Problem 2
Question
In ordinary 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
Verified Answer
Avogadro's number is approximately \(6.022 \times 10^{23}\) entities per mole.
1Step 1: Write down the given information
We are given:
1. Charge on an electron = \(1.6022 \times 10^{-19}\) coulombs
2. Value of a faraday = 96,480 coulombs
2Step 2: Calculate the number of electrons in one mole of charge (Faraday)
Since a coulomb is the amount of electricity passed when a current of one ampere flows for one second, we can find the total number of electrons in one faraday by dividing the value of a faraday by the charge on one electron.
Number of electrons in one faraday (mole of charge) = \(\frac{96,480 \text{ coulombs}}{1.6022 \times 10^{-19} \text{ coulombs/electron}}\)
3Step 3: Calculate Avogadro's number
Since one mole of charge contains the same number of electrons as one mole of any species (e.g., atoms or ions), the number of electrons in one faraday (mole of charge) will be equal to Avogadro's number.
Number of electrons in one faraday = Avogadro's number = \(N_A\)
Therefore, Avogadro's number \((N_A)\) = \(\frac{96,480 \text{ coulombs}}{1.6022 \times 10^{-19} \text{ coulombs/electron}}\)
So, \(N_A = \frac{96,480}{1.6022 \times 10^{-19}}\)
Calculating this gives us,
\(N_A \approx 6.022 \times 10^{23}\)
Avogadro's number is approximately \(6.022 \times 10^{23}\) entities per mole.
Key Concepts
Faraday's ConstantCoulomb's ValueElectron Charge
Faraday's Constant
When studying chemistry and physics, Faraday's constant is a pivotal value that connects the macroscopic world of chemical reactions with the microscopic world of atoms and electrons. Named after the famous scientist Michael Faraday, it represents the total electric charge carried by one mole of electrons. The constant is denoted by the symbol \( F \) and has a value of approximately 96,485 coulombs per mole (C/mol). This value is referred to as one 'faraday' of charge.
Understanding Faraday's constant helps in many practical applications, such as electrochemistry where it's used to calculate the amount of substance that will be produced or consumed during the electroplating process or battery operation. In our exercise, we use Faraday's constant to unravel Avogadro's number, showcasing a direct and elegant connection between the two fundamental constants in chemistry.
Understanding Faraday's constant helps in many practical applications, such as electrochemistry where it's used to calculate the amount of substance that will be produced or consumed during the electroplating process or battery operation. In our exercise, we use Faraday's constant to unravel Avogadro's number, showcasing a direct and elegant connection between the two fundamental constants in chemistry.
Coulomb's Value
The coulomb, named after Charles-Augustin de Coulomb, is the standard unit of electric charge in the system of electrical units. One coulomb of charge is equivalent to the charge of approximately \(6.242 \times 10^{18}\) electrons. It is defined as the charge transported by a steady current of one ampere flowing for one second.
To put it simply, imagine electrons flowing through a wire as water flows through a pipe; the coulomb measures how much 'water' has passed through the 'pipe' in a specific time frame. The coulomb's value is critical in calculating various electrical quantities and in understanding phenomena such as the flow of electricity in circuits, which relates directly to the charge of individual electrons and thereby to the calculation of Avogadro's number.
To put it simply, imagine electrons flowing through a wire as water flows through a pipe; the coulomb measures how much 'water' has passed through the 'pipe' in a specific time frame. The coulomb's value is critical in calculating various electrical quantities and in understanding phenomena such as the flow of electricity in circuits, which relates directly to the charge of individual electrons and thereby to the calculation of Avogadro's number.
Electron Charge
The charge of an electron is a fundamental physical constant denoted by \( e \) and has a value of approximately \(-1.6022 \times 10^{-19}\) coulombs. This charge is considered elementary because it is a single unit of charge and cannot be divided further, making it the basic building block of electric charges in the universe.
The electron charge, though incredibly small, has a monumental impact on the atomic and molecular scale. It influences how atoms bond to form molecules and consequently impacts all of chemistry. In our exercise, understanding the electron's charge is crucial for calculating Avogadro's number, which quantifies the number of units in one mole of substance, forming a bridge from the minutiae of electrons to the large-scale quantities used in chemistry.
The electron charge, though incredibly small, has a monumental impact on the atomic and molecular scale. It influences how atoms bond to form molecules and consequently impacts all of chemistry. In our exercise, understanding the electron's charge is crucial for calculating Avogadro's number, which quantifies the number of units in one mole of substance, forming a bridge from the minutiae of electrons to the large-scale quantities used in chemistry.