Problem 101 - A Complete Resource Book in Chemistry for JEE Main

Question

What is the quantity of electricity (in coulombs) required to deposit all the silver from \(250 \mathrm{~mL}\) of \(1 \mathrm{M}\) \(\mathrm{AgNO}_{3}\) solution? \((\mathrm{Ag}=108)\) (a) \(2412.5\) (b) 24125 (c) \(4825.0\) (d) 48250

Step-by-Step Solution

Answer

48250 C

Step 1: Understand the Chemistry

To deposit silver from a solution of silver nitrate (8 ightarrow ext{Ag}^++ ext{e}^- o ext{Ag}$ (Deposit of 1 mole of Ag requires 1 mole of electrons).

Key Concepts

Electrochemistry

Electrochemistry is the study of the interplay between chemical reactions and electricity. In particular, it involves reactions where electrons are transferred between species, which is crucial for processes like electrolysis where electrical energy is used to drive chemical changes. During electrolysis, ions in a solution are moved towards electrodes by an electric field, and chemical compounds are either decomposed or synthesized.

Let's consider the electrolysis of silver nitrate, as per the problem statement. In this process, silver ions are reduced to silver metal at the cathode. This occurs through the following half-reaction:

• Ag⁺ + e^- → Ag

Here, one mole of electrons is required to reduce one mole of silver ions (Ag⁺) to metallic silver (Ag). The energy for this reaction is provided by the external electric current flowing through the electrolyte solution. Understanding electrochemistry helps us comprehend such transformations, where electrical energy is converted into chemical forms.

Mole Concept

The mole concept is a fundamental chemical principle used to quantify the amount of substance. One mole corresponds to Avogadro's number, which is approximately 6.022 × 10²³ entities, be it atoms, ions, or molecules.

In our exercise, the concentration of silver nitrate solution is given as 1 M, which means that there is 1 mole of AgNO₃ per liter of solution. Since we have 250 mL (or 0.25 L) of the solution, we calculate the number of moles of AgNO₃ present as follows:

• Moles of AgNO₃ = 1 mol/L × 0.25 L = 0.25 moles

Given the 1:1 ratio in the reduction of Ag⁺ to Ag, 0.25 moles of silver ions will require 0.25 moles of electrons to be completely reduced to silver metal. Understanding the mole concept is pivotal in calculating amounts and stoichiometry in chemical reactions.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in a chemical reaction. It is based on the conservation of mass and the mole concept, allowing chemists to predict the quantities involved.

In our problem, stoichiometry will help us determine the quantity of electricity required to stoichiometrically deposit silver from the solution:

• Since 1 mole of electrons corresponds to a charge of 96485 coulombs (Faraday's constant), 0.25 moles of electrons will require:
• Charge required = 0.25 moles × 96485 C/mol = 24121.25 C

This illustrates the direct application of stoichiometry to link the mole concept with actual measurable quantities, like electric charge, in electrolysis reactions. Understanding stoichiometry is crucial for conducting accurate chemical calculations and conversions in various contexts.