Problem 144 - A Complete Resource Book in Chemistry for JEE Main

Question

A current of \(15 \mathrm{amp}\) is employed to plate Nickel in a \(\mathrm{NiSO}_{4}\) bath. Both \(\mathrm{Ni}\) and \(\mathrm{H}_{2}\) are formed at the cathode. If \(9.9 \mathrm{~g}\) of \(\mathrm{Ni}\) are deposited with the simultaneous liberation of \(2.51\) litres of \(\mathrm{H}_{2}\) measured at STP, what is the current efficiency for the deposition of Ni? (Atomic weight of \(\mathrm{Ni}=58.7\) ) (a) \(60 \%\) (b) \(70 \%\) (c) \(80 \%\) (d) \(56 \%\)

Step-by-Step Solution

Answer

The current efficiency for Ni deposition is approximately 60%, option (a).

Step 1: Calculate the Theoretical Charge Required for Ni Deposition

To find the charge required to deposit 9.9 g of Ni, we use Faraday's first law of electrolysis. Nickel is deposited according to the reaction \( ext{Ni}^{2+} + 2e^- \rightarrow ext{Ni} \). Hence, the equivalent weight of Ni is its atomic weight divided by 2, i.e., \( \frac{58.7}{2} = 29.35 \) g/equiv.The number of equivalents of Ni deposited is given by \( \frac{9.9}{29.35} \), which is approximately 0.337 equivalents.The charge required for 1 equivalent is 96500 C (Faraday’s constant), so the charge for 0.337 equivalents is \( 0.337 \times 96500 \approx 32,505 \, \text{C} \).

Step 2: Calculate the Theoretical Charge for H2 Liberation

Hydrogen is liberated according to the reaction \( 2\text{H}^+ + 2e^- \rightarrow \text{H}_2 \). At STP, 1 mole of gas occupies 22.4 L. So, 2.51 L of hydrogen is \( \frac{2.51}{22.4} \approx 0.112 \text{ moles of } \text{H}_2 \).Since 2 moles of electrons are required per mole of \( \text{H}_2 \), the equivalents of electrons used is equal to \( 0.112 \times 2 = 0.224 \text{ equivalents} \).The charge required is \( 0.224 \times 96500 \approx 21,616 \, \text{C} \).

Step 3: Compute the Total Charge Passed

The total charge passed through the solution is equal to the current multiplied by the time: \( Q = I \times t \). Here, current \( I = 15 \, \text{A} \), but we do not have the time in seconds. To find this, we need the sum of the theoretical charges from the previous steps:The total theoretical charge = Charge for Ni + Charge for H2 = \( 32,505 + 21,616 \approx 54,121 \, \text{C} \).

Step 4: Determine the Current Efficiency

The current efficiency for Ni is the ratio of actual charge used for Ni deposition to the total charge passed. Using the theoretical charges:\[ \text{Current Efficiency} = \frac{\text{Charge for Ni}}{\text{Total Theoretical Charge}} \times 100 = \frac{32,505}{54,121} \times 100 \approx 60.07\% \].

Step 5: Identify the Correct Answer

Based on the previous calculations, the current efficiency for the deposition of Nickel is approximately 60.07%, which is closest to answer (a) 60%. Therefore, the correct answer is (a).

Key Concepts

Faraday's Laws of Electrolysis

Faraday's laws of electrolysis provide the foundational understanding of the electrolytic process by defining how substances interact with electric currents to form new compounds or elements in electrochemical reactions. These laws are crucial when thinking about plating metals like nickel.

• Faraday's First Law states that the mass of a substance altered at an electrode during electrolysis is proportional to the amount of electricity passed through the circuit.
• This implies that more electricity (measured in coulombs) results in greater material deposition.
• For our nickel plating example, the equivalent weight of nickel, based on its molar mass and electron transfer in the reaction, defines how much nickel will be deposited for each coulomb of charge.
• Using Faraday's constant ( 96500 C/mol of electrons ), we calculate how much nickel forms given the total charge, linking the atomic level events to macroscopic quantities.

This understanding is vital for predicting outcomes in electroplating processes.

Current Efficiency

Current efficiency refers to the effectiveness of using an electric current for a specific electrochemical reaction, such as nickel deposition in electrolysis. It answers the question: How efficiently is the electric current being used to perform the desired work—depositing nickel?

• It is defined as the ratio of the actual mass of the metal deposited to the theoretical mass expected based on the charge passed, often expressed as a percentage.
• Determining current efficiency involves comparing the charge utilized for the intended reaction (nickel plating) against the total charge theoretically passed through the electrolysis process.
• For example, in the given exercise, the current efficiency calculation showed approximately 60.07%, meaning that only about 60% of the total current contributed directly to nickel deposition, while the rest went towards other reactions, such as hydrogen gas formation.
• Accurate current efficiency calculations can identify areas for process improvement, optimizing resource usage in industrial applications.

Understanding the efficiency helps in correcting and enhancing the electrolysis process.

Nickel Plating Calculations

Nickel plating calculations allow us to determine how much nickel can be plated using a specific current over a given duration. This involves several electrochemical principles, including stoichiometry and Faraday's laws.

• Calculating nickel plating involves understanding the half-reactions, such as Ni²⁺ + 2e⁻ → Ni , meaning nickel ions gain electrons to form metallic nickel.
• The equivalent weight of nickel is employed to find out how many grams per equivalent can be deposited with a known electric charge.
• In practical steps, we first calculate the charge needed for specific reactions, like nickel and hydrogen gas formation, using Faraday’s law. Then, by setting up a proportional relationship between charge and mass (using the atomic weight), we find out the proportion of nickel that is deposited.
• Finally, the total reaction time can be factored, assuming constant current, to assess the detailed effectiveness of the plating process, helping manufacturers understand resource expenditure versus effective output.

This thorough methodological approach enhances both theoretical understanding and practical application in the field of electrochemistry and industrial nickel plating.