5g sulphur is present in 100 g of `CS_(2). DeltaT_(b)` of solution 0.954 and `K_(b)` is 4.88. The molecular formula of sulphur is

Options

A. `S_(2)`
B. `S_(4)`
C. `S_(3)`
D. `S_(8)`

Answer

To solve the problem step by step, we will use the formula for elevation in boiling point and the concept of molality.

### Step 1: Write the formula for elevation in boiling point
The formula for elevation in boiling point (\( \Delta T_b \)) is given by:

\[ \Delta T_b = K_b \cdot m \]

where:
- \( \Delta T_b \) = elevation in boiling point
- \( K_b \) = molal elevation constant
- \( m \) = molality of the solution

### Step 2: Identify the known values
From the problem, we have:
- \( \Delta T_b = 0.954 \, \text{°C} \)
- \( K_b = 4.88 \, \text{°C kg/mol} \)
- Mass of sulfur (solute) = 5 g
- Mass of carbon disulfide (solvent) = 100 g = 0.1 kg

### Step 3: Calculate molality (m)
Molality is defined as the number of moles of solute per kilogram of solvent. We can rearrange the formula for \( m \):

\[ m = \frac{\Delta T_b}{K_b} \]

Substituting the known values:

\[ m = \frac{0.954}{4.88} \approx 0.195 \]

### Step 4: Calculate the number of moles of sulfur
To find the number of moles of sulfur, we use the formula:

\[ m = \frac{\text{number of moles of solute}}{\text{mass of solvent in kg}} \]

Rearranging gives us:

\[ \text{number of moles of solute} = m \cdot \text{mass of solvent in kg} \]

Substituting the values:

\[ \text{number of moles of sulfur} = 0.195 \cdot 0.1 \approx 0.0195 \, \text{moles} \]

### Step 5: Calculate the molecular weight of sulfur
Now, we can find the molecular weight of sulfur using the formula:

\[ \text{Molecular weight} = \frac{\text{mass of solute}}{\text{number of moles of solute}} \]

Substituting the values:

\[ \text{Molecular weight} = \frac{5 \, \text{g}}{0.0195 \, \text{moles}} \approx 256.41 \, \text{g/mol} \]

### Step 6: Determine the molecular formula of sulfur
The atomic weight of sulfur (S) is approximately 32.07 g/mol. To find the number of sulfur atoms in the molecular formula, we divide the molecular weight by the atomic weight:

\[ \text{Number of sulfur atoms} = \frac{256.41}{32.07} \approx 8 \]

Thus, the molecular formula of sulfur is \( S_8 \).

### Final Answer
The molecular formula of sulfur is \( S_8 \).

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