Question

Determine the standard free energy change, ΔG°, for the formation of S₂−(aq) given that the ΔG° for Ag+(aq) and Ag₂S(s) are 77.1 kJ/mol and −39.5 kJ/mol respectively, and the solubility product for Ag₂S(s) is 8 × 10⁻⁵¹.

a) 36.4 kJ/mol
b) -116.6 kJ/mol
c) -3.4 kJ/mol
d) 116.6 kJ/mol

Answer 1

The standard free energy change for the formation of S²⁻(aq) is determined by considering the dissolution of Ag₂S(s) in water and the standard free energies of Ag⁺(aq) and Ag₂S(s), leading to a ΔG° value of -116.6 kJ/mol. The correct option is b.

Step-by-step explanation:

To determine the standard free energy change, ΔG°, for the formation of S²⁻(aq), we must consider the equilibrium reaction for the dissolution of Ag₂S(s) and the fact that the standard free energy of formation for an element in its standard state is zero (which applies to the S²⁻ in this case since we are calculating its formation).

The dissolution of Ag₂S(s) in water can be written as:

Ag₂S(s) ⇌ 2Ag⁺(aq) + S²⁻(aq)

The standard free energy change for this reaction, ΔG°, can be calculated using the standard free energies of formation of Ag⁺(aq) and Ag₂S(s), and the known solubility product (Ksp).

ΔG° for the formation of two moles of Ag⁺(aq) is 2 × 77.1 kJ/mol, and the ΔG° for the dissolution of Ag₂S(s) is -39.5 kJ/mol. Based on the solubility product, we can write the relationship using the formula ΔG° = -RTln(Ksp), where R is the universal gas constant (8.314 J/mol·K), T is the temperature in Kelvin (assumed here to be 298 K), and Ksp is the solubility product.

The correct value for the standard free energy change, ΔG°, for the formation of S²⁻(aq) is -116.6 kJ/mol, which corresponds to option b).