The chloride of a metal (M) contains 65.5% of chlorine. 100 ml of the vapour of the chloride of the metal at STP weights 0.72 g. The molecular formula of the metal chloride is:

Options

A. `MCl_3`
B. `MCl`
C. `MCl_2`
D. `MCl_4`

Answer

To find the molecular formula of the metal chloride (MClN), we will follow these steps:

### Step 1: Determine the molar mass of the metal chloride (MClN)
We know that 100 mL of the vapor weighs 0.72 g at STP. At STP, 1 mole of a gas occupies 22.4 L (or 22400 mL).

Using the formula for molar mass:
\[ \text{Molar Mass} = \frac{\text{mass}}{\text{volume}} \times \text{molar volume} \]
We can calculate the molar mass of the chloride:
\[ \text{Molar Mass} = \frac{0.72 \, \text{g}}{100 \, \text{mL}} \times 22400 \, \text{mL} = 161.28 \, \text{g/mol} \]

### Step 2: Set up the equation for the percentage of chlorine
The problem states that the chloride contains 65.5% chlorine. The mass of chlorine in the compound can be expressed as:
\[ \text{Mass of Cl} = N \times 35.5 \]
where \(N\) is the number of chlorine atoms in the formula.

The total mass of the compound is:
\[ \text{Total mass} = M + N \times 35.5 \]
where \(M\) is the molar mass of the metal.

### Step 3: Set up the equation for the percentage of chlorine
Using the percentage of chlorine:
\[ \frac{N \times 35.5}{M + N \times 35.5} \times 100 = 65.5 \]
Rearranging gives:
\[ N \times 35.5 = 0.655 \times (M + N \times 35.5) \]

### Step 4: Solve for \(N\)
Expanding and rearranging the equation:
\[ N \times 35.5 = 0.655M + 0.655N \times 35.5 \]
\[ N \times 35.5 - 0.655N \times 35.5 = 0.655M \]
\[ N \times (35.5 - 0.655 \times 35.5) = 0.655M \]
\[ N \times 12.85 = 0.655M \]
\[ N = \frac{0.655M}{12.85} \]

### Step 5: Substitute \(M\) and calculate \(N\)
Now we know the molar mass of the chloride is 161.28 g/mol:
\[ M + N \times 35.5 = 161.28 \]
Substituting \(N\):
\[ M + \left(\frac{0.655M}{12.85}\right) \times 35.5 = 161.28 \]
Solving this will give us the value of \(N\).

### Step 6: Calculate \(N\)
After solving the equation, we find that \(N \approx 3\). Therefore, the molecular formula of the metal chloride is:
\[ \text{MCl}_3 \]

### Final Answer
The molecular formula of the metal chloride is **MCl₃**.

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