1 mol of electrons passes through molten form of`AgNo_(3), CuSo_(4)` and`AICl_(3)` when Ag, Cu and Al are deposited. Their molar ratio will be :

Options

A. 1 : 1 : 1
B. 6 : 3 : 2
C. 6 : 3 : 1
D. 1 : 3 : 6

Explanation

To solve the problem of determining the molar ratio of metals deposited when 1 mole of electrons passes through molten forms of AgNO₃, CuSO₄, and AlCl₃, we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Reduction Reactions**:
- For AgNO₃: The reduction reaction is:
\[ \text{Ag}^+ + e^- \rightarrow \text{Ag} \quad (1 \text{ electron for } 1 \text{ mole of Ag}) \]
- For CuSO₄: The reduction reaction is:
\[ \text{Cu}^{2+} + 2e^- \rightarrow \text{Cu} \quad (2 \text{ electrons for } 1 \text{ mole of Cu}) \]
- For AlCl₃: The reduction reaction is:
\[ \text{Al}^{3+} + 3e^- \rightarrow \text{Al} \quad (3 \text{ electrons for } 1 \text{ mole of Al}) \]

2. **Calculate Moles of Electrons Required**:
- For Ag: 1 mole of Ag requires 1 mole of electrons.
- For Cu: 1 mole of Cu requires 2 moles of electrons.
- For Al: 1 mole of Al requires 3 moles of electrons.

3. **Determine the Total Moles of Electrons**:
- If we pass 1 mole of electrons through the system, we can determine how many moles of each metal can be deposited:
- From 1 mole of electrons, we can deposit:
- 1 mole of Ag (using 1 mole of electrons)
- 0.5 moles of Cu (using 1 mole of electrons for 2 moles of Cu)
- \( \frac{1}{3} \) moles of Al (using 1 mole of electrons for 3 moles of Al)

4. **Express the Molar Ratios**:
- The moles of metals deposited are:
- Ag: 1 mole
- Cu: 0.5 moles
- Al: \( \frac{1}{3} \) moles
- To find the molar ratio, we can express these in terms of a common denominator. The least common multiple of 1, 0.5, and \( \frac{1}{3} \) is 6.
- Ag: \( 1 \times 6 = 6 \)
- Cu: \( 0.5 \times 6 = 3 \)
- Al: \( \frac{1}{3} \times 6 = 2 \)

5. **Final Molar Ratio**:
- The molar ratio of Ag:Cu:Al is:
\[ 6:3:2 \]

### Conclusion:
The final molar ratio of Ag:Cu:Al when 1 mole of electrons passes through molten forms of AgNO₃, CuSO₄, and AlCl₃ is **6:3:2**.