2 Al (ℓ) + 1 Cr2O3 (s) → Al2O3 (s alpha-corundum) + 2 Cr (ℓ)

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Stoichiometry

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Al             Mass: g
Cr2O3          Mass: g
Al2O3          Mass: g
Cr             Mass: g

Enthalpy of Reaction

[1ΔHf(Al2O3 (s alpha-corundum)) + 2ΔHf(Cr (ℓ))] - [2ΔHf(Al (ℓ)) + 1ΔHf(Cr2O3 (s))]
[1(-1675.27) + 2(26.1)] - [2(8.66) + 1(-1134.7)] = -505.69 kJ
-505.69 kJ     (exothermic)

Entropy Change

[1ΔSf(Al2O3 (s alpha-corundum)) + 2ΔSf(Cr (ℓ))] - [2ΔSf(Al (ℓ)) + 1ΔSf(Cr2O3 (s))]
[1(50.92) + 2(36.23)] - [2(35.23) + 1(81.17)] = -28.25 J/K
-28.25 J/K     (decrease in entropy)

Free Energy of Reaction (at 298.15 K)

From ΔGf° values:
[1ΔGf(Al2O3 (s alpha-corundum)) + 2ΔGf(Cr (ℓ))] - [2ΔGf(Al (ℓ)) + 1ΔGf(Cr2O3 (s))]
[1(-1581.97) + 2(22.34)] - [2(6.61) + 1(-1053.11)] = -497.4 kJ
-497.40 kJ     (spontaneous)

From ΔG = ΔH - TΔS:
-497.27 kJ     (spontaneous)

Equilibrium Constant, K (at 298.15 K)

1.39816576803027E+87
This process is favorable at 25°C.

Reference(s):

Atkins, Jones, and Laverman. Chemical Principles 6th ed.; W.H. Freeman and Company: New York, NY, 2013; p F94.

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