Cadmium amalgam is prepared by the electrolysis of a solution of CdCl2 using mercury as the cathode. The goal is to prepare an amalgam with 10% by mass of Cd on the cathode, which initially weighs 4.5g. We need to calculate the time required for a current of 4A to pass through the electrolytic cell in order to achieve this desired composition.



1. Calculation of the amount of Cd required:
To calculate the amount of Cd required to prepare the amalgam, we can use the equation:

Mass of Cd = (Mass of CdHg amalgam * % Cd by mass) / 100

Substituting the given values, we get:

Mass of Cd = (4.5g * 10%) / 100
Mass of Cd = 0.45g

2. Calculation of the number of moles of Cd:
Next, we need to calculate the number of moles of Cd using its molar mass. The molar mass of Cd is 112.41 g/mol.

Number of moles of Cd = Mass of Cd / Molar mass of Cd
Number of moles of Cd = 0.45g / 112.41 g/mol
Number of moles of Cd = 0.004 mol

3. Calculation of the total charge required:
Since we know the current passing through the cell and the time required, we can calculate the total charge (Q) using the equation:

Q = I * t

Substituting the given values, we get:

Q = 4A * t

4. Calculation of the amount of electrons required:
The total charge required (Q) is equal to the product of the number of moles of Cd (n) and the Faraday constant (F).

Q = n * F

Substituting the values, we get:

4A * t = 0.004 mol * 96485 C/mol

5. Calculation of the time required:
We can rearrange the equation to solve for time (t):

t = (0.004 mol * 96485 C/mol) / 4A

Simplifying the equation, we get:

t = 9.6485 s

Therefore, a current of 4A should be passed for approximately 9.6485 seconds to prepare an amalgam with 10% by mass of Cd on the cathode.



In summary, the time required for a current of 4A to be passed in order to prepare 10% by mass Cd in CdHg amalgam on a cathode weighing 4.5g of Hg is approximately 9.6485 seconds. This calculation is based on the amount of Cd required, the number of moles of Cd, and the total charge needed for the electrolysis process.