A solution containing 0.050 g of an unknown nonelectrolyte in 2.50 g of cyclohexane (Kf = 20.4 oC/m & F. P. 6.6 oC) was found to freeze at 5.0 oC. What is the molar mass of the unknown substance?

The molar mass of the unknown substance is 255g/mole

Explanation:

Freezing point depression is given by

ΔT = i · Kf · m

Where

m = molality of the solute

i = van't Hoff's factor = i for non electrolyte

Kf = 20.4 °C/m = cryoscopic constant

ΔT = Freezing point depression

Therefore ΔT = 6.6 - 5 = 1.6 °C

1.6 °C = 20.4 °C/m × 1 × m

Therefore m = 1.6/20.4 = 0.0784 m

number of moles in 2.50 g of cyclohexane = 0.0784 m or 0.0784 moles of the substance in 1000 grams of cyclohexane. That is

2.5 ×0.0784/1000 moles in 2.5 graams of cyclohexane  that is

1.96 × 10⁻⁵ moles in 2.5 grams of cyclohexane

1.96 × 10⁻⁵ moles of the substance weighs 0.050 grams

Therefore 1 Mole weighs (0.05 g)/(1.96 × 10⁻⁵ moles) = 255g/mole