Question

Two electrolytic cells containing molten solutions of nickel chloride and aluminium chloride are connected in series. If the same amount of electric current is passed through them, what will be the weight of nickel obtained when 18g of aluminium is obtained? Given: \[{\text{ Al}} = {\text{ }}27{\text{g}}/{\text{mol}},{\text{ Ni}} = 58.5{\text{g}}/{\text{mol }}\].
A.117g
B.$58.5{\text{g}}$
C.$29.25{\text{g}}$
D.$5.85{\text{g}}$

Answer 1

Hint: This question can be solved by using Faraday's second law of electrolysis. As this law deals with the same amount of current applied to different solutions. The amount of product formed will depend on the equivalent mass of the substances.

Complete step by step answer:
Electrolytic cell is the one which converts electrical energy to chemical energy. Current in an electrolytic cell flows due to the movement of ions or electrolyte. For electrolytic cell, Faraday’s law of electrolysis can be applied. First law states that the mass of a substance deposited or the mass of a gas liberated is directly proportional to the amount of charge passing through (electrolyte) solution that is \[{\text{ m}} = {\text{ ZQ }}\]
where m is mass deposited, Q is charge flown and Z is electrochemical equivalent.
Second law states that if the same amount of electric charge is passed through different solutions of electrolyte when connected in series, the amount of substance deposited is directly proportional to its equivalent mass.
\[{\text{Equivalent mass of nickel}} = \dfrac{{{\text{ molecular weight}}}}{{{\text{Valency}}}} = \dfrac{{58.5}}{2}\]
\[{\text{Equivalent mass of aluminium}} = \dfrac{{{\text{ molecular weight}}}}{{{\text{Valency}}}} = \dfrac{{27}}{3}\]
In case of metals, the usual oxidation state can be taken as the valency.
The same amount of electric charge is passed through solutions of nickel chloride and aluminium chloride and the mass of aluminium deposited is 18g as give to us. The mass of nickel deposited can be calculated as using faraday second law as:
\[\dfrac{{{\text{Mass of nickel deposited}}}}{{{\text{Mass of aluminium deposited}}}}\;\;\; = \dfrac{{{\text{equivalent mass of nickel}}}}{{{\text{equivalent mass of aluminium}}}}\;\]
\[ \Rightarrow \dfrac{{{\text{Mass of nickel deposited}}}}{{18{\text{ g}}}}\;\; = \dfrac{{58.2 \times 3}}{{27 \times 2}}\;\]
On solving, mass of nickel deposited = $58.5{\text{g}}$

Thus, the correct option is B.

Note:
 Substance can be classified as electrolytes and nonelectrolytes. An electrolyte is a substance that is an electrical insulator in their solid state but conducts electricity in their molten or aqueous state. An example of electrolyte is metal salts. They dissociate into ions in a solution which act as charge carriers and thus, they conduct electricity.