Sulfur exists in many forms with the general molecular formula Sn. If 1.00 g of sulfur is added to 500.0 g of carbon tetrachloride, and the freezing point of CCl4 is depressed by 0.156 degrees C, what is the molar formula of the sulfur molecule?

S₁₂

Explanation:

The freezing point depression (ΔTf) is a colligative property that can be calculated using the following expression.

ΔTf = Kf × m

where,

Kf: freezing point depression

m: molality

ΔTf = Kf × m

m = ΔTf / Kf

m = 0.156 °C / (29.8 °C/m)

m = 5.23 × 10⁻³ m

The molality is:

m = moles of solute / kilograms of solvent

moles of solute = m × kilograms of solvent

moles of solute = 5.23 × 10⁻³ mol/kg × 0.5000 kg

moles of solute = 2.62 × 10⁻³ mol

1.00 g corresponds to 2.62 × 10⁻³ moles. The molar mass of Sₙ is:

1.00 g/2.62 × 10⁻³ mol = 382 g/mol

We can calculate n.

n = molar mass of Sₙ / molar mass of S

n = (382 g/mol) / (32.0 g/mol)

n = 11.9 ≈ 12

The molar formula is S₁₂.

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