Problem 126 - A Complete Resource Book in Chemistry for JEE Main

Question

Calculate the weight of copper that will be deposited at the cathode in the electrolysis of a \(0.2 \mathrm{M}\) solution of copper sulphate, when quantity of electricity, equal to the required to liberate \(2.24 \mathrm{~L}\) of hydrogen at STP from a \(0.1 \mathrm{M}\) aqueous sulphuric acid, is passed (Atomic mass of \(\mathrm{Cu}=63.5\) ) (a) \(6.35 \mathrm{~g}\) (b) \(3.17 \mathrm{~g}\) (c) \(12.71 \mathrm{~g}\) (d) \(63.5 \mathrm{~g}\)

Step-by-Step Solution

Answer

The weight of copper deposited is 6.35 g, which corresponds to option (a).

Step 1: Use Volume of Hydrogen to Find Moles

First, you need to calculate the moles of hydrogen gas liberated. The volume is given as 2.24 L at STP. At STP, 1 mole of any gas occupies 22.4 L.Number of moles of hydrogen gas = \( \frac{2.24}{22.4} = 0.1 \text{ moles} \).

Step 2: Use Faraday's Laws of Electrolysis

According to Faraday's laws, 2 faradays are needed to liberate 1 mole of hydrogen. Since we have 0.1 moles of hydrogen, the number of faradays required is:\[ 0.1 \times 2 = 0.2 \text{ faradays} \]

Step 3: Calculate Copper Deposited

Copper (Cu) has a valency of 2, meaning 2 faradays will deposit 1 mole of copper. The number of moles of copper deposited by 0.2 faradays is given by:\[ \frac{0.2}{2} = 0.1 \text{ moles} \].Finally, to find the weight of copper deposited, multiply the number of moles by the atomic mass of copper (63.5):\[ 0.1 \times 63.5 = 6.35 \text{ grams} \]

Step 4: Select the Correct Answer

The calculated weight of copper deposited is 6.35 grams. Thus, the correct answer to the problem is option (a) 6.35 grams.

Key Concepts

Faraday's Laws of Electrolysis

Faraday's laws of electrolysis are fundamental for understanding how electricity can cause chemical changes in a solution. These laws help determine the amount of substance that will be deposited during electrolysis.

• The first law states that the amount of a substance deposited or dissolved in an electrolytic process is directly proportional to the amount of electricity that passes through the solution. In simpler terms, the more electricity used, the more material will be deposited.


• The second law explains that when the same amount of electricity is used, different substances will have different amounts deposited based on their equivalent weights. Equivalent weight is the atomic or molecular weight divided by the change in oxidation number during reaction.

In the case of depositing copper, we consider one mole of copper, which is equivalent to two faradays of electricity. That’s because each copper ion requires two electrons to reduce to metal form.

Copper Deposition

Copper deposition is a process where copper ions in the solution are reduced and deposit as a solid on the cathode during electrolysis. This occurs when electricity passes through a copper sulfate solution.

In the solution, the positive copper ions (\( \text{Cu}^{2+} \)) move towards the negative cathode. Here, they gain electrons and are reduced to solid copper (\( \text{Cu} \)).

At the cathode, this reaction can be represented as:\[ \text{Cu}^{2+} + 2 \text{e}^- \rightarrow \text{Cu} \]

• Using Faraday's laws, we calculate the weight of copper by first determining the number of moles deposited.
• Each mole of copper requires two faradays due to copper's valency of two.
• Finally, multiplying the moles of copper by its atomic mass (63.5) gives the weight of copper deposited.

Volume of Hydrogen at STP

Standard Temperature and Pressure (STP) is a fixed reference point in chemistry. At STP, 1 mole of any ideal gas occupies 22.4 liters. This is extremely useful for calculations involving gas volumes.

To find the quantity of electricity required to deposit copper, we first determine the volume of hydrogen liberated at STP from the provided data.

Calculating Moles of Hydrogen

For this problem, 2.24 liters of hydrogen gas is released at STP. We use the molar volume (22.4 L/mol) to find moles of hydrogen released:\[ \frac{2.24}{22.4} = 0.1 \text{ moles} \]

• Hydrogen's liberation gives us information on the number of faradays used since 1 mole of hydrogen corresponds to 2 faradays.
• This electric data is then applied to calculate how many moles of copper would similarly be deposited.

Understanding these calculative steps connects the volume of hydrogen gas at STP to the practical aspects of electrolysis and the deposition of metals like copper.