Question

The weight of silver (atomic weight = 108) displaced by a quantity of electricity which displaces 5600 ml of $O_2$ at STP will be:
A) 5.4 g
B) 10.8 g
C) 54.0 g
D) 108.0 g

Answer 1

It is based upon Faraday's second law of electrolysis, which states that, when the same amount of electricity is passed through several electrolytes, the mass of the substances deposited are directly proportional to their respective chemical equivalent or equivalent weight.
$\dfrac{{W_1}}{{W_2}} = \dfrac{{M_1}}{{M_2}}$
W is proportional to M where, W is the mass of the substance in grams while here M is its chemical equivalent weight in grams per equivalent.

Complete answer:
Given,
Step 1: At STP, 1 mole of oxygen occupies 22400 mL of volume
Therefore, number of moles of oxygen corresponding to 5600 mL $n_{O_2}$ = $\dfrac{{5600}}{{22400}}$= $\dfrac{1}{4}$ = $\dfrac{{W_{O_2}}}{{M_{O_2}}}$= $\dfrac{1}{4}$
Step 2: 1 mole of oxygen produces 4 moles of electrons and 1 mole of silver requires 1 mole of electrons.
According to Faraday's second law:
${\dfrac{{W_{Ag}}}{{M_{Ag}}} = \dfrac{{W_{O_2}}}{{M_{O_2}}}}$
$= {\dfrac{{W_{Ag}}}{{M_{Ag}}} \times 1 = \dfrac{{W_{O_2}}}{{M_{O_2}}} \times 4}$
$= {\dfrac{{W_{Ag}}}{{108}} \times 1 = \dfrac{1}{4} \times 4}$
Thus, $W_{Ag} = 108\;g$

Therefore, the weight of silver displaced by a quantity of electricity which displaces 5600 ml of $O_2$ at STP will be (D) i.e. 108.0 g.

Note: We can determine the equivalent or equivalent weight of a substance by Faraday’s laws of electrolysis and it is defined as the weight of that substance which will combine with or displace the unit weight of hydrogen. It should also be noted that the chemical equivalent of hydrogen is unity. Since, the valency of a substance is equal to the number of hydrogen atoms, which can be replaced or combined, the chemical equivalent of a substance may be defined as the ratio of its atomic weight to its valency.