Specific heat of a metal is `0.031 (Cal)/(g xx^(@)c)` and its equivalent weight is `103.6` calculate the exact atomic weight of metal :-

Options

A. `206.45`
B. `205.2`
C. `207.2`
D. `103.6`

Answer

To calculate the exact atomic weight of the metal given its specific heat and equivalent weight, we can follow these steps:

### Step 1: Use the Long Petit Rule
The Long Petit Rule states that the approximate atomic weight of a substance can be calculated using the formula:
\[ \text{Approximate Atomic Weight} = \frac{6.4}{\text{Specific Heat}} \]
Given that the specific heat of the metal is \(0.031 \, \text{Cal/(g} \cdot \degree C)\), we can substitute this value into the formula:

\[ \text{Approximate Atomic Weight} = \frac{6.4}{0.031} \]

### Step 2: Calculate the Approximate Atomic Weight
Now, we perform the calculation:

\[ \text{Approximate Atomic Weight} = \frac{6.4}{0.031} \approx 206.45 \]

### Step 3: Find the Valency
We know the equivalent weight of the metal is given as \(103.6 \, \text{g/equiv}\). The valency can be calculated using the formula:
\[ \text{Valency} = \frac{\text{Approximate Atomic Weight}}{\text{Equivalent Weight}} \]
Substituting the values we have:

\[ \text{Valency} = \frac{206.45}{103.6} \approx 1.99 \approx 2 \]

### Step 4: Calculate the Exact Atomic Weight
Finally, we can find the exact atomic weight using the formula:
\[ \text{Exact Atomic Weight} = \text{Valency} \times \text{Equivalent Weight} \]
Substituting the values we have:

\[ \text{Exact Atomic Weight} = 2 \times 103.6 = 207.2 \]

### Final Answer
Thus, the exact atomic weight of the metal is:
\[ \boxed{207.2} \]

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