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. Option (b) is the answer.

Step 1: Determine Moles of Electrons for Each Compound

For the electrolytic reaction, we need to determine the moles of electrons required to deposit iron from each electrolyte. \( \text{FeSO}_4 \) dissociates to give iron in its +2 state, requiring 2 moles of electrons for each mole of Fe. \( \text{Fe}_2(\text{SO}_4)_3 \) dissociates to give iron in its +3 state, requiring 3 moles of electrons for each mole of Fe. \( \text{Fe}(\text{NO}_3)_3 \) also dissociates to give iron in its +3 state, requiring 3 moles of electrons for each mole of Fe.

Step 2: Compare Amount of Iron Deposited

Since the same quantity of electricity is passed through each voltameter, the total number of moles of electrons transferred remains constant across all three setups. For \( \text{FeSO}_4 \), the deposited iron will be the highest since it only requires 2 moles of electrons per mole of Fe. For both \( \text{Fe}_2(\text{SO}_4)_3 \) and \( \text{Fe}(\text{NO}_3)_3 \), which require 3 moles of electrons for each mole of Fe, the amount of deposited iron is less and equal for these two compounds.

Step 3: Analyze Statements

Statement (1) is incorrect because \( \text{Fe}_2(\text{SO}_4)_3 \) and \( \text{Fe}(\text{NO}_3)_3 \) both require more moles of electrons, depositing less iron than \( \text{FeSO}_4 \). Statement (2) is correct since the amount of iron deposited from \( \text{Fe}(\text{NO}_3)_3 \) will be \( 2/3 \) of that from \( \text{FeSO}_4 \), given the same electricity. Statement (3) is correct as the iron deposition from \( \text{Fe}_2(\text{SO}_4)_3 \) and \( \text{Fe}(\text{NO}_3)_3 \) is equal.

Key Concepts

Faraday's Laws of Electrolysis

Faraday's Laws of Electrolysis form the foundation of understanding how electric current can cause a chemical change, specifically when passing through an electrolyte solution. There are two basic laws:

• First Law: The amount of chemical change or substance deposited at an electrode is directly proportional to the amount of electricity passed through the electrolyte.
• Second Law: When the same amount of electricity passes through different electrolytes, the masses of substances deposited at the electrodes are proportional to their equivalent weights.

In our problem, this law allows us to calculate and compare the amount of iron deposited from different iron compounds when the same amount of electricity is passed. This stems from the requirement of a certain number of electrons needed for deposition, dependent on the valency of the iron in the compounds being used. Being familiar with Faraday's Laws helps explain why some compounds deposit more iron than others for the same amount of electricity.

Valency and Oxidation States

Understanding the concepts of valency and oxidation states is crucial in electrochemistry. Valency refers to the ability of an atom to bond with other atoms, while oxidation state describes the degree of oxidation of an atom within a compound.
Valency often changes when an atom forms compounds due to the loss or gain of electrons; this directly influences the number of electrons transferred in redox reactions. In our exercise, the difference in iron valency between the compounds, like FeSO₄ and Fe₂(SO₄)₃, is vital. FeSO₄ contains iron in a +2 oxidation state, whereas the latter has iron in a +3 state.
Each oxidation state requires a different number of electrons for a complete reduction to elemental iron.

• Fe in +2 state requires 2 electrons per Fe atom.
• Fe in +3 state requires 3 electrons per Fe atom.

This variance directly impacts the calculation of the amount of iron deposited during electrolysis, as the same amount of electricity supplies a fixed number of electrons across all setups.

Electrolytic Reactions

Electrolytic reactions involve using electricity to drive non-spontaneous chemical reactions. In the context of our exercise, these reactions occur within an electrochemical cell. Here, the application of an electric current causes ions to be reduced and deposited as solid metal onto an electrode.
The specifics of such reactions depend on various factors:

• The nature of the electrolyte—a compound providing ions for the reaction.
• The number of electrons required for the reduction of ions to a neutral metal.
• The structure of the electrode, as well as the power of the electrical source.

In this scenario, the compounds FeSO₄, Fe₂(SO₄)₃, and Fe(NO₃)₃ serve as electrolytes. These compounds dissociate to provide Fe ions for reduction. The efficiency of the iron deposition process within these electrolytic cells is dictated by the number of electrons transferred, emphasizing the direct relation as per Faraday's and electrochemical principles.