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# 5L of 0.1M solution of $CuS{{O}_{4}}$ is to be electrolyzed by a current of 2.0 A. If, before the passing of current, 9.70 g of iron scraps (Fe) are added to the solution, the time (in hrs) elapsed before whole of $C{{u}^{+2}}$ ions are deposited is

Last updated date: 25th Jun 2024
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Hint: When the same amount of current is passed from two electrolytes, the masses liberated from each electrolyte will be directly proportional to the equivalent weight of the substance liberated.

Faraday’s First Law of Electrolysis- The mass of the substance (m) deposited or liberated at any electrode is directly proportional to the quantity of electricity or charge (Q) passed.
Faraday’s Second Law of Electrolysis- the amount of substances deposited by the passage of the same amount of electric current will be proportional to their equivalent weights. When, the electric current (It or Q) remains the same, mass is directly proportional to equivalent weight.
Given, 5L of $CuS{{O}_{4}}$ of 0.1M is electrolysed by current of 2.0A . By Faraday’s Second Law of Electrolysis, the weight of $C{{u}^{+2}}$ can be evaluated.

$\dfrac{{{m}_{1}}}{{{m}_{2}}}=\dfrac{{{E}_{1}}}{{{E}_{2}}}$
Where, ${{m}_{1}}$ is the mass of copper,
${{m}_{2}}$ is the mass of iron , given mass of iron is 9.70g
${{E}_{1}}$ is the equivalent weight of copper, equivalent weight of copper is 31.75g/eq
${{E}_{2}}$ is the equivalent weight of iron,
\begin{align} & {{m}_{1}}={{m}_{2}}\times \dfrac{{{E}_{1}}}{{{E}_{2}}} \\ & {{m}_{1}}=9.70\times \dfrac{31.75}{27.9} \\ & {{m}_{1}}=11.03g \\ \end{align}

The amount of $C{{u}^{+2}}$ is 11.03g. Now applying the Faraday’s First Law of Electrolysis, we get,
\begin{align} & {{m}_{1}}=z\times i\times t \\ & z=\dfrac{{{E}_{1}}}{96500} \\ & \Rightarrow t=\dfrac{{{m}_{1}}}{z\times i} \\ & \Rightarrow t=\dfrac{{{m}_{1}}\times 96500}{{{E}_{1}}\times i} \\ & \Rightarrow t=\dfrac{11.03\times 96500}{31.75\times 2.0} \\ & \Rightarrow t=16762.1s \\ \end{align}
Converting, seconds into hours by dividing the obtained value with 60x60,
\begin{align} & t=\dfrac{16762.1}{60\times 60} \\ & \Rightarrow t=4.6hr \\ \end{align}

Therefore, the time required for the whole $C{{u}^{+2}}$ to be deposited is 4.6 hours.

Note: The time used in the formula of Faraday’s First Law of Electrolysis is in seconds, we have to change the time to hours or minutes according to the requirement of the question. Equivalent weight of a substance can be evaluated by dividing the molecular weight of the substance with its valency.