Problem 141 - A Complete Resource Book in Chemistry for JEE Main

Question

Equal quantities of electricity are passed through three voltameters containing \(\mathrm{FeSO}_{4}, \mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3}\), and \(\mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{3}\). Consider the following statements in this regard (1) the amount of iron deposited in \(\mathrm{FeSO}_{4}\) and \(\mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3}\) is equal (2) the amount of iron deposited in \(\mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{3}\) is two thirds of the amount of iron deposited in \(\mathrm{FeSO}_{4}\) (3) the amount of iron deposited in \(\mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3} \mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{3}\) is equal Of these statements (a) 1 and 2 are correct (b) 2 and 3 are correct (c) 1 and 3 are correct (d) 1,2 and 3 are correct

Step-by-Step Solution

Answer

Statements 2 and 3 are correct (b).

Step 1: Understand Faraday's Law of Electrolysis

Faraday's Law states that the amount of substance deposited or liberated at each electrode is proportional to the amount of electricity that passes through the electrolyte. The amount of substance (m) is given by \( m = \frac{Q}{F} \times \frac{1}{n} \times M \), where \( Q \) is the total charge, \( F \) is Faraday's constant, \( n \) is the number of moles of electrons exchanged, and \( M \) is the molar mass of the substance.

Step 2: Determine Iron Deposition in FeSO4

For \( \text{FeSO}_4 \), iron is deposited via the reduction of \( \text{Fe}^{2+} \) to \( \text{Fe} \). The reaction is \( \text{Fe}^{2+} + 2e^- \rightarrow \text{Fe} \). Here, \( n = 2 \).

Step 3: Determine Iron Deposition in Fe2(SO4)3

For \( \text{Fe}_2(\text{SO}_4)_3 \), iron is deposited via the reduction of \( \text{Fe}^{3+} \) to \( \text{Fe} \). The reaction is \( \text{Fe}^{3+} + 3e^- \rightarrow \text{Fe} \). Here, \( n = 3 \).

Step 4: Determine Iron Deposition in Fe(NO3)3

In \( \text{Fe(NO}_3)_3 \), iron is also deposited from \( \text{Fe}^{3+} \) to iron, the same number \( n = 3 \). The analogous reaction is: \( \text{Fe}^{3+} + 3e^- \rightarrow \text{Fe} \).

Step 5: Analyze the Statements

Given the equal charge passed through each system, the amount of iron deposited is determined by \( \frac{1}{n} \). Independently calculate that:- In \( \text{FeSO}_4 \), \( n = 2 \), so \( \frac{1}{2} \).- In \( \text{Fe}_2(\text{SO}_4)_3 \) and \( \text{Fe(NO}_3)_3 \), both have \( n = 3 \).Hence for equal electricity, \( \text{Fe}_2(\text{SO}_4)_3 \) and \( \text{Fe(NO}_3)_3 \) yield the same deposit, less than \( \text{FeSO}_4 \).

Step 6: Determine Correct Statements

From Step 5,:- Statement 1 is incorrect because \( \text{FeSO}_4 \) would deposit more iron than \( \text{Fe}_2(\text{SO}_4)_3 \).- Statement 2 is correct because \( \text{Fe(NO}_3)_3 \) deposits 2/3 that of \( \text{FeSO}_4 \) (based on \( n \)).- Statement 3 is also correct, as both \( \text{Fe}_2(\text{SO}_4)_3 \) and \( \text{Fe(NO}_3)_3 \) deposited the same amount of iron.

Key Concepts

Electrochemical Deposition

Electrochemical deposition is a process in which metals or other materials are deposited onto a surface using an electric current. This technique is crucial for various industrial applications such as metal plating, semiconductor fabrication, and corrosion prevention. The fundamental principle behind electrochemical deposition is Faraday's Law of Electrolysis, which states that the amount of substance deposited is directly proportional to the quantity of electricity passed through the electrolyte. During this process, ions in the solution gain electrons at the cathode and are reduced to form a solid deposit. Every type of deposition requires a specific set of conditions, including the target material's ionic form in the solution and the number of electrons required to reduce the ions at the electrode surface. An important aspect to note with electrochemical deposition is understanding the mole-to-charge ratio. This ratio, often referred to as the number of moles of electrons exchanged, determines how much of a material can be deposited based on the amount of electrical charge passed through the system.

Voltameter

A voltameter is an apparatus used to measure the magnitude of an electric current by determining the amount of substance deposited or dissolved by electrolysis. It's an essential tool in experiments involving electrochemical deposition.The principle behind a voltameter is based on Faraday's laws of electrolysis. By measuring the weight change of the electrodes, the charge passed through can be calculated. This setup enables the precise examination of the relationship between the electric current and material deposition, which is vital in verifying experimental data.In our exercise, voltameters were used with different solutions, such as \( \mathrm{FeSO}_{4} \) and \( \mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3} \), allowing the determination of the deposited amount of iron based on their respective electron exchanges.

Charge Passage

Charge passage refers to the transfer of electric charge through an electrolyte during the electrolysis process. It is measured in coulombs and directly influences the amount of material deposited at the electrodes.According to Faraday's Law, for a given amount of charge \( Q \) that passes through the system, the mass of a substance \( m \) deposited at an electrode is determined using the formula:\[ m = \frac{Q}{F} \times \frac{1}{n} \times M \]Here, \( F \) is Faraday's constant, \( n \) is the number of moles of electrons exchanged, and \( M \) is the molar mass. This formula illustrates how charge passage interacts with the chemistry of the electrolyte to result in material deposition. The exercise showcases equal charge passage through different setups to compare the deposition outcomes of iron from different iron salts.

Iron Deposition

Iron deposition in electrochemical setups involves reducing iron ions from a solution to form solid iron at an electrode. In the context of our exercise with \( \mathrm{FeSO}_{4} \), \( \mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3} \), and \( \mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{3} \), distinct reduction reactions occur due to differing oxidation states of iron.- For \( \mathrm{FeSO}_{4} \), iron is present as \( \mathrm{Fe}^{2+} \), requiring 2 electrons per iron atom reduced.- For both \( \mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3} \) and \( \mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{3} \), iron is in the \( \mathrm{Fe}^{3+} \) form, needing 3 electrons per atom.Due to these differences, the number of moles of electrons needed to deposit one mole of iron varies between the solutions, influencing the iron deposition amount per unit of charge. This nuanced difference is critical in determining why the statements given in the exercise have various correctness about the levels of iron deposited.

Moles of Electrons Exchanged

The number of moles of electrons exchanged is a fundamental concept in understanding electrochemical reactions, particularly in electrolysis. It tells us how many electrons are required to reduce ions from a solution to solid metals.The exchange number \( n \) is essential for calculating deposition amounts using Faraday's Law. For example, if iron exists as \( \mathrm{Fe}^{2+} \), like in \( \mathrm{FeSO}_{4} \), \( n = 2 \) electrons are needed per iron ion. Conversely, for iron as \( \mathrm{Fe}^{3+} \) in \( \mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3} \), \( n = 3 \) is required.Hence, the total number of moles of electrons exchanged directly affects the calculation of how much iron will be deposited under equal currents. This allows us to analyze the discrepancies between different solutions and understand why equal charges yield differing deposition amounts, as illustrated by the exercise.