Michael Faraday was the first scientist who described the quantitative aspects of electrolysis. Now Faraday’s laws also flow from what has been discussed earlier. Faraday’s Laws of Electrolysis After his extensive investigations on electrolysis of solutions and melts of electrolytes, Faraday published his results during 1833-34 in the form of the following well known Faraday’s two laws of electrolysis:

(i) First Law: The amount of chemical reaction which occurs at any electrode during electrolysis by a current is proportional to the quantity of electricity passed through the electrolyte (solution or melt).

(ii) Second Law: The amounts of different substances liberated by the same quantity of electricity passing through the electrolytic solution are proportional to their chemical equivalent weights (Atomic Mass of Metal ÷ Number of electrons required to reduce the cation).

The density of Ag is 10.5 g/cm³. How long a current of 5A has to be passed through a solution of AgNO₃ to coat a metal surface of area 100 cm₂ with 0.01 mm thick layer? (Ag = 108)

3 minutes 8 seconds

The correct answer is option 2. 3 minutes 8 seconds.

To determine how long a current of 5A needs to be passed through a solution of AgNO3 to coat a metal surface with a specified thickness, we can follow these steps:

Calculate the mass of silver (Ag) to be deposited: First, calculate the volume of silver needed:

\(\text{Volume} = \text{Area} \times \text{Thickness}\)

Given:

\(\text{Area} = 100 \, \text{cm}^2\)

\(\text{Thickness} = 0.01 \, \text{mm} = 0.01 \times 10^{-1} \, \text{cm} = 0.001 \, \text{cm}\)

\(\text{Volume} = 100 \, \text{cm}^2 \times 0.001 \, \text{cm} = 0.1 \, \text{cm}^3\)

Now, calculate the mass of silver:

\(\text{Density of Ag} = 10.5 \, \text{g/cm}^3\)

\(\text{Mass of Ag} = \text{Volume} \times \text{Density} = 0.1 \, \text{cm}^3 \times 10.5 \, \text{g/cm}^3 = 1.05 \, \text{g}\)

Calculate the moles of silver deposited:

\(\text{Molar mass of Ag} = 108 \, \text{g/mol}\)

\(\text{Moles of Ag} = \frac{\text{Mass}}{\text{Molar mass}} = \frac{1.05 \, \text{g}}{108 \, \text{g/mol}} \approx 0.00972 \, \text{mol}\)

Determine the charge required to deposit this amount of silver: The reduction half-reaction for silver ion (\( \text{Ag}^+ \)) to silver metal (Ag) is:

\(\text{Ag}^+ + e^- \rightarrow \text{Ag}\)

1 mole of electrons (1 faraday) is required to deposit 1 mole of silver.

\(\text{Faradays required} = \text{Moles of Ag} = 0.00972 \, \text{mol}\)

Calculate the time required for the current of 5A to pass: Faraday's constant \( F \) is approximately \( 96485 \) C/mol.

\(\text{Charge (C)} = \text{Faradays} \times F = 0.00972 \, \text{mol} \times 96485 \, \text{C/mol} = 938.15 \, \text{C}\)

Current \( I = 5 \) A, so the time \( t \) in seconds can be calculated by:

\(t = \frac{\text{Charge}}{\text{Current}} = \frac{938.15 \, \text{C}}{5 \, \text{A}} = 187.63 \, \text{s} \approx 3 \, \text{minutes} \, 8 \, \text{seconds}\)

Therefore, the answer is: 3 minutes 8 seconds.