consider the following reaction: 2Fe2O3=4Fe+3O2 change of heat==824.2J. The decomposition of 21.0g of Fe2O3 results in:?

In the question, the change of heat should be “+824.2 kJ” instead of “= 824.2 J”.


Molar mass of Fe₂O₃ = (55.8×2 + 16.0×3) g/mol = 159.6 g/mol
No. of moles of 21.0 g of Fe₂O₃ = (21.0 g) / (159.6 g/mol) = 21.0/159.6 mol

2Fe₂O₃ → 4Fe + 3O₂ …… ΔH = +824.2 kJ
Decomposition of 2 mol of Fe₂O₃ requires 824.2 kJ of heat.

Heat required for decomposition of 21.0 g of Fe₂O₃ = (824.2 J) × (21.0/159.6) / 2 = 54.2 kJ

Thermal decomposition of iron(III) oxide..... results in a work of fiction.

You wrote:
"2Fe2O3(s) --> 4Fe(s) + 3O2(g)"
Yet this reaction does not occur. At elevated temperatures oxygen will readily react with metallic iron to make the metal oxide.

You can do the math for this "non-reaction", but what is the point? All it does is reinforce an invalid notion. You would be better served by your teacher choosing a reaction that actually occurs. It would have made more sense to consider a related reaction where "rust" is dehydrated to form Fe2O3. Rust usually takes the form of FeO(OH) which, when it occurs naturally, is the mineral goethite.

2FeO(OH) --heat--> Fe2O3(s) + H2O(g)
21.0g .............. ..........?g

21.0g FeO(OH) x (1 mol FeO(OH) / 88.8g FeO(OH)) x (1 mol Fe2O3 / 2 mol FeO(OH)) x (159.6g Fe2O3 / 1 mol Fe2O3) = 18.9g Fe2O3