Problem 90 - A Complete Resource Book in Chemistry for JEE Main

Question

How much chlorine will be liberated on passing one ampere current for 30 min through \(\mathrm{NaCl}\) solution? (a) \(0.66 \mathrm{~mol}\) (b) \(0.33 \mathrm{~mol}\) (c) \(0.66 \mathrm{~g}\) (d) \(0.33 \mathrm{~g}\)

Step-by-Step Solution

Answer

The mass of chlorine liberated is 0.66 g.

Step 1: Understand the Reaction

Chlorine is liberated at the anode when electrolysis of an aqueous \( \mathrm{NaCl} \) solution occurs. The reaction at the anode is \( 2\mathrm{Cl}^- \rightarrow \mathrm{Cl}_2 + 2e^- \). This means two moles of electrons are needed to liberate one mole of chlorine gas \( \mathrm{Cl}_2 \).

Step 2: Calculate Total Charge Passed

Current \( I = 1 \) ampere and time \( t = 30 \) minutes or \( 1800 \) seconds. Total charge \( Q \) is given by \( Q = I \times t = 1 \times 1800 = 1800 \) coulombs.

Step 3: Use Faraday's Law

According to Faraday's first law, the amount of substance liberated at an electrode is directly proportional to the charge \( Q \). The moles of electrons (Faradays) passed are \( \frac{Q}{F} \), where \( F = 96500 \) coulombs per mole.

Step 4: Calculate Moles of Electrons

Use the formula \( \text{Faradays} = \frac{Q}{96500} = \frac{1800}{96500} \approx 0.0187 \; \text{moles} \).

Step 5: Calculate Moles of Chlorine Liberated

Since 2 moles of electrons are needed to liberate 1 mole of \( \mathrm{Cl}_2 \), the moles of \( \mathrm{Cl}_2 \) liberated is \( \frac{0.0187}{2} = 0.00935 \; \text{moles} \).

Step 6: Convert Moles of Chlorine to Grams

The molar mass of \( \mathrm{Cl}_2 \) is \( 71 \; \text{g/mol} \). Therefore, the mass of \( \mathrm{Cl}_2 \) liberated is \( 0.00935 \times 71 \approx 0.66485 \; \text{g} \).

Step 7: Find the Nearest Option

Round the calculated mass of chlorine to two decimal places, which is \( 0.66 \; \mathrm{g} \). This corresponds to option (c) \( 0.66 \; \mathrm{g} \).

Key Concepts

Faraday's laws of electrolysis

Faraday's laws of electrolysis illustrate the foundational principles of electrochemistry, which govern how electric currents produce chemical changes. These laws, formulated by Michael Faraday in the 19th century, help us understand the quantitative aspects of electrode reactions. Faraday's first law states that the amount of chemical change (or substance liberated or dissolved) at an electrode during electrolysis is directly proportional to the amount of electricity (charge in coulombs) passed through the electrolyte. This means:

• The more electricity you pass, the greater the amount of substance that will be affected at the electrode.
• Mathematically, this is expressed as: \(\text{Weight of substance} = \frac{Q}{F} \times \text{Equivalent weight}\) where \(Q\) is the total charge and \(F\), Faraday's constant, equals 96500 coulombs per mole.

Faraday's second law of electrolysis states that when the same quantity of electricity is passed through different electrolytes, the amounts of substances deposited are in the ratio of their equivalent weights. Understanding Faraday's laws is crucial as they provide insight into how we can predict and calculate the outcomes of electrode processes in electrolysis.

Electrode Reactions

Electrode reactions are the chemical reactions that occur at the electrodes during electrolysis. These reactions are essential to the process because they transform electrical energy into chemical change. Electrolytic cells usually comprise two electrodes:

• The anode, where oxidation occurs. In this problem, it's where chlorine gas is produced from chloride ions.
• The cathode, where reduction happens.

In our example of electrolysis of NaCl, the anode reaction is crucial because it releases chlorine gas. The equation for this reaction is:

• \(2\mathrm{Cl}^- \rightarrow \mathrm{Cl}_2 + 2e^-\)
• This indicates that releasing one mole of \(\mathrm{Cl}_2\) requires two moles of electrons.

Electrode reactions are, therefore, at the core of converting electrical energy to chemical changes. Understanding them allows us to harness and utilize electricity to create specific chemicals, such as releasing chlorine from sodium chloride.

Moles and Molarity

Understanding moles and molarity is fundamental in chemistry, especially when dealing with reactions in solutions like electrolysis. A mole is a unit that measures the amount of a substance. It is equivalent to Avogadro's number, \(6.022 \times 10^{23}\), of atoms, ions, or molecules. This concept simplifies dealing with large numbers of tiny entities in chemistry.In the context of electrolysis, moles are essential because they help calculate the quantities of reactants and products that participate in or result from electrode reactions. For example, for every 2 moles of electrons exchanged, 1 mole of chlorine gas (\(\mathrm{Cl}_2\)) is formed.Molarity, on the other hand, refers to the concentration of a solution. It measures how many moles of a solute are present per liter of solution. While the specific problem does not require us to calculate molarity, understanding it is beneficial when considering the broader implications of electrolysis in solution concentration. Calculating moles and understanding molarity make the quantitative aspect of chemistry clear and provide a framework for predicting the outcomes of chemical reactions.