Question

Make a sketch of a galvanic cell for which the cell notation is $$ \mathrm{Fe}(s)\left|\mathrm{Fe}^{3+}(a q) \| \mathrm{Ag}^{+}(a q)\right| \mathrm{Ag}(s) $$ (a) Label the anode and the cathode. (b) Indicate the charge on each electrode. (c) Indicate the direction of electron flow in the external circuit. (d) Write the equation for the net cell reaction.

Short answer

The anode is Fe(s) with a negative charge, the cathode is Ag(s) with a positive charge, electrons flow from Fe to Ag in the external circuit, and the net cell reaction is \(\mathrm{Fe}(s) + 3\mathrm{Ag}^{+}(aq) \rightarrow \mathrm{Fe}^{3+}(aq) + 3\mathrm{Ag}(s)\).

Step-by-step solution

Draw the Galvanic Cell Setup

Sketch two beakers connected by a salt bridge. On one side, place a solid iron (Fe) electrode immersed in a solution containing Fe3+ ions. On the other side, place a solid silver (Ag) electrode in a solution with Ag+ ions.

Label the Anode and Cathode

The anode is where oxidation occurs and it will be the Fe(s) electrode. The cathode is where reduction occurs, which is the Ag(s) electrode.

Indicate the Charges on Each Electrode

On the anode side, mark the Fe(s) electrode with a negative sign (-) as it loses electrons. On the cathode side, label the Ag(s) electrode with a positive sign (+) as it gains electrons.

Write the Net Cell Reaction Equation

Combine the half-reactions for Fe3+ gaining electrons (reduction) and Ag+ losing electrons (oxidation) to form the overall cell reaction: \[\mathrm{Fe}(s) \rightarrow \mathrm{Fe}^{3+}(aq) + 3e^-\]\[\mathrm{Ag}^{+}(aq) + e^- \rightarrow \mathrm{Ag}(s)\]Multiplying the second equation by 3 to balance the electrons and adding them gives:\[\mathrm{Fe}(s) + 3\mathrm{Ag}^{+}(aq) \rightarrow \mathrm{Fe}^{3+}(aq) + 3\mathrm{Ag}(s)\].

Key concepts

Electrochemical Cells

At the heart of harnessing chemical reactions to produce electricity lies the electrochemical cell, a cornerstone of modern chemistry and power generation. The galvanic cell, also known as a voltaic cell, is a type of electrochemical cell that converts chemical energy into electrical energy through spontaneous redox reactions. It consists of two half-cells, each made up of an electrode and an electrolyte where either oxidation or reduction occurs.

Each half-cell has its own distinct metal and metal ion solution, and the two are connected by a salt bridge to maintain electrical neutrality. The electrons flow through an external circuit from the anode to the cathode, providing a current that can be harnessed for work. Galvanic cells play a crucial role in batteries, powering a myriad of devices from flashlights to electric cars.

Redox Reactions

Redox reactions are the central chemistry behind electrochemical cells. They consist of two processes: reduction, where a substance gains electrons, and oxidation, where a substance loses electrons. In the context of the exercise provided, iron (Fe) undergoes oxidation at the anode, losing electrons to form Fe3+ ions. These electrons then travel through the external circuit to the cathode, where silver ions (Ag+) gain them in a reduction process, becoming solid silver (Ag).

The beauty of redox reactions in a galvanic cell is their self-sustaining nature. As long as there are reactants to oxidize and reduce, the cell can continue to produce electricity. Understanding these reactions allows us to balance chemical equations and predict the direction of electron flow in the circuit.

Standard Cell Notation

Cell notation is a concise way to represent the components and reactions within an electrochemical cell. This shorthand notation lists the anode components first, followed by the cathode components, with each half-cell's contents separated by a vertical line. In the case of the exercise, Fe(s) | Fe3+(aq) || Ag+(aq) | Ag(s) demonstrates standard cell notation.

Starting from the left, solid iron (Fe) is the anode material, in contact with its aqueous iron ions (Fe3+), followed by a double vertical line representing the salt bridge. On the right side, silver ions (Ag+) in solution are depicted before solid silver (Ag) at the cathode. Understanding this notation provides clarity in visualizing the setup of the electrochemical cell and the direction in which the reactions occur.

Electron Flow in Galvanic Cells

In galvanic cells, electrons flow from the anode to the cathode through an external circuit. This movement is driven by the potential difference between the two electrodes, which in turn is caused by the different tendencies of the electrode materials to lose or gain electrons. When identifying the direction of electron flow, it is essential to realize that it's always from the more negative electrode (anode) to the more positive one (cathode).

In our exercise example, the iron electrode is the anode, losing electrons and becoming Fe3+ ions, while the silver electrode is the cathode, gaining electrons to form solid silver. Thus, electrons flow from the Fe electrode to the Ag electrode outside the cell, powering the external circuit on their way. Learning to correctly identify and explain the direction of electron flow is fundamental in understanding how electrochemical cells operate and generate electricity.