Question

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.

Answer 1

Here, ΔT_f = (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

= 0.0146 mol

Therefore, molality of the solution,

= 0.1537 mol kg⁻¹

Applying the relation,

ΔT_f = K_f × m

= 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.

Number of moles of glucose

= 0.0278 mol

Therefore, molality of the solution,

= 0.2926 mol kg⁻¹

Applying the relation,

ΔT_f = K_f × m

= 13.99 K kg mol⁻¹ × 0.2926 mol kg⁻¹

= 4.09 K (approximately)

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