A metal surface of $$100$$ cm$$^2$$ area has to be coated with nickel layer of thickness $$0.001$$ mm. A current of 2A was passed through a solution of Ni(NO$$_3$$)$$_2$$ for 'x' seconds to coat the desired layer. The value of x is _____. (Nearest integer)
($$\rho$$Ni (density of Nickel) is $$10$$ g mL$$^{-1}$$, Molar mass of Nickel is $$60$$ g mol$$^{-1}$$, F $$= 96500$$ C mol$$^{-1}$$)

We need to find the time required to electroplate a nickel layer on a metal surface.

• Surface area = 100 cm$$^2$$
• Thickness = 0.001 mm = 0.0001 cm
• Current $$I = 2$$ A
• Density of Ni, $$\rho = 10$$ g/mL
• Molar mass of Ni = 60 g/mol
• $$F = 96500$$ C/mol

$$V = \text{Area} \times \text{Thickness} = 100 \times 0.0001 = 0.01 \text{ cm}^3 = 0.01 \text{ mL}$$ $$m = \rho \times V = 10 \times 0.01 = 0.1 \text{ g}$$ $$n = \frac{m}{M} = \frac{0.1}{60} \text{ mol}$$

Nickel is deposited as Ni$$^{2+}$$ + 2e$$^-$$ $$\rightarrow$$ Ni, so 2 moles of electrons per mole of Ni.

$$\text{Charge} = n \times 2 \times F = \frac{0.1}{60} \times 2 \times 96500 = \frac{0.2 \times 96500}{60} = \frac{19300}{60}$$ $$Q = It \implies t = \frac{Q}{I} = \frac{19300}{60 \times 2} = \frac{19300}{120} \approx 160.83 \text{ s}$$

Rounding to the nearest integer: $$t = 161$$ seconds.

The answer is $$161$$.