Calculating Gas Products in Extraction

Introduction

Extraction reactions can produce CO₂ or SO₂. A balanced stage equation gives a theoretical amount when feed and conversion are known, but the quantity leaving a plant may differ because gas can be captured, consumed later or mixed with other sources. Choose a clear system boundary before reporting “gas produced.”

Core explanation

Carbonate calcination gives a direct example: CaCO₃ → CaO + CO₂. One mole pure CaCO₃ decomposed makes one mole CO₂. A 100.1 kg pure limestone formula amount is about 1.00 kmol and can release about 44.0 kg CO₂ from this chemical decomposition. If the rock is only 80.0% CaCO₃, use its pure carbonate portion first. CO₂ from burning fuel to heat the kiln is an additional source not counted by the calcination equation.

Sulfide roasting uses incoming oxygen: 2ZnS + 3O₂ → 2ZnO + 2SO₂. One mole ZnS ideally forms one mole SO₂ if fully converted under this model. The sulfur dioxide contains oxygen from air; its mass can exceed the sulfur mass that left the solid. A gas-control system may capture some or all generated SO₂ for treatment or use, so generated mass is not automatically emitted mass.

Iron-oxide reduction by carbon monoxide gives Fe₂O₃ + 3CO → 2Fe + 3CO₂. One mole Fe₂O₃ ideally forms three moles CO₂ from this reduction stage. CO itself may have been produced by upstream carbon reactions, which can generate and consume CO₂. If an overall plant question supplies multiple stage equations, add them and cancel transferred intermediates rather than adding every written CO₂ term as final exhaust.

Gas volumes require conditions. At a stated molar volume of 24.0 L mol⁻¹, 0.0500 mol CO₂ corresponds to 1.20 L, but that volume applies only at the stated temperature and pressure. For a hot furnace gas, use actual conditions or convert to a reference state before comparing volumes. If gas is wet or mixed with air, total measured volume is not pure product gas volume.

Percentage conversion scales the theoretical stage amount. If 0.100 mol CaCO₃ feed is only 70.0% decomposed, the reaction releases 0.0700 mol CO₂ rather than 0.100 mol. If 90.0% of that generated gas is captured, 0.0630 mol is captured and 0.00700 mol remains outside the captured stream under a simplified complete balance. Conversion and capture are different fractions and should be placed at different stages.

Some plants have several gas sources. A zinc feed containing both carbonate and sulfide minerals can make CO₂ in calcination and SO₂ in roasting, but each amount depends on the relevant mineral fraction and equation. A gas analyzer measuring a combined exhaust stream may need flow rate, composition and time to convert concentration into emitted mass. One percentage concentration alone is insufficient.

Environmental interpretation must be careful. SO₂ is an air pollutant and CO₂ is a greenhouse gas, but a theoretical chemistry problem is not a complete emissions inventory. Energy, transport and gas-control processes have additional streams. State what the calculated gas number includes.

Step-by-step reasoning

1. Select a specified stage equation and identify the gas species. 2. Determine reactive feed moles and actual conversion fraction. 3. Apply the gas-to-feed coefficient ratio. 4. Convert to mass or volume at defined conditions. 5. Apply capture or downstream-consumption data separately for emitted amount.

Visual explanation

Draw three boxes: reaction generates gas, capture system removes a fraction, stack releases the remainder. Under the reaction box, list CaCO₃ → CO₂, ZnS → SO₂ and Fe₂O₃ + CO → CO₂ as distinct examples, each with its own coefficient ratio.

Real-world analogy

A factory may produce 100 units of a byproduct, reuse 30 and store 50, leaving 20 to leave the site. “Produced” and “released” are different counts. Reaction gas generation and plant emissions likewise depend on what happens after the chemical stage.

Real-world example

A zinc roaster can generate SO₂ from sulfur in ZnS concentrate. Monitoring both gas formation and capture performance helps a plant estimate what is sent for treatment and what, if anything, reaches the environment. The ore's sulfur content and roast conversion set a chemical upper bound.

Why?

Why can roasting gas weigh more than sulfur removed from ore? Incoming O₂ supplies oxygen atoms to SO₂. Complete mass conservation includes both sulfide feed and air input, not only the solid before and after roasting.

Common misconception

“Every mole of CO₂ written in a process equation is a stack emission.” CO₂ can be captured or consumed in another stage, while fuel can create additional CO₂. Define the boundary and track gas streams before making an emissions claim.

Worked example

Roast 9.74 kg pure ZnS, about 0.100 kmol, completely under 2ZnS + 3O₂ → 2ZnO + 2SO₂. The equation gives 0.100 kmol SO₂, approximately 6.41 kg using 64.1 kg kmol⁻¹. Suppose 95.0% of generated SO₂ is captured. Captured SO₂ is about 6.09 kg, and uncaptured amount is about 0.321 kg under this simplified mass balance. These are not Zn metal amounts; zinc remains in the solid oxide intermediate.

Quick check

1. How many moles CO₂ form from 0.0200 mol CaCO₃ fully decomposed? Answer: 0.0200 mol CO₂ from the 1:1 calcination ratio.

Exam focus

State the equation, feed purity, conversion and gas species. Distinguish generated, captured and emitted amounts. For gas volume, include temperature and pressure or a stated molar volume; do not use a universal volume per mole.

Advanced insight

An emission rate is mass per time, not merely total mass. Continuous-process monitoring combines gas flow rate and concentration over time. Process-gas treatment can convert one chemical species into another, so sulfur or carbon element balances may be more reliable than following a single molecule name through every unit.

Summary

Balanced extraction equations predict gas moles from reacted feed amounts. CO₂ and SO₂ calculations need the correct stage, conversion and gas conditions. Plant emissions require additional accounting for capture, reuse, upstream fuel and downstream reactions.

Practice questions

1. What SO₂ amount forms from 0.0500 mol ZnS in the simplified complete roast? Answer: 0.0500 mol SO₂. 2. At 24.0 L mol⁻¹, what volume is 0.0500 mol gas? Answer: 1.20 L at those stated conditions. 3. If 80% of generated SO₂ is captured, what fraction is uncaptured in a simple balance? Answer: 20% remains outside the captured stream. 4. Why might actual CO₂ exhaust exceed carbonate-only theoretical CO₂? Answer: Fuel combustion and other reactions can add CO₂ beyond carbonate decomposition.