Asolution made by dissolving 14.2g of sucrose in 100g water exhibits a freezing point depression of 0.77 degrees. calculate the molar mass of sucrose

For the purpose we have to know following equation for freezing point depression:

ΔTf=Kf*b

and that Kf of water is 1.86°C/m.

From the formula we can determine molality (b):

b=Δtf/Kf=0.77/1.86= 0.414 mole/kg

Now when we know molality, we can calculate mass of sucrose in solution:

b=n/m(H20)   =>  n(sucrose)=b*m(H20) = 0.414 mole/kg *0.1 kg = 0.0414 mole

Finally, we can determine the molar mass of sucrose:

M=m/n=14.2/0.0414= 343g/mole

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