In 100 g naphthalene 2.56 g sulphur is added boiling point of solution (solid) decreases by `0.68^(@)C`, atomicity of sulphur is
(`K_(f)` of naphthalene=6.8 `Km^(-1)`)

Options

A. 2
B. 4
C. 6
D. 8

Answer

To solve the problem step by step, we will use the formula for the elevation of boiling point and the information provided in the question.

### Step 1: Write down the formula for boiling point elevation
The formula for boiling point elevation is given by:
\[ \Delta T_b = K_b \cdot m \]
where:
- \(\Delta T_b\) = elevation in boiling point
- \(K_b\) = ebullioscopic constant of the solvent (naphthalene in this case)
- \(m\) = molality of the solution

### Step 2: Identify the known values
From the question, we have:
- \(\Delta T_b = 0.68°C\)
- \(K_b = 6.8 \, \text{K kg}^{-1}\)
- Mass of naphthalene (solvent) = 100 g = 0.1 kg
- Mass of sulfur (solute) = 2.56 g

### Step 3: Calculate the molality of the solution
Rearranging the boiling point elevation formula to find molality:
\[ m = \frac{\Delta T_b}{K_b} \]
Substituting the known values:
\[ m = \frac{0.68}{6.8} = 0.1 \, \text{mol/kg} \]

### Step 4: Use the definition of molality
Molality is defined as:
\[ m = \frac{n}{W} \]
where:
- \(n\) = number of moles of solute
- \(W\) = mass of solvent in kg

From the previous calculation, we have:
\[ 0.1 = \frac{n}{0.1} \implies n = 0.1 \times 0.1 = 0.01 \, \text{mol} \]

### Step 5: Calculate the molar mass of sulfur
The number of moles \(n\) can also be expressed as:
\[ n = \frac{m_{\text{solute}}}{M_{\text{solute}}} \]
where \(m_{\text{solute}} = 2.56 \, \text{g}\) and \(M_{\text{solute}}\) is the molar mass of sulfur. Rearranging gives:
\[ M_{\text{solute}} = \frac{m_{\text{solute}}}{n} = \frac{2.56 \, \text{g}}{0.01 \, \text{mol}} = 256 \, \text{g/mol} \]

### Step 6: Determine the atomicity of sulfur
The molar mass of sulfur is approximately \(32 \, \text{g/mol}\). The atomicity \(x\) can be calculated as:
\[ M_{\text{solute}} = 32x \implies 256 = 32x \implies x = \frac{256}{32} = 8 \]

### Conclusion
The atomicity of sulfur is 8.