At `48^(@)C`, the vapour pressure of pure `CS_(2)` is 850torr . A solution of 2.0 g of sulphur in 100g of `CS_(2)` has a vapour pressure 844.9 torr. Determine the atomicity of sulphur molecule :

Options

A. 1
B. 2
C. 4
D. 8

Answer

To solve the problem step by step, we will use Raoult's law and the concept of vapor pressure lowering in a solution.

### Step 1: Understand the Given Data
- Vapor pressure of pure CS₂ (P₀) = 850 torr
- Vapor pressure of the solution (P_solution) = 844.9 torr
- Mass of sulfur (solute) = 2.0 g
- Mass of CS₂ (solvent) = 100 g

### Step 2: Calculate the Relative Lowering of Vapor Pressure
The relative lowering of vapor pressure can be calculated using the formula:
\[ \text{Relative lowering} = \frac{P₀ - P_{\text{solution}}}{P₀} \]
Substituting the values:
\[ \text{Relative lowering} = \frac{850 - 844.9}{850} = \frac{5.1}{850} \approx 0.006 \]

### Step 3: Apply Raoult's Law
According to Raoult's law for dilute solutions:
\[ \text{Relative lowering} = \text{Mole fraction of solute} \]
Let \( n_S \) be the number of moles of sulfur and \( n_{CS₂} \) be the number of moles of CS₂. Thus,
\[ \frac{n_S}{n_{CS₂}} \approx 0.006 \]

### Step 4: Calculate Moles of CS₂
The number of moles of CS₂ can be calculated using its molar mass:
- Molar mass of CS₂ = 76 g/mol
\[ n_{CS₂} = \frac{\text{mass}}{\text{molar mass}} = \frac{100 \, \text{g}}{76 \, \text{g/mol}} \approx 1.316 \, \text{mol} \]

### Step 5: Calculate Moles of Sulfur
From the mole fraction relationship:
\[ n_S = 0.006 \times n_{CS₂} = 0.006 \times 1.316 \approx 0.007896 \, \text{mol} \]

### Step 6: Calculate the Molar Mass of Sulfur
The molar mass of sulfur can be calculated from the mass of sulfur used:
\[ \text{Molar mass of sulfur} = \frac{\text{mass}}{\text{moles}} = \frac{2.0 \, \text{g}}{0.007896 \, \text{mol}} \approx 253.2 \, \text{g/mol} \]

### Step 7: Determine the Atomicity of Sulfur
The atomicity of sulfur can be calculated by dividing the molar mass of sulfur by the atomic mass of a single sulfur atom (approximately 32 g/mol):
\[ \text{Atomicity} = \frac{\text{Molar mass of sulfur}}{\text{Atomic mass of sulfur}} = \frac{253.2 \, \text{g/mol}}{32 \, \text{g/mol}} \approx 7.91 \approx 8 \]

### Conclusion
The atomicity of the sulfur molecule is approximately 8.