Question

The standard free energy of formation, ΔG∘f, of a substance is the free energy change for the formation of one mole of the substance from the component elements in their standard states. These values are applicable at 25 ∘C and are found in thermodynamic tables.

The value of ΔG∘f for a substance gives a measure of the thermodynamic stability with respect to the component elements. Negative values for a formation reaction indicate thermodynamic stability of the product. In other words, the compound formed does not spontaneously decompose back into the component elements. Positive values for a formation reaction indicate thermodynamic instability of the product. Thus, the compound will spontaneously decompose, though the rate may be slow.

The sign of ΔG∘f can be used to predict the feasibility of synthesizing a substance from its component elements. The standard free energy change for a reaction, ΔG∘, is a state function and can be calculated from the standard free energies of formation as follows:

ΔG∘rxn=∑npΔG∘f(products)−∑nrΔG∘f(reactants)

where np and nr represent the stoichiometric coefficients in the balanced chemical equation for the reactants and products respectively.

Based on the standard free energies of formation, which of the following reactions represent a feasible way to synthesize the product?

A. N2(g)+H2(g)→N2H4(g); ΔG∘f=159.3 kJ/mol
B. 2Na(s)+O2(g)→Na2O2(s); ΔG∘f=−451.0 kJ/mol
C. 2C(s)+2H2(g)→C2H4(g); ΔG∘f=68.20 kJ/mol
D. 2SO(g)+O2(g)→2SO2(g); ΔG∘f=−600.4 kJ/mol

Answer 1

B. 2 Na(s) + O₂(g) → Na₂O₂(s); ΔG∘f=−451.0 kJ/mol

D. 2 SO(g) + O₂(g) → 2 SO₂(g); ΔG°f=−600.4 kJ/mol

Step-by-step explanation:

The spontaneity of a reaction is given by the value of the standard Gibbs free energy of the reaction (ΔG°rxn). The more negative is the ΔG°rxn, the more spontaneous is a reaction.

The ΔG°rxn can be calculated using the following expression:

ΔG°rxn = ∑np × ΔG°f(products) − ∑nr × ΔG°f(reactants)

By definition, the standard Gibbs free energy of formation of simple substances in their most stable state is zero. That is why, in the reaction of formation of a compound ΔG°rxn = ΔG°f(product).

Based on the standard free energies of formation, which of the following reactions represent a feasible way to synthesize the product?

A. N₂(g) + H₂(g) → N₂H₄(g); ΔG°f=159.3 kJ/mol.

Not feasible. ΔG°rxn = ΔG°f(product) > 0.

B. 2 Na(s) + O₂(g) → Na₂O₂(s); ΔG°f=−451.0 kJ/mol

Feasible. ΔG°rxn = ΔG°f(product) < 0.

C. 2 C(s) + 2 H₂(g) → C₂H₄(g); ΔG°f=68.20 kJ/mol

Not feasible. ΔG°rxn = ΔG°f(product) > 0.

D. 2 SO(g) + O₂(g) → 2 SO₂(g); ΔG°f=−600.4 kJ/mol

Feasible. ΔG°rxn = ΔG°f(product) < 0.