A solution containing 3.90 g of an unknown nonelectrolyte liquid and 9.60 g water has a freezing point of −3.33 °C. The Kf = 1.86 °C/m for water. Calculate the molar mass of the unknown liquid in g/mol.

The molar mass is 227 g/mol

Explanation:

Step 1: Data given

Mass of unknown nonelectrolyte = 3.90 grams

Mass of water = 9.60 grams

Freezing point of the solution = -3.33 °C

Kf = 1.86°C/m

Nonelectrolyte has a van't Hoff factor = 1

Step 2:

If you know the number of moles, and you know that is equivalent to 1.00 g, you can get molar mass.

∆T =i*m*K f

⇒ ∆T  = difference in temperature between freezing point of solution and pure water = 3.33 °C

⇒ Van't hoff factor of the nonelectrolyte = 1

⇒ molality = moles nonelectrolyte / mass water

⇒ Kf = freezing point constant = 1.86 °C/m

3.33 = (1)(m)(1.86)

m = 1.79 molal = 1.79 moles / kg H2O

Step 3: Calculate moles nonelectrolyte

molality = moles / mass H2O

moles = molality * mass H2O

Moles = 1.79 molal * 0.0096

Moles = 0.017184‬ moles

Step 4: Calculate molar mass of nonelectrolyte

Molar mass = mass / moles

Molar mass = 3.90 grams / 0.017184 moles

Molar mass = 227 g/mol

The molar mass is 227 g/mol