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 exact atomic weight of metal is

Options

A. 50
B. 49.23
C. 19.693
D. 98.12

Answer

To find the exact atomic weight of the metal from the given information, we can follow these steps:

### Step 1: Calculate the Molecular Weight from Vapour Density
The molecular weight (MW) of a compound can be calculated using the formula:
\[ \text{Molecular Weight} = 2 \times \text{Vapour Density} \]

Given that the vapour density (VD) is 95:
\[ \text{Molecular Weight} = 2 \times 95 = 190 \]

### Step 2: Use the Joule-Petit Law to Find Approximate Atomic Weight
According to the Joule-Petit Law:
\[ \text{Atomic Weight} \times \text{Specific Heat} \approx 6.4 \]

We can rearrange this to find the approximate atomic weight (AW):
\[ \text{Approximate Atomic Weight} = \frac{6.4}{\text{Specific Heat}} \]

Given that the specific heat is 0.13 Cal/g:
\[ \text{Approximate Atomic Weight} = \frac{6.4}{0.13} \approx 49.23 \]

### Step 3: Set Up the Equation for the Chloride of the Metal
Assuming the metal is represented as M and the chloride as MClₓ, we can express the molecular weight as:
\[ \text{Molecular Weight} = \text{Atomic Weight of Metal} + x \times \text{Atomic Weight of Chlorine} \]

Where the atomic weight of chlorine is approximately 35.5 g/mol. Thus:
\[ 190 = \text{Approximate Atomic Weight} + x \times 35.5 \]

### Step 4: Solve for x (the number of Chlorine atoms)
Substituting the approximate atomic weight (49.23) into the equation:
\[ 190 = 49.23 + x \times 35.5 \]

Rearranging gives:
\[ x \times 35.5 = 190 - 49.23 \]
\[ x \times 35.5 = 140.77 \]
\[ x = \frac{140.77}{35.5} \approx 3.96 \]

Since x must be a whole number, we round 3.96 to the nearest integer, which is 4.

### Step 5: Calculate the Exact Atomic Weight
Now we can substitute x back into the molecular weight equation:
\[ 190 = \text{Exact Atomic Weight} + 4 \times 35.5 \]
\[ 190 = \text{Exact Atomic Weight} + 142 \]

Rearranging gives:
\[ \text{Exact Atomic Weight} = 190 - 142 = 48 \]

### Conclusion
The exact atomic weight of the metal is **48**.

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