Problem 165 - A Complete Resource Book in Chemistry for JEE Main

Question

Match the following $$ \begin{array}{ll} \hline \text { Column-I } & \text { Column-II } \\ \hline \begin{array}{l} \text { (a) Charge on one mole of } \\ \text { electron. } \end{array} & \text { (p) } 1 \text { Faraday } \\ \text { (b) } 108 \mathrm{~g} \text { of silver deposited } & \text { (q) } 96500 \text { coulomb } \\ \text { at electrode. } & \end{array} $$ $$ \begin{array}{ll} \ \text { (c) } 22.4 \text { L of hydrogen at } & \text { (r) 2 Faraday } \\ \text { STP collected. } & \\ \text { (d) } 8 \text { g of oxygen collected. } & \text { (t) } 5.6 \mathrm{~L} \text { at STP } \\ \hline \end{array} $$

Step-by-Step Solution

Answer

(a) matches with (p), (b) matches with (p), (c) matches with (r), and (d) matches with (t).

Step 1: Understand the Terms and Units

First, identify the terms in Column-I and recall the corresponding values in Column-II. For example, one mole of electrons is equivalent to a known electrical unit, the volume of gases at STP (Standard Temperature and Pressure), and the weight in grams relates to moles of substances.

Step 2: Match Charge on One Mole of Electrons

The charge on one mole of electrons is known as Avogadro's number multiplied by the charge of a single electron, which equals 1 Faraday. Therefore, match (a) with (p).

Step 3: Match 108 Grams of Silver Deposited

Silver has a molar mass of 108 g/mol and requires 1 mole of electrons to deposit 108 g from silver ions. Hence, this corresponds to 1 Faraday of charge: match (b) with (p).

Step 4: Match 22.4 L of Hydrogen at STP

At STP, 22.4 L of any gas represents 1 mole. Since the diatomic hydrogen molecule ({H}_2) is mentioned, it requires 2 Faradays to collect one mole of hydrogen gas. Match (c) with (r).

Step 5: Match 8 Grams of Oxygen Collected

Oxygen molecular weight is approximately 32 g/mol. Thus, 8 grams represent 0.25 moles, which at STP corresponds to 5.6 L. Match (d) with (t).

Key Concepts

Faraday's laws of electrolysis

Faraday's laws of electrolysis are fundamental in electrochemistry, explaining how electrical energy can cause chemical changes. These laws help us understand the relationship between the amount of electric energy applied and the quantity of substance transformed at an electrode.

There are two main laws:

• **First Law of Electrolysis**: This law states that the amount of chemical reaction, or the mass of substance deposited or liberated, is directly proportional to the quantity of electricity passed through the electrolyte. In mathematical terms, we write:\[ m = Z imes Q \]Where: - *m* is the mass in grams. - *Z* is the electrochemical equivalent (ECE). - *Q* is the charge in coulombs.
  
• **Second Law of Electrolysis**: This law states that if the same quantity of electricity is passed through different electrolytes, the mass of ions deposited at each electrode is directly proportional to their equivalent weights.

By understanding these laws, one can predict how much of a substance will be deposited or dissolved when a specific quantity of electricity is used.

Electrochemical equivalent

The electrochemical equivalent (equivalent weight ) represents the amount of a substance deposited or dissolved per unit of charge. It is a constant that tells us how much of an element will change state at an electrode with certain electricity.
To find the electrochemical equivalent, we use the equation:\[ Z = \frac{E}{F} \]Where: - *E* is the equivalent weight of the substance. - *F* is Faraday's constant, approximately 96500 coulombs per mole.
Using this relationship, we can predict how much of a material will be involved in electrolysis when a specific current flows for a given time.

Avogadro's number

Avogadro's number is a fundamental constant in chemistry, denoting the number of constituent particles, usually atoms or molecules, in one mole of a substance. It is approximately:\[ 6.022 \times 10^{23} \]This number allows chemists and physicists to relate macroscopic quantities of material to the individual molecules and atoms they comprise.
It is highly significant in electrochemistry; Avogadro's number connects to Faraday's constant through the charge of a single electron. When multiplied by the elementary charge, you get one Faraday (96485 coulombs), the total charge of one mole of electrons.
This way, Faraday's laws and Avogadro's number form a bridge between electrical charge and chemical quantities, helping predict the extent of reactions during electrolysis.