The properties of solutions which depend on the number of solute particles and are independent of their chemical identity are called colligative properties. These are lowering of vapour pressure, elevation of boiling point, depression of freezing point and osmotic pressure. The process of osmosis can be reversed if a pressure higher than the osmotic pressure is applied to the solution. Colligative properties have been used to determine the molar mass of solutes. Solutes which dissociate in solution exhibit molar mass lower than the actual molar mass and those which associate show higher molar mass than their actual values. Quantitatively, the extent to which a solute is dissociated or associated can be expressed by van’t Hoff factor i. This factor has been defined as ratio of normal molar mass to experimentally determined molar mass or as the ratio of observed colligative property to the calculated colligative property.
18 g of glucose, C6H12O6 (Molar mass: 180 g mol-1) is dissolved in 1 kg of water in a saucepan. At what temperature will this solution boil? (Kb for water = 0.52 K kg mol-1, boiling point of pure water = 373.15 K)
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 373.202 K
A non-volatile solute raises the boiling point of the solvent. For a dilute solution the elevation of boiling point is proportional to the molality m (moles of solute in 1 kg of solvent). Glucose does not dissociate in water, so i = 1:
\( \displaystyle \Delta T_b=K_b\,m \)
Moles of glucose and molality:
\( \displaystyle n=\frac{18\,\mathrm{g}}{180\,\mathrm{g\,mol^{-1}}}=0.1\,\mathrm{mol} \)
\( \displaystyle m=\frac{0.1\,\mathrm{mol}}{1\,\mathrm{kg}}=0.1\,\mathrm{mol\,kg^{-1}} \)
Elevation of boiling point:
\( \displaystyle \Delta T_b=0.52\,\mathrm{K\,kg\,mol^{-1}}\times0.1\,\mathrm{mol\,kg^{-1}}=0.052\,\mathrm{K} \)
Boiling point of the solution:
\( \displaystyle T_b=373.15\,\mathrm{K}+0.052\,\mathrm{K}=373.202\,\mathrm{K} \)