how to find molar mass of an unknown compound

Question

A solution is prepared with 3.85 g of an unknown compound in 100.0 g of cyclohexane. The solution had a freezing point of 4.18 degrees Celsius. what is the molar mass of the unknown compound?

Answer 1

Change in freezing point of a solvent is known as a colligative property, and the equation that can be used to calculate the freezing point change is ∆T = imK where ∆T = change in freezing point; i = van't Hoff factor; m = molality (moles solute per kg solvent) and K = freezing point constant for the particular solvent.  There isn't sufficient information provided to answer the question because we need to know K for cyclohexane and we need to know the normal freezing point of cyclohexane.  Looking these values up, one obtains K = 20.2 ºC Kg/mole and freezing point = 6.5ºC.  Thus, we have

∆T = 6.5 - 4.18 = 2.32

i = 1 for cyclohexane as it is a non electrolyte

K = 20.2

m = ?

Solving for m we have m = ∆T/iK = 2.32/(1)(20.2) = 0.1148 m = 0.1148 moles/kg

Since there are 0.1000 kg of cyclohexane, the number of moles of unknown = 0.1148 moles/kg x 0.1 kg = 0.01148 moles

Molar mass = 3.85 g/0.01148 moles = 335 g/mole