Problem 95 - Advanced Problems in Physical Chemistry for Competitive Examinations

Question

The number of Faradays required to produce 1 g-atom of \(\mathrm{Mg}\) from \(\mathrm{MgCl}_{2}\) is (a) \(\overline{1}\) (b) 2 (c) \(0.5\) (d) 4

Step-by-Step Solution

Answer

The number of Faradays required to produce 1 g-atom of Mg from MgCl2 is 2.

Step 1: Determine the valency of Magnesium

Checking the periodic table, we see that magnesium (Mg) has a valency of 2, as it is in the second group of the periodic table.

Step 2: Understand the concept of a Faraday

A Faraday represents the charge on one mole of electrons, which is equal to Avogadro's number times the elementary charge. One Faraday is used to deposit or dissolve one mole of a monovalent ion. For ions with a valency other than one, the number of Faradays will be equal to the valency of the ion.

Step 3: Calculate the number of Faradays for Mg

Since magnesium has a valency of 2, it will require two Faradays of charge to reduce 1 mole of magnesium ions to magnesium atoms. Therefore, to produce 1 g-atom (which is 1 mole) of Mg, it would require two Faradays.

Key Concepts

Valency of Magnesium

In the realm of chemistry, understanding the term 'valency' is pivotal for students venturing into electrochemistry. Valency can be defined as the combining power of an element, indicating how many atoms of a different element a single atom of the element can combine with. For magnesium (Mg), a lightweight and silvery metal widely used in alloys and compounds, valency is a fundamental characteristic.

Checking the periodic table, one locates magnesium in the second group, commonly referred to as the alkaline earth metals. Magnesium possesses a valency of 2. This means that a magnesium atom can combine with two atoms of a monovalent element, or one atom of a divalent element. When magnesium dissolves in a solution during electrolysis, for example, each magnesium atom will seek to obtain two electrons to transform into a stable magnesium ion (Mg²⁺).

Molar Mass Calculation

To grasp the concept of molar mass calculation, let's dive in by understanding what a 'mole' is in the context of chemistry. A mole corresponds to Avogadro's number, approximately \(6.022 \times 10^{23}\) entities, which could be atoms, molecules, ions, or electrons.

The molar mass represents the mass of one mole of a substance and is expressed in grams per mole (g/mol). The molar mass of an element is numerically equivalent to its atomic weight, which can be found listed on the periodic table. For magnesium, with an atomic number of 24.305, the molar mass is approximately 24.305 g/mol. This calculation is pivotal in stoichiometry, allowing chemists to convert between mass of a substance and the amount in moles, and is equally essential in electrolysis calculations, where specific amounts of a substance are produced or consumed.

Basic Electrochemistry

Basic electrochemistry encompasses a variety of processes in which electricity is related to chemical changes, and one of the fundamentals is the concept of a 'Faraday'.

When delving into electrochemical reactions, Faraday's Law provides the basis to relate electrical charge to the amount of substance altered at the electrode. A Faraday is a unit of charge and is defined as the quantity of electricity required to deposit or dissolve one mole of a monovalent ion (having valency 1). It is equivalent to Avogadro's number times the elementary charge (\(e\), the charge of a single proton), which equates to approximately \(96,485 \text{C/mol}\).

According to Faraday's laws, in order to deposit a divalent ion such as magnesium (Mg²⁺), with a valency of 2, you would need two Faradays of charge. Thus, understanding Faraday's Law of Electrolysis, and the molar mass helps in calculating the necessary charge to produce a certain quantity of an element through electrolytic processes.