Cyclohexae, C6H12, melts at 6.55 oC and has a freezing point depression constant

Question

Cyclohexae, C6H12, melts at 6.55 oC and has a freezing point depression constant of kfp = -20.0 oC/m (where m is molality). You want to determine the molar mass of an unknown pure compound using the colligative property of freezing point depression. You weigh out 83.561 g of cyclohexane, and confirm that its melting point is 6.55 oC. You then mix 2.566 g of your unknown compound with the cyclohexane and find that the solution melting point is now 3.23 oC.

What is the molar mass of the unkown compound? (Identify the freezing point depression, solution molality, and mol of solute)

I'm trying to get this problem started but when I find the freezing point depression I get -7738.89 which I know cannot be correct.

Explanation / Answer

dT = Freezing point of solvent - Freezing point of solution

= 6.55 -3.23 = 3.32

We have formula   dT = i x Kf x m

where i = vantoff foactor = 1 for no dissociative solute

Kf is given 20 C/m , we find m i.e molality

hence 3.32 = 1 x (20) x m

m = 0.166 = molality

solvent is cylcohexane whose mass is 83.561 g = 0.083561 kg

molality = moles of solute / solvent mass in kg

0.166 = moles of solute / 0.083561

moles of solute = 0.01387

Mass of compound = moles of compound x molar mass

               2.566= 0.01387 x Molar mass

Molar mass = 185 g/mol

( Actualy we use Kf = +20 C/m or else we have to use dT = FP ( solution) -FP (solvent)   , so that we get molality in +ve value )

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