determine the freezing point of a solution made by adding 59.6g of methanol to 830.0g of water

Question

I need help for a test coming up this friday in Chemistry 

Answer 1

Freezing Point Depression equation: ΔTF = iKF(H2O)b

Where KF(H2O) = 1.853 K•kg/mol

b is the molality (m) of CH3OH soln

i is the van ’t Hoff factor for CH3OH

First calculate the moles of CH3OH = 59.6g/32.04 g/mol = 1.86 mol CH3OH

Then convert 830.0 g of water to kg: 830.0 g x 1 kg/1000 g = 0.830 kg H2O

Now calculate the Molality of CH3OH solution: 1.86 mol CH3OH/0.830 kg H2O = 2.24 m or 2.24 mol/kg

Lastly, determine the van ‘t Hoff factor(i) for CH3OH: Methanol completely dissociates in water having 2 ions, one is CH3 and the other is OH

Now plug in your values for freezing point depression equation (ΔTF = iKFb) as follows:

ΔTF = iKFb = (2)(1.853 K•kg/mol)(2.24 mol/kg) = 8.30 K

Freezing Point = (normal f.p. of solvent) - ΔTF = 273.15 K – 8.30 K = 264.85 K