Q.(a) 18 g of glucose is dissolved in 1kg of water in a saucepan. At what temperature this solution will boil at 1 atm. pressure? Kb for water is 0.52 K kg mol⁻¹ and boiling point is 373.15 K at 1 atm.

Boiling Point Elevation — From Intuition to Precision

Imagine you're cooking pasta. You add salt to the water, and the water takes longer to boil. That's not your imagination — it's a real physical effect. The salt has raised the boiling point of the water. Pure water boils at 100°C at sea level, but salt water needs a slightly higher temperature to boil. That's boiling point elevation in action.

Why does this happen?

To understand why, you need to think about what boiling actually is. Boiling occurs when the vapour pressure of the liquid equals the surrounding atmospheric pressure. Vapour pressure is the pressure exerted by molecules escaping from the liquid surface into the gas phase.

When you dissolve a non-volatile solute (like salt, which doesn't evaporate) in a solvent (like water), something interesting happens at the surface. Some of the surface molecules are now solute particles — they don't escape into the vapour. This means fewer solvent molecules can leave the liquid per second. The result? The vapour pressure of the solution is lower than that of the pure solvent at the same temperature.

Now, to make this reduced vapour pressure equal to the atmospheric pressure (so the liquid can boil), you need to raise the temperature. That extra heat gives the remaining solvent molecules enough energy to overcome the solute's interference and produce the required vapour pressure.

The precise statement

Boiling point elevation is the increase in the boiling point of a solvent when a non-volatile solute is dissolved in it. The boiling point of the solution is always higher than that of the pure solvent.

The elevation $\Delta T_b$ is given by:

And it depends only on the number of solute particles, not on their chemical identity (for dilute solutions). This is a colligative property — a property that depends on the concentration of particles, not their nature.

What is $K_b$?

The ebullioscopic constant $K_b$ is a property of the pure solvent. It tells you how much the boiling point rises per unit molal concentration. For water, $K_b = 0.512 \, \text{°C kg mol}^{-1}$. So a 1 molal aqueous solution (1 mole of solute per kg of water) boils at $100.512\,°\text{C}$.

What about electrolytes?

If the solute dissociates into ions (like NaCl → Na⁺ + Cl⁻), the number of particles increases. One mole of NaCl gives two moles of particles in solution. So the effective concentration is higher. We account for this using the van't Hoff factor $i$:

For NaCl, $i \approx 2$ (in dilute solutions). For sugar (which doesn't dissociate), $i = 1$. …