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

Using the Faraday's law of electrolysis, we can directly relate the amount of substance deposited (in this case, the nickel layer) with the electric charge passed through the electrolyte. <br/><br/> The formula for Faraday's law of electrolysis is: <br/><br/> $W = z \times i \times t$ <br/><br/> where W is the amount of substance deposited (in grams), z is the electrochemical equivalent (grams per coulomb), i is the current (in amperes), and t is the time (in seconds). <br/><br/> By relating the density and volume of the nickel layer to the electric charge passed through the electrolyte, we can calculate the time needed for the deposition: <br/><br/> $$10 \times 100 \times 0.0001 = \frac{\left(\frac{\text { atomic wt. }}{\text { v.f }}\right) \times 2 \times x}{96500}$$ <br/><br/> where v.f is the valence factor for the reaction (in this case, 2). <br/><br/> Solving for x, we get: <br/><br/> $x = 161 \, \mathrm{sec}$ <br/><br/> So, the value of x is 161 seconds.