# A 5% solution (by mass) of cane sugar in water has freezing point of 271 K. Calculate the freezing point of 5% glucose in water if freezing point of pure water is 273.15 K.

In cane sugar:

ΔTf= (273.15 - 271) K = 2.15 K

Molar mass of sugar (C12H22O11) = 12 × 12 + 22 × 1 + 11 × 16 = 342 g mol- 1

5% solution (by mass) of cane sugar in water means 5 g of cane sugar is present in (100 - 5)g = 95 g of water.

Now, number of moles of cane sugar =5/342 mol

= 0.0146 mol

So, molality of the solution,m=0.0146mol/0.095kg

= 0.1537 kg mol- 1

Relating,

ΔTf= Kf× m

⇒ Kf=  ΔTf  / m

⇒  2.15K / 0.1537 kg mol-1

= 13.99 K kg mol-1

Molar of glucose (C6H12O6) = 6 × 12 + 12 × 1 + 6 × 16 = 180 g mol- 1

5% glucose in water means 5 g of glucose is present in (100 - 5) g = 95 g of water.

∴ No of moles of glucose = 5/180 mol

= 0.0278 mol

So, molality of the solution,m=0.0278 mol / 0.095 kg

= 0.2926 mol kg- 1

Applying the relation,

ΔTf = Kf × m

= 13.99 K kg mol- 1× 0.2926 mol kg- 1

= 4.09 K

Hence, the freezing point of 5% glucose solution is (273.15 - 4.09) K= 269.06 K.

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