Given Data:

• The Gibbs energy formation of M₂O₃(s) is −8.30kJ/mol.

• The Gibbs energy formation of M(s) is 0.0kJ/mol.

• The Gibbs energy formation of O₂(g) is 0.0kJ/mol

• The temperature is 298K.

The decomposition reaction in metal oxide is illustrated below.

M₂O₃(s) ⇌ 2M(s) + 3/2O₂(g)

a) A Gibbs-free energy change can be determined by the formula listed below.

ΔG^orxn = ∑m⋅ΔG^o_f (products) − ∑n⋅ΔG^o_f (reactants)

Where,

• ΔG^o_f(products)  is the Gibbs energy formation of products.

• ΔG^o_f(reactants)  is the Gibbs energy formation of reactants.

• m is the total moles of products.

• n is the total moles of reactants.

For the specific reaction The Gibbs free energy is determined using the formula below.

ΔG^o_rxn = [3/2.ΔG^o_f(O₂(g))+2ΔG^o_f(M(s))]−[1×ΔG^o_f(M₂O₃(s))]

Substitute the required values in above formula.

ΔG^o_rxn = [32×(0.00kJ/mol) + 2×(0.00kJ/mol)]−[1×(−8.30)kJ/mol]

                           = 0kJ/mol−(−8.30kJ/mol)

                           = 8.30kJ/mol

Thus the change in energy free to trigger the reaction is 8.30kJ/mol

b) Since equilibrium constants are established in gaseous form, the term used to describe an equilibrium constant which is based on pressure works:

K=(PO₂)^3/2

Where;

• K is the equilibrium constant.

• PO₂ is the pressure of O₂.

Substitute the values from the formula above.

P_O2 = (0.035)^3/2 = 0.00655atm

Thus the pressure at equilibrium for O₂ is 0.00655atm