Question

Tarnished silver contains \(\mathrm{Ag}_{2} \mathrm{~S} .\) The tarnish can be removed by placing silverware in an aluminum pan containing an inert electrolyte solution, such as \(\mathrm{NaCl}\). Explain the electrochemical principle for this procedure. [The standard reduction potential for the half- cell reaction \(\mathrm{Ag}_{2} \mathrm{~S}(s)+2 e^{-} \longrightarrow 2 \mathrm{Ag}(s)+\mathrm{S}^{2-}(a q)\) is \(\left.-0.71 \mathrm{~V} .\right]\)

Short answer

Electrons from aluminum reduce silver sulfide to silver, cleaning the tarnish.

Step-by-step solution

Understanding the Problem

We need to find the electrochemical principle that explains how tarnished silver, containing \( \mathrm{Ag}_2 \mathrm{S} \), can be cleaned using an aluminum pan and an electrolyte solution such as \( \mathrm{NaCl} \). We will consider the reactions involved and use the given standard reduction potentials to explain the process.

Identify the Reactions

First, determine the relevant reactions for silver tarnish removal. The tarnished silver can be reduced according to the reaction: \( \mathrm{Ag}_2 \mathrm{S}(s) + 2 e^{-} \rightarrow 2 \mathrm{Ag}(s) + \mathrm{S}^{2-}(aq) \), with a reduction potential \( E^0 = -0.71 \mathrm{~V} \). The aluminum will undergo oxidation: \( \mathrm{Al}(s) \rightarrow \mathrm{Al}^{3+}(aq) + 3 e^{-} \), with a reduction potential \( E^0 = -1.66 \mathrm{~V} \).

Calculate Cell Potential

Calculate the cell potential for the reaction. To determine the overall cell potential (\( E_{\text{cell}} \)), subtract the standard reduction potential of the anode reaction (aluminum) from the cathode (silver): \( E_{\text{cell}} = E^{0}_{\mathrm{Ag_2 S/Ag}} - E^{0}_{\mathrm{Al/Al^{3+}}} = (-0.71 \mathrm{~V}) - (-1.66 \mathrm{~V}) = 0.95 \mathrm{~V} \). The positive cell potential indicates the reaction is spontaneous.

Write the Overall Reaction

The overall electrochemical reaction involves the reduction of silver sulfide and the oxidation of aluminum to form sulfur ions and aluminum ions: \[ \mathrm{3Ag}_2\mathrm{S}(s) + 2\mathrm{Al}(s) \rightarrow 6\mathrm{Ag}(s) + 2\mathrm{Al}^{3+}(aq) + 3\mathrm{S}^{2-}(aq) \].

Explain the Electrochemical Principle

This process is based on the principle of galvanic cells where a spontaneous redox reaction occurs. The aluminum metal acts as the anode, losing electrons, while the silver sulfide acts as the cathode, gaining electrons to be reduced back to silver. The flow of electrons from aluminum to silver sulfide through the electrolyte causes the tarnish to be converted back into metallic silver.

Key concepts

Redox Reactions

Redox reactions are at the heart of many chemical processes, including those involved in tarnish removal from silver. The term "redox" is short for reduction-oxidation reaction. It involves two half-reactions: one where a substance gains electrons (reduction) and another where a substance loses electrons (oxidation). In our silver tarnish scenario, silver sulfide (\( \mathrm{Ag}_2 \mathrm{S} \)) is reduced to silver (\( \mathrm{Ag} \)), while aluminum (\( \mathrm{Al} \)) oxidizes to aluminum ions (\( \mathrm{Al}^{3+} \)). This exchange of electrons is what drives the chemical process.

• Reduction involves the gain of electrons, converting tarnished silver back to bright silver metal.
• Oxidation involves the loss of electrons, as aluminum changes to aluminum ions.

Understanding these reactions gives us insights into how substances can change their oxidation states and transform during chemical reactions.

Cell Potential

Cell potential, often symbolized by \( E_{ ext{cell}} \), is a key factor in determining whether a redox reaction is spontaneous. It is calculated based on the difference between the standard reduction potentials of the two half-reactions involved. The cell potential tells us if the reaction will occur on its own without any external input of energy.
In the case of tarnish removal, the cell potential formula used is:

• \[ E_{ ext{cell}} = E^{0}_{ ext{cathode}} - E^{0}_{ ext{anode}} \]

For silver tarnish, the calculated cell potential is \( 0.95 \) volts, which is positive. A positive cell potential means that the reaction will proceed spontaneously, efficiently converting the tarnish back to silver.
This spontaneous reaction is what makes using the aluminum pan effective in removing the tarnish without the need for extra energy.

Standard Reduction Potential

The standard reduction potential, \( E^0 \), is a measure of the tendency of a chemical species to gain electrons and be reduced. It is crucial for predicting the direction of redox reactions and for calculating the cell potential.
Each half-reaction in a redox process has its own standard reduction potential, measured under standard conditions (all concentrations at 1 mol/L, gases at 1 atm, and a specified temperature, usually 25°C). In our example:

• The silver sulfide reaction has a standard reduction potential of \(-0.71 \) volts.
• The aluminum reaction has a more negative standard reduction potential of \(-1.66 \) volts.

The more positive the potential, the greater the species' ability to gain electrons. The difference in these values allows us to compute the overall cell potential and deduce the feasibility of the reaction.
Knowing these potentials helps in designing electrochemical cells that harness the reactivity of different materials.

Galvanic Cells

Galvanic cells, also known as voltaic cells, are devices that convert chemical energy into electrical energy through spontaneous redox reactions. They are essential for powering many everyday devices and for understanding electrochemical processes.
In the case of tarnished silverware, the arrangement can be thought of as a galvanic cell with aluminum acting as the anode (site of oxidation) and silver sulfide serving as the cathode (site of reduction). The process includes:

• The anode, where aluminum undergoes oxidation, losing electrons.
• The cathode, where silver ions gain electrons and are reduced back to silver metal.
• The electrolyte, which facilitates the flow of ions without permitting the solutions to mix directly.

This setup allows the flow of electrons from aluminum to silver, leading to the degradation of tarnish and restoration of the original shiny appearance of the silver.
Understanding the principles of galvanic cells provides insight into creating effective and practical electrochemical systems.