## Fe2O3 (s hematite) + 3 C (s graphite) → 2 Fe (s alpha) + 3 CO (g)

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## Stoichiometry

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 Heat Added: kJ Fe2O3          Mass: g C              Mass: g Fe             Mass: g CO             Mass: g or Gas Volume: L

## Enthalpy of Reaction

[2ΔHf(Fe (s alpha)) + 3ΔHf(CO (g))] - [1ΔHf(Fe2O3 (s hematite)) + 3ΔHf(C (s graphite))]
[2(0) + 3(-110.54)] - [1(-824.25) + 3(0)] = 492.63 kJ
492.63 kJ     (endothermic)

## Entropy Change

[2ΔSf(Fe (s alpha)) + 3ΔSf(CO (g))] - [1ΔSf(Fe2O3 (s hematite)) + 3ΔSf(C (s graphite))]
[2(27.28) + 3(197.9)] - [1(87.4) + 3(5.69)] = 543.79 J/K
543.79 J/K     (increase in entropy)

## Free Energy of Reaction (at 298.15 K)

From ΔGf° values:
[2ΔGf(Fe (s alpha)) + 3ΔGf(CO (g))] - [1ΔGf(Fe2O3 (s hematite)) + 3ΔGf(C (s graphite))]
[2(0) + 3(-137.28)] - [1(-742.24) + 3(0)] = 330.4 kJ
330.40 kJ     (nonspontaneous)

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

## Equilibrium Constant, K (at 298.15 K)

1.2977872179e-058
This process is not favorable at 25°C.

## Reference(s):

Zumdahl, Steven and Zumdahl, Susan A. Chemistry 9th ed.; Brooks/Cole: Belmont, CA, 2014; p 134.