Problem 35 - A Complete Resource Book in Chemistry for JEE Main

Question

For reducing 1 mol of \(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}\) to \(\mathrm{Cr}^{31}\), the charge required is (a) \(3 \times 96500\) coulomb (b) \(6 \times 96500\) coulomb (c) \(0.3 \mathrm{~F}\) (d) \(0.6 \mathrm{~F}\)

Step-by-Step Solution

Answer

The charge required is (b) \(6 \times 96500\) coulombs.

Step 1: Identify the Reaction and Change in Oxidation State

In the provided reduction reaction, one mole of dichromate ion \(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}\) is reduced to form \(\mathrm{Cr}^{3+}\). Here, chromium changes its oxidation state from +6 in dichromate to +3. Thus, each chromium atom undergoes a change of 3 units in its oxidation state.

Step 2: Calculate Electrons Required for Full Change

Since the dichromate ion \(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}\) contains two chromium atoms, the total change for the pair is from \(+12\) to \(+6\) across both chromium atoms. This totals a transfer of \(2 \times 3 = 6\) moles of electrons required to change the oxidation state.

Step 3: Relate Electrons to Faraday's Constant

The charge of one mole of electrons (1 Faraday) is equivalent to 96500 coulombs. Since 6 moles of electrons are needed, the total charge required is \(6 \times 96500\) coulombs.

Key Concepts

Oxidation state

Understanding oxidation states is fundamental in the study of electrochemistry. An oxidation state is a number assigned to an element in a compound, which represents the number of electrons lost or gained by an atom of that element.
In our example, the dichromate ion \(\mathrm{Cr}_{2}\mathrm{O}_{7}^{2-}\), each chromium atom originally has an oxidation state of +6.
When it is reduced to \(\mathrm{Cr}^{3+}\), the oxidation state of chromium decreases to +3. This reduction process involves a change of 3 units per chromium atom. Since there are two chromium atoms involved in the reaction, the total change across both atoms is from +12 to +6, making it a change of 6 units.

• Oxidation state helps determine the electron transfer in a chemical reaction.
• The ability to identify changes in oxidation states is crucial to balance redox reactions accurately.

By understanding oxidation states, you can easily track electron movements and predict reaction outcomes.

Faraday's constant

Faraday’s constant is a key player in linking the amount of substance altered in a redox reaction with the electric charge involved. This constant represents the charge of one mole of electrons.
Its value is approximately 96,500 coulombs per mole (C/mol), which is crucial for calculating the total electric charge required to drive a chemical reaction.

• When you know the number of moles of electrons needed in a redox reaction, multiplying by Faraday's constant gives the total charge in coulombs.
• This is particularly handy in electroplating and electrochemical conversion processes, where precise charge measurements are needed.

In our exercise, knowing that 6 moles of electrons are required to complete the reaction allows us to calculate that \(6 \times 96500\) coulombs are needed for the electron transfer. Faraday’s constant is an indispensable tool for connecting chemical change with electrical voltage.

Redox reactions

Redox reactions, short for reduction-oxidation reactions, are essential chemical processes where the oxidation state of molecules changes. They involve the transfer of electrons between substances.
One substance gets oxidized (loses electrons) while another gets reduced (gains electrons).
In our example, the dichromate ion \(\mathrm{Cr}_{2}\mathrm{O}_{7}^{2-}\) is reduced to \(\mathrm{Cr}^{3+}\), while electrons are gained and the oxidation state decreases.

• Redox reactions are widely utilized in everyday products, including batteries and combustion engines.
• Understanding these reactions enables the development of energy storage systems and pollution control methods.

These balanced electron exchanges form the foundation of electrochemical cells and fuel various industrial processes. Mastering redox reactions enhances your ability to interpret chemical changes and their applications in real-world scenarios.