Question

The faraday is a unit of charge frequently encountered in electrochemical applications and named for the British physicist and chemist Michael Faraday. It consists of exactly 1 mole of elementary charges. Calculate the number of coulombs in 1.000 faraday.

Short answer

Answer: There are approximately 96485.3383 coulombs in 1 faraday.

Step-by-step solution

Understand the relation between faraday, elementary charge, and coulombs

In this problem, we need to convert faradays to coulombs using the following conversion: 1 faraday = 1 mole of elementary charges To perform this conversion, we need to know the elementary charge (charge of a single electron or proton) and Avogadro's number (the number of atoms/molecules in one mole). The elementary charge is 1.602176634×10^(-19) C, and the Avogadro's number is 6.02214076×10^(23) particles/mole.

Calculate the charge in coulombs for 1 faraday

To find the charge in coulombs of 1 faraday, we will multiply the elementary charge by Avogadro's number: Charge in coulombs = (elementary charge) × (Avogadro's number) Charge in coulombs = (1.602176634×10^(-19) C) × (6.02214076×10^(23) particles/mole)

Perform the calculation

Now, perform the multiplication: Charge in coulombs = (1.602176634×10^(-19) C) × (6.02214076×10^(23) particles/mole) = 96485.3383 C

Write the final answer

The charge in 1.000 faraday is approximately 96485.3383 coulombs.

Key concepts

Understanding Electrochemistry

Electrochemistry is a branch of chemistry that deals with the movement of electrons and ions, and the chemical reactions that involve electrical charges. This discipline is the foundation of various technological advancements, including batteries, fuel cells, and electrolysis. In the context of our problem, electrochemistry is important as it underpins the understanding of Faraday's constant, which links electrical charge to the amount of a substance that has been electrolyzed.

Electrochemistry is often explored through the use of Faraday's laws of electrolysis, which quantify the relation between electric charge and substance change during an electrolytic process. The relationship between electrical current, time, and the quantity of material transformed or produced at an electrode during electrolysis is central to grasping electrochemical applications. Faraday's constant is a bridge between macroscopic quantities (like the amount of a substance) and the microscopic, quantized world of atoms and charges. It enables calculations like determining the charge in coulombs associated with a given number of faradays.

Elementary Charge

The concept of 'elementary charge', denoted by 'e', is crucial in the study of both electrochemistry and physics. It represents the smallest unit of electric charge that is considered indivisible in classical electromagnetic theory. This charge is carried by elementary particles such as electrons and protons, with a single electron or proton holding a charge of \( -1.602176634\times10^{-19} \text{C} \) or \( 1.602176634\times10^{-19} \text{C} \) respectively.

The elementary charge is fundamental in the calculation of electrical charge in systems like atoms, ions, or in our case, faradays. In simpler terms, the elementary charge is like the DNA of electrical charge; it's the basic component from which all larger charges are made up. This discrete nature of electric charge is what allows scientists to precisely calculate and predict the behavior of electrically charged particles in various scenarios.

Avogadro's Number

Avogadro's number, often symbolized as \( N_A \) or \( L \), is one of the cornerstone constants in chemistry. It represents the number of particles, usually atoms or molecules, that are contained in one mole of a substance. One mole is defined as \( 6.02214076\times10^{23} \text{particles/mole} \) and is the bridge between microscopic and macroscopic scales of substances.

Understanding Avogadro's number is essential for converting measurements between individual particles and macroscopic amounts of a chemical substance. For example, it allows us to relate individual particles to faradays, as was necessary in our textbook example. This conversion is often essential in chemistry, and specifically in electrochemistry, as it enables us to link electrochemical processes at the microscopic level (such as electron transfer reactions) to observable quantities like weight and volume.