QJEEM24Ch5248: JEE Main 2024 Chemistry - Class 12 JEEM24Ch5248 Solution: The mass of silver (Molar mass of ) displaced by a quantity of…

First, we need to determine the amount of $\mathrm{O}_2$ (oxygen gas) in moles that is displaced by the quantity of electricity mentioned. To do this, we'll use the molar volume of a gas at Standard Temperature and Pressure (S.T.P.), which is approximately $22.4 \mathrm{~L/mol}$ (or $22400 \mathrm{~mL/mol}$ ).

The volume of $\mathrm{O}_2$ is given as $5600 \mathrm{~mL}$ . Now, we convert this volume to moles:

Next, we'll use Faraday's laws of electrolysis to relate the moles of $\mathrm{O}_2$ to the moles of silver being displaced. In electrolysis, silver is deposited at the cathode according to the following half-reaction:

This tells us that for each mole of $\mathrm{Ag}^+$ ions, only 1 mole of electrons is required to reduce it to silver metal $\mathrm{Ag}$ . However, the liberation of oxygen gas involves the following half-reaction:

From this reaction, we can see that 1 mole of $\mathrm{O}_2$ gas requires 4 moles of electrons to be produced. Therefore, the number of moles of electrons associated with the $0.25 \mathrm{~mol}$ of $\mathrm{O}_2$ will be:

Now, since it takes 1 mole of electrons to reduce 1 mole of $\mathrm{Ag}^+$ . The moles of electrons required is equal to the moles of $\mathrm{Ag}$ produced. Hence, we have 1 mole of $\mathrm{Ag}$ being deposited.

Finally, to calculate the mass of this silver, we use the molar mass of silver:

So, the mass of silver displaced by the quantity of electricity that displaces 5600 mL of $\mathrm{O}_2$ at S.T.P. will be $108 \mathrm{~g}$ .