Problem 19 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

How many electrons would be required to deposit \(6.35 \mathrm{~g}\) of copper at the cathode during the electrolysis of an aqueous solution of copper sulphate? (Atomic mass of copper \(=63.5 \mathrm{u}, \mathrm{N}_{\mathrm{A}}=\) Avogadro's constant): (a) \(\frac{\mathrm{N}_{\mathrm{A}}}{20}\) (b) \(\frac{\mathrm{N}_{\mathrm{A}}}{10}\) (c) \(\frac{\mathrm{N}_{\mathrm{A}}}{5}\) (d) \(\frac{\mathrm{N}_{\mathrm{A}}}{2}\)

Step-by-Step Solution

Answer

Option (b): \(\frac{\mathrm{N}_{\mathrm{A}}}{10}\).

Step 1: Identify the Reaction

The electrolysis of copper sulfate involves the deposition of copper at the cathode. The reaction can be represented as \( \text{Cu}^{2+} + 2\text{e}^- \rightarrow \text{Cu} \). This equation shows that two electrons are required for each copper ion.

Step 2: Calculate Moles of Copper

First, determine the number of moles of copper deposited. Given the mass of copper deposited is \( 6.35 \, \text{g} \) and the atomic mass of copper is \( 63.5 \, \text{g/mol} \), we calculate the moles as follows: \( \text{moles of Cu} = \frac{6.35}{63.5} = 0.1 \).

Step 3: Calculate Moles of Electrons

Since two electrons are required for each copper ion \( (\text{Cu}^{2+}) \), the moles of electrons needed are twice the number of moles of copper. Thus, \( \text{moles of electrons} = 2 \times 0.1 = 0.2 \text{ moles} \).

Step 4: Calculate Number of Electrons

To find the total number of electrons, multiply the moles of electrons by Avogadro's constant \( (\text{N}_{\text{A}} = 6.022 \times 10^{23} \, \text{mol}^{-1}) \). Therefore, the number of electrons is \( 0.2 \times 6.022 \times 10^{23} = 1.2044 \times 10^{23} \text{ electrons} \).

Step 5: Choose the Correct Option

Next, compare \( 1.2044 \times 10^{23} \) with the given options. Option (b) is \( \frac{\mathrm{N}_{\mathrm{A}}}{10} = \frac{6.022 \times 10^{23}}{10} = 6.022 \times 10^{22} \), which is indeed \( 0.1 \times 6.022 \times 10^{23} \). Hence, option (b) is correct.

Key Concepts

Number of Electrons

When discussing the electrolysis of copper sulfate, a fundamental concept is understanding the number of electrons involved in the reaction. During electrolysis, copper ions (\(\text{Cu}^{2+}\)) gain electrons at the cathode, resulting in the deposition of copper metal. The specific reaction occurring is:
\[ \text{Cu}^{2+} + 2\text{e}^- \rightarrow \text{Cu} \]
This equation highlights a crucial point: every copper ion (\(\text{Cu}^{2+}\)) requires two electrons to form a copper atom. This means for any amount of copper being deposited, twice that number of electrons is needed.

To concretely understand how many electrons are required, we go through the process of calculating the moles of electrons first (as discussed in the following sections) and then using Avogadro's constant. By multiplying the moles of electrons by \(\text{N}_{\text{A}}\), which is Avogadro's number (\(6.022 \times 10^{23}\)), we can determine the total number of electrons involved in the process.

Atomic Mass

The concept of atomic mass is critical when considering how much of an element reacts. The atomic mass of copper is given as \(63.5 \, \text{u}\), which we use to convert the mass of copper into moles. The atomic mass unit (u) provides a way to express the mass of atoms and subatomic particles.
In this task, knowing the atomic mass allows us to calculate the number of copper moles present in \(6.35 \, \text{g}\) of deposited copper:

• First, identify the given mass of copper, which is \(6.35 \, \text{g}\).
• Then, use the formula for moles calculation: \[ \text{moles of Cu} = \frac{\text{mass of Cu}}{\text{atomic mass of Cu}} \]
• Substitute the values into the formula: \( \frac{6.35}{63.5} \), leading to \(0.1\) moles of copper.

The ability to convert mass to moles is a foundational skill in chemistry and essential when doing calculations related to electrolysis.

Moles Calculation

Moles are central to understanding chemical reactions, particularly during electrolysis. Calculating moles allows us to determine how much of a substance is involved in a reaction.
To find out how many moles are formed or needed, use the formula:
\[ \text{moles} = \frac{\text{mass}}{\text{molar mass}} \]

Steps in Calculation:

• First, find the amount of copper deposited, given as \(6.35\) grams.
• The atomic mass of copper (molar mass), as provided, is \(63.5 \, \text{g/mol}\).
• Use the above formula to find moles of copper: \( \text{moles of Cu} = \frac{6.35}{63.5} = 0.1 \text{ moles}\).

Next, consider the moles of electrons needed for each mole of copper ionized. Since two electrons are required per copper atom, the moles of electrons are double the copper:

• Multiply by 2 to account for the electrons per copper: \(0.1 \, \text{moles of Cu} \times 2 = 0.2 \, \text{moles of electrons}\).

By understanding these calculations, you can derive the number of electrons required in electrolysis, connecting it to Avogadro's constant and ensuring accurate predictions in experiments.