1. Find moles of silver deposited

Given mass of silver deposited = $108\,\text{g}$ and molar mass of silver = $108\,\text{g mol}^{-1}$.

$n(Ag)=\frac{108}{108}=1\,\text{mol}$

2. Find charge required for silver deposition

At cathode:

$Ag^+ + e^- \rightarrow Ag$

So, $1$ mol of $Ag$ requires $1$ mol of electrons.

Hence, the quantity of electricity used corresponds to:

$1\,\text{mol } e^- = 1\,F$

3. Relate same charge to oxygen production from water

Oxygen is produced at anode by oxidation of water:

$2H_2O \rightarrow O_2 + 4H^+ + 4e^-$

From the equation, $4$ mol electrons produce $1$ mol $O_2$.

Therefore, with $1$ mol electrons:

$n(O_2)=\frac{1}{4}\,\text{mol}$

4. Calculate volume of oxygen at 273 K and 1 bar

At $273\,\text{K}$ and $1\,\text{bar}$, molar volume of an ideal gas is approximately:

$22.71\,\text{L mol}^{-1}$

So,

$V(O_2)=\frac{1}{4}\times 22.71$

$V(O_2)=5.6775\,\text{L}$

Thus, the required volume is approximately:

$\boxed{5.68\,\text{L}}$

5. Comparison with stored correct answer

Stored correct answer: $5.66$ to $5.68$

Our derived answer $5.68\,\text{L}$ lies within this range, so it agrees.