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 1 mole of elementary charges. Calculate the number of coulombs in 1.000 faraday.

Short answer

Answer: There are approximately 96500 coulombs in 1.000 faraday.

Step-by-step solution

Recall the Definition of a Faraday

A faraday consists of 1 mole of elementary charges. To calculate the number of coulombs in a faraday, we must first recall the elementary charge and Avogadro's number. The elementary charge (charge of an electron or proton) is approximately 1.602 x 10^(-19) C (coulombs). Avogadro's number (number of particles in a mole) is approximately 6.022 x 10^23 particles per mole.

Multiply Avogadro's number with the elementary charge

Now that we have the values for the elementary charge and Avogadro's number, we can calculate the number of coulombs in 1.000 faraday. To do this, we multiply the value of Avogadro's number with the elementary charge: Number of coulombs in 1 faraday = (1.602 x 10^(-19) C) x (6.022 x 10^23 particles per mole)

Compute the Result and Put in Proper Units

Multiplying the values from Step 2, we get: Number of coulombs in 1 faraday = (1.602 x 10^(-19) C) x (6.022 x 10^23 particles per mole) = 96485.336 C We can round this value to 3 significant figures: Number of coulombs in 1 faraday ≈ 96500 C So, there are approximately 96500 coulombs in 1.000 faraday.

Key concepts

Electrochemistry

Electrochemistry is a fascinating branch of chemistry that delves into the relationship between electricity and chemical reactions. It plays a critical role in various applications such as batteries, fuel cells, and electrolysis. At its core, electrochemistry deals with the flow of electrons between different substances through an electric circuit. This electron transfer leads to chemical changes, a process known as a redox reaction.

Understanding Faraday's laws of electrolysis, which govern the relationship between the amount of electrical charge passed through a solution and the amount of substance deposited at the electrodes, is crucial. The faraday unit itself is central to electrochemistry as it represents the charge of one mole of electrons and is a critical concept when calculating the energies involved in electrochemical reactions.

Elementary Charge

The elementary charge is the smallest unit of electric charge that is considered indivisible in classical electromagnetism, symbolized as 'e'. Precisely, one elementary charge is the charge possessed by a single proton or the negative of the charge possessed by a single electron, with its value approximately equal to \( 1.602 \times 10^{-19} \text{C} \).

This minuscule charge might seem insignificant, but it is the cornerstone of many calculations in electrochemistry and physics. The concept of elementary charge is paramount when we consider transferring charges in processes like the one evaluated when dealing with the faraday as a unit of electrical charge in electrochemical applications.

Avogadro's Number

Avogadro's number, commonly denoted as \( N_A \), is a fundamental constant used extensively in chemistry. This constant represents the number of atoms, ions, or particles present in one mole of a substance and is approximately equal to \( 6.022 \times 10^{23} \text{particles/mole} \).

In terms of electrochemistry, Avogadro's number allows us to connect the macroscopic world that we can measure—the moles of a substance—with the microscopic world of atoms, ions, and electrons. When we talk about 1.000 faraday, we refer to the charge of one mole of elementary charges; hence, Avogadro's number plays an essential role in translating moles into an actual number of particles or charges.

Coulomb's Law

Coulomb's Law is a principle within electromagnetism, formulated by Charles-Augustin de Coulomb in the 18th century. It states that the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. Mathematically, it is represented as \( F = k \frac{|q_1 q_2|}{r^2} \), where \( F \) is the force, \( q_1 \) and \( q_2 \) are the point charges, \( r \) is the separation distance, and \( k \) is Coulomb's constant.

While Coulomb's Law is more commonly associated with the forces between charges, it provides the foundation for understanding the interaction of charged particles and is indirectly related to the concept of a faraday in electrochemistry. The charge values derived from calculations using Avogadro's number and the elementary charge express the quantitative aspect of these electrostatic interactions in chemical processes.