Problem 74 - A Complete Resource Book in Chemistry for JEE Main

Question

A solution of \(\mathrm{CuSO}_{4}\) is electrolyzed for 7 minutes with a current of \(0.6 \mathrm{~A}\). The amount of electricity passed equal to (a) \(26 \mathrm{C}\) (b) \(4.2 \mathrm{C}\) (c) \(2.6 \times 10^{-4} \mathrm{~F}\) (d) \(2.6 \times 10^{-3} \mathrm{~F}\)

Step-by-Step Solution

Answer

252 C of charge was passed, none of the options directly match. Check for unit mismatch.

Step 1: Understand the Question

The question asks us to calculate the amount of electricity in Coulombs that has passed when a copper sulfate solution is electrolyzed for 7 minutes. We want to find the charge in Coulombs (C) using the given current.

Step 2: Recall the Formula

We will use the formula that relates current, charge, and time, which is given by:\[ Q = I \times t \]where \( Q \) is the charge in Coulombs, \( I \) is the current in Amperes, and \( t \) is the time in seconds.

Step 3: Convert Time to Seconds

The time is given in minutes, so we need to convert it to seconds. Since there are 60 seconds in a minute, calculate the total time by multiplying:\[ 7 \text{ minutes} \times 60 \text{ seconds/minute} = 420 \text{ seconds} \]

Step 4: Calculate the Charge

Insert the values for the current and time into the formula:\[ Q = 0.6 \, \text{A} \times 420 \, \text{s} \]Calculate the result:\[ Q = 252 \, \text{Coulombs} \]

Step 5: Compare with Options

Look at the options provided and compare the calculated charge. The calculated value is 252 C, which does not directly match any of the given options. Go through each answer to determine if there might be a conversion or different unit expected that fits any other choice.

Key Concepts

Coulombs

Coulombs is the unit of electric charge in the International System of Units (SI), symbolized by C. Understanding how this unit is defined is crucial for solving electrochemistry problems. The charge of a particle, like an electron, is extremely small. Therefore, Coulombs are used to represent much larger quantities of charge which is easier to work with in scientific equations.

• One Coulomb is equivalent to the charge transferred by a steady current of one ampere in one second.
• Coulombs are determined using the formula: \[ Q = I \times t \] where \( Q \) is the charge in Coulombs, \( I \) is the current in amperes, and \( t \) is the time in seconds.

In electrolysis processes, we calculate the total charge passed through the solution during the electrolysis period, which helps determine things like how much material will be deposited or dissolved in response to the electric current.

Faraday's Law

Faraday's Law of Electrolysis is a fundamental principle used to describe the relationship between the amount of substance altered at an electrode during electrolysis and the amount of electricity passed through a circuit.Faraday’s Law consists of two parts:

• The first states that the amount of chemical change, or deposition, is directly proportional to the electricity passed.
• The second part indicates that the amounts of different substances deposited or changed by the same quantity of electricity are proportional to their equivalent weights.

Faraday's Law is mathematically expressed as: \[ Q = n \times F \]where \( Q \) is the charge in Coulombs, \( n \) is the number of moles of electrons, and \( F \) is Faraday's constant, approximately 96485 C/mol.With this, it becomes clearer why calculating the charge in Coulombs is pivotal. It tells us how much reaction occurs quantitatively at the electrodes during the process of electrolysis.

Electrolysis

Electrolysis is a chemical process where electrical energy is used to drive a non-spontaneous chemical reaction. This process is fundamental in electrochemistry, and it plays a significant role in various industrial applications, such as electroplating, extraction of metals, and chemical synthesis. During electrolysis:

• An electric current is passed through a solution or molten compound (electrolyte), causing cations to migrate to the cathode and anions to the anode.
• At the electrodes, redox reactions take place, leading to the deposition or dissolution of materials.
• The amount of substance produced at each electrode is proportional to the quantity of electricity (measured in Coulombs) that flows through the circuit, which ties back to Faraday's Laws of Electrolysis.

This knowledge not only helps to comprehend why certain substances are released or deposited during the electrolysis but also how we can control these reactions for desired outcomes. Knowing how to apply the concept of Coulombs in calculations is essential to predict the results of electrolysis in various chemical processes.