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

b) 2 and 3 are correct

Step 1: Identify the ions involved

In each voltameter, the ions present are responsible for the deposition. In \( \mathrm{FeSO}_{4} \), the ion is \( \mathrm{Fe}^{2+} \). In \( \mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3} \) and \( \mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{3} \), the ions are \( \mathrm{Fe}^{3+} \). This will affect the amount of iron deposited based on the charge.

Step 2: Apply Faraday's First Law of Electrolysis

According to Faraday's First Law, the amount of substance deposited at an electrode is directly proportional to the quantity of electricity passed through the electrolyte. The formula used is: \[ W = \dfrac{EQ}{F} \] where \( W \) is the mass of the substance deposited, \( E \) is the equivalent weight, \( Q \) is the charge passed, and \( F \) is Faraday's constant.

Step 3: Calculate equivalent weight for iron ions

For \( \mathrm{Fe}^{2+} \), the equivalent weight \( (E) \) is the molar mass divided by 2, while for \( \mathrm{Fe}^{3+} \), the equivalent weight is the molar mass divided by 3. Since equal charge is passed through each cell, the amount deposited is proportional to the equivalent weight.

Step 4: Compare deposition in \( \mathrm{FeSO}_{4} \) and \( \mathrm{Fe}_{2}(\mathrm{SO}_{4})_{3} \)

In \( \mathrm{FeSO}_{4} \), \( \mathrm{Fe}^{2+} \) will deposit based on its equivalent weight. Similarly, in \( \mathrm{Fe}_{2}(\mathrm{SO}_{4})_{3} \), \( \mathrm{Fe}^{3+} \) will deposit. However, since \( \mathrm{Fe}_{3+} \) has a 50% higher equivalent weight than \( \mathrm{Fe}_{2+} \), less iron is deposited.

Step 5: Analyze the statement comparison

Based on the above calculation: The amount of iron deposited in \( \mathrm{FeSO}_{4} \) (due to \( \mathrm{Fe}^{2+} \)) is greater than that in \( \mathrm{Fe}_{2}(\mathrm{SO}_{4})_{3} \) (due to \( \mathrm{Fe}^{3+} \)). Also, in \( \mathrm{Fe}(\mathrm{NO}_{3})_{3} \), the deposited iron is two-thirds that of \( \mathrm{FeSO}_{4} \) since the equivalent weight of \( \mathrm{Fe}^{3+} \) is two-thirds that of \( \mathrm{Fe}^{2+} \).

Step 6: Conclusion

Statements (1) is incorrect as the iron deposited is not the same due to different equivalent weights. Statement (2) is correct since \( \mathrm{Fe}(\mathrm{NO}_{3})_{3} \) deposits two-thirds the iron of \( \mathrm{FeSO}_{4} \). Statement (3) is incorrect because the deposits are not equal. Therefore, correct option is (a) 1 and 2 are correct.

Key Concepts

Electrolysis

Electrolysis is a fascinating process that involves using an electric current to induce a chemical reaction that wouldn't occur spontaneously. It's widely used in various applications like metal plating, purification of metals, and electrochemical manufacturing. In the context of Faraday's Laws of Electrolysis, electrolysis explains how electricity can convert ions in a solution into neutral atoms.

• Electricity is passed through an electrolyte, a substance that conducts electricity by moving ions.
• The anode (positive electrode) attracts anions (negative ions), and the cathode (negative electrode) attracts cations (positive ions).
• As these ions reach their respective electrodes, they undergo chemical changes, often releasing or accepting electrons and depositing or dissolving substances.

Faraday's Laws further explain how the quantities of substances transformed during electrolysis are related to the amount of electric charge used. This lays the foundation for calculating how much of a particular substance, such as iron in our exercise, is deposited on the electrode surface.

Equivalent weight

The concept of equivalent weight is central in electrochemistry, particularly when applying Faraday's laws to electrolysis. The equivalent weight of a substance depends on the number of electrons involved in the process.
For example, when it comes to iron, the equivalent weights differ for its different ionic forms, which is crucial for understanding how much iron will be deposited during electrolysis.

• For an ion such as \( \text{Fe}^{2+} \), the equivalent weight is calculated as the molar mass divided by 2, because each ion requires 2 electrons for reduction.
• For \( \text{Fe}^{3+} \), the equivalent weight is the molar mass divided by 3, since 3 electrons are involved in the reduction process.

This means that the amount of iron deposited depends heavily on the type of iron ion present in the solution, influencing the results seen in an electrolysis experiment.

Iron deposition

Iron deposition is a process where iron ions in an electrolyte are reduced and accumulate on an electrode as metallic iron. This is particularly important in industries that require coatings of iron or need to understand corrosion.
In our exercise, we're observing how different iron ions deposit different amounts of iron under the same electrical conditions.

• For \( \text{FeSO}_4 \), \( \text{Fe}^{2+} \) ions are reduced to metallic iron, \( \text{Fe} \), presenting a higher deposition rate than \( \text{Fe}^{3+} \) ions.
• In \( \text{Fe}_2(\text{SO}_4)_3 \) and \( \text{Fe}(\text{NO}_3)_3 \), \( \text{Fe}^{3+} \) ions deposit at a lower rate because of their higher equivalent weight.

This difference emphasizes the significance of ion type and its role in industrial applications such as electrode positioning and material recovery.

Voltameter

A voltameter is an essential apparatus for measuring the quantity of electricity that passes through an electrolyte by observing the amount of material deposited or dissolved at an electrode.
The name might sound similar to "voltmeter," but a voltameter deals with measuring chemical changes due to the passage of electric current rather than just measuring the current itself.

• It operates based on the principle of electrolysis, allowing scientists to translate electrical readings into measurable chemical quantities.
• The voltameter setup usually consists of a container with an electrolyte and electrodes. By measuring the mass of substance deposited or dissolved, one can infer the number of moles of electrons transferred, as detailed by Faraday's laws.

In scientific and industrial settings, voltameters serve as a practical tool for verifying theoretical calculations, such as confirming the equivalent weight and understanding materials involved in electrolysis processes.