Given:
Mass of sulphur (S) = 3.795 g
Mass of CS2 solvent = 100 g
Boiling point of CS2 solvent = 319.45 K
Boiling point of the solution = 319.81 K
Kb (molal boiling point elevation constant) for CS2 = 2.42 kg mol⁻¹
Atomic mass of S = 32 g mol⁻¹

To find:
Molecular formula of sulphur in the solution

Explanation:

1. Calculate the molality (m) of the solution:
Molality is defined as the number of moles of solute (S) per kilogram of solvent (CS2). The formula to calculate molality is:

m = (moles of solute) / (mass of solvent in kg)

First, let's calculate the moles of S in the solution:
moles of S = (mass of S) / (atomic mass of S)
= 3.795 g / 32 g mol⁻¹
= 0.1186 mol

Now, let's calculate the mass of CS2 in kg:
mass of CS2 = 100 g / 1000
= 0.1 kg

Now, we can calculate the molality of the solution:
m = (0.1186 mol) / (0.1 kg)
= 1.186 mol kg⁻¹

2. Calculate the change in boiling point (ΔTb):
The change in boiling point is given by the formula:

ΔTb = Kb * m

Substituting the values, we get:
ΔTb = 2.42 kg mol⁻¹ * 1.186 mol kg⁻¹
= 2.86892 K

3. Calculate the boiling point of the pure solvent (CS2):
The boiling point of the pure solvent is given as 319.45 K.

4. Calculate the boiling point of the solution:
The boiling point of the solution is given as 319.81 K.

5. Calculate the change in boiling point of the solvent:
The change in boiling point of the solvent can be calculated by subtracting the boiling point of the pure solvent from the boiling point of the solution:

Change in boiling point of solvent = Boiling point of solution - Boiling point of solvent
= 319.81 K - 319.45 K
= 0.36 K

6. Calculate the van't Hoff factor (i):
The van't Hoff factor (i) can be calculated using the formula:

i = ΔTb / Change in boiling point of solvent

Substituting the values, we get:
i = 0.36 K / 2.86892 K
= 0.1255

7. Calculate the effective number of moles of solute:
The effective number of moles of solute (S) can be calculated using the formula:

Effective moles of solute = (moles of solute) / i

Substituting the values, we get:
Effective moles of solute = 0.1186 mol / 0