The atomic mass of an element is 27. If valency is 3, the vapour density of the volatile metal chloride will be :

Options

A. 66.75
B. 6.675
C. 667.5
D. 81

Explanation

To find the vapor density of the volatile metal chloride, we can follow these steps:

### Step 1: Determine the molecular formula of the metal chloride.
Given that the atomic mass of the element is 27 and its valency is 3, we can deduce the formula for the metal chloride. The general formula for a metal chloride where the metal has a valency of 3 is:
\[ \text{MCl}_3 \]
where M represents the metal.

### Step 2: Calculate the molar mass of the metal chloride.
To find the molar mass of the metal chloride (MCl₃), we need to add the atomic mass of the metal and the mass of the chlorine atoms. The atomic mass of chlorine (Cl) is approximately 35.5 g/mol.

Thus, the molar mass of MCl₃ is calculated as follows:
\[ \text{Molar mass of MCl}_3 = \text{Atomic mass of M} + 3 \times \text{Atomic mass of Cl} \]
\[ = 27 + 3 \times 35.5 \]
\[ = 27 + 106.5 = 133.5 \, \text{g/mol} \]

### Step 3: Calculate the vapor density.
The vapor density (VD) of a substance is defined as half of its molar mass. Therefore, we can calculate the vapor density of the metal chloride as follows:
\[ \text{Vapor Density} = \frac{\text{Molar mass}}{2} \]
\[ = \frac{133.5}{2} = 66.75 \, \text{g/L} \]

### Final Answer:
The vapor density of the volatile metal chloride is **66.75 g/L**.

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