Thermal decomposition of calcium carbonate: How many kilograms of CaCO3 must be heated to produce 56 kg of quicklime (CaO)?

Introduction / Context:
This stoichiometry question checks your ability to relate reactants and products for the calcination reaction used in cement and lime manufacture: CaCO3 decomposes to CaO (quicklime) and CO2. Understanding molar masses and fixed mass ratios is essential in chemical process calculations.

Given Data / Assumptions:

• Reaction: CaCO3 → CaO + CO2 (complete conversion).
• Molar mass: CaCO3 = 100 kg per kmol, CaO = 56 kg per kmol, CO2 = 44 kg per kmol.
• Product CaO required = 56 kg.

Concept / Approach:
The balanced reaction shows a 1:1 molar ratio between CaCO3 and CaO. Therefore the mass ratio follows directly from molar masses. For each 56 kg of CaO formed, 100 kg of CaCO3 are consumed and 44 kg of CO2 are released.

Step-by-Step Solution:

Verification / Alternative check:
Mass conservation: 100 kg (CaCO3) = 56 kg (CaO) + 44 kg (CO2). Numbers balance perfectly, confirming the calculation.

Why Other Options Are Wrong:

• 56: Confuses product mass with reactant requirement; ignores CO2 mass.
• 144 or 1000: Do not match the fixed stoichiometric ratio from molar masses.

Common Pitfalls:
Using atomic rather than formula masses, or assuming 1:1 by mass instead of 1:1 by moles. Always convert through molar masses for solids and gases in reactions.

Final Answer:
100