Question

Consider the following electrochemical cell: a. If silver metal is a product of the reaction, is the cell a galvanic cell or electrolytic cell? Label the cathode and anode, and describe the direction of the electron flow. b. If copper metal is a product of the reaction, is the cell a galvanic cell or electrolytic cell? Label the cathode and anode, and describe the direction of the electron flow. c. If the above cell is a galvanic cell, determine the standard cell potential. d. If the above cell is an electrolytic cell, determine the minimum external potential that must be applied to cause the reaction to occur.

Short answer

In summary, when silver metal is a product of the reaction, the cell is a galvanic cell, and electrons flow from the anode (Cu) to the cathode (Ag). The standard cell potential is +0.46 V. If copper metal is a product of the reaction, the cell is an electrolytic cell, and electrons flow from the cathode (Cu) to the anode (Ag). The minimum external potential required is -0.46 V.

Step-by-step solution

Part A: Silver metal as a product

1. Understand the definitions - A galvanic cell is a spontaneous electrochemical cell in which the electrical energy is produced by a spontaneous redox reaction. - An electrolytic cell is a non-spontaneous electrochemical cell in which the electrical energy is used to drive a non-spontaneous redox reaction. - Cathode: an electrode where reduction takes place - Anode: an electrode where oxidation takes place 2. Identify the redox half-reactions If silver metal is a product of the reaction, the following half-reaction occurs: \[Ag^+ + e^- \to Ag\] Since the reduction reaction takes place, this electrode is considered as the cathode. 3. Determine the type of cell and electron flow Since reduction takes place at the cathode and oxidation takes place at the anode in a galvanic cell, this cell is most likely a galvanic cell if silver metal is a product. Electrons flow from the anode to the cathode in a galvanic cell.

Part B: Copper metal as a product

1. Identify the redox half-reaction If copper metal is a product of the reaction, the following half-reaction occurs: \[Cu^{2+} + 2e^- \to Cu\] Since the reduction reaction takes place, this electrode will be considered the cathode. 2. Determine the type of cell and electron flow Since reduction takes place at the cathode and oxidation takes place at the anode in an electrolytic cell, this cell is most likely an electrolytic cell if copper metal is a product. Electrons flow from the cathode to the anode in an electrolytic cell.

Part C: Standard cell potential

1. Identify the half-reactions In a galvanic cell, the following half-reactions occur: - Anode (oxidation): \(Cu \to Cu^{2+} + 2e^-\) - Cathode (reduction): \(Ag^+ + e^- \to Ag\) 2. Determine the standard potentials The standard reduction potentials for the half-reactions are: - Anode: \(E^\circ_{Cu^{2+}/Cu} = +0.34 V\) - Cathode: \(E^\circ_{Ag^+/Ag} = +0.80 V\) 3. Calculate the standard cell potential The standard cell potential for a galvanic cell is given by the following equation: \[E^\circ_{cell} = E^\circ_{cathode} - E^\circ_{anode}\] Using the standard potentials, we calculate the standard cell potential: \[E^\circ_{cell} = (+0.80 V) - (+0.34 V) = +0.46 V\]

Part D: Minimum external potential

1. Determine the half-reactions In an electrolytic cell, the following half-reactions occur: - Anode (oxidation): \(Ag \to Ag^+ + e^-\) - Cathode (reduction): \(Cu^{2+} + 2e^- \to Cu\) 2. Calculate the minimum external potential The minimum external potential required for an electrolytic cell can be obtained from the standard cell potential calculated in Part C, but with the opposite sign: \[E^\circ_{ext} = -E^\circ_{cell} = -(+0.46 V) = -0.46 V\] A potential of at least -0.46 V must be applied to cause the reaction to occur in the electrolytic cell.

Key concepts

Galvanic Cell

A galvanic cell, also known as a voltaic cell, is a type of electrochemical cell that generates electrical energy through spontaneous redox reactions. It is the powerhouse of many batteries used in everyday devices.
A typical galvanic cell consists of two different metals connected by a salt bridge or a porous membrane. This setup allows ions to move between the two half-cells. The spontaneous nature of the redox reaction means no external voltage is needed. Instead, the cell itself creates electricity by transferring electrons from one electrode to another.
The anode in a galvanic cell is where oxidation occurs—electrons are lost here. Electrons travel through the external circuit to the cathode, where reduction occurs, meaning electrons are gained. The movement of electrons from the anode to the cathode drives the generation of electric current, which can be harnessed for work.

• The anode is typically a negative electrode because it releases electrons.
• The cathode is a positive electrode because it receives electrons.

This flow of electrons continues until the reactants are used up or the circuit is broken.

Electrolytic Cell

An electrolytic cell is the opposite of a galvanic cell when it comes to functionality. Instead of generating energy, it requires external electrical energy to drive chemical reactions that aren't spontaneous.
Electrolytic cells are mostly used for electrolysis processes, such as splitting water into hydrogen and oxygen, or plating metals. These cells have a similar setup using two electrodes, an anode, and a cathode, submerged in an electrolyte solution.
In an electrolytic cell, the anode is connected to the positive terminal of an external voltage source, while the cathode is connected to the negative terminal. Here, the direction of electron flow is reversed when compared to a galvanic cell:

• Electrons flow from the cathode to the anode.
• The anode is the positive electrode because electrons are forced out by the external voltage.
• The cathode becomes the negative electrode as it gains electrons.

This setup forces non-spontaneous reactions to occur, making it ideal for applications like electroplating and electrorefining.

Standard Cell Potential

The standard cell potential is a crucial concept to understand the effectiveness of an electrochemical cell. It is denoted by the symbol \(E^\circ_{cell}\) and quantified in volts (V). This value is calculated under standard conditions, which typically involve 1 M concentration for all aqueous ions, a pressure of 1 atm for any gases involved, and a temperature set at 25 °C (298 K).
The standard cell potential is calculated by subtracting the standard reduction potential of the anode from that of the cathode. In formulaic terms:\[E^\circ_{cell} = E^\circ_{cathode} - E^\circ_{anode}\]
In a galvanic cell, if \(E^\circ_{cell}\) is positive, it indicates a spontaneous reaction which can generate electricity. Conversely, in an electrolytic cell, the process is non-spontaneous and requires an opposing external potential at least as large as the negative of this \(E^\circ_{cell}\) value to drive the reaction.
Generally, higher \(E^\circ_{cell}\) means a more vigorous reaction, able to provide more electrical power or needing less external power in case of electrolysis.

Redox Reactions

Redox reactions, or oxidation-reduction reactions, are fundamental to the operation of electrochemical cells. These reactions involve the transfer of electrons between substances.
At the core of every redox process are two half-reactions: oxidation, where a substance loses electrons, and reduction, where a substance gains electrons. Together, these reactions ensure the continuity of an electron flow from the anode to the cathode in an electrochemical cell.
In the context of a galvanic cell:

• The substance at the anode gets oxidized, losing electrons.
• The substance at the cathode accepts these electrons and gets reduced.

These reactions are critically balanced, meaning the amount of electrons lost by the oxidizing agent must equal the amount gained by the reducing agent.
Understanding redox reactions is key to mastering electrochemistry, as they determine the feasibility and direction of electron flow in cells. Every application, from battery technology to metal refining, hinges on these reactions.