Problem 2 - Chemical Principles in the Laboratory

Question

In standard, IUPAC units, the faraday is equal to 96,480 coulombs. A coulomb is the amount of electricity passed when a current of one ampere flows for one second. Given the charge on an electron, \(1.6022 \times 10^{-19}\) coulombs, calculate a value for Avogadro's number.

Step-by-Step Solution

Answer

Avogadro's number is approximately \(6.022 \times 10^{23}\) entities/mol.

Step 1: Understanding the Problem

We are given the value of a faraday and the charge of an electron, and we need to find Avogadro's number, which tells us how many elementary entities there are per mole.

Step 2: Identifying the Relationship

One faraday corresponds to the charge of one mole of electrons. Therefore, Avogadro's number can be determined by dividing the total charge of a mole of electrons (a faraday) by the charge of one electron.

Step 3: Calculating Avogadro's Number

Avogadro's number, \(N_A\), can be calculated using the formula: \[N_A = \frac{96,480 \text{ C/mol}}{1.6022 \times 10^{-19} \text{ C/electron}}\] where 96,480 C/mol is the charge of one mole of electrons in coulombs, and 1.6022 \times 10^{-19} C/electron is the charge of a single electron.

Step 4: Performing the Division

Divide the faraday by the charge of a single electron: \[N_A = \frac{96,480}{1.6022 \times 10^{-19}}\] This results in an approximate value of \[N_A \approx 6.022 \times 10^{23} \text{ entities/mol}\].

Key Concepts

Faraday Constant

The Faraday constant is a key concept in electrochemistry, essential for understanding how electric charge is transferred during chemical reactions. Named after the scientist Michael Faraday, the Faraday constant represents the total electric charge of one mole of electrons. In the International System of Units (SI), its value is approximately 96,485 coulombs per mole.

Here's why this is important:

• Relationship with Avogadro's Number: The Faraday constant's value can be directly linked to Avogadro's number, which tells us how many particles are in a mole of substance. It helps us calculate the number of electrons (or other charge carriers) in reactions.
• Practical Applications: The Faraday constant is used in electroplating, battery technology, and various other fields where control of electron transfer is required.
• Calculation: Using the Faraday constant, we can easily convert between the quantity of electric charge and the amount of substance. It's calculated by multiplying the charge of an electron by Avogadro's number.

The concept is foundational for calculating charge in chemical equations and processes.

Electron Charge

The electron charge is the basic unit of electric charge in many electrochemical equations. Each electron carries a negative charge, found to be precisely \(1.6022 \times 10^{-19} \,\text{coulombs}\), which is surprisingly small but has vast implications in chemistry and physics.

Understanding electron charge is crucial in several aspects:

• Fundamental Nature: As a fundamental particle, the electron's charge is integral to atomic and molecular interactions. It's the smallest discrete charge present in nature.
• Role in Electricity: Electric currents are essentially flows of electrons, and understanding the electron charge helps us quantify the amount of charge carried by electrical currents.
• Use in Calculations: Knowing the charge of an electron allows scientists to calculate significant quantities like the total charge in a mole of substance, using Avogadro's number.

Without understanding electron charge, it would be more challenging to predict and explain many natural and technological processes.

Coulomb

The coulomb is the SI unit of electric charge. It's a derived unit, meaning it’s based on the ampere, which is a base unit, and time in seconds. In simpler terms, one coulomb is the amount of electrical charge that flows through a wire if 1 ampere of current is maintained for 1 second.

There are several reasons why the coulomb is important:

• Measuring Charge Flow: It's used to express the quantity of electricity transported. For example, in a battery, the amount of charge it can store or deliver might be expressed in coulombs.
• Scientific Research: Understanding coulombs is essential in scientific fields that involve electricity, magnetism, and circuits.
• Units in Equations: Many equations in physics and chemistry use the coulomb to describe electron interactions and charge quantities, such as Coulomb's Law in physics, which describes the force between two charged objects.

The coulomb helps in bridging the gap between theoretical electrical concepts and real-world applications.