$5 \, A$ current is passed through an electrolytic cell filled with $AgNO_3$ solution for $2.7$ hours. If $1$ spoon requires $0.01 \, g$ of silver to get coated,calculate how many spoons can be coated by the silver obtained at the cathode? $[Ag = 108 \, u]$

(5439) Step $1$: Calculate the total charge $Q$ passed through the cell.
$Q = I \times t = 5 \, A \times (2.7 \times 3600 \, s) = 48600 \, C$.
Step $2$: Calculate the mass of silver deposited using Faraday's law of electrolysis.
$m = \frac{M \times Q}{n \times F} = \frac{108 \times 48600}{1 \times 96500} \approx 54.387 \, g$.
Step $3$: Calculate the number of spoons coated.
$\text{Number of spoons} = \frac{\text{Total mass of Ag}}{\text{Mass of Ag per spoon}} = \frac{54.387 \, g}{0.01 \, g/\text{spoon}} \approx 5438.7$.
Rounding to the nearest whole number,we get $5439$ spoons.