Question

When same quantity of electricity is passed through two different cells containing copper sulfate and silver nitrate, if \(0.99\) g Ag and \(0.29\) g Cu are deposited, calculate the molar mass of Ag (Molar mass of Cu = \(63.2\) g/mol)

• A. \(63.5\) g/mol
• B. \(10.78\) g/mol
• C. \(107.8\) g/mol
• D. \(31.6\) g/mol

Hint:

The same charge deposits masses in the ratio of their equivalent weights; copper has valency 2 and silver has valency 1.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
By Faraday's second law, \(\dfrac{W_{Ag}}{W_{Cu}}=\dfrac{E_{Ag}}{E_{Cu}}\), where \(E\) is the equivalent weight.

Step 2: Equivalent Weights
For Cu, \(\text{Cu}^{2+}\) so \(E_{Cu}=\dfrac{63.2}{2}=31.6\).
For Ag, \(\text{Ag}^{+}\) so \(E_{Ag}=M_{Ag}\).

Step 3: Calculation
\(\dfrac{0.99}{0.29}=\dfrac{M_{Ag}}{31.6}\)
\(M_{Ag}=\dfrac{0.99\times31.6}{0.29}=107.9\,\text{g/mol}\)

Step 4: Compare the options
The closest value is \(107.8\) g/mol, option (C).

Final Answer:
The molar mass of silver is about 107.8 g/mol. \[ \boxed{\text{(C) }107.8\text{ g/mol}} \]