2 Ca3(PO4)2 (s beta) + 6 SiO2 (s quartz) + 10 C (s graphite) → P4 (g) + 6 CaSiO3 (s wollastonite) + 10 CO (g)

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Stoichiometry

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Ca3(PO4)2      Mass: g
SiO2           Mass: g
C              Mass: g
P4             Mass: g  or Gas Volume: L
CaSiO3         Mass: g
CO             Mass: g  or Gas Volume: L

Enthalpy of Reaction

[1ΔHf(P4 (g)) + 6ΔHf(CaSiO3 (s wollastonite)) + 10ΔHf(CO (g))] - [2ΔHf(Ca3(PO4)2 (s beta)) + 6ΔHf(SiO2 (s quartz)) + 10ΔHf(C (s graphite))]
[1(128.87) + 6(-1634.94) + 10(-110.54)] - [2(-4120.82) + 6(-910.94) + 10(0)] = 2921.11 kJ
2,921.11 kJ     (endothermic)

Entropy Change

[1ΔSf(P4 (g)) + 6ΔSf(CaSiO3 (s wollastonite)) + 10ΔSf(CO (g))] - [2ΔSf(Ca3(PO4)2 (s beta)) + 6ΔSf(SiO2 (s quartz)) + 10ΔSf(C (s graphite))]
[1(128.87) + 6(81.92) + 10(197.9)] - [2(235.98) + 6(41.84) + 10(5.69)] = 1819.49 J/K
1,819.49 J/K     (increase in entropy)

Free Energy of Reaction (at 298.15 K)

From ΔGf° values:
[1ΔGf(P4 (g)) + 6ΔGf(CaSiO3 (s wollastonite)) + 10ΔGf(CO (g))] - [2ΔGf(Ca3(PO4)2 (s beta)) + 6ΔGf(SiO2 (s quartz)) + 10ΔGf(C (s graphite))]
[1(72.38) + 6(-1549.71) + 10(-137.28)] - [2(-3884.84) + 6(-856.67) + 10(0)] = 2311.02 kJ
2,311.02 kJ     (nonspontaneous)

From ΔG = ΔH - TΔS:
2378.63 kJ     (nonspontaneous)

Equilibrium Constant, K (at 298.15 K)

0
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 F94.

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