Metallurgy Problem Set

Introduction

Metallurgy problems often mix a qualitative question about reactivity with a quantitative question about ore mass or gas output. Solve the chemistry first: identify the mineral, write a plausible stated route and name the target metal. Then follow the metal atoms through formula fractions, balanced equations and stage recoveries. Keep environmental and corrosion questions on their own evidence basis.

Core explanation

Start with an ore grade problem. If 1000 kg rock is 40.0% Fe₂O₃, it contains 400 kg hematite. Iron fraction within hematite is about 111.7/159.7 = 0.699, so contained iron is about 280 kg. A furnace recovery of 85.0% gives about 238 kg elemental iron content. The mass of tapped crude iron may differ because carbon and impurities accompany iron. The distinction among rock, mineral, contained element and metal product is essential.

A reaction-demand problem uses the amount of reacting oxide . Under Fe₂O₃ + 3CO → 2Fe + 3CO₂, 1.00 kmol hematite requires 3.00 kmol CO and ideally makes 2.00 kmol Fe. If a 10% CO excess is supplied, input CO is 3.30 kmol per kmol hematite, while stoichiometric consumption remains 3.00 kmol for full reduction in the isolated model. Excess does not increase iron beyond the oxide's atoms.

An ore-conversion problem may begin with ZnS. Roasting 2ZnS + 3O₂ → 2ZnO + 2SO₂ forms SO₂ and ZnO. It does not yet form Zn metal. A later leach/electrowinning or thermal reduction stage must be specified for zinc output. If 0.100 mol ZnS is roasted and 80% of zinc reaches metal, product is 0.0800 mol Zn. The SO₂ generated by complete roast is 0.100 mol, but emitted SO₂ depends on gas capture.

Reactivity guides extraction choice but cannot replace an equation. Aluminium's stable oxide points toward electrolytic extraction in a molten bath, while iron oxide can be reduced by CO under furnace conditions. A balanced but impractical carbon equation is not evidence that the route is used. Similarly, copper may be processed by different routes depending on whether the feed is sulfide or oxide-rich.

Corrosion questions need mechanism. A zinc coating protects iron as barrier and sacrificial metal; a paint film mainly blocks access. A sacrificial anode needs an electrical connection and electrolyte path, and it is consumed. If a question gives 0.100 mol Zn oxidized, electron release is 0.200 mol; this does not by itself quantify how much iron mass was spared.

Mixed problems may give percentages with ambiguous names. Write each as a fraction with explicit numerator and denominator. Ore grade is valuable component over ore mass; concentrate recovery is target captured over target in feed; product purity is target mass over total product mass. Multiplying aligned recoveries can give overall recovery, while a supplied overall figure must not be multiplied by its component stages again.

Check conclusions. A metal amount greater than contained metal needs another feed source or an arithmetic correction. A gas mass greater than solid mass lost may be possible when oxygen entered from air, as in roasting. A high-quality answer states system boundary, gas conditions and whether amounts are theoretical, captured or emitted.

Step-by-step reasoning

1. Identify mineral and target product, then select a chemically supported route. 2. Convert ore grade and formula fraction to contained target metal. 3. Write balanced stage equations and calculate reagent or gas ratios in moles. 4. Apply recoveries and purities only on their stated material-flow bases. 5. Check atom conservation, limiting inputs and whether output is metal, compound or gas.

Visual explanation

Draw a decision map with branches “oxide,” “sulfide” and “native metal.” Each branch enters a box labeled “contained metal,” then the appropriate conversion or separation route. Recovery fractions sit on arrows between stages; gas and slag leave as separate arrows, never as additions to metal mass.

Real-world analogy

Planning a meal from a crate requires knowing how much is edible, how much is lost in preparation and what recipe uses the edible part. A metallurgy problem similarly combines composition, process efficiency and reaction proportions in a definite order.

Real-world example

A plant report may state tonnes of ore, iron grade, coke use and tapped iron. Comparing the figures requires the ore assay, reaction model and other coke roles. An engineer will not equate tonnes of ore with tonnes of metal or explain all coke use by one reduction equation.

Why?

Why name every stream before arithmetic? A percentage applied to concentrate mass can mean something different from one applied to contained metal. Labels reveal whether a factor belongs to rock, mineral, element, gas or final product.

Common misconception

“The last number in the question is the final answer's denominator.” A percentage must be tied to its defined physical basis. Guessing its role from position in a word problem can double count losses or confuse grade with purity.

Worked example

An ore batch of 500 kg is 50.0% ZnS by mass. Pure ZnS is 250 kg and contains about 0.671 × 250 = 168 kg Zn. Roasting retains 90.0% of the zinc in useful oxide, and later recovery captures 80.0% of that zinc as metal. Final Zn content is 168 × 0.900 × 0.800 ≈ 121 kg. If all pure ZnS roasted, ideal SO₂ generated is 250/97.4 ≈ 2.57 kmol, about 165 kg SO₂. This gas mass exceeds some solid mass differences because incoming oxygen contributes to SO₂. Actual emitted SO₂ requires capture data; metal output uses the two zinc recovery fractions.

Quick check

1. What is the first step if ore grade is reported as a mineral percentage rather than elemental metal percentage? Answer: Find mineral mass, then use its formula to calculate contained metal before applying recovery.

Exam focus

Draw a short amount pathway with named substances and units. Distinguish thermal conversion from metal reduction, and distinguish generated gas from emitted gas. Explain reactivity as a route clue, not as a substitute for balanced stoichiometry.

Advanced insight

Independent assays of feed, concentrate, slag and final metal can overdetermine an element balance. If they disagree beyond uncertainty, the discrepancy can reveal unmeasured dust, sampling bias or a wrong mineral assumption. Reconciliation is a practical extension of textbook stoichiometry.

Summary

Mixed metallurgy problems require chemical route selection followed by element-based accounting. Ore grade and mineral formula set contained metal, balanced equations set reagent and gas ratios, and recovery sets captured output. Clear stream labels prevent most conceptual errors.

Practice questions

1. How much Fe is contained in 100 kg pure Fe₂O₃ at 69.9% Fe by mass? Answer: 69.9 kg Fe. 2. What is recovered at 80.0% recovery? Answer: 55.9 kg Fe content. 3. Does roasting ZnS to ZnO yield Zn metal? Answer: No. A later reduction or electrowinning stage is needed. 4. What must accompany a claimed SO₂ emission from roasting? Answer: Conversion and capture or treatment information, not only the balanced generation equation.