An electrolytic cell is composed of Cu and Zn. A current of 9.65A is drawn from a cell for 1 hour. Then the loss in mass at anode and gain in mass at cathode, respectively could be

Options

A. 11.77g, 11.43g
B. 11.77g, 10g
C. 22.86g, 23.54g
D. 23.54g, 22.86g

Answer

To solve the problem of calculating the loss in mass at the anode and the gain in mass at the cathode in an electrolytic cell composed of Cu and Zn, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Reactions**:
- At the anode (oxidation):
\[ \text{Zn} \rightarrow \text{Zn}^{2+} + 2e^- \]
- At the cathode (reduction):
\[ \text{Cu}^{2+} + 2e^- \rightarrow \text{Cu} \]

2. **Determine the Current and Time**:
- Current (I) = 9.65 A
- Time (t) = 1 hour = 3600 seconds (since 1 hour = 60 minutes and 1 minute = 60 seconds).

3. **Calculate the Total Charge (Q)**:
\[ Q = I \times t = 9.65 \, \text{A} \times 3600 \, \text{s} = 34740 \, \text{C} \]

4. **Use Faraday's Law of Electrolysis**:
The mass loss or gain can be calculated using the formula:
\[ W = \frac{M \times Q}{n \times F} \]
where:
- \( W \) = mass (in grams)
- \( M \) = molar mass (g/mol)
- \( Q \) = total charge (C)
- \( n \) = number of electrons transferred (n-factor)
- \( F \) = Faraday's constant (approximately 96500 C/mol)

5. **Calculate the Loss of Mass at the Anode (Zinc)**:
- Molar mass of Zinc (M) = 65.38 g/mol
- n-factor for Zn = 2 (since 2 electrons are involved in the oxidation).
\[ W_{\text{Zn}} = \frac{65.38 \times 34740}{2 \times 96500} \]
\[ W_{\text{Zn}} = \frac{2270521.2}{193000} \approx 11.77 \, \text{g} \]

6. **Calculate the Gain of Mass at the Cathode (Copper)**:
- Molar mass of Copper (M) = 63.546 g/mol
- n-factor for Cu = 2 (since 2 electrons are involved in the reduction).
\[ W_{\text{Cu}} = \frac{63.546 \times 34740}{2 \times 96500} \]
\[ W_{\text{Cu}} = \frac{2207860.84}{193000} \approx 11.43 \, \text{g} \]

7. **Final Results**:
- Loss in mass at the anode (Zn): **11.77 g**
- Gain in mass at the cathode (Cu): **11.43 g**

### Summary:
The loss in mass at the anode is approximately **11.77 g**, and the gain in mass at the cathode is approximately **11.43 g**.