A metallic oxide contains `60%` metal by mass.The vapour density of volatile chloride of this metal is `47.48`. The molecular formula of the chloride of metal is `:-`

Options

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

Explanation

To solve the problem step-by-step, let's break it down:

### Step 1: Determine the mass of the metal oxide
We know that the metallic oxide contains 60% metal by mass. This means that the remaining 40% is oxygen.

Let’s assume the mass of the metallic oxide is \( x \) grams.

Given:
- Percentage of metal = 60%
- Percentage of oxygen = 40%

From this, we can express the mass of oxygen in terms of \( x \):
\[ \text{Mass of oxygen} = 0.40x \]

### Step 2: Calculate the mass of the metal
Since we know that the mass of the oxide is composed of both the metal and oxygen, we can express the mass of the metal as:
\[ \text{Mass of metal} = 0.60x \]

### Step 3: Relate the mass of oxygen to a known value
We can set the mass of oxygen to a known value. For example, if we assume the mass of oxygen is 16 grams (which is the molar mass of oxygen), we can set up the equation:
\[ 0.40x = 16 \]

### Step 4: Solve for \( x \)
Now we can solve for \( x \):
\[ x = \frac{16}{0.40} = 40 \text{ grams} \]

### Step 5: Calculate the mass of the metal
Now that we have the total mass of the metallic oxide, we can find the mass of the metal:
\[ \text{Mass of metal} = 0.60 \times 40 = 24 \text{ grams} \]

### Step 6: Calculate the molar mass of the volatile chloride
We are given that the vapor density of the volatile chloride is 47.48. The molar mass can be calculated using the formula:
\[ \text{Molar mass} = \text{Vapor density} \times 2 \]
Substituting the given vapor density:
\[ \text{Molar mass} = 47.48 \times 2 = 94.96 \text{ grams} \]

### Step 7: Determine the mass of chlorine in the chloride
Now we can find the mass of chlorine in the chloride:
\[ \text{Mass of chlorine} = \text{Molar mass of chloride} - \text{Mass of metal} \]
Substituting the values we have:
\[ \text{Mass of chlorine} = 94.96 - 24 = 70.96 \text{ grams} \]

### Step 8: Calculate the number of chlorine atoms
The molar mass of chlorine (Cl) is approximately 35.5 grams. To find the number of chlorine atoms in the chloride, we can use:
\[ \text{Number of Cl atoms} = \frac{\text{Mass of chlorine}}{\text{Molar mass of Cl}} = \frac{70.96}{35.5} \approx 2 \]

### Step 9: Write the molecular formula of the chloride
Since we have determined that there are approximately 2 chlorine atoms for every metal atom, the molecular formula of the chloride can be written as:
\[ \text{Molecular formula} = MCl_2 \]

### Conclusion
Thus, the molecular formula of the chloride of the metal is \( \text{MCl}_2 \).

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