A solution was prepared by mixing together 5.80 g of a nonelectrolyte solute with 28.0 g of solvent. The freezing point depression, ∆T, for the solution was determined to be 7.30 oC. Kf = 3.91 oC/m for the pure solvent. What is the molecular weight (molar mass) of the solute? Enter your answer as a decimal number.

110.9 g/mol is the molar mass of the solute

Explanation:

ΔT = Kf . m  → Colligative property of freezing point depression

7.30°C = 3.91 °C/m . m

Kf is the cryoscopic constant for the solvent

m is molality (moles of solute in 1kg of solvent)

7.30°C / 3.91m/°C = m → 1.87 mol/kg

This moles of the solute are in 1kg of solvent, but our mass of solvent is 28 g. We convert the mass of solvent from g to kg

28 g . 1kg / 1000g = 0.028 kg

We find out the moles →  1.87 mol/kg . 0.028kg = 0.0523 moles

This moles are the amount of 5.80 g. We can determine the molar mass:

g/mol = 5.80 g /0.0523 mol =  110.9 g/mol

The molar mass of the solute is 110.9 g/mol

Explanation:

Step 1: Data given

Mass of a nonelectrolyte = 5.80 grams

Mass of solvent = 28.0 grams

freezing point depression ∆T = 7.30 °C

Freezing point depression constant = 3.91 °C /m

Step 2: Calculate molality

∆T = i*Kf * m

⇒∆T = the freezing point depression = 7.30 °C

⇒i = the van't Hoff factor = 1

⇒Kf = the freezing point depression constant = 3.91 °C/m

⇒m = molality = moles solute / mass solvent

m = 7.30 /3.91

m = 1.867 molal

Step 3: Calculate moles solute

Moles solute = molality * mass of solvent

Moles solute = 1.867 molal * 0.028 kg

Moles solute = 0.0523 moles

Step 4: Calculate molar mass

Molar mass = mass / moles

Molar mass = 5.80 grams / 0.0523 moles

Molar mass = 110. 9 g/mol

The molar mass of the solute is 110.9 g/mol