallurgy · Extractive Metallurgy

Electrometallurgy

Electrometallurgy deposits metal by electrolysis — Faraday law sizes mass from current and time; cell voltage exceeds E° due to overpotential and IR drop. Hall-Héroult process produces aluminium; copper electrowinning follows SX in Indian plants.
Exam tip: keep SI units consistent end-to-end, write the governing relation symbolically before substituting, and sanity-check magnitude and sign.

Key formulas & points

Skim these first — then read the full notes below.

  • Electrowinning from purified electrolyte
  • Hall-Héroult aluminium from alumina
  • Energy cost dominates electrometallurgy

Topic details

Introduction

NALCO and Hindalco smelters consume massive grid power — aluminium economics tied to ₹/kWh and anode effect frequency. Copper EW cells at Khetri — purity 99.99% cathode for wire rod.

Scope in B.Tech and GATE syllabus

Current efficiency 90–98% typical — side reactions (H₂ evolution, Fe co-deposition) reduce CE. Exam Faraday problems often give CE < 100% to adjust mass.

Why this topic matters in practice

Hartman extractive metallurgy compares pyro vs hydro vs electro route for same metal.

Key relations & formulas

Formulas (Indian textbook notation)

  • Faradaym=(I×t×M)(n×F)Faraday m = \frac{(I\times t\times M)}{(n\times F)}

Formulas (Indian textbook notation)

  • cellvoltageV=E§K0§+overpotentials+IRdropcell voltage V = E^{§K0§} + overpotentials + IR drop

Formulas (Indian textbook notation)

  • currentefficiencyCE=actualtheoreticalmass×100current efficiency CE = \frac{actual}{theoretical} mass \times 100%

Notation and sign conventions

Relation 1 —
Faradaym=Faraday m =

Formulas (Indian textbook notation)

  • Faradaym=(I×t×M)(n×F)Faraday m = \frac{(I\times t\times M)}{(n\times F)}
Write this relation with symbols exactly as in Rosenqvist Extractive Metallurgy — Standard reference before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 2 —
cellvoltageV=E§K0§+overpotentials+IRdropcell voltage V = E^{§K0§} + overpotentials + IR drop

Formulas (Indian textbook notation)

  • cellvoltageV=E§K0§+overpotentials+IRdropcell voltage V = E^{§K0§} + overpotentials + IR drop
Write this relation with symbols exactly as in Rosenqvist Extractive Metallurgy — Standard reference before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 3 —
currentefficiencyCE=actualtheoreticalmass×100current efficiency CE = \frac{actual}{theoretical} mass \times 100%

Formulas (Indian textbook notation)

  • currentefficiencyCE=actualtheoreticalmass×100current efficiency CE = \frac{actual}{theoretical} mass \times 100%
Write this relation with symbols exactly as in Rosenqvist Extractive Metallurgy — Standard reference before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Fundamentals and definitions

Faraday: m = I t M / (n F) — M molar mass, n electrons per ion, F = 96485 C/mol. Multiple cells in series same current; parallel splits current.

Governing relations in practice

Cell voltage V = E_cathode − E_anode + η_anode + η_cathode + I R — overpotentials η exceed equilibrium to drive kinetics at practical rate.

Design and analysis considerations

Hall-Héroult: alumina dissolved in cryolite bath ~950°C — carbon anode consumes, CO₂ evolved. Energy ~13–15 kWh/kg Al.

Advanced theory and extensions

CE = actual mass / theoretical mass × 100% — shortfall from parallel reactions and re-dissolution of cathode. Plant tracks kg Al per kWh as efficiency KPI.

Assumptions and validity limits

State assumptions explicitly before using any relation for electrometallurgy — steady state, uniform properties, linear elastic material, ideal gas, incompressible flow, etc., as applicable.
Wrong assumptions invalidate the entire solution even when the formula is correct. In Extractive Metallurgy viva and GATE descriptive questions, listing valid assumptions often earns separate marks.

Step-by-step problem approach

1. Read the question and list given data with SI units (common in Extractive Metallurgy papers).
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to electrometallurgy.
4. Use equation 1:
Faradaym=Faraday m =
.
5. Use equation 2:
cellvoltageV=E§K0§+overpotentials+IRdropcell voltage V = E^{§K0§} + overpotentials + IR drop
.
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.

Applications & exam relevance

Electrometallurgy appears in smelters and refineries. In Indian mining curricula this topic is tested because it connects theory to pyro, hydro, and electrometallurgy.
GATE and semester exams often combine electrometallurgy with earlier units — revise prerequisites before attempting mixed problems.
Industry interview panels sometimes ask: "Where did you use electrometallurgy?" — answer with a lab, mini-project, or plant visit example if possible.

Common mistakes in exams

• Faraday n wrong (Cu²⁺ n=2 not 1)
• Theoretical mass without CE correction
• Hall-Héroult temperature with aqueous electrolyte confusion
• IR drop omitted in required cell voltage

Quick revision checklist

Before attempting electrometallurgy problems, confirm you can:
1. Electrowinning from purified electrolyte
2. Hall-Héroult aluminium from alumina
3. Energy cost dominates electrometallurgy
Revise the solved examples in Rosenqvist Extractive Metallurgy — Standard reference and one previous-year GATE or university paper for this unit.

Worked examples

Try the problem first — open the solution when you are ready to check.

Copper electrowinning mass

Problem

I = 20000 A, t = 24 h, CE = 96%. Find Cu deposited (M=63.5, n=2).

Solution

m_theoretical = I t M/(nF) = 20000×86400×63.5/(2×96485) ≈ 569 kg
m_actual = 0.96 × 569 ≈ 546 kg

Conceptual check — Electrometallurgy

Problem

In a Extractive Metallurgy semester or GATE paper you are asked: "State the main assumption, the governing relation, and one practical consequence of electrometallurgy." What should a complete answer include?

📖 Standard books (India)

  • Rosenqvist Extractive Metallurgy — Standard reference

    Read: Syllabus unit

    Referenced in Indian B.Tech syllabus

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