Question

108 g of silver (molar mass 108 \[{\text{g mo}}{{\text{l}}^ - }\] ) is deposited at cathode from \[{\text{AgN}}{{\text{O}}_3}\left( {{\text{aq}}} \right)\] solution by a certain quantity of electricity. The volume (in L) of oxygen gas produced at 273 K and 1 bar pressure from water by the same quantity of electricity is:

Answer 1

Hint: The above question is based on Faraday law of electrolysis. We will first calculate the electricity consumed by silver ions. Then we will calculate the number of moles produced during hydrolysis for water with the same electricity. Using the ideal gas equation we will get the volume.
Formula used:
\[{\text{PV}} = {\text{nRT}}\]
Here P is pressure, V is volume, n is number of moles, R is universal gas constant and T is temperature.

Complete step by step solution:
One Faraday is the charge carried by 1 mole of electrons. The reaction of decomposition of silver ion occurs as:
\[{\text{A}}{{\text{g}}^ + } + {{\text{e}}^ - } \to {\text{Ag}}\]
As we can see, one mole of electrons is required to deposit the silver. This means that 1 Faraday of electricity must have been consumed.
The same amount that is 1 Faraday of electricity must have been given to water.
The decomposition of water occurs as:
\[{{\text{H}}_2}{\text{O}} \to \dfrac{1}{2}{{\text{O}}_2} + 2{{\text{H}}^ + } + {\text{2}}{{\text{e}}^ - }\]
Here the exchange of 2 moles of electrons is taking place. 2 Faraday of electricity is consumed to form \[\dfrac{1}{2}\] moles of oxygen. But we have only passed 1 F of electricity. So 1 F of electricity will give us \[\dfrac{1}{4}\] moles of oxygen.
Using the ideal gas equation we will get:
\[{\text{V}} = \dfrac{1}{4} \times \dfrac{{0.082 \times 273}}{1} = 5.5965{\text{ L}}\]

Note:
The faraday law states that the amount of change produced by current in an electrolytic cell is based on the amount of electricity passed through it. The second law stated that the change produced by the same quantity of electricity is passed through different solutions then the amount produced is proportional to their equivalent weight.