An acidic solution of `Cu^(2+0` salt containing `0.4g` of `Cu^(2+)` is electrolyzed until all the copper is deposited. The electrolysis is continued for seven more minutes with the volume of solution kept at `100mL` and the current at `1.2A`. Calculate the volume of gases evolved at `STP` during the entire electrolysis.

Explanation

To solve the problem step by step, we will break it down into two parts: the electrolysis until all the copper is deposited and the electrolysis continued for an additional 7 minutes.

### Step 1: Calculate the moles of Cu deposited

1. **Given Data**:
- Mass of Cu = 0.4 g
- Molar mass of Cu = 63.5 g/mol

2. **Calculate moles of Cu**:
\[ \text{Moles of Cu} = \frac{\text{Mass of Cu}}{\text{Molar mass of Cu}} = \frac{0.4 \, \text{g}}{63.5 \, \text{g/mol}} = 0.006299 \, \text{mol} \]

### Step 2: Calculate the equivalents of Cu

3. **Since Cu²⁺ requires 2 electrons to deposit**:
\[ \text{Equivalents of Cu} = \text{Moles of Cu} \times 2 = 0.006299 \, \text{mol} \times 2 = 0.012598 \, \text{equiv} \]

### Step 3: Calculate the equivalents of O₂ produced during Cu deposition

4. **From the reaction**:
\[ 2H_2O \rightarrow O_2 + 4H^+ + 4e^- \]
- 1 equivalent of O₂ is produced for every 4 equivalents of electrons.
- Therefore, the equivalents of O₂ produced:
\[ \text{Equivalents of O₂} = \frac{0.012598}{4} = 0.0031495 \, \text{equiv} \]

### Step 4: Calculate the volume of O₂ at STP

5. **Using the volume of gas at STP**:
\[ \text{Volume of O₂} = \text{Equivalents of O₂} \times 22.4 \, \text{L/equiv} = 0.0031495 \times 22.4 \, \text{L} = 0.0706 \, \text{L} = 70.6 \, \text{mL} \]

### Step 5: Calculate the current for the second part of electrolysis

6. **Given Data**:
- Current (I) = 1.2 A
- Time (t) = 7 minutes = 7 × 60 = 420 seconds

7. **Calculate the charge (Q)**:
\[ Q = I \times t = 1.2 \, \text{A} \times 420 \, \text{s} = 504 \, \text{C} \]

### Step 6: Calculate the equivalents of H₂ produced

8. **Using Faraday's law**:
\[ \text{Equivalents} = \frac{Q}{F} = \frac{504 \, \text{C}}{96500 \, \text{C/equiv}} = 0.00522 \, \text{equiv} \]

### Step 7: Calculate the volume of H₂ at STP

9. **From the reaction**:
\[ 2H_2O + 2e^- \rightarrow H_2 + 2OH^- \]
- 1 equivalent of H₂ is produced for every 2 equivalents of electrons.
- Therefore, the volume of H₂ produced:
\[ \text{Volume of H₂} = \text{Equivalents of H₂} \times 22.4 \, \text{L/equiv} = 0.00522 \times 22.4 \, \text{L} = 0.1175 \, \text{L} = 117.5 \, \text{mL} \]

### Step 8: Total volume of gases evolved

10. **Total volume of gases**:
\[ \text{Total Volume} = \text{Volume of O₂} + \text{Volume of H₂} = 70.6 \, \text{mL} + 117.5 \, \text{mL} = 188.1 \, \text{mL} \]

### Final Answer:
The total volume of gases evolved at STP during the entire electrolysis is **188.1 mL**.

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