When a 20.0 g sample of an unknown compound is dissolve in 500. G of benzene, the freezing point of the resulting solution is 3.77 o C. The freezing point 9f pure benzene is 5.48 o C and Kf for benzene is 5.12 o C/m. Calculate the molar mass of the unknown

The correct answer is 116.3 g/mol

Explanation:

When a solute is added to a solvent, the freezing point decreases. That is called freezeing point depression and is given by the following expression:

ΔTf= Kf x m

Where ΔTf is the decrease in freezing point (final temperature - initial temperature), Kf is the freezeing point constant, m is the molality of the solution.

We have the following data:

Kf= 5.12ºC/m

ΔTf= 5.48ºC - 3.77ºC = 1.71ºC

We can calculate the molality of the solution from the mathematical expression for freezeing point as follows:

m = ΔTf/Kf = 1.71ºC/(5.12º C/m)= 0.334 m

The molality is the number of moles of solute in 1 kg of solvent. The solute was added to 500 g of solvent (benzene), so we can multiply the molality by the grams of solvent (500 g = 0.5 kg) to obtain the number of moles:

0.334 mol/kg x 0.5 kg = 0.172 moles

We know that the molar mass is equal to the mass of compound per mole, so we divide the mass into the moles to obtain the molar mass as follows:

MM = mass/moles= 20.0 g/0.172 moles = 116.3 g/mol