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 electric charge passed when a current of one ampere flows for one second. Given the charge on the electron is \(1.6022 \times 10^{-19}\) coulombs, calculate a value for Avogadro's number. ____________________

Step-by-Step Solution

Answer

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

Step 1: Understand the Relationship Between Current and Charge

A coulomb is the amount of electric charge passed when a current of one ampere flows for one second: 1 Coulomb = 1 Ampere × 1 Second. This provides a basis for understanding how charge flow is measured in terms of ampere and time.

Step 2: Comprehend the Relationship Between Faraday and Electrons

A faraday is defined as 96,480 coulombs, which is the total charge for one mole of electrons. Therefore, 96,480 coulombs represents the total charge carried by a mole of electrons, connecting coulombs to the charge of electrons.

Step 3: Calculate the Number of Electrons in One Faraday

Given the charge on one electron is 1.6022 × 10^{-19} coulombs, divide the total charge in one faraday by the charge of a single electron to determine the number of electrons in one mole: \[ \text{Number of electrons} = \frac{96480 \text{ coulombs}}{1.6022 \times 10^{-19} \text{ coulombs/electron}} \].

Step 4: Compute Avogadro's Number

Perform the division from the previous step: \[ \text{Number of electrons} = \frac{96480}{1.6022 \times 10^{-19}} \approx 6.022 \times 10^{23} \]. This result represents Avogadro's number, the number of particles in a mole of substance.

Key Concepts

Faraday Constant

The Faraday constant is a fundamental concept in electrochemistry. It represents the total charge carried by one mole of electrons. Understanding this constant is crucial in calculating Avogadro's number, as it bridges electrical charge and the quantity of substance. - **Value of Faraday Constant**: The Faraday constant is approximately 96,480 coulombs. - **Role in Electrochemistry**: It helps in quantifying the charge required for electrochemical reactions. Since one mole of electrons carries 96,480 coulombs, knowing the charge each electron carries allows us to determine how many electrons are in a mole. This is a vital step when calculating Avogadro's number, linking macroscopic and molecular measurements.

Coulombs

Coulombs are the SI unit of electric charge, which quantifies the amount of electricity transferred. The concept of coulombs is essential for anyone working with electricity, as it defines how charge is measured and transferred. - **Definition**: A coulomb is the total charge transferred in one second by a current of one ampere. - **Usage**: This unit is used in electrical circuits to calculate the total charge flow over time, which can be crucial for determining energy usage. In the context of the Faraday constant, coulombs help us measure and understand the total electric charge carried by a mole of electrons. This understanding is essential for practical calculations such as determining Avogadro's number by estimating the total mole of electrons.

Electron Charge

The electron charge is a fundamental property of electrons, defining their electrical energy. This is crucial for calculations involving particles at the atomic or subatomic levels.- **Value of Electron Charge**: The charge of a single electron is approximately \(1.6022 \times 10^{-19} \) coulombs.- **Significance**: By knowing this minute charge, we can extrapolate to find large scale quantities, like the number of electrons in a mole.In calculations, the electron charge assists in converting between the macro-level Faraday constant and the micro-level single electron measurements. By dividing the total coulombs in a Faraday constant by the electron charge, we derive the number of electrons in a mole, hence arriving at Avogadro's number.