Molar Mass using Molality?

Question

Molar Mass of:

1. compound A if a solution of 1.00 g in 225 g of water freezes at -0.102 degrees celsius

2. compound B if a solution of 1.00 g in 100 g of cyclohexane freezes at 6.02 degrees celsius

very confusing need help!!

Answer 1

1.  ∆T = imK 

Assuming compound A is a non electrolyte, then i = 1 and ...

0.102 = (1)(m)(1.86)

m = 0.102/1.86 = 0.0548 m = 0.0548 moles/kg

0.0548 moles/kg x 0.225 kg = 0.0123 moles

1.00 g/0.0123 moles = 81.3 g/mole = Molar Mass

 

2.  ∆T = imK

Again, if you assume the compound B is a non electrolyte, i = 1

Since the normal freezing point of cyclohexane is 6.5ºC the ∆T = 6.5 - 6.02 = 0.48

The freezing point constant (K) for cyclohexane is 20.0 

0.48 = (1)(m)(20.0)

m = 0.48/20 = 0.024 m = 0.024 moles/kg

0.024 moles/kg x 0.1 kg = 0.0024 moles

1.00 g/0.0024 moles = 417 g/mole = molar mass