Question

How much time is required to deposit \[1\times {{10}^{-3}}cm\] thick layer of silver(density is \[1.05g/c{{m}^{3}}\]) on a surface of area \[100c{{m}^{2}}\] by passing a current of \[5A\] through the \[AgN{{O}_{3}}\] solution ?
A. \[125s\]
B. \[115s\]
C. \[18.7s\]
D. \[27.25s\]

Answer 1

Hint: According to Faraday’s first law the amount of substance produced at an electrode during electrolysis is directly proportional to the quantity of electricity passed though the electrolyte. 

Hence, we can write as:
\[ W\propto Q\Rightarrow Q=it\]
\[ W\propto it\]
\[\Rightarrow W=Zit\]
W = Deposited weight
Q = Quantity of electricity passed
I = Current required to electrolysis
T = Time required for the process
Z = Electro-chemical equivalent of the substance

Complete step by step answer:
Here we have the electrolysis of silver nitrate solution(\[AgN{{O}_{3}}\])
So we have to find the mass of silver deposited from the question by using density and volume
We have known that;
\[ Mass=Density\times Volume\]
\[Mass=Density\times surface.area\times thickness\]
We have density, thickness and surface area as \[1.05g/c{{m}^{3}}\],\[1\times {{10}^{-3}}cm\] and \[100c{{m}^{2}}\] respectively. So we could write as;
\[ Mass=1.05\times 100\times 1\times {{10}^{-3}}\]
\[\Rightarrow Mass=0.105g\]
So, we have to find the required time to deposit \[0.105g\] of silver by passing \[5A\] using the equation of Faraday’s first law. According Faraday’s first law
\[ W=Zit\]
From this equation we have to find the required time. Hence we could rewrite the equation as;
\[ t=\dfrac{W}{Zi}\]
\[ Z=\dfrac{\text {Equivalent.weight}}{96500}\], here the equivalent weight of silver is 108
\[W=0.105g\]
\[\Rightarrow i=5A\]
Substitute these values in the above equation. 

So we get,
\[\Rightarrow t=\dfrac{0.105\times 96500}{5\times 108}\]
\[\Rightarrow t=18.7s\]

Hence we get the time required is \[18.7s\] to deposit \[0.105g\] by passing \[5A\] of current through the silver nitrate solution

So, the correct answer is Option C.

Note: Also, Other than Faraday’s first law we have Faraday’s second law which states that Masses of different substances liberated or dissolved by the same amount of electricity passed is directly proportional to their chemical equivalent. Hence we have to be damn sure about the question where law has to be used in the questions to solve it.