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Faraday's First Law

How long has ...

Question

How long has a current of $3$ ampere to be applied through a solution of silver nitrate to coat a metal surface of $80 c m^{2}$ with $0.005 m m$ thick layer? Density of silver is $10.5 g / c m^{3}$ .

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Solution

Mass of silver to be deposited
$= v o l u m e \times d e n s i t y$
$= a r e a \times t h i c k n e s s \times d e n s i t y$
Given: $A r e a = 80 c m^{2}, t h i c k n e s s = 0.0005 c m$ and $d e n s i t y = 10.5 g / c m^{3}$
Mass of silver to be deposited $= 80 \times 0.0005 \times 10.5$
$= 0.42 g$
Applying to silver $E = Z \times 96500$
$Z = \frac{108}{96500} g$
Let the current be passed for $t$ seconds.
We know that, $W = Z \times I \times t$
So, $0.42 = \frac{108}{9600} \times 3 \times t$
or $t = \frac{0.42 \times 96500}{108 \times 3} = 125.09 s e c o n d$ .

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