Problem 22 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Electrolysis of dilute aqueous \(\mathrm{NaCl}\) solution was carried out by passing 10 milli ampere current. The time required to liberate \(0.01\) mol of \(\mathrm{H}_{2}\) gas at the cathode is \(\left(1\right.\) Faraday \(\left.=96500 \mathrm{C} \mathrm{mol}^{-1}\right)\) [2008S] (a) \(9.65 \times 10^{4} \mathrm{sec}\) (b) \(19.3 \times 10^{4} \mathrm{sec}\) (c) \(28.95 \times 10^{4} \mathrm{sec}\) (d) \(38.6 \times 10^{4} \mathrm{sec}\)

Step-by-Step Solution

Answer

The answer is (b) \(19.3 \times 10^4\) sec.

Step 1: Understanding Electrolysis of NaCl

In the electrolysis of a dilute aqueous solution of NaCl, water is reduced at the cathode, producing hydrogen gas, while Cl ions produce chlorine gas at the anode. The half-reaction at the cathode can be represented as: \[ 2H_2O + 2e^- \rightarrow H_2 + 2OH^- \], indicating that 2 moles of electrons produce 1 mole of hydrogen gas.

Step 2: Calculate Charge Needed to Liberate H₂

According to the reaction, 2 moles of electrons are needed to produce 1 mole of \( H_2 \), so 1 mole of electrons is needed for 0.5 moles of \( H_2 \). Thus, 2 Faradays (\(2 \times 96500\) Coulombs) are required for 1 mole of \( H_2 \). Thus, for 0.01 mol of \( H_2 \), the required charge is \(2 \times 96500 \times 0.01 = 1930 \) Coulombs.

Step 3: Calculate Time Required

We know current (I) is charge (Q) per unit time (t). Rearranging \( Q = I \times t \) gives \( t = \frac{Q}{I} \). Substituting the known values, \( t = \frac{1930 \text{ C}}{10 \times 10^{-3} \text{ A}} = 193000 \text{ seconds} \).

Step 4: Select the Correct Option

The calculated time is \( 193000 \text{ seconds} \), which matches option (b) \(19.3 \times 10^4 \text{ sec}\).

Key Concepts

Dilute Aqueous Solution

In electrolysis, a dilute aqueous solution refers to a mixture where a small amount of a substance, like sodium chloride (NaCl), is dissolved in water. The water provides a medium for ions to move freely, enabling them to conduct electricity.
This is essential because electrolysis relies on the movement of ions to the electrodes through the solution. In the case of NaCl, when it dissolves in water, it splits into Na⁺ and Cl⁻ ions.
Understanding the nature of a dilute solution helps in predicting the behavior of ions during electrolysis, such as which ions will participate in the reactions occurring at the electrodes.
Keep in mind:

• Water is not just a passive solvent; it actively participates in reactions.
• Dilution impacts the concentration of ions, affecting the reactions at electrodes.

NaCl

Sodium chloride, commonly known as salt, plays a critical role in electrolysis. When NaCl is dissolved in water, it breaks apart into sodium ions (Na⁺) and chloride ions (Cl⁻).
The presence of these ions allows the solution to conduct electricity, which is necessary for electrolysis to occur.
This splitting is crucial because the electrodes will facilitate separate reactions, involving different ions, thereby producing gases like hydrogen and chlorine.
Here are key points about NaCl in electrolysis:

• NaCl increases the electrical conductivity of the water.
• Cl⁻ ions migrate to the anode, where they participate in oxidation reactions.
• Na⁺ ions do not participate directly in gas production at the cathode.

Cathode Reaction

The cathode reaction is a key part of electrolysis, especially when dealing with a dilute aqueous solution of NaCl. At the cathode, reduction occurs.
In this case, water molecules are reduced to produce hydrogen gas and hydroxide ions: \[ 2H_2O + 2e^- \rightarrow H_2 + 2OH^- \].
This implies that for every 2 moles of electrons, 1 mole of hydrogen gas is produced.
This reaction is crucial because it dictates the amount of hydrogen gas that can be collected. The factors that affect this include:

• The concentration of ions available from the dissolution of NaCl.
• The flow of electrons provided by the current.

Electrode Process

The electrode process involves the reactions that take place at the cathode and anode during electrolysis. For a dilute NaCl solution, specific processes occur:

• At the cathode, water is reduced, producing hydrogen gas and hydroxide ions.
• At the anode, Cl⁻ ions are oxidized, forming chlorine gas.

These processes are fundamental to understanding how electrolysis converts electrical energy into chemical changes.
The rates of these processes depend on various factors such as:

• The current supplied to the system, determining how fast ions are reduced or oxidized.
• The type of ions present and their ability to conduct electricity.

Understanding each electrode's specific reaction helps predict what substances will form, underscoring the importance of balancing electrochemical equations to determine the products of electrolysis.