Balancing a Combustion Reaction Under Constraint
A technician burns propane (C₃H₈) in a sealed 10 L vessel to heat a small sample. The vessel initially contains 0.30 mol of propane and 1.20 mol of oxygen gas. After ignition, the reaction goes to completion and the vessel cools to room temperature. The technician writes the unbalanced equation C₃H₈ + O₂ → CO₂ + H₂O and claims that because 1.20 mol of oxygen is present, all the propane will burn and 0.30 mol of CO₂ will form. A supervisor questions the claim and asks for a mass balance and a limiting-reactant analysis. Molar masses: C = 12.0, H = 1.0, O = 16.0 g/mol.
1. Balance the combustion equation and determine the limiting reactant.
Read the worked answer
Balanced equation: C₃H₈ + 5O₂ → 3CO₂ + 4H₂O. Check: C 3 = 3; H 8 = 8; O 10 = 6 + 4 = 10. ✓
Oxygen needed for 0.30 mol propane: 0.30 × 5 = 1.50 mol O₂. Only 1.20 mol is available, so O₂ is limiting and propane is in excess.
Propane actually consumed: 1.20 ÷ 5 = 0.24 mol. Propane left: 0.30 − 0.24 = 0.06 mol.
2. Calculate the moles and masses of CO₂ and H₂O produced, and show that mass is conserved.
Read the worked answer
From 1.20 mol O₂: CO₂ = 1.20 × (3/5) = 0.72 mol; mass = 0.72 × 44.0 = 31.68 g. H₂O = 1.20 × (4/5) = 0.96 mol; mass = 0.96 × 18.0 = 17.28 g.
Reactants consumed: propane 0.24 × 44.0 = 10.56 g; oxygen 1.20 × 32.0 = 38.40 g. Total = 48.96 g. Products: 31.68 + 17.28 = 48.96 g. Mass is conserved. ✓
Unreacted propane remains: 0.06 × 44.0 = 2.64 g, which is not part of the reaction and must be excluded from the balance.
3. The technician's claim that 0.30 mol CO₂ forms is wrong. Explain the error in reasoning and state the corrected yield.
Read the worked answer
The technician assumed propane is fully consumed and multiplied by the 1:3 ratio without checking oxygen supply. But each mole of propane requires 5 mol O₂, and only 1.20 mol O₂ is present, enough for just 0.24 mol propane. The correct CO₂ yield is 0.72 mol, not 0.30 mol. The error is failing to identify the limiting reactant before applying stoichiometric ratios.