Question

In 2 hours, a certain current liberates 0.504 g hydrogen. How many grams of copper can be deposited by the same current flowing for the same time in a $CuSO_4$ solution?
(Molar mass of Cu $= 63.5\ \text{g mol}^{-1}$, $H_2 = 2.0\ \text{g mol}^{-1}$)

• A. $31.8\ \text{g}$
• B. $32.0\ \text{g}$
• C. $63.5\ \text{g}$
• D. $16.0\ \text{g}$

Hint:

For electrolysis problems, always compare substances using their equivalent weights when the same charge flows.

Answer 1

The Correct Option is D

Step 1: Apply Faraday’s law of electrolysis.
For the same quantity of electricity, the masses of substances liberated are proportional to their equivalent weights.
Step 2: Calculate equivalent weights.
Hydrogen:
\[ \text{Equivalent weight of } H = \frac{2}{2} = 1 \]
Copper (from $Cu^{2+}$):
\[ \text{Equivalent weight of Cu} = \frac{63.5}{2} = 31.75 \]
Step 3: Use proportionality relation.
\[ \frac{\text{Mass of Cu}}{\text{Mass of H}} = \frac{31.75}{1} \]
\[ \text{Mass of Cu} = 0.504 \times 31.75 \]
\[ \text{Mass of Cu} \approx 16.0\ \text{g} \]
Step 4: Conclusion.
The mass of copper deposited by the same current in the same time is $16.0\ \text{g}$.