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Cadmium amalgam is prepared by electrolysis of a solution of ${ CdCl }_{ 2 }$ using a mercury cathode. Find how long current of ${ 5 amperes }$ should be passed in order to prepare ${ 12 }$ % Cd-Hg amalgam on a cathode of 2g mercury. The atomic mass of Cd = ${ 112.40 }$.

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Last updated date: 20th Jun 2024
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Answer
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Hint: Electrolysis refers to a process in which a chemical change is brought about by passing an electric current through a solution of electrolytes so that the electrolyte's ions move toward the negative and positive electrodes and react with them.

Complete step by step answer:
Amount of Cd required by ${ 2g }$ Hg to prepare ${ 12 }$ % amalgam =$\frac { 12 }{ 88 } { \times 2 }$ = ${ 0.273 g }$
The half-reaction of the cathode will be:
${ Cd }^{ 2+ }{ +2e }^{ - }{ \rightarrow Cd }$
It is given that;
The molar mass of Cd = ${ 112.40 }$
As 1mole of an electron gives ${ 96500C }$ charge
So, 2 moles of an electron gives ${ 2\times 96500C }$ charge

Now, to deposit ${ 1 mole }$ or ${ 112.4 }$ g of Cd we require ${ 2 moles }$ of electrons = ${ 2\times 96500C }$ charge area will be required.
To deposit ${ 1g }$ of Cd we require = ${ 2\times 96500C\times 112.40 }$ of charge area will be required
Charge required to deposit ${ 0.273 g }$ of Cd = ${ \frac { 2\times 96500 }{ 112.40 } { \times 0.273 } }$ of charge area will be required.
Therefore, Charge = ${ 468.76C }$
As we know, Charge = ${ current\times time }$
By putting the values in a formula, we can calculate the time (s).
Time = $\frac { charge }{ current } $
Time = ${ 468.76\times 5A }$ = ${ 93.75 seconds }$.

Therefore, the time required will be = ${ 93.75seconds }$.

Note: The possibility to make a mistake is that here in this reaction ${ 2 moles }$ of electrons are required, so don’t forget to multiply Faraday's constant with two.