Final answer:
The standard free energy of formation, Δ∘f, for phosphoric acid is -1828.72 kJ/mol. The calculated value can be compared to the value in Appendix G to assess the accuracy of the calculation.
Step-by-step explanation:
The standard free energy of formation, Δ∘f, for phosphoric acid (H3PO4) can be determined by using the standard free energy values given in the equations provided. The balanced equation for the formation of phosphoric acid is:
6H₂O(g) + P₄O₁₀(s) ⟶ 4H₃PO₄(l)
From the given data, the standard free energies for the reactions are:
ΔG° for P₄()+5O₂()⟶P₄O₁₀() = -2697.0 kJ/mol
ΔG° for 2H₂()+O₂()⟶2H₂O() = -457.18 kJ/mol
ΔG° for 6H₂O()+P₄O₁₀()⟶4H₃PO₄() = -428.66 kJ/mol
Using Hess's Law, we can add the free energies of the reactions to obtain the total standard free energy change for the formation of phosphoric acid:
ΔG° for 4H₃PO₄(l) formation = (4 x ΔG° for 2H₂()+O₂()) + (ΔG° for P₄()+5O₂()) - (ΔG° for 6H₂O()+P₄O₁₀())
= (4 x -457.18 kJ/mol) + (-2697.0 kJ/mol) - (-428.66 kJ/mol)
= -1828.72 kJ/mol
Therefore, the standard free energy of formation, Δ∘f, for phosphoric acid is -1828.72 kJ/mol.
(b) The calculated standard free energy of formation for phosphoric acid can be compared to the value in Appendix G to determine the accuracy of the calculation. The value obtained (-1828.72 kJ/mol) can be compared to the value in Appendix G to assess the accuracy of the calculation.