Problem 135 - A Complete Resource Book in Chemistry for JEE Main

Question

When a quantity of electricity is passed through \(\mathrm{CuSO}_{4}\) solution, \(0.16 \mathrm{~g}\) of copper gets deposited. If the same quantity of electricity is passed through acidulated water, then the volume of \(\mathrm{H}_{2}\) liberated at STP will be (At. wt of \(\mathrm{Cu}=64\) ) (a) \(4.0 \mathrm{~cm}^{3}\) (b) \(56 \mathrm{~cm}^{3}\) (c) \(604 \mathrm{~cm}^{3}\) (d) \(8.0 \mathrm{~cm}^{3}\)

Step-by-Step Solution

Answer

The volume of \(\text{H}_2\) liberated is \(56 \text{ cm}^3\).

Step 1: Find the Moles of Copper Deposited

The atomic weight of copper (Cu) is given as 64. First, we calculate the number of moles of copper deposited using the formula: \[ \text{Moles of Cu} = \frac{\text{Mass of Cu}}{\text{Atomic weight of Cu}} = \frac{0.16}{64} = 0.0025 \text{ moles} \]

Step 2: Relate Copper Deposition to Electricity Quantity

Each mole of Cu is deposited by 2 moles of electrons (since Cu is in 2+ state in \(\text{CuSO}_4\)). Thus, \(0.0025\) moles of Cu corresponds to \(2 \times 0.0025 = 0.005\) moles of electrons.

Step 3: Determine Moles of Hydrogen Gas Liberated

In the electrolysis of water, 2 moles of electrons are required to produce 1 mole of hydrogen gas (\(\text{H}_2\)). Therefore, \(0.005\) moles of electrons will liberate \(0.005/2 = 0.0025\) moles of \(\text{H}_2\).

Step 4: Calculate Volume of Hydrogen at STP

According to the ideal gas law, at STP, 1 mole of any gas occupies 22400 \(\text{cm}^3\). Thus, the volume of \(0.0025\) moles of \(\text{H}_2\) is \[ \text{Volume of } \text{H}_2 = 0.0025 \times 22400 = 56 \text{ cm}^3 \]

Key Concepts

Faraday's Laws of Electrolysis

Faraday's laws of electrolysis are fundamental principles that help us understand how electric current influences chemical change. These laws, introduced by Michael Faraday, provide insight into the quantitative aspects of electrolysis.

• The **first law** states that the mass of a substance deposited or dissolved at an electrode during electrolysis is proportional to the total electric charge passed through the substance. This means the more electricity you pass, the more material gets deposited.
• The **second law** tells us that the masses of different substances deposited or dissolved by the same quantity of electricity are proportional to their chemical equivalents. A chemical equivalent is the ratio of the molar mass of the substance to its valency.

Understanding these laws is essential in processes such as electroplating, where a specific amount of a metal is deposited on an item by passing an electric current through a solution containing the metal.

Electrolysis

Electrolysis is a fascinating process through which electrical energy is used to drive a non-spontaneous chemical reaction. It takes place in an electrolytic cell, where an electric current is passed through a liquid or solution containing ions. This causes the ions to move towards the electrodes, resulting in chemical changes.

• At the **cathode**, reduction reactions take place, where cations gain electrons to form stable elements or compounds.
• At the **anode**, oxidation occurs, and anions lose electrons, often producing gases or other elements.

Electrolysis is not only vital for extracting metals from ores but also for splitting water into hydrogen and oxygen — an important process for producing clean energy.

STP Conditions

Standard Temperature and Pressure (STP) conditions are a set of agreed-upon parameters that allow scientists to compare different experimental results. STP is defined as a temperature of 273.15 K (0°C) and a pressure of 1 atm.
These conditions are crucial for calculations involving gases, as they standardize the gas volume for comparison. For example, at STP, one mole of any ideal gas occupies a volume of 22,400 cm³. This standard volume helps when calculating the amount of gas produced or consumed in a reaction, ensuring comparisons and conversions are consistent and accurate.

Moles and Mole Concept

The mole concept is a fundamental principle in chemistry, crucial for quantifying substances in chemical reactions. A **mole** is a unit that represents exactly 6.022 x 10²³ elementary entities (such as atoms, molecules, ions, etc.).

• This number is known as Avogadro's number and allows chemists to count atoms and molecules by weighing measurable amounts of material.
• The concept allows chemists to convert between the mass of a substance and the number of particles it contains, facilitating the precise formulation of chemical reactions.

In electrolysis, the mole concept helps us determine how many moles of a product like a gas are generated for a given number of electrons (or charges) passed through the system. This relationship is often illustrated in electrochemical calculations involving gases and reactions at electrodes.