Answer: To calculate the molecular weight of the unknown non-electrolyte, we can use the formula for freezing point depression:
ΔTf = Kf * m
where:
ΔTf = freezing point depression (change in freezing point)
Kf = freezing point depression constant (given as 5.12°C/kg/mol for benzene)
m = molality of the solution (moles of solute per kilogram of solvent)
Step 1: Calculate the molality (m) of the solution.
Molality (m) = moles of solute / mass of solvent (in kg)
Given mass of the unknown non-electrolyte solute = 1.048 g
Given mass of benzene solvent = 36.21 g
Convert the masses to kilograms:
Mass of solute = 1.048 g / 1000 g/kg = 0.001048 kg
Mass of solvent = 36.21 g / 1000 g/kg = 0.03621 kg
Step 2: Calculate the freezing point depression (ΔTf).
ΔTf = freezing point of pure benzene - freezing point of the solution
The freezing point of pure benzene is 5.50°C, and the freezing point of the solution is 1.39°C. Therefore:
ΔTf = 5.50°C - 1.39°C
ΔTf = 4.11°C
Step 3: Calculate the molality (m) of the solution.
m = moles of solute / mass of solvent (in kg)
To find the moles of solute, we need to use the molar mass of the unknown non-electrolyte (Molar mass = m/Moles)
Step 4: Use the formula to find the molar mass of the unknown non-electrolyte:
ΔTf = Kf * (molar mass / molar mass of benzene) * molality
molar mass = ΔTf * molar mass of benzene / (Kf * molality)
molar mass = 4.11°C * 78.11 g/mol (molar mass of benzene) / (5.12°C/kg/mol * 0.001048 kg)
molar mass ≈ 203.45 g/mol
So, the molecular weight of the unknown non-electrolyte is approximately 203.45 g/mol.