Question

Which of the following solutions will have the highest boiling point?
(A) 1% glucose in water
(B) 1% sucrose in water
(C) 1% NaCl in water
(D) 1% urea in water

Answer 1

Hint: Use the formula of elevation in boiling point: $\Delta {T_b} = i{K_b}m$. All the solutions in the options have the same concentration and ${K_b}$ values, so boiling point is proportional to ‘i’. Now find out the number of solute particles after ionization (i) and the compound having highest value of ‘i’ will have the highest boiling point.

Complete step by step answer:
-First of all we will see what boiling point is.
It is basically the temperature at which the vapour pressure of the liquid equals the pressure around the liquid and the liquid converts into vapour state.
Boiling point increases with increase in external pressure and the liquids having greater intermolecular forces have high boiling points.
-We will now talk about the concept of elevation in boiling point after dissolution of solute.
The elevation in boiling point ($\Delta {T_b}$) is the difference between boiling point of solution (${T_b}$) and boiling point of pure solvent ($T_b^ \circ $). It is a colligative property. Mathematically it can be written as:
$\Delta {T_b} = {T_b} - T_b^ \circ $
The elevation in boiling point is directly proportional to concentration (molality ‘m’). So:
$\Delta {T_b}\alpha m$
$\Delta {T_b} = i{K_b}m$ (1)
Where, ${K_b}$ = boiling point elevation constant;
i = van’t Hoff factor of solute;
m = molality.
-Now coming back to the question, we can see that all have a concentration of 1% and so the molality will be same for all and the value of ${K_b}$ depends on solvent and the solvent is water in all, so even ${K_b}$ will be same for all. But the value of ‘i’ is different for all and so the boiling point elevation depends on ‘i’.
$\Delta {T_b} \propto i$ ………………………………. (2)
Hence we can also say that here boiling point will depend on ‘i’ or the van’t Hoff factor. We know that the van't Hoff factor is the number of particles produced after dissolution or ionization.
So, more is the number of particles, more will be the value of ‘i’ and so higher will be the boiling point.
-We will now check the options to see which of them has the highest value of ‘i’:
For (A) 1% glucose in water: We know that glucose is a non-electrolyte and so does not dissociate. For it the value of i = 1
For (B) 1% sucrose in water: We know that sucrose is a non-electrolyte and so does not dissociate. For it the value of i = 1
For (C) 1% NaCl in water: NaCl is a strong electrolyte and so ionizes to form $N{a^ + }$ and $C{l^ - }$ ions. So for NaCl the value of i = 2
For (D) 1% of urea in water: We know that sucrose is a non-electrolyte and so does not dissociate. For it the value of i = 1
 Since in the above discussion we have seen that the value of ‘i’ is highest for NaCl (i = 2) and so it will have the highest boiling point.

Hence the correct option will be: (C) 1% NaCl in water.

Note: The colligative properties depend only on the number of solute particles present and not on the nature of the solute particles. There are 4 colligative properties:
1) Elevation in boiling point
2) Depression in freezing point
3) Lowering of vapour pressure
4) Osmotic pressure