Solid fuel used in rocket is a mixture of Fe₂ O₃ and Al (in ratio 1 : 2). The heat evolved (kJ) per gram of the mixture is ____________. (Nearest integer)
Given: Δ H_f^θ(Al₂ O₃)=-1700 kJ mol⁻¹
Δ H_f^θ(Fe₂ O₃)=-840 kJ mol⁻¹
Molar mass of Fe, Al and O are 56, 27 and 16 g mol⁻¹ respectively.

Solution

Chemistry ma’am · 4 steps

Write the thermite reaction, get its ΔH from formation enthalpies, then divide by the mass of both reactants.

1. The reaction. A 1:2 mole ratio of Fe₂O₃ to Al is exactly the balanced thermite reaction: Fe₂O₃ + 2Al → Al₂O₃ + 2Fe.
2. Enthalpy of reaction. Elements in their standard state have Δ H_f° = 0, so only the two oxides count.

   Δ Hᵣ = Δ H_f°(Al₂O₃) - Δ H_f°(Fe₂O₃) = -1700 - (-840) = -860 kJ

3. Mass of mixture. This heat comes from 1 mol Fe₂O₃ (2 × 56 + 3 × 16 = 160 g) plus 2 mol Al (2 × 27 = 54 g), which is 214 g of mixture in total.
4. So. Heat evolved per gram = 860/214 = 4.02 kJ g⁻¹, which rounds to 4.

The common slip: 5. Dividing 860 kJ by the mass of Fe₂O₃ alone (160 g) gives 5.4, which rounds to 5. The aluminium is part of the mixture too, so its 54 g must be added.

The idea to keep. For heat per gram of a fuel mixture, divide the reaction's ΔH by the total mass of every reactant in the balanced equation, not just one of them.

Answer from the NTA final answer key. Solution by PrepWiser.