Problem 32 - Chemistry: The Central Science in SI Units, Global Edition

Question

(a) Which electrode of a voltaic cell, the cathode or the anode, corresponds to the higher potential energy for the electrons? (b) What are the units for electrical potential? How does this unit relate to energy expressed in joules?

Step-by-Step Solution

Answer

(a) In a voltaic cell, the anode has a higher potential energy for electrons as they are released from the anode and move toward the cathode. (b) The units for electrical potential are volts (V), and their relation to energy expressed in joules can be summarized by the equation \( E = Q×V \), where E represents electric energy in joules, Q represents charge in coulombs, and V represents potential difference in volts.

Step 1: (a) Identifying the electrode with higher potential energy for electrons

In a voltaic cell, an oxidation reaction occurs at the anode, and a reduction reaction takes place at the cathode. During this process, at the anode, electrons are released as the species undergoes the oxidation reaction. These electrons transfer and move through the external circuit toward the cathode, where they are accepted by the species undergoing the reduction reaction. The potential energy for electrons is higher at the electrode from where they are being released. As the electrons are released from the anode and move toward the cathode, the anode has a higher potential energy for electrons.

Step 2: (b) Units for electrical potential and their relation to energy expressed in joules

The units for electrical potential are volts (V). The volt represents the potential difference between two points in an electric circuit, which is required to move one coulomb (C) of charge, producing one joule (J) of electrical energy. The relationship between volts, coulombs, and joules can be summarized in the following equation: \[Electric\: Energy (Joules) = Charge (Coulombs) × Potential\: Difference (Volts) \] \[ E = Q×V \] In this equation, E represents the electric energy in joules, Q represents the charge in coulombs, and V represents the potential difference in volts. This equation demonstrates the relationship between the unit of electrical potential (volt) and energy expressed in joules.

Key Concepts

Electrodes

In a voltaic cell, electrodes play a critical role in the flow of electrons. The electrodes are the two terminals where the electron transfer reactions occur, enabling the device to generate electricity.

• There are two types of electrodes in a voltaic cell: the anode and the cathode.
• The anode is the electrode where oxidation takes place, which means it loses electrons during the chemical reaction.
• The cathode is the electrode where reduction occurs and gains electrons.

The primary function of electrodes is to facilitate these redox reactions in the cell. Electrons are generated at the anode and travel through an external circuit to reach the cathode. This electron movement creates an electric current, which voltaic cells utilize to do work.
Electrode materials and their respective chemical reactions are vital to the efficiency and effectiveness of electrical energy production.

Oxidation and Reduction Reactions

Understanding oxidation and reduction reactions is essential for grasping how a voltaic cell functions. These reactions, collectively known as redox processes, involve the transfer of electrons between substances.

• Oxidation is characterized by the loss of electrons from a substance, which increases its oxidation state.
• Reduction, on the other hand, is the gain of electrons by a substance, causing its oxidation state to decrease.

In a voltaic cell:

• At the anode, the oxidation reaction takes place, releasing electrons into the external circuit.
• Electrons then flow to the cathode, where a reduction reaction occurs, accepting these electrons.

These complementary processes are what ensure a continuous flow of electrons, allowing the voltaic cell to maintain electrical output. The anode and cathode are connected through the conductive wire, completing the circuit and enabling the same electron flow repeatedly.

Electrical Potential

Electrical potential, often described in terms of voltage, represents the ability of an electric field to do work on charges, moving them from one point to another. In a voltaic cell, this is crucial as it determines how well the cell can pump electrons through an external circuit.

• Voltage (V) is the measure of electrical potential difference between two points.
• It is what "pushes" electrons through the circuit and quantifies the cell’s capacity to perform electrical work.

The higher the voltage, the greater the ability of the voltaic cell to drive electron flow in a circuit. Voltage can be thought of as the electric "pressure" that moves electrons from the anode to the cathode. This potential difference is created by the redox reactions occurring at the electrodes, specifically between the anode possessing high potential energy for electrons and the cathode having the lower potential energy.

Relationship between Volts and Joules

The relationship between volts and joules is pivotal to understand how electrical energy is quantified.

• A volt is the unit of electrical potential, representing the potential difference required to impart one joule of energy to a charge of one coulomb.
• The formula for this relationship is expressed as \((V = \frac{J}{C})\) where V stands for volts, J for joules, and C for coulombs.

This formula states that the product of a charge pushed through an electric potential difference equals the energy it delivers. In practical terms, this means:

• More volts imply a greater ability to do work electrically, transferring higher energy per charge.
• This energy is what powers devices connected to the voltaic cell and is a direct conversion from the chemical energy involved in the redox reactions.

Understanding this relationship is crucial for appreciating how a voltaic cell functions to provide electrical energy from chemical reactions.