7. Consider the decomposition of a metal oxide to its elements, where M represents a generic metal. M3O4(s)↽−−⇀ 3M(s)+2O2(g)

Question

Consider the decomposition of a metal oxide to its elements, where M represents a generic metal. M3O4(s)↽−−⇀ 3M(s)+2O2(g)

	SubstanceΔG°f(kJ/mol)
M3O4(s)	−6.80
M(s)	0
O2(g)	0

What is the standard change in Gibbs energy for the reaction, as written, in the forward direction? Δ𝐺∘rxn= ? kJ/mol

What is the equilibrium constant of this reaction, as written, in the forward direction at 298 K? 𝐾=?

What is the equilibrium pressure of O2(g) over M(s) at 298 K? 𝑃O2= ? atm

Answer 1

M₃O₄(s) <==> 3M(s) + 2O₂(g)

What is ∆Gº_rxn?

∆Gº_rxn = ∑∆Gº_f products - ∑∆Gº_f reactants = 0 + 0 - (-6.80)

∆Gº_rxn = +6.80 kJ/mole (positive value means not a spontaneous reaction). Expect Keq to be low value.

What is Keq?

∆Gº = -RT ln K

6.80 kJ/mol = -(0.008314 kJ/molK)(298K) ln K

ln K = -2.623

K = 0.0726 (low value as expected, again suggesting products are not favored)

What is equilibrium pressure of O2?

K = (O₂)² / 1

0.0726 = (2x)² = 4x²

x² = 0.01815

x = 0.135 atm

Note: pO₂ suggests the negative log of O₂, whereas P_O2 suggests partial pressure of O₂. Guessing the question wants the latter.