Final answer:
To find the standard free energy change for the formation of S2-(aq), use the provided standard free energies of formation for Ag+(aq) and Ag2S(s), as well as the solubility product of Ag2S(s). Calculate the reaction free energy and then solve for the unknown ΔG°f of S2-(aq) by rearranging the equation used to determine ΔG°rxn.
Step-by-step explanation:
To determine the standard free energy change (ΔG°f) for the formation of S2-(aq), we use information provided for the compounds and ions involved in its formation reaction. In this case, we are interested in the precipitation reaction of Ag2S(s) which can be represented as follows:
Ag2S (s) → 2Ag+ (aq) + S2- (aq)
The standard free energy change of the reaction ΔG°rxn can be related to the solubility product (Ksp) by the equation ΔG°rxn = -RT ln(Ksp), where R is the universal gas constant and T is the temperature in Kelvin. Substituting provided values including R (8.314 J·mol-1·K-1) and T (298.15 K for room temperature), we can calculate ΔG°rxn for the dissolution of Ag2S(s).
Next, using the given ΔG°f for Ag+(aq) and Ag2S(s), we can find the ΔG°f of S2-(aq) through the formula ΔG°rxn = ΣΔG°f(products) - ΣΔG°f(reactants).
By rearranging this equation to solve for ΔG°f of S2-(aq), we get ΔG°f(S2-(aq)) = ΔG°rxn - 2ΔG°f(Ag+(aq)) + ΔG°f(Ag2S(s)). Plugging in the calculated ΔG°rxn and the provided ΔG°f values allows us to solve for the unknown ΔG°f for S2-(aq).