Problem 71 - A Complete Resource Book in Chemistry for JEE Main

Question

A certain current liberates \(0.504 \mathrm{~g}\) of hydrogen in 2 hour. The amount (or mass) of copper deposited at the cathode during the electrolysis of \(\mathrm{CuSO}_{4}\) (aq) solution by the same current flowing for the same time is (atomic masses \(\mathrm{H}=1.0, \mathrm{Cu}=63.5\) ) (a) \(16.0 \mathrm{~g}\) (b) \(32.0 \mathrm{~g}\) (c) \(8.6 \mathrm{~g}\) (d) \(1.60 \mathrm{~g}\)

Step-by-Step Solution

Answer

The mass of copper deposited is 16.0 g (option a).

Step 1: Determine Hydrogen Equivalent

The equivalent weight of hydrogen is 1 because hydrogen gas (\(\mathrm{H}_2\)) has a molar mass of 2 and a valency of 1. 1 mole of hydrogen gas is liberated by 2 Faradays of charge, so for 1 gram-equivalent of hydrogen, we need 1 Faraday.

Step 2: Calculate Faraday Current for Hydrogen

We are given that 0.504 g of hydrogen is liberated by the current. Since hydrogen's equivalent mass is 1 g/equiv, 0.504 grams correspond to 0.504 equivalents, requiring 0.504 Faradays of charge (since 1 Faraday is needed per equivalent).

Step 3: Determine Copper Equivalent

Copper (\(\mathrm{Cu}\)) has a valency of 2. Its atomic mass is 63.5, so its equivalent weight is \(\frac{63.5}{2} = 31.75\) g/equiv.

Step 4: Calculate Copper Mass Deposited

Since 0.504 Faradays is used, the equivalent mass of copper deposited would be \(0.504 \times 31.75 = 16.002\) grams.

Step 5: Review Options and Solution

Given the available options, option (a) 16.0 g matches our calculated amount of 16.002 g for copper deposited at the cathode.

Key Concepts

Faraday's Laws of Electrolysis

When studying electrolysis, there are two fundamental principles referred to as Faraday's Laws. These laws help us understand how electrolysis works on a quantitative level.

• First Law: The mass of a substance altered at an electrode during electrolysis is proportional to the quantity of electricity passed through the electrolyte. Simply put, more electricity equals more material change.
• Second Law: The mass of various substances altered by the same electric quantity relates directly to their equivalent weights. This means that each substance, depending on its chemical characteristics, requires a specific amount of electricity for change.

These laws allow scientists to determine how much of a substance will be deposited or dissolved during electrolysis, which is crucial for many applications, including industrial electroplating and battery technology.

Equivalent Weight Calculation

Equivalent weight plays a key role in electrochemistry, particularly when applying Faraday's laws. It represents the mass of a substance that would combine with or displace 1 gram of hydrogen. Calculating equivalent weight involves dividing the molar mass of a substance by its valency.
For example, hydrogen has an equivalent weight of 1 because one mole of \( ext{H}_2\) (molar mass 2) has a valency of 1. On the other hand, for copper (Cu), with a molar mass of 63.5 and a valency of 2, the equivalent weight is \( \frac{63.5}{2} = 31.75 \) g/equiv.
Knowing the equivalent weight is essential when calculating the amount of charge (in Faradays) required to alter a specific mass of a substance. It also enables us to predict the mass of material deposited in reactions like the copper electroplating process.

Electroplating

Electroplating is a fascinating application of electrolysis where a material is coated with a thin layer of metal by passing electrical current through an electrolyte. This process enhances properties like appearance, corrosion resistance, and surface hardness.
The process involves submerging the object to be plated (cathode) and the plating metal (anode) in an electrolyte solution. As the current is applied, metal ions from the anode dissolve into the solution, then migrate to the cathode, forming a uniform metallic layer.
Factors influencing electroplating include the concentration of metal ions, current density, and the time duration of current application. By controlling these parameters, industrial applications ranging from jewelry to automotive parts can achieve desired plating thickness, ensuring durability and aesthetics.

Electrochemistry Calculations

Electrochemistry calculations form the backbone of understanding how much material can be changed in electrochemical reactions like electrolysis. These calculations often rely on Faraday’s laws and sometimes on equivalent weight.
For instance, using Faraday's first law, we calculate the mass of a substance altered as \[ m = rac{Q}{F} imes E_w \] where \( m \) is mass, \( Q \) is total charge in coulombs, \( F \) is Faraday's constant (approximately 96,500 C/mol), and \( E_w \) is the equivalent weight.
Using Faraday's second law and equivalent weights, we determine the substance's mass based on the provided electrical charge. These calculations ensure precision in applications like electroplating, battery design, and metallurgical processes, offering efficiency and cost-effectiveness.