`2.56g` of sulfur in `100 g` of `CS_(2)` of has depression in freez point of `0.01^(@)C.K_(f)=0.1^(@)` mol `al^(-1)`. Hence, he atomicity of sulfur is `CS_(2)` is

Options

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

Explanation

To solve the problem, we need to determine the atomicity of sulfur in carbon disulfide (CS₂) based on the given data.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Mass of sulfur (solute) = 2.56 g
- Mass of CS₂ (solvent) = 100 g
- Depression in freezing point (ΔTf) = 0.01 °C
- Kf (freezing point depression constant) = 0.1 °C kg/mol

2. **Use the Freezing Point Depression Formula:**
The formula for freezing point depression is:
\[ \Delta T_f = K_f \times \text{molality} \]
Rearranging this gives us:
\[ \text{molality} = \frac{\Delta T_f}{K_f} \]

3. **Calculate the Molality:**
Substituting the values into the equation:
\[ \text{molality} = \frac{0.01}{0.1} = 0.1 \text{ mol/kg} \]

4. **Convert the Mass of Solvent to Kilograms:**
The mass of the solvent (CS₂) is given as 100 g, which needs to be converted to kilograms:
\[ \text{mass of solvent} = \frac{100 \text{ g}}{1000} = 0.1 \text{ kg} \]

5. **Relate Molality to Moles of Solute:**
Molality is defined as:
\[ \text{molality} = \frac{\text{moles of solute}}{\text{mass of solvent in kg}} \]
Therefore, we can express the moles of solute as:
\[ \text{moles of solute} = \text{molality} \times \text{mass of solvent in kg} \]
Substituting the values:
\[ \text{moles of solute} = 0.1 \times 0.1 = 0.01 \text{ moles} \]

6. **Calculate the Molecular Mass of Sulfur:**
The number of moles can also be expressed as:
\[ \text{moles} = \frac{\text{mass}}{\text{molecular mass}} \]
Rearranging gives:
\[ \text{molecular mass} = \frac{\text{mass}}{\text{moles}} = \frac{2.56 \text{ g}}{0.01 \text{ moles}} = 256 \text{ g/mol} \]

7. **Determine the Atomicity of Sulfur:**
The atomic mass of sulfur (S) is known to be 32 g/mol. The atomicity can be calculated as:
\[ \text{atomicity} = \frac{\text{molecular mass}}{\text{atomic mass}} = \frac{256}{32} = 8 \]

### Final Answer:
The atomicity of sulfur in CS₂ is **8**.