`A` transition metal `M` forms a volatile chloride which has a vapour density of `94.8`. If it contains `74.75%` of chlorine the formula of the metal chloride will be

Options

A. `MCl_(2)`
B. `MCl_(4)`
C. `MCl_(5)`
D. `MCl_(3)`

Answer

To find the formula of the transition metal chloride \( MCl_x \), we will follow these steps:

### Step 1: Calculate the mass of the metal chloride
Given that the volatile chloride contains 74.75% chlorine, we can determine the mass of chlorine in 100 grams of the chloride:
\[ \text{Mass of Cl} = 74.75 \text{ g} \]
The remaining mass will be the mass of the metal \( M \):
\[ \text{Mass of M} = 100 \text{ g} - 74.75 \text{ g} = 25.25 \text{ g} \]

### Step 2: Calculate the equivalent weight of the metal
The equivalent weight of the metal can be calculated using the formula:
\[ \text{Equivalent weight} = \frac{\text{Weight of metal}}{\text{Weight of chlorine}} \times 35.5 \]
Substituting the values:
\[ \text{Equivalent weight} = \frac{25.25 \text{ g}}{74.75 \text{ g}} \times 35.5 \]
Calculating this gives:
\[ \text{Equivalent weight} = 12 \text{ g/equiv} \]

### Step 3: Calculate the valency of the metal
Using the formula for the valency of the metal:
\[ \text{Valency} = \frac{2 \times \text{Vapor Density}}{\text{Equivalent Weight} + 35.5} \]
Substituting the given vapor density (94.8) and the calculated equivalent weight (12):
\[ \text{Valency} = \frac{2 \times 94.8}{12 + 35.5} \]
Calculating this gives:
\[ \text{Valency} = \frac{189.6}{47.5} = 4 \]

### Step 4: Determine the formula of the metal chloride
Since the valency of the metal \( M \) is 4, the formula of the metal chloride will be:
\[ MCl_4 \]

### Final Answer
The formula of the metal chloride is \( MCl_4 \).

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