Question

Zn Amalgam is prepared by electrolysis of aqueous \(\mathrm{ZnCl}_{2}\) using \(\mathrm{Hg}\) cathode \((9 \mathrm{gm})\). How much current is to be passed through \(\mathrm{ZnCl}_{2}\) solution for 1000 seconds to prepare a Zn Amalgam with \(25 \% \mathrm{Zn}\) by wt. \((\mathrm{Zn}=65.4)\) (1) \(5.6\) amp (2) \(7.2 \mathrm{amp}\) (3) \(8.85 \mathrm{amp}\) (4) \(11.2 \mathrm{amp}\)

Short answer

Option (3) 8.85 amp

Step-by-step solution

- Calculate the mass of Zinc needed

Given that the amalgam is 25% Zn by weight, 75% of the amalgam mass is Hg. Define the total mass of the amalgam as the mass of Hg (\text{9 gm}) plus the mass of Zn (\text{m}). Since 25% of the total mass is Zn, we can write:\[ 0.25 \times (\text{9} + \text{m}) = \text{m} \]Rearrange to solve for m:\[ 0.25 \times 9 + 0.25 \times \text{m} = \text{m} \]\[ 2.25 = 0.75 \times \text{m} \]\[ \text{m} = 3 \text{ gm} \]Thus, the mass of Zinc needed to prepare the amalgam is 3 grams.

- Determine moles of Zn required

Using the atomic mass of Zinc (65.4 g/mol), calculate the moles of Zinc needed:\[ \text{moles of Zn} = \frac{3 \text{ gm}}{65.4 \text{ g/mol}} = 0.0459 \text{ mol} \]

- Relate moles of Zn to Faraday’s law

Faraday’s law of electrolysis states that the mass of substance deposited at an electrode is directly proportional to the quantity of electricity passed. One mole of Zn deposits from ZnCl\(_2\) with 2 moles of electrons (2 Faraday):\[ \text{Q} = \text{n} \times \text{F} \]where Q is the charge, n is the moles of electrons, and F is the Faraday constant (96500 C/mol). For Zn:\[ \text{Q} = 0.0459 \text{ mol} \times 2 \times 96500 \text{ C/mol} = 8855 \text{ C} \]

- Relate charge to current

The current (I) needed to deliver a charge (Q) over time (t) is given by:\[ \text{I} = \frac{\text{Q}}{\text{t}} = \frac{8855 \text{ C}}{1000 \text{ s}} = 8.855 \text{ A} \]

- Choose the correct option

Among the provided options, the closest to the calculated current (8.855 A) is:Option (3) 8.85 amp.

Key concepts

Faraday's law of electrolysis

Faraday's law of electrolysis is a fundamental principle in the field of electrochemistry. It states that the amount of substance deposited or dissolved at an electrode during electrolysis is directly proportional to the amount of electric charge passed through the electrolyte. There are two laws:
1. The amount of chemical change is proportional to the amount of electricity that flows through the electrolyte.
2. To deposit a single mole of a substance, a fixed amount of charge must be passed, known as the Faraday constant, which is approximately 96500 coulombs per mole (C/mol).
In the given problem, we needed to prepare a zinc amalgam using ZnCl\(_2\) solution. To find out how much current is required, we first needed to determine the amount of zinc to be deposited. Using Faraday's laws, we calculated the charge (\textbf{Q}) needed by multiplying the moles of zinc required by the Faraday constant and the number of electrons needed for the deposition.

zinc amalgam preparation

Zinc amalgam is a mixture of zinc and mercury, and it's a common reagent in organic chemistry for amalgamating various reactions. In this problem, the zinc amalgam is prepared using the process of electrolysis of aqueous ZnCl\(_2\).
Steps to prepare zinc amalgam:
1. Calculate the mass of zinc needed based on the given percentage by weight.
2. Calculate the moles of zinc using its atomic mass.
3. Apply Faraday’s law to relate the moles of zinc to the required charge.
For this exercise, the goal was to create a 25% zinc amalgam by weight with a 9 gm mercury substrate. By solving the mass equations, we found that 3 gm of zinc is required. This allows students to understand not just the electrochemical principle but also the stoichiometric calculations involved in preparing specific materials.

current calculation

Calculating the current (I) for electrolysis involves understanding the relationship between charge (\textbf{Q}), time (\textbf{t}), and current. The formula linking these three parameters is:
\( I = \frac{Q}{t} \)
From the previous calculations, we determined that the total charge (\textbf{Q}) required is 8855 coulombs. The time (\textbf{t}) provided in the problem is 1000 seconds. Substituting these values into the formula gives us the current:
\( I = \frac{8855 \text{ C}}{1000 \text{ s}} = 8.855 \text{ A} \)
The correct current needed to achieve the desired zinc deposition is, therefore, approximately 8.85 amps. This calculation is crucial as it translates the theoretical concepts of electrolysis and Faraday's laws into practical terms that can be directly applied in experimental or industrial scenarios.