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Answer to Question #69450 in Molecular Physics | Thermodynamics for John

Question #69450
Hi there, I I have a question about Physics/chemistry.

If I have a bag of iron oxide(lll) and powdered aluminium in the ratio of 3:1 totalling 72g, with 54g being Fe2O3 and 18g of 2Al, what would the temperature be when it burns during the exothermic reaction? Can you provide full working out please?

Thank you very much

P.S the powder would be mixed and put in a plant pot.
Expert's answer
Solution:
Fe_2 O_3+Al→2Fe+Al_2 O_3
Gibbs Free Energy:
∆G=∆H-T∆S (1), where ΔH is the enthalpy of reaction, T is the temperature in Kelvin, ΔS is the entropy change
Enthalpy of reaction
[2ΔHf(Fe (ℓ)) + 1ΔHf(Al2O3)] - [2ΔHf(Al (s)) + 1ΔHf(Fe2O3)]
[2(13.13) + 1(-1675.27)] - [2(0) + 1(-824.25)] = -824.76 kJ
ΔH = -824.76 kJ
Entropy change
[2ΔSf(Fe (ℓ)) + 1ΔSf(Al2O3)] - [2ΔSf(Al (s)) + 1ΔSf(Fe2O3)]
[2(34.29) + 1(50.92)] - [2(28.33) + 1(87.4)] = -24.56 J/K
ΔS =-24.56 J/K (decrease in entropy)
Free energy of reaction
[2ΔGf(Fe (ℓ)) + 1ΔGf(Al2O3)] - [2ΔGf(Al (s)) + 1ΔGf(Fe2O3)]
[2(11.05) + 1(-1581.97)] - [2(0) + 1(-742.24)] = -817.63 kJ
ΔG = -817.63 kJ
Of (1) T=(∆G-∆H)/∆S (2)
Of (2) T=298 K
Answer:
298 K

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