Question

What mass of silver (Atomic mass = 108 g/mol) deposited by a quantity of electricity which displaces 5600 mL of \(\text{O}_2\) at STP ?

• A. \(5.4 \text{g}\)
• B. \(10.8 \text{g}\)
• C. \(54.0 \text{g}\)
• D. \(108.0 \text{g}\)

Hint:

Same charge deposits equal equivalents; find equivalents of O2 first.

Answer 1

The Correct Option is D

Step 1: Find moles of O2
At STP one mole of gas occupies \(22400\ \text{mL}\). So \(n(O_2) = \frac{5600}{22400} = 0.25\ \text{mol}\).

Step 2: Find the charge in moles of electrons
Oxygen is released by \(2H_2O \rightarrow O_2 + 4H^+ + 4e^-\), so 1 mol of \(O_2\) needs \(4\) mol of electrons.
\(0.25 \times 4 = 1\ \text{mol}\) of electrons, which is 1 faraday.

Step 3: Silver deposited
\(Ag^+ + e^- \rightarrow Ag\), so 1 mol of electrons deposits 1 mol of silver.
\[ m = 1 \times 108 = 108\ \text{g} \]

Step 4: Check the options
\(54\) g would need 0.5 F and \(10.8\) g would need 0.1 F. Only \(108\) g matches 1 F.

Final Answer:
The same one faraday of charge deposits 108 g of silver. \[ \boxed{\text{(D)}\ 108.0\ \text{g}} \]