Q.How will you determine the molar mass of solute from elevation of boiling point? OR Define:

Why does salt make water boil hotter?

You already know that pure water boils at $100^\circ\text{C}$ at 1 atm pressure. But if you dissolve salt or sugar in that water, the boiling point goes up. Not by much — a pinch of salt raises it by a fraction of a degree — but measurably. The question is: why?

Think about what boiling actually is. A liquid boils when its vapour pressure equals the surrounding atmospheric pressure. At that point, bubbles of vapour can form anywhere inside the liquid, not just at the surface. So boiling temperature is really the temperature at which the liquid's vapour pressure hits the external pressure.

Now add a non-volatile solute — something like salt or sugar that does not itself evaporate. The solute particles stay behind in the liquid. They get in the way of solvent molecules trying to escape into the vapour phase. Fewer solvent molecules make it to the surface per second, so the vapour pressure of the solution is lower than that of the pure solvent at the same temperature.

If the vapour pressure is lower, you need to heat the solution to a higher temperature to bring that vapour pressure back up to atmospheric pressure. That higher temperature is the new boiling point. The difference between this new boiling point and the pure solvent's boiling point is the elevation of boiling point, denoted $\Delta T_b$.

The precise statement

For dilute solutions of a non-volatile solute, the elevation of boiling point is directly proportional to the molal concentration of the solute. Molality ($m$) is the number of moles of solute per kilogram of solvent.

Introducing the proportionality constant $K_b$, called the ebullioscopic constant (or boiling point elevation constant) of the solvent:

Here:

• $\Delta T_b$ is the boiling point elevation (in K or °C — the numerical difference is the same)
• $K_b$ is a property of the solvent alone, not the solute. For water, $K_b = 0.512\ \text{K kg mol}^{-1}$
• $m$ is the molality of the solution

So if you dissolve 1 mole of a non-volatile solute in 1 kg of water, the boiling point rises by $0.512^\circ\text{C}$ — from $100^\circ\text{C}$ to $100.512^\circ\text{C}$.

Why proportional to molality, not molarity?

Because boiling point elevation depends on the number of solute particles relative to the mass of solvent, not the volume of the solution. Temperature changes affect volume (and therefore molarity), but mass stays constant. Molality is temperature-independent, making it the natural choice for a property that itself depends on temperature.

A concrete example

Suppose you dissolve 58.44 g of NaCl (table salt, molar mass 58.44 g/mol) in 500 g of water. That is 1 mole of NaCl in 0.5 kg of water, so molality $m = 2\ \text{mol/kg}$.

But NaCl dissociates in water into Na⁺ and Cl⁻ ions — two particles per formula unit. For ionic solutes, the effective number of particles is given by the van't Hoff factor $i$. For NaCl, $i \approx 2$. …