High School

An aqueous solution containing 35.9 g of an unknown molecular (nonelectrolyte) compound in 150.0 g of water has a freezing point of \(-1.3 \degree C\). Calculate the molar mass of the unknown compound.

Answer :

Answer:

molr mass (mm):

mm = 342.43 g/mol

Explanation:

freezing point (ΔTf):

  • ΔTf = - Kf*mb

∴ ΔTf = - 1.3°C

∴ a: water (solvent)

∴ b: solute

∴ mb: molality of the solute [=] mol/Kg

∴ Kf: cryoscopic constant

⇒ Kf water = 1.86 °C.Kg/mol

∴ wb = 35.9 g

∴ wa = 150.0 g = 0.150 Kg

∴ molar mass solute (mm) [=] g/mol

⇒ mb = - ΔTf/Kf

⇒ mb = - ( - 1.3°C)/(1.86 °CKg/mol)

⇒ mb = 0.6989 mol/Kg

∴ moles solute (nb):

⇒ nb = (0.6989 mol/Kg)(0.150 Kg) = 0.1048 mol

molar mass:

⇒ mm = (35.9 g)/(0.1048 mol) = 342.43 g/mol

Final answer:

The molar mass of the unknown compound is calculated using the freezing point depression formula, which involves the depression constant for water and the molality of the solution. By determining the moles of solute and dividing the mass of the solute by the number of moles, the molar mass is found to be 342.39 g/mol.

Explanation:

To calculate the molar mass of the unknown compound from the freezing point depression, we need to use the formula ΔTf = i * Kf * m, where ΔTf is the freezing point depression, i is the van't Hoff factor (which is 1 for a nonelectrolyte), Kf is the freezing point depression constant for water (1.86 °C/m), and m is the molality of the solution.

First, we calculate the freezing point depression: ΔTf = (0 °C - (-1.3 °C)) = 1.3 °C.

Next, we find the molality (m): m = ΔTf / (Kf * i) = 1.3 °C / (1.86 °C/m) = 0.6989 m.

Then, we determine the moles of solute (mol): mol = (mass of solute in grams) / (molar mass of solute), which we rearrange to find the molar mass: molar mass = (mass of solute in grams) / (mol).

Molality is also defined as moles of solute per kilogram of solvent. Since we have 0.6989 mol/kg and 150.0 g (0.150 kg) of water, we get: moles of solute = 0.6989 m * 0.150 kg = 0.10484 mol.

Finally, we calculate the molar mass: molar mass = (mass of solute in grams) / (moles of solute) = 35.9 g / 0.10484 mol = 342.39 g/mol.

The molar mass of the unknown compound is therefore determined to be 342.39 g/mol.

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