The black silver sulfide discoloration of silverware can be removed by heating the silver article in a sodium carbonate solution in an aluminum pan. The reaction is

3 Ag 2 S ( s ) + 2 Al ( s )   ⇌   6 Ag ( s )   +   3 S 2 − ( a q ) + 2 Al 3 + ( a q )

a. Using data in Appendix 4, calculate ∆G°, K, and  for the above reaction at 25°C. [For Al³⁺(aq), Δ G f ° = −480. kJ/mol.]

b. Calculate the value of the standard reduction potential for the following half-reaction:

2 e − + Ag 2 S ( s )   →   2 Ag ( s ) + S 2 − ( a q )

Interpretation: The standard Gibbs free energy, equilibrium constant and cell potential for the given reaction are to be calculated. Also the standard reduction potential for the given half cell reaction is to be calculated.

Concept introduction: Equilibrium constant is defined as the ratio of the concentration of products and the concentration of the reactants and Gibbs free energy is a thermodynamic quantity that is used to calculate the maximum work of reversible reaction performed by a system. It is equal to the difference between the enthalpy and the product of entropy at absolute temperature. Cell potential is defined as the measure of energy per unit charge available from the redox reaction to carry out the reaction.

To determine: The standard Gibbs free energy, equilibrium constant and cell potential for the given reaction.

Explanation

Given

ΔGfο=−480 kJ/mol.

The given reaction is,

3Ag2S(s)+2Al(s)⇌6Ag(s)+3S2−(aq)+2Al3+(aq).

The standard Gibbs free energy (ΔGο) is the change in free energy when one mole of a compound is formed from its constituent elements in their standard states. It is represented as follows,

ΔGrxnο=∑ΔGProductο−∑ΔGreactantο

Where,

∑ΔGProductο is the sum of free energies of products.

∑ΔGreactantο is the sum of free energies of reactants.

The table representing the values of standard free energy of formation (ΔGfο) of reactants and products is as follows,

SubstanceΔGfοAg2S(s)−40Ag(s)0Al(s)0S−2(aq)86Al+3(aq)−480.

The ΔGrxnο is calculated by using the expression

ΔGrxnο=∑ΔGProductο−∑ΔGreactantο

Substitute the value of ΔGreactantο and ΔGproductο in the above expression

ΔGrxnο=∑ΔGProductο−∑ΔGreactantοΔGrxnο=[(6)ΔGf(Ag)ο+(3)ΔGf(S2−)ο+(2)ΔGf(Al3+)ο]−[(3)ΔGf(Ag2S)ο+(2)Δ

Interpretation: The standard Gibbs free energy, equilibrium constant and cell potential for the given reaction are to be calculated. Also the standard reduction potential for the given half cell reaction is to be calculated.

Concept introduction: Equilibrium constant is defined as the ratio of the concentration of products and the concentration of the reactants and Gibbs free energy is a thermodynamic quantity that is used to calculate the maximum work of reversible reaction performed by a system. It is equal to the difference between the enthalpy and the product of entropy at absolute temperature. Cell potential is defined as the measure of energy per unit charge available from the redox reaction to carry out the reaction.

To determine: The standard reduction potential for the given half cell reaction.