Question

Silver is monovalent and has an atomic mass of 108 g. Copper is divalent and has an atomic mass of 63.6 g. the same current is passed, for the same length of time through a silver coulometer and a copper coulometer. If 27.0 g of silver is deposited, then the corresponding amount of copper deposited is:
(A) 31.08 g
(B)15.908 g
(C) 7.95 g
(D) None of these

Answer 1

Hint: This question is based on faraday's second law of electrolysis. It can be solved by equating the ratio of the mass of both the substances deposited to the ratio of the equivalent mass of both the substances.

Complete step by step solution:
Faraday's second law states that: If we pass the same quantity of electricity through the solution containing different electrolytes that are connected in series, then the mass or weight of the substance produced at the electrodes is directly proportional to their equivalent weight.
Equivalent weight or mass is the quantity of the substance that will combine with or displace another substance.
So, according to the question, the formula will be:
$\dfrac{\text{Eq}\text{. wt}\text{. of Ag}}{\text{Eq}\text{. wt}\text{. of Cu}}\text{=}\dfrac{\text{Mass of Ag deposited}}{\text{Mass of Cu deposited}}$
Equivalent weight can be calculated by dividing the mass of the substance to its valency.
The equivalent weight of Ag = 108 g (because it is a monovalent atom)
The equivalent weight of Cu = $\dfrac{63.6}{2}=31.8\text{ g}$ (because copper is divalent atom)
The mass of silver deposited is 27.0 g.
Putting all these in the formula, we get:
$\dfrac{\text{Eq}\text{. wt}\text{. of Ag}}{\text{Eq}\text{. wt}\text{. of Cu}}\text{=}\dfrac{\text{Mass of Ag deposited}}{\text{Mass of Cu deposited}}$
$\dfrac{108}{31.8}\text{=}\dfrac{27}{x}$
$x=7.95\,\text{g}$

So, the correct answer is an option (C)- 7.95 g.

Note: The equivalent weight can also be calculated by multiplying the Faraday’s value to the ratio weight of the substance to the quantity of electricity. The value of Faraday is 96500.
$Eq.\text{ }wt.=\dfrac{W}{Q}\text{ x 96500}$.