Question

Assertion (A): Passage of 48,250 coulombs of electricity through cupric sulphate and ferrous sulphate solutions result in the deposition \(0.5\) moles each of iron and copper at the respective cathodes. Reason (R): Number of equivalents of a metal deposited at cathode is equal to the number of faradays of electricity passed through the electrolyte. (a) Both "A" and "R" are true and "R" is the correct explanation of "A". (b) Both "A" and "R" are true and "R" is not the correct explanation of "A". (c) "A" is correct and "R" is wrong. (d) "A" is wrong and "R" is correct.

Short answer

Explain your answer using Faraday's laws of electrolysis. Answer: No, the passage of 48,250 coulombs of electricity results in the deposition of 0.25 moles each of iron and copper at the respective cathodes, not 0.5 moles. This is determined using Faraday's laws of electrolysis, which states that the number of equivalents of a metal deposited at the cathode is equal to the number of faradays of electricity passed through the electrolyte.

Step-by-step solution

Analyze Assertion (A)

First, we need to determine if the passage of 48,250 coulombs of electricity through cupric sulfate and ferrous sulfate solutions result in the deposition of 0.5 moles each of iron and copper at the respective cathodes. Copper (Cu) has a valency of +2, and hence its equivalent weight is atomic mass / 2 = 63.5 / 2. Iron (Fe) also has a valency of +2, and its equivalent weight is atomic mass / 2 = 55.8 / 2. Using Faraday's Law, we know that the number of equivalents = charge passed (in coulombs) / (n * Faraday's constant), where n is the valency of the metal. Faraday's constant is approximately 96,500 C/mol.

Calculate the number of equivalents of Cu and Fe deposited on the respective cathodes

For copper: Number of equivalents of Cu = Charge passed / (2 * 96,500) = 48,250 / (2 * 96,500) = 0.25 mol For iron: Number of equivalents of Fe = Charge passed / (2 * 96,500) = 48,250 / (2 * 96,500) = 0.25 mol Since we have calculated the number of moles of each metal deposited at the cathodes and it doesn't match the amount stated in Assertion (A), we can conclude that Assertion (A) is incorrect.

Analyze Reason (R)

Now let's analyze the Reason (R). The statement says that "Number of equivalents of a metal deposited at cathode is equal to the number of faradays of electricity passed through the electrolyte." This statement describes Faraday's Law of electrolysis and it's correct. According to Faraday's law, the amount of substance transformed in an electrolytic cell is proportional to the amount of electrical charge passed through the cell.

Determine the relationship between "A" and "R"

Now we have the conclusions about Assertion (A) and Reason (R). 1. Assertion (A) is incorrect, as the passage of 48,250 coulombs of electricity will not result in the deposition of 0.5 moles each of iron and copper at the respective cathodes, but instead 0.25 moles each. 2. Reason (R) is correct, as it accurately describes Faraday's Law of electrolysis. Therefore, the correct answer is (d) "A" is wrong and "R" is correct.

Key concepts

Equivalents in Electrolysis

When we talk about electrolysis, the term "equivalents" plays an important role. It reflects the amount of a substance that will react with or displace a fixed amount of another substance. In context of electrolysis, the equivalents can be calculated using the formula:

Number of equivalents = \( \frac{\text{Charge passed (in coulombs)}}{n \times \text{Faraday's constant}} \)

where \( n \) is the valency of the ion.

Here's how it works: you divide the total electric charge (in coulombs) by the product of the ion's valency and Faraday's constant, which is 96,500 C/mol. This gives you the number of equivalents deposited at the cathode during electrolysis. For instance, if 48,250 coulombs are passed, this value helps determine the number of moles of the metal deposited.

Cupric Sulphate Electrolysis

Cupric sulphate, with the chemical formula \( \text{CuSO}_4 \), contains copper ions with a valency of +2.

During electrolysis, copper ions gain electrons at the cathode and are deposited as metallic copper. The reaction at the cathode can be represented as:

\( \text{Cu}^{2+} + 2e^- \rightarrow \text{Cu} \).

To calculate the number of equivalents of copper deposited, you use the valency (2) in the formula for equivalents. For example, with the passage of 48,250 coulombs in a solution of cupric sulphate, you'd find:

\( \frac{48,250}{2 \times 96,500} = 0.25 \text{ moles} \)

This equation shows that only 0.25 moles of copper are deposited rather than the 0.5 moles mentioned in the assertion.

Ferrous Sulphate Electrolysis

In the case of ferrous sulphate, \( \text{FeSO}_4 \), iron also has a valency of +2. During electrolysis, ferrous ions \( \text{Fe}^{2+} \) receive electrons at the cathode, forming solid iron. The reaction is:

\( \text{Fe}^{2+} + 2e^- \rightarrow \text{Fe} \).

By using the equivalent formula, and considering the valency (2), the equivalents of iron deposited are calculated similarly to copper:

\( \frac{48,250}{2 \times 96,500} = 0.25 \text{ moles} \)

This tells us that 0.25 moles of iron are deposited, which again doesn't match the 0.5 moles claimed in the assertion.

Valency and Equivalent Weight

Understanding valency and equivalent weight is crucial for electrolysis calculations. Valency refers to the ability of an atom to combine with other atoms, which in electrolysis, determines how many electrons are needed for a reaction.

Equivalent weight is calculated by dividing the atomic mass of an element by its valency. For example:

• Copper (Cu) has an atomic mass of 63.5 and valency of \(+2\). Thus, its equivalent weight is \( \frac{63.5}{2} \).
• Iron (Fe) has an atomic mass of 55.8 and valency of \(+2\), making its equivalent weight \( \frac{55.8}{2} \).

These values simplify calculations used in electrolysis, showing how much of a substance can be deposited with a given charge.

Coulombs and Moles Conversion

Transforming coulombs into moles involves using Faraday's Law, a key principle in electrolysis. First, identify the total electric charge in coulombs and then apply the formula to find how many moles are produced.

The conversion is straightforward:

• Calculate the number of equivalents using \( \frac{\text{Charge (coulombs)}}{n \times \text{Faraday's Constant}} \).
• Remember, Faraday's Constant is 96,500 C/mol, representing the charge of one mole of electrons.

This conversion is crucial for understanding how much of a substance is deposited during the process of electrolysis, revealing the actual moles involved compared to theoretical predictions.