Question

Which of the following statement(s) is(are) true? a. Copper metal can be oxidized by \(\mathrm{Ag}^{+}\) (at standard conditions). b. In a galvanic cell the oxidizing agent in the cell reaction is present at the anode. c. In a cell using the half reactions \(\mathrm{Al}^{3+}+3 \mathrm{e}^{-} \longrightarrow\) Al and \(\mathrm{Mg}^{2+}+2 \mathrm{e}^{-} \longrightarrow \mathrm{Mg}\) , aluminum functions as the anode. d. In a concentration cell electrons always flow from the compartment with the lower ion concentration to the compartment with the higher ion concentration. e. In a galvanic cell the negative ions in the salt bridge flow in the same direction as the electrons.

Short answer

Statements a and d are true. Statement a is true because the reaction between \(\mathrm{Cu}\) and \(\mathrm{Ag}^{+}\) is thermodynamically possible due to the difference in their reduction potentials. Statement d is true because in a concentration cell, electrons flow from the compartment with the higher ion concentration (anode) to the compartment with the lower ion concentration (cathode).

Step-by-step solution

Statement a

Copper metal can be oxidized by \(\mathrm{Ag}^{+}\) (at standard conditions). If a redox reaction occurs, the reaction will involve the transfer of electrons. We can determine the feasibility of this reaction by comparing the reduction potentials of the two species in question. The reduction potential of \(\mathrm{Cu}^{2+}\) is \(+0.34V\) and the reduction potential for \(\mathrm{Ag}^{+}\) is \(+0.80V\). Since the reduction potential of \(\mathrm{Ag}^{+}\) is more positive, this reaction is thermodynamically possible, with \(\mathrm{Cu}\) being oxidized to \(\mathrm{Cu}^{2+}\) and \(\mathrm{Ag}^{+}\) being reduced to \(\mathrm{Ag}\). Therefore, statement a is true.

Statement b

In a galvanic cell, the oxidizing agent in the cell reaction is present at the anode. In a galvanic cell, the anode is where the oxidation half-reaction occurs, and the cathode is where the reduction half-reaction takes place. The oxidizing agent accepts electrons in the process, so it undergoes reduction. Since reduction takes place at the cathode, the oxidizing agent is present at the cathode. Therefore, statement b is false.

Statement c

In a cell using the half reactions \(\mathrm{Al}^{3+}+3 \mathrm{e}^{-} \longrightarrow\) Al and \(\mathrm{Mg}^{2+}+2 \mathrm{e}^{-} \longrightarrow \mathrm{Mg}\), aluminum functions as the anode. Here, we have two half-reactions: one involving \(\mathrm{Al}^{3+}\) and one involving \(\mathrm{Mg}^{2+}\). In a galvanic cell, the half-cell with a more negative reduction potential functions as the anode (where oxidation occurs). The standard reduction potentials for \(\mathrm{Al}^{3+}\) and \(\mathrm{Mg}^{2+}\) are \(-1.66V\) and \(-2.37V\), respectively. Since the reduction potential of \(\mathrm{Mg}^{2+}\) is more negative, the anode in this cell will consist of magnesium undergoing oxidation to \(\mathrm{Mg}^{2+}\). Therefore, statement c is false.

Statement d

In a concentration cell, electrons always flow from the compartment with the lower ion concentration to the compartment with the higher ion concentration. In a concentration cell, the flow of electrons is driven by concentration differences, producing a voltage. The anode compartment will have a higher ion concentration and will undergo oxidation, releasing electrons into the external circuit. The cathode compartment will have a lower ion concentration and will undergo reduction, accepting these electrons. Electrons flow from the anode to the cathode, so this statement is true.

Statement e

In a galvanic cell, the negative ions in the salt bridge flow in the same direction as the electrons. The purpose of the salt bridge in a galvanic cell is to maintain overall electrical neutrality. As electrons flow from the anode to the cathode, a cation from the salt bridge must migrate towards the cathode compartment to balance the charge. As electrons flow back from the cathode to the anode, an anion from the salt bridge migrates towards the anode compartment to balance the charge. Therefore, the movement of anions in the salt bridge is opposite to the direction of electron flow and statement e is false. In summary, statements a and d are true, while statements b, c, and e are false.

Key concepts

Galvanic Cells

A galvanic cell is a device that converts chemical energy into electrical energy through redox reactions. It consists of two half-cells connected by a salt bridge. Each half-cell contains an electrode immersed in an electrolyte solution.
The anode is where oxidation occurs and electrons are released. These electrons flow through an external circuit to the cathode, where reduction takes place.

• Anode: Site of oxidation, releases electrons.
• Cathode: Site of reduction, receives electrons.
• Salt Bridge: Maintains electrical neutrality by allowing ions to flow between the half-cells.

In a galvanic cell, the flow of electrons generates an electric current that can be harnessed to do work.

Half-Reactions

Half-reactions are the individual oxidation or reduction reactions that occur in a redox process. Each half-reaction represents a part of the full redox reaction, showing either the loss or gain of electrons.
By coupling them, we get the entire balanced redox equation.

• Oxidation Half-Reaction: Shows how electrons are lost. For example, \( \mathrm{Mg} \rightarrow \mathrm{Mg}^{2+} + 2\mathrm{e}^{-} \).
• Reduction Half-Reaction: Shows how electrons are gained, e.g., \( \mathrm{Al}^{3+} + 3\mathrm{e}^{-} \rightarrow \mathrm{Al} \).

By combining these half-reactions, the galvanic cell generates an electric current as electrons move from the anode (oxidation site) to the cathode (reduction site).

Reduction Potentials

Reduction potential, often called electrode potential, is a measure of the tendency of a chemical species to gain electrons and be reduced. Each half-reaction has its own standard reduction potential, which helps predict the direction of electron flow in a galvanic cell.
The more positive the reduction potential, the greater the tendency to gain electrons.

• Determining Feasibility: Comparing reduction potentials helps us determine which species will be oxidized or reduced in a reaction.
• Example: Copper and silver ions can react, with silver ions having a higher reduction potential, leading to copper oxidizing and silver reducing.

Understanding reduction potentials allows us to predict the behavior of galvanic cells and construct balanced chemical equations for redox reactions.

Concentration Cells

Concentration cells are a type of galvanic cell where the electrodes are identical, but the ion concentrations in the half-cells differ. This difference in concentration creates a potential that drives electron flow.
Electrons will move from the side of lower concentration to the side of higher concentration.

• Anode: Higher ion concentration, where oxidation occurs.
• Cathode: Lower ion concentration, where reduction occurs.

In essence, it is the concentration gradient that generates the electric potential, and this flow continues until the concentrations equalize. Concentration cells illustrate the importance of ion concentration in electrochemical reactions.