13 C (s graphite) + 3 Cr2O3 (s) → 2 Cr3C2 (s) + 9 CO (g)

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Stoichiometry

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Cr2O3          Mass: g
C              Mass: g
Cr3C2          Mass: g
CO             Mass: g  or Gas Volume: L

Enthalpy of Reaction

[2ΔHf(Cr3C2 (s)) + 9ΔHf(CO (g))] - [13ΔHf(C (s graphite)) + 3ΔHf(Cr2O3 (s))]
[2(-85.35) + 9(-110.54)] - [13(0) + 3(-1134.7)] = 2238.54 kJ
2,238.54 kJ     (endothermic)

Entropy Change

[2ΔSf(Cr3C2 (s)) + 9ΔSf(CO (g))] - [13ΔSf(C (s graphite)) + 3ΔSf(Cr2O3 (s))]
[2(85.44) + 9(197.9)] - [13(5.69) + 3(81.17)] = 1634.5 J/K
1,634.50 J/K     (increase in entropy)

Free Energy of Reaction (at 298.15 K)

From ΔGf° values:
[2ΔGf(Cr3C2 (s)) + 9ΔGf(CO (g))] - [13ΔGf(C (s graphite)) + 3ΔGf(Cr2O3 (s))]
[2(-86.32) + 9(-137.28)] - [13(0) + 3(-1053.11)] = 1751.17 kJ
1,751.17 kJ     (nonspontaneous)

From ΔG = ΔH - TΔS:
1751.21 kJ     (nonspontaneous)

Equilibrium Constant, K (at 298.15 K)

1.5531678825e-307
This process is not favorable at 25°C.

Reference(s):

Atkins, Jones, and Laverman. Chemical Principles 6th ed.; W.H. Freeman and Company: New York, NY, 2013; p F95.

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