The vapour density of a volatile chloride of a metal is 95 and the specific heat of the metal is 0.13 cal/g. The equivalent mass of the metal will be approximately.

Options

A. 6 g
B. 12.3 g
C. 18 g
D. 24 g

Answer

To find the equivalent mass of the metal from the given information, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Vapor Density (VD) of the volatile chloride = 95
- Specific Heat of the metal = 0.13 cal/g

2. **Calculate the Molar Mass of the Metal Chloride:**
- We know that Vapor Density (VD) is related to Molar Mass (M) by the formula:
\[ \text{VD} = \frac{M}{2} \]
- Rearranging this gives:
\[ M = 2 \times \text{VD} \]
- Substituting the given vapor density:
\[ M = 2 \times 95 = 190 \text{ g/mol} \]

3. **Calculate the Atomic Mass of the Metal:**
- The equivalent mass of the metal can be calculated using the specific heat and the formula:
\[ \text{Atomic Mass} = \frac{6.4}{\text{Specific Heat}} \]
- Substituting the specific heat:
\[ \text{Atomic Mass} = \frac{6.4}{0.13} \approx 49.23 \text{ g/mol} \]

4. **Determine the Formula of the Metal Chloride:**
- The molar mass of the metal chloride (MClₓ) is 190 g/mol.
- Let the atomic mass of chlorine be 35.5 g/mol. The formula can be expressed as:
\[ 49.23 + x \times 35.5 = 190 \]
- Rearranging gives:
\[ x \times 35.5 = 190 - 49.23 \]
\[ x \times 35.5 = 140.77 \]
\[ x = \frac{140.77}{35.5} \approx 4 \]
- Thus, the formula of the metal chloride is MCl₄.

5. **Calculate the Equivalent Mass of the Metal:**
- The equivalent mass is given by:
\[ \text{Equivalent Mass} = \frac{\text{Atomic Mass}}{\text{Valency}} \]
- The valency of the metal in MCl₄ is +4 (since there are 4 chlorine atoms, each with a -1 charge).
- Therefore:
\[ \text{Equivalent Mass} = \frac{49.23}{4} \approx 12.31 \text{ g} \]

6. **Final Result:**
- The equivalent mass of the metal is approximately 12 g.