Vapour density of a metal chloride is 66. Its oxide contains `53%` metal. The atomic weight of the metal is

Options

A. 21
B. 54
C. 27.06
D. 2.086

Explanation

To find the atomic weight of the metal, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Vapor density of the metal chloride (VD) = 66
- Percentage of metal in the oxide = 53%

2. **Assume the Weight of the Metal Oxide:**
- Let the weight of the metal oxide be 100 grams.

3. **Calculate the Weight of the Metal:**
- Weight of metal = 53% of 100 g = \( \frac{53}{100} \times 100 = 53 \) g

4. **Calculate the Weight of Oxygen:**
- Weight of oxygen = Total weight of oxide - Weight of metal
- Weight of oxygen = \( 100 - 53 = 47 \) g

5. **Calculate the Equivalent Weight of the Metal Oxide:**
- The equivalent weight of an oxide can be calculated using the formula:
\[ \text{Equivalent Weight of Oxide} = \frac{\text{Molar Mass of Oxide}}{\text{Valence Factor}} \]
- For \( O^{2-} \), the valence factor = 2.
- The atomic weight of oxygen = 16 g/mol, so for \( O_2 \):
\[ \text{Equivalent Weight of O} = \frac{16}{2} = 8 \, \text{g/equiv} \]

6. **Calculate the Equivalent Weight of the Metal:**
- Using the formula for equivalent weight:
\[ \text{Equivalent Weight of Metal} = \frac{\text{Weight of Metal}}{\text{Weight of Oxygen}} \times \text{Equivalent Weight of Oxide} \]
- Substitute the values:
\[ \text{Equivalent Weight of Metal} = \frac{53}{47} \times 8 \]
- Calculate this:
\[ \text{Equivalent Weight of Metal} = \frac{424}{47} \approx 9.02 \, \text{g/equiv} \]

7. **Calculate the Equivalent Weight of Chloride:**
- The equivalent weight of chloride \( Cl^- \) is calculated as:
\[ \text{Equivalent Weight of Cl} = \frac{35.5}{1} = 35.5 \, \text{g/equiv} \]

8. **Use the Vapor Density to Find Valency:**
- The formula relating valency, vapor density, and equivalent weights is:
\[ \text{Valency} = \frac{2 \times \text{Vapor Density}}{\text{Equivalent Weight of Metal} + \text{Equivalent Weight of Chloride}} \]
- Substitute the known values:
\[ \text{Valency} = \frac{2 \times 66}{9.02 + 35.5} \]
- Calculate this:
\[ \text{Valency} = \frac{132}{44.52} \approx 2.96 \approx 3 \]

9. **Calculate the Atomic Weight of the Metal:**
- The atomic weight of the metal can be calculated using:
\[ \text{Atomic Weight} = \text{Equivalent Weight} \times \text{Valency} \]
- Substitute the values:
\[ \text{Atomic Weight} = 9.02 \times 3 \approx 27.06 \]

### Final Answer:
The atomic weight of the metal is approximately **27.06 g/mol**.