Question

A solution of 2.95 g of sulphur in 100 g of cyclohexane had a freezing point of 4.18°C. The freezing point of pure cyclohexane is 6.50°C. What is the molecular formula of sulphur in the solution?

Answer 1

Given: Mass of sulphur (solute) = 2.95 g

Mass of cyclohexane (solvent) = 100 g = 0.1 kg

Freezing point of pure cyclohexane = 6.50°C

Freezing point of solution = 4.18°C

ΔT_f = 6.50 − 4.18 = 2.32°C

Molality (m) = `(DeltaT_f)/K_f`

= `2.32/20.2`

= 0.11485 mol/kg

Moles of sulphur = 0.11485 × 0.100 = 0.011485 mol

Molar mass of sulphur = `"Mass of sulphur"/"Moles of sulphur"`

= `2.95/0.011485`

= 256.85 g/mol

Number of sulphur atoms = `256.85/32.06` = 8.01

Since the number of atoms must be an integer, it is 8.

The molecular formula of sulphur is S₈.