A metal surface of $100 \mathrm{~cm}^{2}$ area has to be coated with nickel layer of thickness 0.001 mm. A current of 2 A was passed through a solution of $\mathrm{Ni}\left(\mathrm{NO}_{3}\right)_{2}$ for '$x$' seconds to coat the desired layer. The value of $x$ is $\_\_\_\_$ (Nearest integer) ($\rho_{\mathrm{Ni}}$ (density of Nickel) is $10 \mathrm{gmL}^{-1}$, Molar mass of Nickel is $60 \mathrm{gmol}^{-1}$ $\mathrm{~F}=96500 \mathrm{C} \mathrm{mol}^{-1}$)

JEE Main · 2023 · 13 Apr 2023 · Shift 1 · Redox Reactions and Electrochemistry

A metal surface of

100 cm^{2}

area has to be coated with nickel layer of thickness 0.001 mm. A current of 2 A was passed through a solution of

Ni (NO_{3})_{2}

for '

x

' seconds to coat the desired layer. The value of

x

____

(Nearest integer)
(

ρ_{Ni}

(density of Nickel) is

10 gmL^{- 1}

, Molar mass of Nickel is

60 gmol^{- 1}

F = 96500 C mol^{- 1}

)

Answer: 161

Using Faraday's law of electrolysis:

W = \frac{E \times i \times t}{F}

, where

E

is the equivalent weight.

First, calculate the mass of nickel needed:

Volume = Area × thickness = $100 cm^{2} \times 0.0001 cm = 0.01 cm^{3} = 0.01 mL$
Mass = density × volume = $10 \times 0.01 = 0.1$ g

For

Ni X^{2 +}

reduction, valence factor = 2, so equivalent weight

E = \frac{60}{2} = 30

g/equiv.

Using the equation:

0.1 = \frac{30 \times 2 \times t}{96500}

t = \frac{0.1 \times 96500}{60} = 160.83 \approx 161 seconds

JEE Main · 2023 · 13 Apr 2023 · Shift 1 · Integer answer