Question

A metal surface of 100 cm2 area has to be coated with nickel layer of thickness 0.001mm. A current of 2A was passed through a solution of Ni (NO₃)₂ for 'x' seconds to coat the desired layer. The value of x is_____ (Nearest integer)
 (P_Ni (density of Nickel) is 10 gmL^-1, Molar mass of Nickel is 60 gmol^-1 F = 96500 C mol^-1)

Answer 1

Correct Answer: 161

Solution:
To find the time required to coat the metal surface, we use Faraday's law of electrolysis: \[ m = \frac{M I t}{n F}, \] where:

\( m \) is the mass of the substance deposited,

\( M \) is the molar mass of the substance (nickel, 60 g/mol),

\( I \) is the current (2 A),

\( t \) is the time in seconds,

\( n \) is the valency of the substance (for nickel, \( n = 2 \)),

\( F \) is the Faraday constant (96500 C/mol).

We are given that the thickness of the nickel layer is 0.001 mm (0.0001 cm), so the volume of the nickel deposited is: \[ V = \text{Area} \times \text{Thickness} = 100 \, \text{cm}^2 \times 0.0001 \, \text{cm} = 0.01 \, \text{cm}^3. \] Using the density of nickel \( \rho_{\text{Ni}} = 10 \, \text{g/mL} \), we can calculate the mass of the deposited nickel: \[ m = \rho_{\text{Ni}} \times V = 10 \times 0.01 = 0.1 \, \text{g}. \] Now, substitute into Faraday’s equation: \[ 0.1 = \frac{60 \times 2 \times t}{2 \times 96500}. \] Solving for \( t \): \[ t = \frac{0.1 \times 2 \times 96500}{60 \times 2} = 160.83 \, \text{seconds}. \] Thus, the time required to coat the desired layer is approximately 161 seconds.